Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.
What is meant by rate?
In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.
If the new exhibit is 3 1/2 times larger than the old one, then its volume is:
[tex]V_{new} = 3.5 * V_{old[/tex]
We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:
576,000 gallons / 24 hours = 24,000 gallons per hour
To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:
Flow rate = [tex]V_{new[/tex] / time
Plugging in the values we have:
Flow rate = (3.5 * [tex]V_{old[/tex]) / time
We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:
24,000 = (3.5 * [tex]V_{old[/tex]) / time
To solve for time, we can multiply both sides by time:
24,000 * time = 3.5 * [tex]V_{old[/tex]
Then we can divide both sides by 24,000:
time = (3.5 * [tex]V_{old[/tex]) / 24,000
Plugging in [tex]V_{old[/tex] = 576,000, we get:
time = (3.5 * 576,000) / 24,000 = 84 hours
Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:
[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).
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Answer:
To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.
To do this, we divide the total gallons by the number of hours:
576,000 gallons / 24 hours = 24,000 gallons per hour
Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.
Let's assume the volume of the old exhibit is x gallons.
The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.
To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.
So, the volume of the new exhibit is 7/2 * x.
Now, we can determine the amount of water circulated per hour in the new exhibit.
To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):
(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour
Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.
Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.
Step-by-step explanation:
<3
Sam has a deck that is shaped like a triangle with a base of 18 feet and a height of 7 feet. He plans to build a 2:5 scaled version of the deck next to his horse’s water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work.
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work.
Part C: Compare the ratio of the area to the scale factor. Show every step of your work.
Answer:
A) The dimensions of the new triangular deck are:
base = 45 feetheight = 17.5 feetB) Area of original deck = 63 square feet
Area of new deck = 393.75 square feet
C) The ratio of the area is 4 : 25. This is the square of the scale factor.
Step-by-step explanation:
Part AThe given scale is 2 : 5. This means that the ratio of the measurements of the corresponding sides of two objects is 2 to 5. In other words, if one object has a length of 2 units, the corresponding length of the other object is 5 units. So in this scenario, a 2 : 5 scaled version means that for every 2 foot of the original deck, there is 5 foot of the new deck.
Therefore, if the original base of the triangle is 18 feet, the new base, b, will be:
[tex]\implies \sf 2 : 5 = 18 : b[/tex]
[tex]\implies \sf \dfrac{2}{5} = \dfrac{18}{b}[/tex]
[tex]\implies \sf 2 \cdot b=18 \cdot 5[/tex]
[tex]\implies \sf b=\dfrac{18 \cdot 5}{2}[/tex]
[tex]\implies \sf b=45\;ft[/tex]
Similarly, if the original height of the triangle is 7 feet, the new height, h, will be:
[tex]\implies \sf 2 : 5 = 7 : h[/tex]
[tex]\implies \sf \dfrac{2}{5} = \dfrac{7}{h}[/tex]
[tex]\implies \sf 2 \cdot h=7 \cdot 5[/tex]
[tex]\implies \sf h=\dfrac{7\cdot 5}{2}[/tex]
[tex]\implies \sf h=17.5\;ft[/tex]
Therefore, the dimensions of the new triangular deck are:
base = 45 feetheight = 17.5 feet[tex]\hrulefill[/tex]
Part BThe area of a triangle is half of the product of its base and height:
[tex]\boxed{\sf A=\dfrac{1}{2}bh}[/tex]
Area of the original deck:
[tex]\implies \sf A=\dfrac{1}{2} \cdot 18 \cdot 7[/tex]
[tex]\implies \sf A=9 \cdot 7[/tex]
[tex]\implies \sf A=63\;ft^2[/tex]
Area of the new deck:
[tex]\implies \sf A=\dfrac{1}{2} \cdot 45\cdot 17.5[/tex]
[tex]\implies \sf A=22.5 \cdot 17.5[/tex]
[tex]\implies \sf A=393.75\;ft^2[/tex]
Therefore, the areas of the two decks are:
Area of original deck = 63 square feetArea of new deck = 393.75 square feet[tex]\hrulefill[/tex]
Part CThe ratio of the area of the original deck to the area of the new deck is:
[tex]\implies \textsf{Area original deck}:\textsf{Area new deck}=\sf 63 : 393.75[/tex]
To rewrite the ratio in its simplest form, multiply both sides of the ratio by 16:
[tex]\implies \sf 63 \cdot 16: 393.75 \cdot 16=1008 :6300[/tex]
Then divide both sides of the ratio by 252:
[tex]\implies \sf \dfrac{1008}{252}:\dfrac{6300}{252}=4:25[/tex]
Therefore, the ratio of the area of the original deck to the area of the new deck in its simplest terms is 4 : 25.
If we compare this to the original scale factor 2 : 5 (which is the ratio of length), we can see that the ratio of area is the square of the scale factor:
[tex]\implies \sf 2^2:5^2=4:25[/tex]
you have a summer job that pays time and a half for overtime. that is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. what does the slope of a line segment represent in the context of this situation?
The slope of a line segment represent in the context of this situation is the total wages for the week.
We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the
x-coordinate are denoted by y and x, respectively.
Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is
[tex]m=\frac{y}{x} =\frac{change \ in \ y}{change\ in\ x}[/tex]
You are a crew at a Convenience store that pays an hourly wage $ 7 and 1.5 times the hours wage for the extra hours if you work for more than 40 hours a week. Write a piecewise function that gives the weekly pay P in term of the number of hours h your work.
→ wages for 1 hours = $ 7
So,
we can say that, wages for 40 hours, = 7 x 40 = 280 .
Therefore,
→ Total wages of week is = 280.
Piecewise function is :-
P(h) = 280 , where h ≤ 40.
Now, we have given that, store gives 1.5 times the hours wage for the extra hours if you work for more than
40 hours a week.
So,
→ wages per hour now = 1.5 x 7 = 10.5 .
Therefore,
→ Total wages of week
= 280 + 10.5(h - 40)
= 280 + 10.5h - 420
= 10.5h - 140.
and,
Piecewise function that gives the weekly pay P in term of the number of hours h your work is:
P(h) = 280 + 10.5(h - 40), where [h > 40].
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What is the area of the rectangle?
What is the product of (-a + 3)(a + 4)? Oa²-a +12 Oa2-a-12 O-a²-a-12 O-a ²-a + 12
The product of equation (-a + 3)(a + 4) is -a² - a + 12.
What is product of equation?
Using the distributive property, we can expand the product of (-a + 3)(a + 4) as follows:
(-a + 3)(a + 4) = -a(a) - a(4) + 3(a) + 3(4)
Simplifying, we get:
(-a + 3)(a + 4) = -a² - 4a + 3a + 12
Combining like terms, we get:
(-a + 3)(a + 4) = -a² - a + 12
Therefore, the product of (-a + 3)(a + 4) is -a² - a + 12.
What is distributive property?
The distributive property is a property of arithmetic operations that is used to simplify expressions by distributing one term over another term inside parentheses.
In particular, the distributive property states that:
a × (b + c) = (a × b) + (a × c)
or
(a + b) × c = (a × c) + (b × c)
This property applies to both multiplication and addition, and can be extended to subtraction and division by adding or subtracting the distributive term to both sides of the equation.
For example, using the distributive property, we can simplify the expression:
3 × (4 + 5)
as follows:
3 × (4 + 5) = 3 × 4 + 3 × 5
= 12 + 15
= 27
In this example, we used the distributive property to distribute the term 3 over the sum (4 + 5), resulting in the equivalent expression 3 × 4 + 3 × 5.
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I need this for a quiz to pass my grade HELP!!!!!
Jake plans to use a ramp to make it easier to move a piano out of the back of his truck. The back of the truck is
83
8383 centimeters tall and the ramp is
158
158158 centimeters long.
What is the horizontal distance from the end of the ramp to the back of the truck?
Round your answer to the nearest tenth of a centimeter.
Answer:
Step-by-step explanation:
This can be solved using Pythagorean Theorem.
a² + b² = c²
8383² + b² = 158158²
70274689 + b² = 25013952964
70274689 - 70274689 + b² = 25013952964 - 70274689
b² = 24943678275
√b² = √24943678275
b = 157935.7 cm
using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected. group startstrue or false
The given statement "Using p-value rule for a population proportion or mean, if the level of significance is less than p-value, null hypothesis is rejected." is True because the hypothesis is rejected in this case.
In hypothesis testing, the p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, assuming that the null hypothesis is true. The level of significance, denoted by alpha, is the maximum probability of rejecting the null hypothesis when it is actually true.
If the p-value is less than the level of significance, it means that the observed test statistic is unlikely to have occurred by chance alone, assuming the null hypothesis is true. Therefore, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.
For example, suppose we are testing the hypothesis that the population mean is equal to a certain value. If the p-value is 0.02 and the level of significance is 0.05, we would reject the null hypothesis because the p-value is less than the level of significance.
This means that there is strong evidence against the null hypothesis and we can conclude that the population mean is likely different from the hypothesized value.
In summary, if the level of significance is less than the p-value, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.
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If the point D is the center of dilation, what is the scale factor?
With D as Center of dilation, the scale factor is √2.
What exactly is scaling factor?In mathematics, a scaling factor is a ratio that describes how much a figure or object has been enlarged or reduced in size. A scaling factor is typically expressed as a fraction or decimal that represents the relative change in size between the original figure and the new, scaled figure.
Now,
To find the scale factor of dilation, we can use the distance formula to find the ratio of corresponding sides in the original and dilated triangles.
The distance between points A and B in the original triangle is:
[tex]\rm AB = \sqrt{(x_2 - x_1)\² + (y_2 - y_1)\²}[/tex]
[tex]= \sqrt{(0 - (-1))\² + (1 - (-1))\²} \\\\= \sqrt{1\² + 2\²}[/tex]
= √5
The distance between points A' and B' in the dilated triangle is:
[tex]\rm A'B' = \sqrt{(x_2' - x_1')\² + (y_2' - y_1')\²}[/tex]
[tex]= \sqrt{(-2 - (-1))\² + (-5 - (-2))\²}[/tex]
[tex]= \sqrt{1\² + 3\²}[/tex]
= √10
Therefore, the scale factor for the dilation is:
Scale factor = A'B' / AB = √10 / √5 = √2
Hence, the scale factor of dilation is √2.
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If you select two marbles from a bag in a row, what is probability that the first was blank and the second was orange?
NOTE: you are not replacing any marbles after each selection.
The probability of selecting a blank marble on the first draw and an orange marble on the second draw is:
[tex](bo)/[(b+o)(b+o-1)][/tex]
Let B be the event that the first marble selected is blank and let O be the event that the second marble selected is orange. Since we are not replacing the marbles after each selection, the probability of the second marble being orange depends on the outcome of the first selection.
Let's assume that the bag contains b blank marbles and o orange marbles. The probability of selecting a blank marble on the first draw is b/(b+o), and the probability of selecting an orange marble on the second draw, given that the first marble was blank, is o/(b+o-1) (since there is one less marble in the bag after the first draw).
Therefore, the probability of selecting a blank marble on the first draw and an orange marble on the second draw is:
[tex]P(B\ and\ O )= P(B)*P(O|B)\\\\=b/(b+o)*o/(b+o-1)\\\\=(bo)/[(b+o)(b+o-1)][/tex]
Note that this assumes that there are no marbles that are both blank and orange. If there are such marbles in the bag, the calculation will be different.
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I NEED HELP ASAP! The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Mean 82.3°
Median 86.5°
Range 48°
IQR 34°
Answer:
The new value of the list after changing 71° to 93° would be:
58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57
The measure that changes the most would be the median. Without the change, the median was 86.5°, which was the average of the 7th and 8th values in the list (100 + 77) / 2. However, after changing 71° to 93°, the median becomes 91°, which is the average of the 6th and 7th values in the list (91 + 91) / 2.
Therefore, the median has changed by 4.5° (from 86.5° to 91°).
Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax 2 + bx + c where c = 40. The middle “b” term is unknown.
The correct area models are 4e and none of the given models for 4d and 4c.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.
The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).
When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.
The area model of 4d is incorrect because it does not properly represent a factorable polynomial.
It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.
Therefore, the correct area models are 4e and none of the given models for 4d and 4c.
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a. There are different
ways to tell whether an equation
represents a proportional
relationship. Is there one way that is
always best?
b.Explain your reasoning.
Which of the equations y = 2x and
y = 2x + 15, if either, represents a
proportional relationship?
A. only y = 2x + 15
B. neither equation
C. both equations
D. only y = 2x
Pls and thx
The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
A. There is no one optimum approach to determine if an equation indicates a proportionate connection. One popular method is to test if the equation can be stated in the form y = kx, where k is a constant. A proportional connection is represented by an equation that may be expressed in this format.
A. Because it can be expressed as y = kx with k = 2, the equation y = 2x represents a proportional connection. As a result, D is the right answer: just y = 2x.
The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.
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an integer is randomly chosen from the integers $1$ through $100$, inclusive. what is the probability that the chosen integer is a perfect square or a perfect cube, but not both? express your answer as a common fraction.
The probability that the chosen integer is a perfect square or a perfect cube but not both is therefore 13/100.
When choosing an integer from 1 to 100, there are 10 perfect squares (1² to 10²) and 4 perfect cubes (1³ to 4³). However, the number 1 is both a perfect square and a perfect cube. To avoid counting it twice, we use the formula for the union of two sets: |A∪B| = |A| + |B| - |A∩B|. In this case, |A∪B| represents the number of integers that are either a perfect square or a perfect cube. Plugging in the values, we get |A∪B| = 10 + 4 - 1 = 13. The probability is therefore 13/100.
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Find the values of sin a and tan a, if a is the measure of an acute
angle in a right triangle and
cos a= 0.6
Step-by-step explanation:
Acute angle means less than 90 degrees....so it is in the first Quadrant and sin and cos will be positive values
Trig identity
sin^2 + cos^2 = 1
sin^2 + .6^2 = 1 shows sin = .8
The tan = sin/ cos = .8/.6 = 1.33
the extract of a plant native to taiwan has been tested as a possible treatment for leukemia. one of the chemical compounds produced from the plant was analyzed for a particular collagen. the collagen amount was found to be normally distributed with a mean of 61 and standard deviation of 9.8 grams per mililiter. a. what is the probability that the amount of collagen is greater than 60 grams per mililiter? b. what is the probability that the amount of collagen is less than 90 grams per mililiter? c. what percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
a. The probability that the amount of collagen is greater than 60 grams per mililiter is 0.5398
b. The probability that the amount of collagen is less than 90 grams per mililiter is 0.9985.
c. Approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.
a. To find the probability that the amount of collagen is greater than 60 grams per milliliter, we'll use the z-score formula:
z = (X - μ) / σ
where X is the value we're interested in, μ is the mean, and σ is the standard deviation.
z = (60 - 61) / 9.8 ≈ -0.1
Now, we'll use a z-table or calculator to find the probability corresponding to this z-score.
A z-score of -0.1 corresponds to a probability of approximately 0.4602.
Since we're looking for the probability that the amount of collagen is greater than 60 grams per milliliter, we need to find the area to the right of this z-score:
P(X > 60) = 1 - P(X ≤ 60) = 1 - 0.4602 ≈ 0.5398
b. To find the probability that the amount of collagen is less than 90 grams per milliliter, we'll again use the z-score formula:
z = (90 - 61) / 9.8 ≈ 2.96
A z-score of 2.96 corresponds to a probability of approximately 0.9985.
Since we're looking for the probability that the amount of collagen is less than 90 grams per milliliter, we'll use this probability directly:
P(X < 90) ≈ 0.9985
c. To find the percentage of compounds formed from the extract of this plant that fall within 1 standard deviation of the mean, we'll use the empirical rule (68-95-99.7 rule), which states that approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.
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i need help solving these questions step by step, I can't figure out question 15! PLEASE HELP IT DUES TODAY!!
After factorization we get:
14. (m²+ 4)(m + 2)(m - 2).
15. (x + 2y + 2z)(x + 2y - 2z).
16. m²(m + 1)(m - 1) - 12.
17. (2x + 3)² - 3(2x + 3).
What is factorization?Factorization is the process of breaking down a mathematical expression, equation, or number into its constituent parts or factors. In algebra, factorization involves finding the factors of a polynomial expression, which are the individual terms that can be multiplied together to yield the original polynomial.
14. To factor m⁴ - 16, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, we can rewrite the expression as (m²)² - 4², and use the formula:
m⁴ - 16 = (m² + 4)(m² - 4)
Now, we can use the difference of squares formula again to factor m^2 - 4:
m⁴ - 16 = (m²+ 4)(m + 2)(m - 2)
15. x² + 4xy + 4y² - 4z² = (x + 2y)² - 4z²
(x + 2y)² - 4z² = (x + 2y + 2z)(x + 2y - 2z)
Therefore, the factored form of x² + 4xy + 4y² - 4z² is (x + 2y + 2z)(x + 2y - 2z).
16. To factor m⁴ + m² - 12, we can start by factoring out m^2:
m⁴ + m² - 12 = m²(m² + 1) - 12
Now we have a difference of squares in the parentheses, which we can factor using the formula a² + b² = (a + b)(a - b):
m²(m² + 1) - 12 = m²(m + 1)(m - 1) - 12
Therefore, the factored form of m⁴ + m² - 12 is m²(m + 1)(m - 1) - 12.
17. To factor (2x + 3)² + 2(2x + 3) - 15, we can recognize that it is a quadratic expression in the form of ax² + bx + c. We can first simplify the expression by using the distributive property:
(2x + 3)² + 2(2x + 3) - 15 = (2x + 3)(2x + 3) + 4x + 6 - 15
= (2x + 3)² + 4x - 9
Now, we can factor out the common factor of (2x + 3)² :
(2x + 3)² + 4x - 9 = (2x + 3)²+ 4x - 12x - 9
= (2x + 3)² - 8x - 9
= (2x + 3)² - (3)(3 + 2x)
Finally, we can factor out the common factor of (3 + 2x) from the two terms:
(2x + 3)² - (3)(3 + 2x) = (2x + 3)² - (3 + 2x)(3)
= (2x + 3)² - 3(2x + 3).
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obsessivex avatar
obsessivex
17 hours ago
Mathematics
High School
Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
obsessivex
Based on the IQR values, we conclude that Bus 18 is more consistent than Bus 47, as it has smaller IQR. This means the travel times of students on Bus 18 are more tightly clustered around the median, and are fewer outliers in data.
What is line plots?A line plot is a type of graph that displays data as points or dots along a number line. Each dot or point represents a single data value, and the number line shows the range of the data. Line plots are useful for displaying small to moderate-sized data sets and for identifying the central tendency and variability of the data.
To determine which bus is the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the middle 50% of the data.
From the given data, we can calculate the IQR for both buses as follows:
For Bus 18:
Lower quartile (Q1) = 8
Upper quartile (Q3) = 24
IQR = Q3 - Q1 = 24 - 8 = 16
For Bus 47:
Lower quartile (Q1) = 10
Upper quartile (Q3) = 34
IQR = Q3 - Q1 = 34 - 10 = 24
The range, which is the difference between the maximum and minimum values, is not as appropriate a measure of variability for this purpose, as it is heavily influenced by outliers. Therefore, we cannot use the range to determine the consistency of the data for either bus.
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Decide what are the rates are equivalent. (30 beats per 20 seconds, 90 beats per 60 seconds)
Find the missing dimension of the cone. Volume=1/18
r=2/3
Answer:
Step-by-step explanation:
The formula to calculate the volume of a cone is:
v = h * π * r ^ 2/3
Where,
h: height
r: radio
We then clear the value of h:
h = (3 * v) / (π * r ^ 2)
We substitute the values:
h = (3 * (118π)) / (π * ((2/3) / (2)) ^ 2)
h = 3186 ft
Answer:
The height of the cone is:
h = 3186 ft
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Answer:151
Step-by-step explanation:
Addition of 107 and 44
The value of the angle m∠EFG is 151.
We have,
From the figure,
m∠EFG = m∠EFH + m∠HFG
Now,
Substituting the values in the angle.
m∠EFG
= m∠EFH + m∠HFG
= 44 + 107
= 151
Thus,
The value of the angle m∠EFG is 151.
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Find measure of angle 14. (Just enter the number, no symbols)
A
The measure of angle 14 is 83° in the parallel line t and s and transversal n.
What is parallel line?Parallel lines are a pair of lines in a two-dimensional plane that never intersect or cross each other, regardless of how far they are extended in either direction. Parallel lines have the same slope, which determines their steepness or inclination, and they maintain the same slope throughout their length.
What is transversal?A transversal is a line that intersects two or more other lines in a plane at distinct points. Specifically, if two or more lines in a plane are intersected by a third line, that third line is called a transversal. The lines being intersected are referred to as the "transversed lines".
According to the given information:
Given the parallel lines are t and s, the transversal are line m and n
the given angles are ∠2 = 97° and ∠6 = 83°
In the parallel lines t and s , line n is transversal
By the property that "corresponding angles are equal"
we can say that ∠5 =∠13, ∠7 =∠15, ∠6= ∠14, ∠8=∠16
given ∠6 = 83°, We know that ∠6= ∠14
∠14 = 83° (Corresponding angles are equal)
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suppose a simple random sample of 150 students is drawn from a population of 3000 college students. among sampled students, the average iq score is 115 with a standard deviation of 10. what is the point estimate? group of answer choices 3000 115 unable to tell. not enough information given. 10
115.
The point estimate for the average IQ score of the population of 3000 college students based on a simple random sample of 150 students with an average IQ score of 115 and a standard deviation of 10 is 115.
Therefore, the correct option is 115.
A point estimate is an estimate of a population parameter based on a single value or point. It is obtained by using statistics collected from a sample to infer population values. It can be a single value or a range of values that best represents the unknown population parameter.
Based on the given information, a simple random sample of 150 students is drawn from a population of 3000 college students.
Among sampled students, the average IQ score is 115 with a standard deviation of 10. The point estimate, in this case, is the average IQ score of the population, which is estimated to be 115 based on the sample data.
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Sarah visited a tree nursery. She measured and recorded the heights of some young trees. This line plot shows her results.
How much taller is one of the tallest trees than one of the shortest trees?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
3 and 1/2
Step-by-step explanation:
7 and 1/2 - 4
An economist would like to estimate the average household income in Martin county. The mean household
income of a random sample of 227 families in Martin county was found to be $52,939. The standard
deviation of the household incomes of all households in Martin county is known to be $1,227.
Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the average
household income in Martin county. Report the confidence interval using interval notation. Round solutions
to two decimal places, if necessary.
Therefore , the solution of the given problem of average comes out to be 96% confidence interval is ($52,791.38, $53,086.62).
What is average?The result of a collection, also known as the arithmetic mean, is the sum of all values split by all of the values. One of the most commonly used primary trend indicators, it is frequently referred to as "mean." Multiply the total number of numbers in the collection by each value to get the result. Calculations can be performed using either the raw data or data that has been merged into frequency charts.
Here,
The error margin (E) is equal to z* (standard deviation / sqrt(n)).
Interval of confidence equals sample mean E
Where n is the sample size, z* is the critical value for the required confidence level, and s is the population standard deviation.
We can enter the provided values into the margin of error formula as follows:
=> E = 2.05 * (1227 / sqrt(227))
=> E ≈ 147.62
Therefore, the error range is roughly $147.62.
Next, we can create the confidence interval using the group mean and margin of error:
Interval of confidence equals sample mean E
=> Confidence range is between $52,939 and $147.62.
=> Interval of confidence = ($52,791.38, $53,086.62)
Therefore, the range of the typical household income in Martin County within the 96% confidence interval is ($52,791.38, $53,086.62).
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The radius of a sphere is increasing at a constant rate of 2 inches per minute. At the instant when the radius of the sphere is 9 9 inches, what is the rate of change of the volume? The volume of a sphere can be found with the equation � = 4 3 � � 3 . V= 3 4 πr 3 . Round your answer to three decimal places.
Answer:
2035.752 in³/min
Step-by-step explanation:
To find the rate of change of the volume of the sphere at the instant its radius is 9 inches, we need to work out dV/dt when r = 9.
The equation for the volume of a sphere is:
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Differentiate the expression for volume with respect to r:
[tex]\begin{aligned}V&=\dfrac{4}{3}\pi r^3\\\\\implies\dfrac{\text{d}V}{\text{d}r}&=3 \cdot \dfrac{4}{3} \pi r^{3-1}\\\\\dfrac{\text{d}V}{\text{d}r}&=4 \pi r^2\end{aligned}[/tex]
We know that that the radius of a sphere is increasing at a constant rate of 2 inches per minute, so the rate of change of the radius of sphere is:
[tex]\dfrac{\text{d}r}{\text{d}t}=2[/tex]
To find an expression for dV/dt, use the chain rule:
[tex]\boxed{\dfrac{\text{d}V}{\text{d}t}=\dfrac{\text{d}V}{\text{d}r} \times \dfrac{\text{d}r}{\text{d}t}}[/tex]
Substitute the expressions for dV/dr and dr/dt to create an expression for dV/dt:
[tex]\begin{aligned}\implies \dfrac{\text{d}V}{\text{d}t}&=4 \pi r^2 \times 2\\&=8 \pi r^2\end{aligned}[/tex]
To find the value of dV/dt when r = 9, substitute r = 9 into the equation for dV/dt:
[tex]\begin{aligned}\dfrac{\text{d}V}{\text{d}t}\;\textsf{at}\;r=9\implies \dfrac{\text{d}V}{\text{d}t}&=8 \pi (9)^2\\&=8\pi (81)\\&=648\pi\\&=2035.752\; \sf in^3/min\;(3\;d.p.)\end{aligned}[/tex]
Therefore, the rate of change of the volume of the sphere at the instant when its radius is 9 inches is 2035.752 in³/min (rounded to three decimal places).
Eliminate the x term
The solution to the system of equations is x = -1, y = 2.
What is a linear equation?A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation of two variables."
What characterizes a linear equation?The adjective "linear" comes from the fact that the collection of solutions to such an equation forms a straight line in the plane.
These are the three types of linear equations:
Slope Intercept Form Standard Form Point Slope FormHow do we eliminate variables?By multiplying each equation by an appropriate constant, we may use the method of elimination to make the coefficients of x in both equations equal in size but opposite in sign. The following results from multiplying the first equation by 3 and the second equation by -2 in this situation:
a. 6x + 12y = 18
b. -6x - 10y = -14
To get rid of x, we can now combine these two equations:
a. 6x + 12y = 18
b. (-6x - 10y = -14)
2y = 4
By finding y, we obtain:
y = 2
We can find x by adding this value of y back into either of the initial equations:
2x + 4y = 6
2x + 4(2) = 6
2x + 8 = 6
2x = -2 x ⇒ -1
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the solution to the system of equations 2x+4y=6 and 3x+5y=7, after eliminating the x term, is x = -1 and y = 2.
The x term, we can multiply the first equation by -3 and the second equation by 2, so that the x term will have opposite coefficients and will cancel out when we add the two equations together.
[tex]-3(2x+4y=6) gives -6x - 12y = -18[/tex]
[tex]2(3x+5y=7) gives 6x + 10y = 14[/tex]
Adding these two equations gives:
[tex]-6x - 12y = -18[/tex]
[tex]+6x + 10y = 14[/tex]
[tex]-2y = -4[/tex]
Solving for y, we get:
[tex]y = 2[/tex]
Substituting this value of y back into either of the original equations, we can solve for x:
[tex]2x + 4y = 6[/tex]
[tex]2x + 8 = 6[/tex]
[tex]2x = -2[/tex]
[tex]x = -1[/tex]
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(X^3+x^2+x+2)/(x^2-1)
According to the given question quotient of a given equation [tex](x^{3} +x^{2} +x+2)/(x^{2} -1)[/tex] is [tex]x[/tex] [tex]+ (3x+2)/ (x^{2} -1)[/tex]
What is equation?When the roots and solutions of two equations coincide, the two equations are compared.
The same quantity, symbol, or expression must be added to or subtracted from both of the equation's two sides in order to produce an equivalent equation.
By multiplying or dividing each side of such an equation by a nonzero number, we can also produce a comparable equation.
Given
[tex](x^{3} +x^{2} +x+2)/(x^{2} -1)[/tex] by using polynomial long devision
After dividing we get
[tex]x+ (3x+2)/ (x^{2} -1)[/tex]
Therefore the given question quotient of a given equation [tex](x^{3} +x^{2} +x+2)/(x^{2} -1)[/tex] is [tex]x[/tex] [tex]+ (3x+2)/ (x^{2} -1)[/tex]
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give the required elements of the hyperbola y^2/9-x^2/81=1
The hyperbola opens:
Vertically
Horizontally
By answering the presented question, we may conclude that equation Asymptotes: y = ±(3/9)x and y = ±(-3/9)x, which simplify to y = ±(1/3)x and y = ∓(1/3)x. and The hyperbola opens Vertically.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation[tex]"x2 + 2x - 3 = 0,[/tex]" the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Center: (0,0)
Transverse axis length: 2a = 2*3 = 6
Conjugate axis length: 2b = 2*9 = 18
Vertices: (0,±3)
Foci: (0,±√18)
Asymptotes: y = ±(3/9)x and y = ±(-3/9)x, which simplify to y = ±(1/3)x and y = ∓(1/3)x.
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Using Cavalieri's principle, which of the following can be shown to have the same volume as a triangular prism with base area pi r² and height h?
Hence, a cylinder with height h and base area [tex]\pi r^{2}[/tex] may be proven to have the same volume as a triangular prism.
What is a cylinder?Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.
When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.
A cylinder's volume may be calculated using the formula V = [tex]r^{2}[/tex]h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.
Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.
Let's consider the given triangular prism with base area [tex]\pi[/tex][tex]r^2[/tex] and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:
[tex]A(y) = \pi r^2 + (2r)(y) / 2[/tex]
Simplifying, we get:
[tex]A(y) = \pi r^2 + ry[/tex]
Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:
[tex]A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh[/tex]
By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:
[tex]\pi r^² + ry = \pi r^² + 2rh[/tex]
[tex]ry = 2rh[/tex]
[tex]y = 2r[/tex]
So, we see that the areas are equal for all y between 0 and h, except at [tex]y = 2r.[/tex] However, this is just a single point and has no effect on the volume,
Therefore, the cylinder with base area [tex]\pi[/tex][tex]r²[/tex] and height h has the same volume as the triangular prism, with base area [tex]\pi[/tex]r² and height h.
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1. What is the range of this data set?
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 22
2. 7.5
3. 11
4. 16
2. Use the list below to find the lower quartile.
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 7
2. 7.5
3. 8
4. 8.5
3. Use the list below to find the upper quartile.
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 11
2. 13
3. 14
4. 16
4. What is the interquartile range of the data set?
5, 5, 6, 7, 9, 11, 14, 17, 21, 23
1. 7
2. 9
3. 11
4. 13
5. What is the interquartile range of this data set?
4, 5, 7, 9, 10, 14, 16, 24
1. 6
2. 7
3. 8
4. 9
Answer:I think the answer should be 22 because you subtract 27 the largest number from the smallest number which is 5 which gives you 22
Step-by-step explanation:
1) 27-5=22
A storage company sells their moving boxes for x dollars each. For every dollar the price is increased, the quantity sold decreases by 49. When the price is zero, there are 567 moving boxes in demand to be sold. Which of the following functions could be used to determine the total amount of revenue the company earns from selling moving boxes?
A.
r(x) = -49x2 + 567
B.
r(x) = -49x2 + 567x
C.
r(x) = 49x2 + 567x
D.
r(x) = -49x2
A function which could be used to determine the total amount of revenue the company earns from selling moving boxes include the following: B. r(x) = -49x² + 567x.
How to calculate the total amount of revenue?From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (equation):
R(x) = x × P(x)
Where:
x represents the number of units sold.p(x) represents the unit price.Since it is a revenue function, we would simply substitute the value of the unit price and evaluate as follows:
Revenue, R(x) = x × P(x)
P(0) = 567
By substituting the given parameters into the formula, we have;
Revenue, R(x) = x × (567 - 49x)
Revenue, R(x) = -49x² + 567x
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