Standard deviation
a) The distribution of IQ is exactly normal.Trueb) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54c) The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886e) The probability that the sample mean IQ is between 117 and 123 is 0.773Step-by-step explanationa) The distribution of IQ is exactly normalGiven population mean IQ, µ = 119Standard deviation, σ = 18b) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54The standard error of the sample is calculated as:SE = σ/√nwhere σ = 18 and n = 50SE = 18/√50SE = 2.54The distribution of the sample means is approximated to normal with the help of central limit theorem. The mean of sample means is μ = 119 and standard deviation of sample means is σ/√n = 2.54.c) The probability that the sample mean IQ is less than 117 is 0.114We need to calculate the z-score using the formula:z = (x-μ)/SEz = (117-119)/2.54z = -0.79Now, using z-table, the probability is calculated as:P(Z < -0.79) = 0.2146The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886The probability that the sample mean IQ is greater than 117 is equal to one minus the probability of less than 117:P(Z > -0.79) = 1 - 0.2146 = 0.786The probability that the sample mean IQ is greater than 117 is 0.886.e) The probability that the sample mean IQ is between 117 and 123 is 0.773We need to calculate the z-score for 117 and 123 as:z1 = (117-119)/2.54 = -0.79z2 = (123-119)/2.54 = 1.57The probability of sample means between 117 and 123 can be found as:P(-0.79 < Z < 1.57) = 0.773The probability that the sample mean IQ is between 117 and 123 is 0.773.
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The cone-shaped paper cup is 2/3 full of sand. What is the volume of the part of the cone that is filled with sand?
The volume of the part of the cone that is filled with sand is 2/9 times the total volume of the cone.
To do this, we need to first determine the total volume of the cone. The formula for the volume of a cone is:
V = 1/3 x π x r² x h
Where V is the volume, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant (approximately equal to 3.14).
Since we know that the paper cup is cone-shaped, we can assume that it has a circular base. Let's say that the radius of the base of the cone is r and the height of the cone is h.
The total volume of the cone can be calculated using the formula above:
V = 1/3 x π x r² x h
Now we need to determine the volume of the part of the cone that is filled with sand. We know that the cup is 2/3 full of sand, so the volume of sand in the cup is 2/3 of the total volume of the cup. We can express this as:
V = 2/3 x V
We can substitute the formula for V into this equation to get:
V = 2/3 x (1/3 x π x r² x h)
Simplifying this equation, we get:
V = 2/9 x π x r² x h
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mathematics homework
The angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.
Describe 16- notch socket?The 16-notch socket has a cylindrical shape with 16 notches or recesses machined into the interior of the socket. Each notch corresponds to a flat side of a 16-sided nut or bolt head. The notches are evenly spaced around the socket, providing a secure grip on the nut or bolt head and allowing for easy application of torque using a ratchet or wrench.
16-notch sockets are commonly used in automotive and industrial applications, particularly in heavy machinery where large bolts and nuts with 16-sided heads are often used. They are available in a range of sizes to fit different nut and bolt sizes and are typically made of durable materials such as chrome vanadium steel or high-grade aluminum.
Premise 1: Deondra is designing a 16-notch socket wrench.
Premise 2: The notches will be the same size.
Conclusion: Therefore, Deondra needs to know the angle measure for each notch.
To determine the angle measure for each notch, we can use the formula for the interior angle of a regular polygon, which is:
Interior angle = (n-2) x 180 / n
where n is the number of sides (or notches) in the polygon.
Applying this formula to a 16-sided polygon (or hexadecagon), we get:
Interior angle = (16-2) x 180 / 16
Interior angle = 1680 / 16
Interior angle = 105 degrees
Therefore, the angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.
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For each statement below, state whether the lengths, angles or both are invariant.
Translation
Reflection
Rotation
Enlargement
What would be the best way to display the data below to see specific data but still see the shape of the data? line plot bar graph line graph stem-and-leaf graph
A number has three prime factors. Two of its prime factors are 3 and 5. The other prime factor is even
what is the number?
The other prime factor is even, the number is 30, and its prime factors are 2, 3, and 5.
To find the third prime factor and ultimately the number, we can use the fact that any integer greater than 1 can be expressed as a unique product of prime factors. We know that the number has three prime factors, and two of them are 3 and 5. So, we need to find the third prime factor.
Since the other prime factor is even, it must be 2 (the only even prime number). Therefore, the number can be calculated as:
Number = 3 x 5 x 2 = 30
So, the number is 30, and its prime factors are 2, 3, and 5.
Prime factors are the prime numbers that divide a given number exactly without leaving any remainder. For example, the prime factors of 12 are 2, 2, and 3, because 2 x 2 x 3 = 12 and these are the only prime numbers that divide 12 exactly. To factorize a number into its prime factors, we can use a method called prime factorization. We start by dividing the number by the smallest prime number that divides it exactly. We keep dividing the quotient by the smallest prime number that divides it exactly until we obtain only prime numbers. The prime factors are then the product of these prime numbers
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Find a polynomial \( f(x) \) of degree 4 with leading coefficient 1 such that both \( -4 \) and 2 are zeros of multiplicity 2 . \[ f(x)=x \]
Polynomial with a degree 4 and leading coefficient 1 is to be found. Also, -4 and 2 are the zeros of multiplicity 2.
Given the roots, the polynomial can be expressed in factored form as:
\[f(x) = (x + 4)^2(x - 2)^2\]
Expanding this:
\begin{align*}
f(x) &= (x + 4)^2(x - 2)^2\\
&= (x^2 + 8x + 16)(x^2 - 4x + 4)\\
&= x^4 + 4x^3 - 4x^3 - 32x^2 + 16x^2 + 128x + 64\\
&= x^4 - 16x^2 + 128x + 64
\end{align*}
Thus, the polynomial is:
\[f(x) = x^4 - 16x^2 + 128x + 64\]Therefore, the answer is \[f(x) = x^4 - 16x^2 + 128x + 64\].
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Please answer with formula and how to find it
Radius is the distance in a straight line from the centre of the circle to its circumference. The diameter is twice the radius. Therefore, radius and diameter of the circle are 7 and 14 yards respectively.
How to find area of a circle?The above figure is a circle. The area of the circle is given as 49π yard squared. The question want us to find the radius and diameter of the circle.
Hence,
area of a circle = πr²
where
r = radius of a squareTherefore,
area of the circle = 49π
Hence,
49π = π × r²
divide both sides by π
r² = 49
square root both sides
r = √49
r = 7 yards
The diameter of a circle is twice the radius.
Hence,
diameter of the circle = 7 × 2 = 14 yards
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Rachel, Sam and Thomas applied for a common position at the company. Only one of them will be hired for the position. The probabilities that each of them is hired for the role are given by 1 out of 7, 2 out of 7, and 4 out of 7 respectively.
The probabilities that Rachel, Sam and Thomas can help boost the company’s revenue are given by 4 out of 5, 1 out of 2, and 3 out of 10 respectively if they are hired.
(a) Find the probability that Thomas is selected for the position given that the company’s revenue did not improve.
(b) Find the probability, p, that the company’s revenue will generally improve.
Rachel, Sam and Thomas interviewed at another company for another position. The probabilities that each of them is hired for the role are now given by x, 2x and 4x respectively.
It can be assumed that the hiring process for each individual candidate are independent of one another.
(c) Suppose there is no limit to the number of hires the company can make (i.e. the company can hire any one of them, any two of them, all three of them or no one at all). Find an inequality that must satisfied by x.
7x ≤ 1, or x ≤ 1/7
(a) The probability that Thomas is selected for the position given that the company’s revenue did not improve is 4 out of 7.
(b) The probability that the company’s revenue will generally improve is the sum of the probabilities that Rachel, Sam and Thomas are hired multiplied by the probability that the company’s revenue will improve given that each individual is hired. This probability is given by (1/7)*(4/5) + (2/7)*(1/2) + (4/7)*(3/10) = 0.5.
(c) For the probabilities given for the second hiring process to be valid, the inequality x + 2x + 4x ≤ 1 must be satisfied. This inequality can be written as 7x ≤ 1, or x ≤ 1/7.
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The football booster club raised $750 to take a group of students to a football game. The booster club will pay for the bus to transport the students to the game, the admission tickets to the game, and a meal at the concession stand for each student. The bus to transport the students to the game costs $200. Each admission ticket to the game costs $6.50.If the booster club pays for a medium sandwich, drink, and popcorn for each student, how many more students can go to the game than if the booster club pays for a large sandwich, drink, and popcorn for each student?
Let's first find the total cost of transportation and admission tickets:
$200 (transportation) + $6.50 (admission ticket) x n (number of students) = $750
$6.50n = $550
n = 84.62
So, the maximum number of students that can go to the game is 84.62. However, we cannot have a fractional number of students, so we can round down to 84 students.
Now, let's find the cost of the meal for each student:
$2.50 (medium sandwich) + $2.00 (drink) + $1.50 (popcorn) = $6.00
If the booster club pays for a large sandwich, drink, and popcorn for each student, the cost will be:
$3.00 (large sandwich) + $2.50 (drink) + $2.00 (popcorn) = $7.50
The difference in cost between the two options is $1.50 per student.
To find how many more students can go to the game with the cheaper meal option, we can divide the total amount of money available ($750) by the difference in cost per student ($1.50):
$750 ÷ $1.50 = 500
So, with the cheaper meal option, the booster club can take 500/6 students = 83 students.
Therefore, the booster club can take 1 more student to the game if they pay for a medium sandwich, drink, and popcorn for each student.
Lisa’s job pays $8 per hour, but if she works more than 35 hours per week she is paid 11 times her regular salary for the overtime hours. How much is she paid if she works hours 42 hours in one week?
Total pay = Regular pay + Overtime pay = $280 + $616 = $896. Therefore, if Lisa works 42 hours in one week, she would be paid $896
The first step is to calculate Lisa's regular pay for the week. We know that her regular hourly rate is $8 per hour. If she works 35 hours or less in a week, then her pay is simply her hourly rate times the number of hours worked. Therefore, her regular pay for a week where she works 35 hours or less would be:
Regular pay = $8/hour * 35 hours = $280
However, we know that Lisa worked 42 hours in one week, which is more than 35 hours. This means she also worked 7 overtime hours. According to the problem, Lisa is paid 11 times her regular salary for any overtime hours worked. This means her overtime pay for the 7 overtime hours would be:
Overtime pay = $8/hour * 11 * 7 hours = $616
To get Lisa's total pay for the week, we simply add her regular pay and overtime pay together:
Total pay = Regular pay + Overtime pay = $280 + $616 = $896
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find the perimeter of 18.6 18.9 6.9
The perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.
What is the perimeter?
The perimeter of a polygon is the total distance around its boundary, which is equal to the sum of the lengths of all its sides. To find the perimeter of a polygon, you simply add up the lengths of all its sides.
The perimeter of any polygon is the sum of the lengths of its sides. In this case, we have three sides of lengths 18.6, 18.9, and 6.9.
To find the perimeter, we simply add these lengths together:
Perimeter = 18.6 + 18.9 + 6.9
Perimeter = 44.4
Therefore, the perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.
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Find the area of the triangle. A drawing of a triangle with base of 12 and a half feet and height of 4 feet.
Answer:
[tex]\large\boxed{ \sf Area = 25\ ft .^2}[/tex]
Step-by-step explanation:
We need to find out the area of the triangle which has a base of 12.5ft and s height of 4ft.
We know that the formula for calculating the area of the triangle is ,
[tex]\sf:\implies \pink{Area_{\triangle}=\dfrac{1}{2}\times (b)\times (h)}\\[/tex]
where,
b is the base .h is the height .F I G U R E : -
[tex] \setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){$\large\bf 4\ ft $}\put(2.8,.3){$\large\bf 12.5\ ft$}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}[/tex]
Now on substituting the respective values, we have;
[tex]\sf:\implies Area = \dfrac{1}{2}\times (12.5) \times (4) \ ft.^2 \\[/tex]
Simplify,
[tex]\sf:\implies \underline{\underline{\boxed{\sf Area = \frak{25\ ft.^2} }}} \\[/tex]
Hence the area of the triangle is 25ft.²
SOMEBODY PLEASE HELP ME I'M DROWNING IN THIS WORK
The surface area of the triangular prism is 156.5 inches².
How to find the surface area of a prism?The surface area of a triangular prism can be found as follows:
Therefore, the prism is a triangular prism. The prism has two triangular base with side length 5 inches each. The height of the triangular bases are 4.3 inches each.
The height of the triangular prism is 9 inches. The surface area of the triangular prism is the sum of the whole individual area of each surface of the prism.
Hence,
surface area of the prism = bh + l(s₁ + s₂ + s₃)
Therefore,
surface area of the prism = 4.3 × 5 + 9(5 + 5 + 5)
surface area of the prism = 21.5 + 9(15)
surface area of the prism = 21.5 + 135
surface area of the prism = 156.5 inches²
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Thuli wants to buy TV R8 500 A bank offers to loan her the money at an interest of 5 percent she decide to pay her TV off 3 years. Calculate the simpled interest she will have to pay also calculate the total she will pay
The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.
Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.
Principal, P = R 8,500
Interest Rate, R = 5%
Time, t = 3 year
Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100
Here, SI = Simple interest
P = Principal (sum of money borrowed)
R = Rate of interest p.a
T = Time (in years)
We have to calculate simpled interest she will have to pay also calculate the total she will pay.
So, Simple interest = (8500×3×5)/100
= 85× 15 = R 1275
Now, total she will have to pay = Principle + SI
= 8500 + 1275
= R 9775
Hence, required total she will pay is R9775.
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the iron bank offers a range of financial services and investment opportunities. of its customers, 36% invest in stocks, 22% invest in futures, and 15% invest in both stocks and futures. use this information and the rules of probability to answer the following:Part A: What proportion of Iron Bank customers invest in neither Stocks nor Futures? Part B: Of the Iron Bank customers who invest in Futures, what percentage invest in Stocks? Part C: What is the probability that a randomly selected Iron Bank customer invests in Stocks aud does not invest in Futures?
Part A: The proportion of Iron Bank customers who invest in neither stocks nor futures is 27%.
Part B: Of the Iron Bank customers who invest in futures, 61.54% also invest in stocks.
Part C: The probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%.
Part A: This can be calculated by subtracting the combined proportion of those who invest in stocks (36%) and those who invest in futures (22%) from 100%.
Part B: This can be calculated by dividing the proportion of those who invest in both stocks and futures (15%) by the proportion of those who invest in futures (22%).
Part C: This can be calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
Given, that 36% of the customers are investing in stocks and 15% of those customers are also investing in futures.
So, 21% of the customers invest in stocks and not futures, while 79% of the customers either invest in futures, or in neither stocks nor futures.
Therefore, the probability is 21/100, or 18.18%.
In conclusion, the probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%. This is calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
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ANSWER FAST!!!
find the missing y value in the table
x y
4 2.5
11 9.5
15 13.5
21 y
The missing y value in the table can be found to be 19. 5.
How to find the missing value in the table?To find the missing value, you need to find the relationship that x and y have with each other on the table.
We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:
= 11 - 4 = 9. 5 - 2.5
= 7 = 7
We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.
The y value corresponding to 21 as x would be:
= ( 21 - 15 ) + 13. 5
= 19. 5
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A golf coach bought g golf balls. The balls came in 7 packages. Write an expression that shows how many golf balls were in each package.
Answer:
g/7
Step-by-step explanation:
Answer:G/7
Step-by-step explanation:G/7
Which is an example of a suggestive survey question?
What do you like and don’t like about the CEO?
Do you own a car or a truck?
What is your favorite brand of soda?
How much credit card debt do you owe?
The answer of the given question based of a suggestive survey the answer is "What do you like and don’t like about the CEO?"
Who is CEO?The CEO or Chief Executive Officer is highest-ranking executive in company who is responsible for making major corporate decisions, managing overall operations, and leading organization towards achieving its goals and the objectives. The CEO reports to board of directors and is responsible for success or failure of company.
The suggestive survey question is: "What do you like and don’t like about the CEO?"
This question is suggestive because it implies that the respondent should have opinions about the CEO, and it encourages the respondent to share both positive and negative opinions. This can bias the responses towards certain answers, rather than allowing the respondent to express their own thoughts freely.
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60% of all Americans live in cities with population greater than 100,000 people. If 34 Americans are randomly selected, find the probability that
a. Exactly 23 of them live in cities with population greater than 100,000 people.
b. At most 23 of them live in cities with population greater than 100,000 people.
c. At least 22 of them live in cities with population greater than 100,000 people.
d. Between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.
What is the probability of selecting the required numbers?Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.
Then X follows a binomial distribution with n = 34 and p = 0.6.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:
P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:
P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)
= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23
= 0.0332
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:
P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)
= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21
= 0.9876
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:
P(18 <= X <= 24) = P(X <= 24) - P(X < 18)
= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24
- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17
= 0.8782
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f:g → 10 - g. Find f-1: g
pls i need this
The inverse function is [tex]f^{-1} (g) = 10 - g[/tex]
What is the Composition function?Composition function is a type of function that is formed by combining two or more functions, where the output of one function becomes the input of another function. Composition function shown by the symbol "∘".
The composition function is a mathematical operation that combines two functions to produce a new function. Specifically, given two functions f and g, the composition function (also called function composition) creates a new function h(x) = f(g(x)) that applies the function g to an input x, and then applies the function f to the output of g(x).
We can start by finding the inverse function of f(g), which is [tex]f^{-1} (g)[/tex]. To do so, we need to solve the equation:
[tex]f(g) = x = 10 - g[/tex]
for g, in terms of x:
x = 10 - g
g = 10 - x
This gives us the inverse function:
[tex]f^{-1} (x) = 10 - x[/tex]
Now we can find f^-1(g) by replacing x with g in the above equation:
[tex]f^{-1} (g) = 10 - g[/tex]
Therefore, the function [tex]f^{-1} (g)[/tex] is given by:
[tex]f^{-1} (g) = 10 - g[/tex]
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Complete question is: f:g → 10 - g. Find f-1: g.
Let \( A=\left[\begin{array}{rrr}-2 & -5 & -13 \\ 4 & 5 & 11 \\ 1 & 2 & 6\end{array}\right] \) Find the third column of \( A^{-1} \) without computing the other two columns. How can the third column o
The third column of the inverse of the matrix, A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 &5 &11 \\1 &2 &6 \\\end{bmatrix}[/tex], obtained using the product of A and the third column of A⁻¹ is; [tex]\begin{bmatrix} 1 \\ -3\\ 1 \\\end{bmatrix}[/tex]
What is an inverse of a matrix?The product of a matrix and the inverse of the matrix is the multiplicative identity.
The specified matrix can be presented as follows;
A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}[/tex]
The third columns of the inverse of the matrix, A, A⁻¹, can be obtained without computing the other two columns, as follows;
The inverse of the matrix A, A⁻¹ is the solution of the following matrix equation;
Ax = [tex]e_i[/tex]
Where;
[tex]e_i[/tex] = The column i of the identity matrix
x = The third column of the inverse matrix
Therefore, for the third column, we get;
[tex]e_i[/tex] = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]
Ax = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]
Therefore;
x = [tex]e_i[/tex]/X, which using a graphing calculator, indicates;
[tex]x = \frac{\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}}{\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}} = \begin{bmatrix}1 \\ -3\\1\\\end{bmatrix}[/tex]
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A study of the amount of time it takes a specialist to repair a mobile MRI shows that the mean is 8. 4 hours and the standard deviation is 1. 8 hours. If 40 broken mobile MRIs are randomly selected, find the probability that their mean repair time is less than 8. 9 hours
Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
[tex]Z=\frac{x-u}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]
u=8.4, sigma=1.8 n=32 s=0.3182
The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:
Z=1.57
Z = 1.57 has a p-value of 0.9418.
1 - 0.9418 = 0.0582.
0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
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Find the value of the unknown in the figure below
b =(17,6x 8,9):19,7=7,95
In rectangle QRST , QS=30-2x and RT=9+x . Find the lengths of the diagonals of QRST
Answer:
Each of the diagonals is 16
Step-by-step explanation:
The diagonals of a rectangular are equal
The two diagonals are QS and RT
QS = RT
→ 30 - 2x = 9 + x
Subtract 30 both sides:
30 - 30 - 2x = 9 - 30 + x
- 2x = -21 + x
Subtract x both sides
-2x - x = -21 + x - x
-3x = -21
x = -21/-3 = 7
So the diagonal RT = 9 + 7 =16
should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16
What is the equation of parabola with focus (4,5) and a directrix y =-1
The equation of the parabola with focus (4,5) and directrix y=-1 is
[tex](y-5)^2=4(x-4) or (y+1)^2=4(x-4).[/tex]
The equation of a parabola is defined by its focus and directrix. The focus is the point on the parabola that is used to determine its shape, while the directrix is the line used to determine its orientation. The equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex]. This equation can be expressed in terms of the focus and directrix by substituting the x and y values of the focus and directrix into the equation. Substituting the x value of the focus (4) into the equation gives us[tex](y-5)^2=4(4-4)[/tex], which simplifies to[tex](y-5)^2=0[/tex]. This equation can be rearranged to give us y=5, which is the y value of the focus. Substituting the y value of the directrix (-1) into the equation gives us [tex](y+1)^2=4(x-4)[/tex]. This equation can also be rearranged to give us y=-1, which is the y value of the directrix. Therefore, the equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex] or[tex](y+1)^2=4(x-4)[/tex].
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Amore scored 15 out of 20 in a test.Write as a percentage
Answer:
75%
Step-by-step explanation:
write it as a fraction first, so 15/20.
make the bottom number 100 to get the mark out of 100.
to do this, multiply the bottom by 5 (20x5=100) and then do the same to the top.
you get 75/100. this equals 75%
Answer:
75%
Step-by-step explanation:
In this question, 20 is the highest score you can get on the test so 20 is 100%. We will now want to divide 100 by 20.
100 ÷ 20 = 5
Each score Amore got on the test was worth 5% of the test.
We know he scored 15 on the text, so now we want to multiply 15 with 5.
15 × 5 = 75
Amore scored 75% on his test.
PLEASE HELP WITH THE PROBLEM !!
Answer:
the answer is 18
Step-by-step explanation:
volume of triangular prism =l×w×h
9×2×1=18
Whats the distance between (-1,-2) and (3,4)
Answer:
the answer is 7,21
Step-by-step explanation:
Distance formula is d=√(x1-x2)²+(y1-y2)²√(-1-3)²+(-2-4)²√(-4)²+(-6)²√16+36√527.21Statistics grades: In a statistics class of 42 students, there were 11 men and 31 women. Six of the men and seven of the women received an A in the course. A student is chosen at random from the class.
Give all answers as decimals rounded to 4 digits after the decimal point
(a) Find the probability that the student is a woman.
(b) Find the probability that the student received an A.
(c) Find the probability that the student is a woman or received an A.
(d) Find the probability that the student did not receive an A.
A is 0.8218
A is 0.6905.
(a) The probability that the student is a woman.The number of women in the class is 31 while the total number of students is 42. The probability of a randomly selected student being a woman is given as:P(woman) = (Number of women in the class) / (Total number of students in the class)P(woman) = 31 / 42P(woman) = 0.7381(b) The probability that the student received an A.The number of men and women that received an A is given as follows:Men that received an A = 6Women that received an A = 7The total number of students that received an A is:Total number of students that received an A = (Number of men that received an A) + (Number of women that received an A)Total number of students that received an A = 6 + 7Total number of students that received an A = 13The probability of a randomly selected student receiving an A is given as:P(A) = (Number of students that received an A) / (Total number of students in the class)P(A) = 13 / 42P(A) = 0.3095(c) The probability that the student is a woman or received an A.The probability of the student being a woman or received an A is given as:P(woman or A) = P(woman) + P(A) - P(woman and A)From parts (a) and (b), we know that:P(woman) = 0.7381P(A) = 0.3095Now, we have to determine the probability that the student is a woman and received an A.The number of women that received an A = 7 while the total number of women in the class is 31.The probability of a woman receiving an A is given as:P(woman and A) = (Number of women that received an A) / (Total number of women in the class)P(woman and A) = 7 / 31P(woman and A) = 0.2258Therefore:P(woman or A) = P(woman) + P(A) - P(woman and A)P(woman or A) = 0.7381 + 0.3095 - 0.2258P(woman or A) = 0.8218(d) The probability that the student did not receive an A.The probability that the student did not receive an A is given as:P(not A) = 1 - P(A)From part (b), we know that:P(A) = 0.3095Therefore:P(not A) = 1 - P(A)P(not A) = 1 - 0.3095P(not A) = 0.6905Therefore, the answers are given as follows:(a) The probability that the student is a woman is 0.7381.(b) The probability that the student received an A is 0.3095.(c) The probability that the student is a woman or received an A is 0.8218.(d) The probability that the student did not receive an A is 0.6905.
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Renting a roller rink for your birthday costs $ 150 plus $6 per person. The total charge for your party was $282 Translate this information into an equation using x to represent the number of guests at your party.
The equation to represent the number of guests at your party is 150 + 6x = 282 where, the number of guests at the party, x is 22.
How to write and solve equation?Let
Cost of renting a roller rink = $150
Cost per person = $6
Total charge of the party = $282
Number of persons at the birthday party = x
The equation:
150 + 6x = 282
subtract 150 from both sides
6x = 282 - 150
6x = 132
divide both sides by 6
x = 132/6
x = 22
Therefore, there are 22 guests at the birthday party.
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