Answer:
3
Step-by-step explanation:
To estimate the number of students out of the next 10 who will support Julian, we can use the proportion of students who have supported Julian so far.
The total number of students who have been surveyed is:
15 + 9 + 16 + 10 = 50
Out of these 50 students, 15 have supported Julian. Therefore, the proportion of students who have supported Julian so far is:
15/50 = 0.3
To estimate how many of the next 10 students surveyed will support Julian, we can multiply the proportion of students who have supported Julian so far by 10:
0.3 x 10 = 3
Therefore, we can estimate that out of the next 10 students surveyed, about 3 will support Julian.
1. When you turn on the hot water tap in your kitchen, the temperature T of the
water depends on how long the water has been running. If we want to model T as
a function of time t, what do you think a rough graph of T would look like? You
can sketch T on a piece of paper if you like, scan and then insert the image as the
answer to this question
A rough graph of T as a function of time t for hot water running from a tap would likely show an exponential decay curve.
Initially, the temperature of the water will be close to the temperature of the hot water supply in the house. However, as the water continues to flow, the temperature will gradually decrease due to heat loss through the pipes and the ambient temperature of the surrounding air. This decay will likely be exponential, with a relatively steep initial drop in temperature followed by a more gradual decrease over time. The graph would show an asymptotic approach towards room temperature as the water continues to flow. The exact shape of the curve will depend on a variety of factors, such as the length and material of the pipes, the ambient temperature, and the temperature of the hot water supply.
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I need a step by step process for to find out what, "x" is in this problem. y = -3x +5
when y = 5 in the equation y = -3x + 5, the value of variable x is 0.
Define equationAn equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.
the steps to find out what x is in the equation y = -3x + 5 for y = 5:
Substitute y = 5 in the equation: y = -3x + 5Replace y with 5: 5 = -3x + 5Subtract 5 from both sides of the equation: 5 - 5 = -3x + 5 - 5Simplify: 0 = -3xDivide both sides by -3: 0/-3 = -3x/-3Simplify: 0 = xTherefore, x = 0 when y = 5 in the equation y = -3x + 5.To know more about Divide, visit:
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The complete question is:
I need a step by step process for to find out what, "x" is in this problem. y = -3x +5 for y=5
statement: if two noncollinear rays join at a common endpoint, then an angle is created. which geometry term does the statement represent?
The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
The two rays are called the sides of an angle, and the common endpoint is called the vertex.
The angle that lies in the plane does not have to be in the Euclidean space.
An angle is formed when two non-collinear rays join at a common endpoint.
This endpoint is called the vertex of the angle.
The two rays are referred to as the arms of the angle.
Angles can be classified according to their degree measurement.
An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle
measures between 90 and 180 degrees.
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You’ve been making student loan payments consistently for the past year, and your credit score has increased. Now, your APR is lower, 18%. If you owe $777, what is the amount of interest you will owe?
To find the amount of interest you will owe, we need to calculate the interest using the formula:
Interest = Principal * Rate * Time
Where:
- Principal = $777 (the amount you owe)
- Rate = 18% per year (expressed as a decimal, or 0.18)
- Time = 1 year (since you have been making payments for a year)
Plugging in these values, we get:
Interest = $777 * 0.18 * 1
Interest = $139.86
So, the amount of interest you will owe is approximately $139.86.
how can we simplify algebric expressions?
There are various techniques to simplify algebraic expressions, including:
1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.
2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.
3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.
4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).
Equation for line of best fit
correlation positive/negative
r=
Therefore , the solution of the given problem of equation comes out to be y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect
What is an equation?
Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.
Here,
The least squares technique can be used to determine the equation of the line, presuming that the line of best fit is a linear regression line.
The findings that we get using a calculator or statistical software are as follows:
=> y = -0.9x + 5.5 is the equation of the line of best fit.
=> R = -0.83 is the correlation coefficient (r).
We can infer that there is a negative link between the two variables because the correlation coefficient (r) is negative.
This implies that the value of y tends to decline as the value of x rises.
As a result, y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.
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find the 5th term of this sequence: 3/2,4/3,5/4,6/5
how many different committees with 4 members can be formed from a group of 10 people? (order is not important.)
The number of committees with 4 members can be formed from a group of 10 people are 210 different committees
To find the number of different committees with 4 members that can be formed from a group of 10 people we can use the combination formula which is,
nCr = n!/r!(n-r)!
where:
nCr = number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
from the given data:
n = 10
r = 4
From the above formula, we can write the equation as:
= 10C4
=C(10,4)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Therefore, 210 different committees with 4 members can be formed from a group of 10 people.
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Can someone please help me
:3
The area of the base (B) to be 15.588 cm², the height of the prism (h) to be 22 cm, and the volume (V) of the prism to be 343.996 cm³.
What is area?Area is a measure of the size of a two-dimensional surface or shape. It is measured in square units such as square meters (m2), square centimeters (cm2), square kilometers (km2), and square miles (mi2). Area can also be calculated for three-dimensional shapes, such as cubes and spheres, by multiplying length, width, and height. For example, the area of a cube with sides of length 10 cm would be 1000 cm2. Area is an important concept in mathematics and has many practical uses in real life.
Base Area (B):
To calculate the area of the base, we use the formula for the area of an equilateral triangle: B = (√3/4) × a², where a is the side length.
In this case, a = 6 cm. Therefore, B = (√3/4) × 6² = 15.588 cm².
Height (h):
The height of the prism is the height of the triangle (12 cm) plus the height of the floor (10 cm). Therefore, h = 12 cm + 10 cm = 22 cm.
Volume (V):
The volume of the prism is equal to the area of the base times the height of the prism. Therefore, V = B × h = 15.588 cm² × 22 cm = 343.996 cm³.
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Opposite vertices of a rectangle in the standard (x, y) coordinate plane have coordinates (6, 38) and (18, 8) respectively. What are the coordinates of the center of this rectangle?
(12, 23) are the coordinates of the center of the rectangle with coordinates (6, 38) and (18, 8).
To find the coordinates of the center of the rectangle in the standard (x, y) coordinate plane, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are:
((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the opposite vertices of the rectangle have coordinates (6, 38) and (18, 8). We can use these coordinates to find the midpoint of the rectangle as follows:
The x-coordinate of the midpoint is (6 + 18) / 2 = 12.
The y-coordinate of the midpoint is (38 + 8) / 2 = 23.
Therefore, the coordinates of the center of the rectangle are (12, 23)
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At a school social, parents attended with their children. Everyone had a choice between a sweet snack and a salty snack. Here is a two-way table showing the number of adults and children who made each choice of snack. sweet snack salty snack total adult 57 88 145 child 77 31 108 total 134 119 253 Make a segmented bar graph to represent the data in your table. Use one bar for each row of the table
The horizontal axis of the graph represents the total number of individuals who made a choice, and the vertical axis represents the type of snack.
The graph has two bars, one for sweet snacks and one for salty snacks. Each bar is segmented to represent the number of adults and children who chose each type of snack. For the first row of the table, the sweet snack bar is segmented into two parts: one representing the 57 adults who chose a sweet snack, and the other representing the 77 children who chose a sweet snack. The total length of the bar is 134, representing the total number of individuals who made a choice.
For the second row of the table, the salty snack bar is segmented into two parts: one representing the 88 adults who chose a salty snack, and the other representing the 31 children who chose a salty snack. The total length of the bar is 119, representing the total number of individuals who made a choice.
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The complete question is:
At a school social, parents attended with their children. Everyone had a choice between a sweet snack and a salty snack. Here is a two-way table showing the number of adults and children who made each choice of snack.
Make a segmented bar graph to represent the data in your table. Use one bar for each row of the table
hi i need help checking i already know the answer!!
x/7 - 4 = 4
Answer:
x=56
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 56
Step-by-step explanation:
Given that-
x/7 - 4 = 4
x/7 - 4 + 4 = 4 + 4 >> Add 4 to both sides
x/7 = 8
7x/7 = 8 × 7 >> Multiply both sides by 7
x = 56
Check Answer-
Substitute x in the equation the check.
56/7 - 4 = 4 >> 56/7 = 8
8 - 4 = 4 >> 8 - 4 = 4
4 = 4 >> Correct
RevyBreeze
could someone explain this to me so I can do it? It's dividing decimals by whole numbers.
First thing you need to do is raise the decimal. Once you've raised the decimal then you should continue through the problem as if it were a standard long division question.
Start with the first number which is 6.
6 divided by 3 is 2. That means you can subtract 6 from the first number.
Then, you bring down 3 and do the same thing.
3 divided by 3 is 1. Subtract 3 from 3 and then bring down the next number.
Finally, 3 divided by 9 is three.
By following this process, you should get 2.13 as your final answer.
Look at the image below for more reference.
When flying out of a place your expected to fly to 1500 feet before leaving the airspace in a pilots plane their distance measuring equipment says they have traveled 2 miles before they reached this altitude what angle was the pilot flying as they took off from the runway?
Answer: To solve this problem, we can use trigonometry and the relationship between angle, distance, and altitude in a right triangle.
Let's denote the angle the pilot was flying at takeoff as θ. We can then use the tangent function to find θ, since:
tan(θ) = opposite/adjacent
In this case, the opposite side is the altitude the pilot reached (1500 feet), and the adjacent side is the distance the pilot traveled before reaching that altitude (2 miles = 10560 feet). So we can plug in these values and solve for θ:
tan(θ) = 1500/10560
θ = tan⁻¹(1500/10560)
θ ≈ 7.67 degrees
So the pilot was flying at an angle of approximately 7.67 degrees at takeoff from the runway.
Step-by-step explanation:
according to the u.s. department of agriculture, the mean yield of corn per acre in the u.s. is 107 bushels with a standard deviation of 15 bushels. suppose 80 one-acre plots of corn are selected at random. (a) what is the probability that the mean yield of the 80 one-acre plots chosen will be between 104 and 111 bushels? (b) what is the probability that the mean yield of the 80 one-acre plots chosen will be greater than 105 bushels? (c) what is the probability that a randomly selected one-acre plot has a yield less than 100 bushels? (2) the average age of millionaires in the us is to be determined. twenty us millionaires are randomly selected to find a mean age of 58.5 years. assume the standard deviation of all us millionaires is 12.8 years. assume the population of ages of us millionaires is normally distributed. find a 95% confidence interval for the mean age of all millionaires. round your answer to 2 decimal places if necessary. interpret your answer in a sentence.
The probability that the mean yield of the 80 one acre plots chosen will be within 2 bushels of the population mean is 0.9332. The assumptions made to answer part (a) are that the population standard deviation is known, the sample is randomly selected, and the sample size is large (n>=30)
a) We can use the central limit theorem to approximate the distribution of the sample mean. The distribution of the sample mean can be approximated as a normal distribution with a mean of 107 bushels and a standard deviation of 12/√80=1.34 bushels. Therefore, we can find the probability that the sample mean falls within 2 bushels of the population mean using the standard normal distribution.
P(105 ≤ X ≤ 109) = P(Z ≤ (109-107)/1.34) - P(Z ≤ (105-107)/1.34)
= P(Z ≤ 1.49) - P(Z ≤ -1.49)
= 0.9319 - 0.0681
= 0.8638
Therefore, there is an 86.38% probability that the mean yield of the 80 one acre plots will be within 2 bushels of the population mean.
b) Assumptions made:
The sample of 80 one acre plots is selected at random.
The one acre plots are independent of each other.
The population standard deviation is known and remains constant.
The distribution of the yield of corn per acre is approximately normal.
The sample size is large enough (n≥30) to apply the central limit theorem.
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Distributive property
3(r+2)+5(r+t-2)?
1. 3r+6+5r+t-10
2. 3r+2+5r+5t-10
3. 3r+6+5r+5t-10
4. 3r+6+5r+t-2
Answer:
Step-by-step explanation:
Using the distributive property, we can simplify the expression as follows:
3(r+2) + 5(r+t-2)
= 3r + 3(2) + 5r + 5t - 5(2)
= 3r + 6 + 5r + 5t - 10
= 8r + 5t - 4
Therefore, the simplified expression is:
8r + 5t - 4
a container is shaped like a triangular prism. each base of the container is an equilateral triangle with the dimensions shown. image the container has a height of 15 centimeters. what is the lateral surface area of the container in square centimeters?
The lateral surface area of the triangular prism container is 270 cm².
We will begin with the calculation of perimeter of equilateral triangle.
Perimeter = 3 × sides
Perimeter = 3 × 6
Perimeter = 18 cm
Now calculating the lateral surface = perimeter of base × height
Keep the values in formula
Lateral surface of equilateral triangle prism = 18 × 15
Performing multiplication again
Lateral surface area = 270 cm²
Thus, the lateral surface area of the container is 270 cm².
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The picture is added of equilateral triangle with dimensions.
a group of rats ran faster after receiving a steroid drug supplement compared to a group of rats that received no steroid drug supplement. which type of statistical test should be used to report these results?
An independent samples t-test would be appropriate to analyze the difference in running speed between rats that received a steroid drug supplement and those that did not.
The appropriate statistical test to analyze the difference in running speed between two groups of rats (one receiving a steroid drug supplement and one not receiving it) would be a t-test. Specifically, an independent samples t-test would be suitable for this type of comparison, assuming that the data meets the assumptions for parametric testing.
This test would compare the means of the two groups and assess the probability that the observed difference is due to chance alone. A significant result would indicate that the difference in running speed is unlikely to be due to chance and is instead likely to be a true effect of the steroid drug supplement
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Jared is building a tree house. He pays $75 for materials and pays his friend $12 per hour to help him. If Jared spends a total of $129 on building his tree house, for how many hours did his friend work on it?
What are the values of x and y?
We can therefore find the other angle of right angle triangle by
Pythagoras , then x = 142 - y and y = 142 - x
What is the Pythagoras ?A fundamental theorem in geometry that deals with the sides of a right triangle is known as the Pythagorean theorem. In it, it is said:
a+ b² = c²
where the lengths of the right triangle's legs are a, b, and c, and the length of the hypotenuse (the side across from the right angle) is c
Nevertheless, if we know the other two, we can use the fact that the total of the angles in a triangle is always 180 degrees to determine one of the angles. We are aware that angle C in this situation is 38 degrees.
We thus have:
x + y + 38 = 180
Calculating x and y results in:
x = 142 - y
y = 142 - x
We can therefore find the other angle if we know the value of one. To determine the real figures, we still want further details.
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Write the slope-intercept form of the equation of the line through the given point with the given slope.
Point: (-1,4) , Slope=3/4
Answer:
[tex]y-y_1=m(x-x_1)\\\y-4=\frac{3}{4} (x-(-1))\\\\y-4=\frac{3}{4} x+\frac{3}{4} \\y=\frac{3}{4} x+\frac{19}{4}[/tex]help i am stuck in this question.
The proof of the sum of the triangles ΔPMS + ΔMQT and ΔSOR + ΔNRT is shown below
Proving the sum of the triangles are equalGiven that
PQRS and MNOP are parallelograms
We have the following congruent sides by the theorem of CPCTC
QT = RT and MQ = NR
PM = SO and MS = SR
This is alse true because of the SSS congruent theorem
When the sides are added, we get
PMS + MQT = SOR + NRT
So, we have
ΔPMS + ΔMQT = ΔSOR + ΔNRT
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in this expression, assume that y=0.
4y^2•2y^4
which is an equivalent expression?
A.)6y^6
B.)6^8
C.)8y^6
D.)8y^8
Answer:
If y=0, then 4y^2•2y^4 = 4(0)^2•2(0)^4 = 0.
Therefore, any of the options that involve y, such as A) 6y^6 or C) 8y^6, would also be equal to 0.
The only option that is still a valid answer is B) 6^8, which is simply 6 to the 8th power, or 1679616.
Hope This Helps!
Given: ​quadrilateral abcd​ is inscribed in circle o. prove: m∠a m∠c=180° a quadrilateral is inscribed in a circle o. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c, and d. drag an expression or phrase to each box to complete the proof. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. statements reasons ​quadrilateral abcd​ is inscribed in circle o. given mbcdî…î…‘î…"î…"î…"î…"=2(m∠a) response area response area inscribed angle theorem mbcdî…î…‘î…"î…"î…"î…" mdabî…î…‘î…"î…"î…"î…"=360° response area 2(m∠a) 2(m∠c)=360° substitution property ​​response area division property of equality
The angle m∠A + m∠C = 180° in the inscribed quadrilateral ABCD.
To prove that m∠A + m∠C = 180° in an inscribed quadrilateral ABCD with circle O, follow these steps:
1. Statement: Quadrilateral ABCD is inscribed in circle O.
Reason: Given.
2. Statement: m∠BCD = 2(m∠A) and m∠DAB = 2(m∠C).
Reason: Inscribed Angle Theorem
3. Statement: m∠BCD + m∠DAB = 360°.
Reason: The sum of the measures of the angles in a circle is 360°.
4. Statement: 2(m∠A) + 2(m∠C) = 360°.
Reason: Substitution Property (from steps 2 and 3).
5. Statement: m∠A + m∠C = 180°.
Reason: Division Property of Equality (divide both sides of the equation in step 4 by 2).
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Please help me I don't know this ?
1. the equation of the quadratic function is: y = (8/65)(x + 5)(x - 13)
2. The axis of symmetry is the line x = 0 (the y-axis).
What is quadratic function?
The quadratic equation with roots -5 and 13 can be written as:
y = a(x + 5)(x - 13)
where a is a constant that depends on the coefficient of the quadratic term.
To find the value of a, we can use the fact that the coefficient of the quadratic term is the sum of the roots, multiplied by -1:
a = -(sum of roots) / (product of roots)
a = -(-5 + 13) / (-5 * 13)
a = 8 / 65
Therefore, the equation of the quadratic function is:
y = (8/65)(x + 5)(x - 13)
What is symmetry?
2. The axis of symmetry is the line x = 0 (the y-axis).
To find the axis of symmetry, we can use the formula:
x = -(b / 2a)
where a and b are the coefficients of the quadratic function. In this case, a = 8/65 and b = 0, since there is no linear term.
Substituting these values, we get:
x = -(0 / (2 * (8/65)))
x = -0
Therefore, the axis of symmetry is the line x = 0 (the y-axis).
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suppose that the bac of students who drink five beers varies from student to student according to a normal distribution with mean 0.07 and standard deviation of 0.01. show your work. a. the middle 99.7% of students who drink five beers have bac between what two numbers? b. what is the range for the 16% of lowest bacs? c. what percent of students have a bac above 0.09?
a. The middle 99.7% of students between 0.04 and 0.10.
b. The range for the 16% of lowest BACs is 0.06 or below.
c. 2.28% of students have a BAC above 0.09.
a. How to find range?To find the range, use the properties of the normal distribution and the given mean (0.07) and standard deviation (0.01).
99.7% of the data lies within 3 standard deviations from the mean in a normal distribution.Calculate the lower bound: mean - 3 * standard deviation = 0.07 - 3 * 0.01 = 0.07 - 0.03 = 0.04Calculate the upper bound: mean + 3 * standard deviation = 0.07 + 3 * 0.01 = 0.07 + 0.03 = 0.10The middle 99.7% of students between 0.04 and 0.10.
To find the range use the z-score corresponding to the 16th percentile (z ≈ -1).
Calculate the BAC value corresponding to the z-score: BAC = mean + z * standard deviation = 0.07 + (-1) * 0.01 = 0.07 - 0.01 = 0.06The range for the 16% of lowest BACs is 0.06 or below.
c. How to find percentage?To find the percentage, find the z-score for 0.09 first.
Calculate the z-score: z = (BAC - mean) / standard deviation = (0.09 - 0.07) / 0.01 = 2Look up the area under the curve to the left of the z-score in a z-table (which is about 0.9772).Calculate the percentage of students above 0.09: 100% - 97.72% = 2.28%Approximately 2.28% of students have a BAC above 0.09.
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Please help
see below
The value of angle ∠α in the triangle ΔPQR is 22.1°. Therefore, the answer is option (C) i.e. 22.1°.
What is triangle?A closed triangle is a two-dimensional shape with three angles and three straight sides.
Three non-collinear points are connected with line segments to create one of the fundamental shapes in Three non-collinear points are connected with line segments to create one of the fundamental shapes in geometry Triangles can be categorized by their sides and angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.
The sum of a triangle's internal angles is always 180 degrees.
We can use trigonometry to solve for the angle α in the right triangle PQR.
We know that tan α = PQ/QR, where PQ is the opposite side and QR is the adjacent side.
Substituting the given values, we get:
tan α = 5.2/13.4
Taking the inverse tangent of both sides, we get:
α = tan⁻¹(5.2/13.4)
Using a calculator, we get:
α ≈ 22.1°
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the tensile strength of a certain metal component is normally distributed with a mean of 10,000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centimeter. a) what proportion of these components exceed 10,200 kilograms per square centimeter in ten- sile strength? b) what is the probability that a randomly chosen metal component has a tensile strength of less than 9,500 kilograms per square centimeter?
The probability calculation resulted in (a) 2.28% (b) zero.
a) To find the proportion of components that exceed 10,200 kilograms per square centimeter in tensile strength, we need to find the area to the right of 10,200 under the normal distribution curve. Using the z-score formula, we have:
z = (x - mu) / σ
z = (10,200 - 10,000) / 100
z = 2
Looking up the area to the right of z = 2 in a standard normal distribution table or using a calculator, we find this to be approximately 0.0228. Therefore, about 2.28% of the components exceed 10,200 kilograms per square centimeter in tensile strength.
b) To find the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter, we need to find the area to the left of 9,500 under the normal distribution curve. Using the z-score formula, we have:
z = (x - mu) / σ
z = (9,500 - 10,000) / 100
z = -5
Looking up the area to the left of z = -5 in a standard normal distribution table or using a calculator, we find this to be approximately 0.
Therefore, the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter is essentially 0.
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The area, a, of an ellipse can be determined using the formula a = Ï€xy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. which is an equivalent equation solved for y? y = a · Ï€x y = a (Ï€x) y = a â€" Ï€x y = a ÷ (Ï€x)
The correct equivalent equation solved for y is y = a ÷ (πx).
The equivalent equation solved for y in the given formula
a = πxy is y = a ÷ (πx).
1. Start with the original formula:
a = πxy
2. To solve for y, we need to isolate y on one side of the equation.
3. Divide both sides of the equation by πx:
a ÷ (πx) = (πxy) ÷ (πx)
4. The πx terms cancel out on the right side of the equation, leaving:
y = a ÷ (πx).
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Please help me with this Trigonometry question: its about inequalities
t ≈ 0.59, 2.09, 3.68, 5.18, 6.77, 8.27, ... These are the times when the block is 5 cm above equilibrium.
What is arccosine?The arccosine function, denoted as arccos(x) or acos(x), is the inverse function of the cosine function. In other words, given a value of x between -1 and 1, arccos(x) returns the angle whose cosine is x, in radians or degrees.
According to question:To find the times when the block is 5 cm above equilibrium, we need to solve the equation:
9cos((2π/3)t) = -5
Dividing both sides by 9, we get:
cos((2π/3)t) = -5/9
There are two solutions for cos(t) = -5/9 within the interval [0, 2π], which we can find using the inverse cosine function:
t = acos(-5/9) ≈ 2.498 or t = -acos(-5/9) ≈ -2.498
Since the function is periodic with a period of 6 seconds (as we can see from the coefficient of t in the cosine function), we can add integer multiples of the period to these solutions to get all possible solutions. Therefore, the general formula for all the solutions is:
t = (2kπ ± acos(-5/9))/2π, for any integer k ≥ 0
where ± is chosen according to the quadrant in which the solution lies. Since we want non-negative solutions, we can use only the positive value of t given by the formula above:
t = (2kπ + acos(-5/9))/2π, for any integer k ≥ 0
Rounding to two decimal places, we have:
t ≈ 0.59, 2.09, 3.68, 5.18, 6.77, 8.27, ...
These are the times when the block is 5 cm above equilibrium.
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