Thus, the number of months when the revenue earned will be equal to the business's expenses is 8 months approx)
Explain about the quadratic function;f(x) = ax² + bx + c, from which a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Even though "width" or "steepness" of a parabola can vary as well as its path of opening, they all share so same fundamental "U" form.
Given data:
monthly expenses's function: y = 2.75x + 7.5 .
revenue function: y = 0.2x² + 1.5x
x is the number of months
y is the amount of money (dollars)
monthly expenses = revenue function
2.75x + 7.5 = 0.2x² + 1.5x
On simplification:
0.2x² + 1.5x - 2.75x - 7.5 = 0
0.2x² - 1.25x - 7.5 = 0
Divide equation by 0.2
x² - 6.25x - 37.5 = 0
standard form of quadratic eq: ax² + bx + c = 0
On comparing:
a = 1, b = -6.25 and c = -7.5
Using the quadratic formula:
x = [tex](-b + \sqrt{b^{2} - 4 ac } )/ 2a[/tex] and x = [tex](-b - \sqrt{b^{2} - 4 ac } )/ 2a[/tex]
Put the values:
x = [tex](6.25 + \sqrt{-6.25^{2} - 4 *1*(-7.5) } )/ 2*1[/tex]
x = (6.25 + 8.31)/2
x = 7.28 (number of months)
x = 8 months approx
and x = [tex](6.25 - \sqrt{-6.25^{2} - 4 *1*(-7.5) } )/ 2*1[/tex]
x = (6.25 - 8.31)/2
x = -1.03 (negative value not taken)
Thus, the number of months when the revenue earned will be equal to the business's expenses is 8 months approx)
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complete question:
The monthly expenses of a business can be modeled by y = 2.75x + 7.5 The revenue generated by the business can be represented by the function y = 0.2x² + 1.5x. In each function, x is the number of months since the business opened and y is the amount of money in thousands of dollars. After how many months will the revenue earned be equal to the business's expenses.
Use the function f(x) to answer the questions.
f(x) = −16x2 + 60x + 16
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answer: Part A:
To find the x-intercepts of the graph of f(x), we need to set f(x) equal to zero and solve for x:
-16x2 + 60x + 16 = 0
Divide both sides by -4 to simplify:
4x2 - 15x - 4 = 0
We can use the quadratic formula to solve for x:
x = (-b ± sqrt(b2 - 4ac)) / 2a
Where a = 4, b = -15, and c = -4.
x = (-(-15) ± sqrt((-15)2 - 4(4)(-4))) / 2(4)
x = (15 ± sqrt(385)) / 8
Therefore, the x-intercepts are approximately 0.256 and 3.194.
Part B:
The coefficient of the x2 term in f(x) is -16, which is negative. This means that the graph of f(x) opens downward, so the vertex is a maximum.
The x-coordinate of the vertex can be found using the formula:
x = -b / 2a
Where a = -16 and b = 60.
x = -60 / 2(-16) = 1.875
To find the y-coordinate of the vertex, we can plug in this value of x into the equation for f(x):
f(1.875) = -16(1.875)2 + 60(1.875) + 16 = 80.25
Therefore, the coordinates of the vertex are (1.875, 80.25).
Part C:
To graph f(x), we can use the information we obtained in Part A and Part B. We know that the x-intercepts are approximately 0.256 and 3.194, and the vertex is at (1.875, 80.25).
We can also find the y-intercept by plugging in x = 0:
f(0) = -16(0)2 + 60(0) + 16 = 16
Therefore, the y-intercept is (0, 16).
Using all of this information, we can sketch the graph of f(x) as a downward-opening parabola with x-intercepts at approximately 0.256 and 3.194, a vertex at (1.875, 80.25), and a y-intercept at (0, 16).
Step-by-step explanation:
Create a real life example that includes function composition in it and solve it?
how can you multiply binomial with a trinomial? Give an example about it and solve it.
For instance: Let f(x) = 2x + 1 and g(x) = x^2. Find (f ∘ g)(3). First, we need to find g(3) which is 3^2 = 9. Then we plug this value into f: f(g(3)) = f(9) = 2(9) + 1 = 19. Therefore, (f ∘ g)(3) = 19.
What is the description of a function composition?Function composition is a mathematical concept that is used to combine two or more functions into a single function. This concept is widely used in real life situations, such as in computer programming, engineering, and physics.
For example, in computer programming, function composition is used to break down complex programs into smaller, more manageable parts. By using function composition, programmers can create complex programs that are easier to read and maintain. Therefore, function composition is a powerful tool that is used in various fields to simplify complex problems and create more accurate models of the world around us.
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PLEASE HELP
find the first 5 terms of each sequence (see picture)
The first five terms of the sequences are 2, 3, 5, 9, 17. and 1, 4, 7, 10, 13
Using the formula, an = 2an-1 - 1 where a1 = 2, we can find the first few terms of the sequence as follows:
a2 = 2a1 - 1 = 2(2) - 1 = 3
a3 = 2a2 - 1 = 2(3) - 1 = 5
a4 = 2a3 - 1 = 2(5) - 1 = 9
a5 = 2a4 - 1 = 2(9) - 1 = 17
Therefore, the first five terms of the sequence are: 2, 3, 5, 9, 17.
For the second sequence, the first five terms are
1, 4, 7, 10, 13
Because the common difference is 3
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///////////////lelelelelelelelel//////
Answer: I do not understand this question
Step-by-step explanation: Enjoy your day today
HELP PLEASE EASY 20 POINTS!!
After running a marathon,Alvin reduced his training by 18 miles per week on a period of 3 weeks. Which equation can be used to represent the average weekly change in his training?
A) -18 ÷ -3 = +6
B) +18 ÷ -3= -6
C) +18 ÷ +3 = +6
D) -18 ÷ 3 = -6
Micheal is a swimmer. In 2009,he swam the men's 50-meter freestyle in 23.04 seconds. In the same year,he swam the 100 meter freestyle in 47.77 seconds. How much faster,in meters,was his 50-meter freestyle time then his 100-meter freestyle time?
The answer is C) +18 ÷ +3 = +6. Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.
What is speed?Measure of how far an object travels in a certain amount of time. Speed is calculated by dividing the distance traveled by the time it took to travel that distance.
The answer is C) +18 ÷ +3 = +6.
This is because Alvin decreased his training by 18 miles over a period of 3 weeks.
Dividing the decrease by the number of weeks gives us 6 miles, which is the average weekly change in his training.
That is 18/3= 6.
To answer the second question, Micheal's 50-meter freestyle was 24.73 meters faster than his 100-meter freestyle.
To calculate this, we subtract the time of the 50-meter freestyle (23.04 seconds) from the time of the 100-meter freestyle (47.77 seconds) to get 24.73 seconds.
We then multiply this time by the speed of a meter per second (1 meter/second) to get 24.73 meters.
Therefore, Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.
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Can someone please help me ASAP? It’s due today!! Read the question. I will give brainliest if it’s all correct
The order from least to greatest is:
Neither the letters nor the numbers can be repeated.The letters can repeat, but the numbers cannot repeat.The number can repeat, but the letters cannot repeat.The letter "O" cannot be used, but there are no restrictions on repeating the other letters or numbers.What are the possible license situation?The number of possible license plates for each situation:
Neither the letters nor the numbers can be repeated: 26 x 25 x 9 x 8 x 7 = 327,600
The letters can repeat, but the numbers cannot repeat: 26 x 26 x 9 x 8 x 7 = 405,504
The number can repeat, but the letters cannot repeat: 26 x 25 x 9³ = 5,153,250
The letter "O" cannot be used, but there are no restrictions on repeating the other letters or numbers: 25 x 25 x 9 x 9 x 9 = 15,187,500
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Image transcribed:
Use the arrows to move each item into the correct order. Click the "up" arrow to move the item up, or click the "down" arrow to move the item down. Once all the items are in the correct order, submit your response.
A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then order them from least to greatest.
↑ ↓The letters can repeat, but the numbers cannot repeat.
↑ ↓The numbers can repeat, but the letters cannot repeat.
↑ ↓Neither the letters nor the numbers can be repeated.
↑ ↓The letter "o" cannot be used, but there are no restrictions on repeating the other letters or numbers.
claims filed under auto insurance policies follow a normal distribution with mean 19,400 and standard deviation 5,000. what is the probability that the average of 25 randomly selected claims exceeds 20,000?
To find the probability that the average of 25 randomly selected claims exceeds 20,000, we need to first determine the mean and standard deviation of the sample distribution.
Given:
- Mean of the population (μ) = 19,400
- Standard deviation of the population (σ) = 5,000
- Sample size (n) = 25
Step 1: Calculate the mean of the sample distribution (μ_sample)
Since the sample mean is an unbiased estimator of the population mean, μ_sample = μ = 19,400.
Step 2: Calculate the standard deviation of the sample distribution (σ_sample)
σ_sample = σ / √n = 5,000 / √25 = 5,000 / 5 = 1,000
Now, we need to find the probability that the sample mean exceeds 20,000. We can do this using the Z-score formula:
Z = (X - μ_sample) / σ_sample
where X is the sample mean we want to find the probability for (20,000 in this case).
Step 3: Calculate the Z-score
Z = (20,000 - 19,400) / 1,000 = 600 / 1,000 = 0.6
Step 4: Find the probability
Now, we need to find the area to the right of the Z-score in the standard normal distribution table or use a calculator/software that provides the probability.
The area to the right of Z = 0.6 is approximately 0.2743. So, the probability that the average of 25 randomly selected claims exceeds 20,000 is approximately 0.2743 or 27.43%.
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please help need both answers please will give 30 points please i need both answered i dont need work shown i just need both answers please
Answer:
Angle A = Angle L
Angle D = Angle M
Angle C = Angle N
Segment AB = Segment LB
Segment CD = Segment NM
Segment DA = Segment ML
2nd part
Quadrilateral URST has moved by a translation of (x-5,y+2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
The proportion of the rise to the run for each of the similar slope triangles is given by:
h / b = mh' / mb' = mh / b
What is proportion?
A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.
To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.
Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:
a / a' = b / b' = c / c'
Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.
In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.
We can write the proportion of the rise to the run for each triangle as:
h / b = mh' / mb'
Simplifying this proportion, we can cancel out the common factor of b:
h / b = mh' / mb'
h / 1 = mh' / m'
h = bmh'
Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:
h / b = mh' / mb' = mh / b
The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.
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Brandi bought 3 pies and 2 cup cakes for $17.5. Ronnie
bought 4 pies and 2 cup cakes for $22.00 How much does
the pies cost?
O $2.00
O $3.25
O $1.75
O $4.50
Answer: 4.50
Step-by-step explanation: first of start with simple multiplacation to find wich adds up to 17.5 first you multiplye 4.50x3=13.5 then 1.72x2=3.5
add them together to get 13.5+3.5= 17.5 therfor the Answer will be 4.50
A
Samuel's specialty is fences. He has a standard fence he likes to build. It's
perimeter is 76 2/3 feet. If Samuel builds eight of these fences, how many feet of
material will he need? Explain how you found your answer.
Answer:
Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.
PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer: it is going to be 1/100
The scale factor is basically like saying ratio.
60 millimeters is 60/1000 of a meter.
since there are 6 meters multiply by 6
60/6000
6/600
1/100
The movie was played in a scale factor of 1/100
Step-by-step explanation:
Can someone solve this for me please I need it fast
The value of the indicated sides of the shape given above are as follows:
Scale factor = 1.67
X = 15
Y = 9
Z = 9
How to calculate the scale factor of the given shape above?To call the scale factor of a given shape the formula used is given below;
Scale factor = Dimension of new shape(bigger)/dimension of the old shape(smaller).
Dimension of new shape = BC = 30
Dimension of old shape = FE = 18
scale factor = 30/18 = 1.67
X = AD/1.67
X = 25/1.67
X = 15 (approximately)
Y = DC/1.67
Y = 15/1.67
Y = 9 (approximately)
Z = AB/1.67
Z = 15/1.67
Z = 9(approximately)
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The heights of 11 plants, in inches, are listed. 14, 15, 16, 16, 17, 17, 17, 18, 18, 19, 22 If another plant with a height of 14 inches is added to the data, how would the range be impacted? The range would decrease to 8 inches. The range would stay the same value of 8 inches. The range would increase to 17 inches. The range would stay the same value of 18 inches.
The range wοuld stay the same value οf 8 inches.
What is average?Let's lοοk at the average fοrmula in mοre detail in this part and use sοme examples tο illustrate hοw it may be used. The fοllοwing is an example οf the average fοrmula fοr a specific set οf data οr οbservatiοns: Average = (Sum οf Observatiοns) ÷ (Tοtal Numbers οf Observatiοns).
In the οriginal data set, the maximum value is 22 inches and the minimum value is 14 inches, sο the range is:
22 - 14 = 8 inches
If anοther plant with a height οf 14 inches is added tο the data, the minimum value will still be 14 inches, but the maximum value will nοw be 22 inches (since there are twο plants with a height οf 22 inches).
Therefοre, the range will increase:
22 - 14 = 8 inches
Sο the cοrrect answer is: The range wοuld stay the same value οf 8 inches.
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One leg of a right triangle is twice the length of the other leg. The length of the hypotenuse is √45 centimeters. Let x represent the length of the shorter leg. Use the Pythagorean Theorem to write and solve an equation to find the length of the legs.
Answer:
Let's use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given that one leg (let's call it the shorter leg) is twice the length of the other leg. So, if we let x represent the length of the shorter leg, then the longer leg has a length of 2x.
We are also given that the length of the hypotenuse is √45 centimeters. We can simplify this by noticing that √45 = √(9 × 5) = √9 × √5 = 3√5. So the length of the hypotenuse is 3√5 centimeters.
Now we can write the Pythagorean Theorem equation:
x^2 + (2x)^2 = (3√5)^2
Simplifying, we get:
x^2 + 4x^2 = 45
5x^2 = 45
x^2 = 9
x = 3
So the shorter leg has a length of 3 centimeters, and the longer leg has a length of 2x = 2(3) = 6 centimeters.
Pls help ill offer 12 points
Answer:
Point L
Step-by-step explanation:
Which point represent the ordered pair
(2, -[tex]\frac{7}{2}[/tex])
-7/2 = -3.5
Looking at it we see point L is the answer.
Help solve anyone you can help me with
The surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.
How to solveTo calculate the surface area and volume of the frustum of a pyramid, we first need to determine the slant height of the frustum, which we can do using the Pythagorean theorem.
Calculate the slant height of the frustum:
Let s1 and s2 be the side lengths of the top and bottom squares, and h be the height of the frustum.
The slant height (l) can be calculated using the Pythagorean theorem:
l = sqrt(h^2 + ((s2 - s1)/2)^2)
l = sqrt(5^2 + ((6 - 3)/2)^2)
l = sqrt(25 + 1.5^2)
l = sqrt(25 + 2.25)
l = sqrt(27.25)
l ≈ 5.22 cm
Calculate the surface area of the frustum:
Surface area = top square area + bottom square area + lateral surface area
Top square area = s1^2 = 3^2 = 9 cm^2
Bottom square area = s2^2 = 6^2 = 36 cm^2
Lateral surface area = 0.5 * (s1 + s2) * l = 0.5 * (3 + 6) * 5.22 ≈ 23.49 cm^2
Total surface area ≈ 9 + 36 + 23.49 = 68.49 cm^2
Calculate the volume of the frustum:
We can use the following formula to calculate the volume of a frustum:
Volume = (h/3) * (A1 + A2 + sqrt(A1 * A2))
Where A1 and A2 are the areas of the top and bottom squares, respectively:
A1 = 3^2 = 9 cm^2
A2 = 6^2 = 36 cm^2
Volume = (5/3) * (9 + 36 + sqrt(9 * 36))
Volume = (5/3) * (45 + sqrt(324))
Volume = (5/3) * (45 + 18)
Volume = (5/3) * 63
Volume ≈ 105 cm^3
So, the surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.
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A farmer is constructing a small fenced in area that can be describe with the ordered pairs (2,3), (2,8), (6,8), and (6,3). The units for both x and y are feet. Make a graph. The find the amount of fencing he will need.
We need to find the perimeter of the shape given by the coordinates. Let's start by drawing a Cartesian coordinate system and identifying the points. This will give us information about the geometric shape.
A Cartesian coordinate system is given in the photos below and the indicated points [(2,3), (2,8), (6,3) and (6,8)] are marked.
We can see that this shape is a rectangle. A rectangle is home to two sides of different lengths, long and short. To find the perimeter of a rectangle, we add the length of the long side and the length of the short side and multiply the result by [tex]2[/tex]. (Because a rectangle must have [tex]2[/tex] long sides and [tex]2[/tex] short sides).
The rectangle in the figure has a long side length of [tex]5[/tex] feet and a short side length of [tex]4[/tex] feet.
Perimeter: [tex]2(L+S) = 2(5+4)=18ft.[/tex]
an air line reports the 94% of its flights arrive on time describe the complement of the flight arriving on time
The percentage of flights that do not arrive on time is 6%.
If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the
percentage means, a part per hundred. The word per cent means per 100.
An air line reports the 94% of its flights arrive on time.
The complement of the flight arriving on time would be the percentage of flights that do not arrive on time.
To calculate the complement, you can subtract the percentage of flights arriving on time from 100%.
The complement of the flight arriving on time = 100% - 94% = 6%
Therefore, the percentage of flights that do not arrive on time is 6%.
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Suppose a new cross section was created in each solid, both at the same height, using some scale factor k. How would the areas of these 2 cross sections compare? Explain your reasoning.
The areas of the two cross-sections would be proportional to k².
If a new cross-section was created in each solid, both at the same height using a scale factor k, the areas of the two cross sections would be proportional to k².
The reason for this is that when a scale factor is applied to a two-dimensional figure, the area of the resulting figure increases by a factor of k². This is because the linear dimensions of the figure (length and width) are multiplied by k, and since the area is calculated by multiplying length and width, the area of the figure is multiplied by k².
Therefore, if the two cross sections are created at the same height and are scaled by the same factor k, their areas will be proportional to k². For example, if k=2, the area of each cross-section will be four times the original area; if k=3, the area of each cross-section will be nine times the original area, and so on.
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Please help!! this is rizzcalc
The curve described by these parametric equations is the graph of the Cartesian equation: x = 2e^[(1 - y)/5]
What is the Cartesian equation?To eliminate the parameter t, we need to find a way to express t in terms of x and y, and then substitute that expression into one of the equations to eliminate t.
x(t) = 2e^t
y(t) = 1 - 5t
Let's start by solving the second equation for t:
y = 1 - 5t
Adding 5t to both sides, we get:
5t = 1 - y
Dividing both sides by 5, we get:
t = (1 - y)/5
Now we can substitute this expression for t into the first equation:
x = 2e^t
x = 2e^[(1 - y)/5]
This is the Cartesian equation in terms of x and y. We have eliminated the parameter t and expressed the equation solely in terms of x and y.
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Evaluate the expression. (4−7)4 − 52
Answer: -64
Step-by-step explanation:
In a green house basil is grown in planters that have a base of 3 1/2 by 1 3/4. If there is a 3x3 array of these planters with no space between them, what is the are covered by the planters?
seven new employees, two of whom are married to each other, are to be assigned seven desks that are lined up in a row. if the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks? (round your answer to the nearest tenth of a percent.)
The probability that the married couple will have adjacent desks is 0.72.
Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say it will happen or not. The result often has good applications in sports, business as a result of forecasting, and the result is also widely used in the field of new intelligence.
Mathematically, the number of ways to assign 6 desks to 6 employees is equal to 8!
Now,
the number of ways the couple can interchange their desks is just 2 ways
Thus,
the number of ways to assign desks such that the couple has adjacent desks is 2(6!)
The number of ways to assign desks among all six employees randomly is 7!
Thus, the probability that the couple will have adjacent desks would be ;
2(6!)/7! = 2/7
This means that the probability that the couple have non adjacent desks is 1-2/7 = 5/7 = 0.71428 ≈ 0.72
Which is 0.72 to the nearest tenth of a percent
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High Order Thinking Skills (HOTS) Q10. The amount of petrol in a tank is twice of that in another tank. If we draw out 25 litres from firs & add it the other, the amount of petrol in both the tanks will be the same. Find the amount o petrol in each tank now. ** Downloaded from www.studiestoday.com
According to the problem, the amount of petrol in the second tank is twice that in the first tank, which means the amount of petrol in the second tank is 2x liters.
If we draw out 25 liters from the first tank and add it to the second tank, the amount of petrol in both tanks will be the same. Therefore, the total amount of petrol in both tanks after the transfer is (x - 25) + (2x + 25) = 3x.
Since the amount of petrol in both tanks is the same after the transfer, we can set up an equation:
x - 25 = (2x + 25) / 2
Simplifying this equation, we get:
2x - 50 = 2x + 25
2x - 2x = 25 + 50
x = 75
Therefore, the amount of petrol in the first tank is 75 liters, and the amount of petrol in the second tank is 2x = 2*75 = 150 liters.
A tortoise takes 141 hours to walk 65 miles. At this rate, how long does it take her to walk 1 mile
The number of hours for the tortoise to walk 1 mile will be 1.5 hours.
Speed:
Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration. The pie divides the dimension of distance by time. The SI unit of speed is meter per second (m/s), but the most common unit of speed in everyday use is kilometer per hour (km/h), or in the US and UK United, the mile per hour (mph). air And for sea travel, knots are commonly used.
We know that the speed formula
Speed = Distance/Time
A tortoise takes 1 1/4 hours to walk 5/6 miles.
Convert the mixed fraction number into a decimal number.
1 ¹/₄ = 1.25 hours
Then the speed of the tortoise will be calculated as,
⇒ Speed = (5/6) / 1.25
⇒ Speed = 0.667 miles per hour
The number of hours for the tortoise to walk 1 mile will be calculated as,
⇒ T = 1 / 0.667
⇒ T= 1.5 hours
The number of hours for the tortoise to walk 1 mile will be 1.5 hours.
Complete Question:
A tortoise takes 1 1/4 hours to walk 5/6 miles. At this rate, how long does it take her to walk 1 mile?
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most computer languages include a function that can be used to generate random numbers. in excel, the rand function can be used to generate random numbers between and . if we let denote a random number generated using rand, then is a continuous random variable with the following probability density function. a. select the probability density function. 1. 2. 3. 4. choose the correct graph from above: - select your answer - b. what is the probability of generating a random number between and (to 1 decimal place)? c. what is the probability of generating a random number with a value less than or equal to (to 1 decimal place)? d. what is the probability of generating a random number with a value greater than (to 1 decimal place)? e. using random numbers given below, compute the mean and standard deviation. 0.931806 0.398110 0.216843 0.826248 0.323101 0.235342 0.105300 0.203744 0.973537 0.181343 0.848380 0.602418 0.013789 0.495464 0.365786 0.027959 0.782500 0.232680 0.913043 0.689042 0.399642 0.982936 0.724617 0.088320 0.152830 0.303524 0.706177 0.076412 0.937273 0.367035 0.155910 0.003958 0.442786 0.769659 0.098387 0.995570 0.953256 0.497222 0.428427 0.531733 0.895690 0.717929 0.257446 0.478400 0.810417 0.666180 0.071199 0.876201 0.545347 0.159312 mean (to 6 decimals) standard deviation (to 6 decimals)
a. The probability density function of the random variable generated using rand in Excel is:1:b. The probability of generating a random number between 0.2 and 0.8 can be found by calculating the area under the probability density function between those values:P(0.2 ≤ X ≤ 0.8) = ∫0.8 0.2 f(x) dxP(0.2 ≤ X ≤ 0.8) ≈ 0.6Therefore, the probability of generating a random number between 0.2 and 0.8 is approximately 0.6.c. The probability of generating a random number with a value less than or equal to 0.5 can be found by calculating the area under the probability density function up to that value:P(X ≤ 0.5) = ∫0.5 0 f(x) dxP(X ≤ 0.5) ≈ 0.5Therefore, the probability of generating a random number with a value less than or equal to 0.5 is approximately 0.5.d. The probability of generating a random number with a value greater than 0.8 can be found by calculating the area under the probability density function above that value:P(X > 0.8) = ∫1 0.8 f(x) dxP(X > 0.8) ≈ 0.1Therefore, the probability of generating a random number with a value greater than 0.8 is approximately 0.1.e. Using the given random numbers, we can calculate the mean and standard deviation as follows:Mean:μ = (0.931806 + 0.398110 + 0.216843 + ... + 0.545347 + 0.159312) / 50μ ≈ 0.464257Therefore, the mean of the given random numbers is approximately 0.464257.Standard deviation:s = sqrt([(0.931806 - μ)^2 + (0.398110 - μ)^2 + ... + (0.545347 - μ)^2 + (0.159312 - μ)^2] / (50 - 1))s ≈ 0.316221Therefore, the standard deviation of the given random numbers is approximately 0.316221.
a. The probability density function is 1.
b. The probability of generating a random number between 0.2 and 0.8 is 0.6.
c. The probability of generating a random number with a value less than or equal to 0.5 is 0.5.
d. The probability of generating a random number with a value greater than 0.7 is 0.3.
e. The mean is 0.472817 and the standard deviation is 0.316211.
A customer purchased a book that had an original price for $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book?
Enter your answer in the box.
$30.21 is the total amount, in dollars, the customer pays for the discounted book.
If the original price of the book was $38, and it was discounted by 25%, then the discounted price of the book would be:
Discounted price = Original price - Discount
Discounted price = $38 - 0.25 x $38
Discounted price = $28.50
Now, the customer must pay a 6% sales tax on the discounted price of the book. The sales tax can be calculated as:
Sales tax = 0.06 x Discounted price
Sales tax = 0.06 x $28.50
Sales tax = $1.71
Therefore, the total amount the customer pays for the discounted book is the sum of the discounted price and the sales tax:
Total amount = Discounted price + Sales tax
Total amount = $28.50 + $1.71
Total amount = $30.21
So, the customer pays $30.21 for the discounted book
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Let ²-13x - 30 = (x+p) (x+q). If the absolute value of p is greater than the absolute
value of q, which number, p or q, is a negative integer? Explain your answer.
Answer: We can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients, and use this relationship to find the values of p and q.
Given the equation ²-13x - 30 = (x+p)(x+q), we can see that the coefficient of the x^2 term is 1, the coefficient of the x term is -13, and the constant term is -30.
By comparing the coefficients with the formula for the sum and product of the roots of a quadratic equation, we have:
p + q = -(-13)/1 = 13
p*q = -30/1 = -30
Since the absolute value of p is greater than the absolute value of q, we know that either p is positive and q is negative, or p and q are both negative. We can eliminate the possibility of p being positive and q being negative, since their product would be negative, and we know that p*q = -30. Therefore, both p and q must be negative integers.
We also know that the sum of p and q is 13, which means that the absolute value of q is less than the absolute value of p. Since p and q are both negative, this means that q has a larger absolute value (i.e., is farther from zero) than p. Therefore, q is the negative integer in this case.
Step-by-step explanation:
c/0.5 - 3.2 = 2.6 I dont get it
Answer:
c/0.5= 2.6+3.2
c= 5.8×0.5
c=2.9