You are interested in the average amount of money students made during the summer. Assume the population mean is μ and variance σ 2
. You don't want to ask everyone in the population (all Queen's students), so you decide to randomly ask 5 people. Denote their summer income as Y 1
​
,Y 2
​
,Y 3
​
,Y 4
​
, and Y 5
​
Consider another estimator, W 2
​
which is just simply equal to the first student you asked (Y 1
​
). What are the expected value and variance of W 2
​
in terms of μ and σ 2
? Is this estimator of the population mean unbiased

The product of all three numbers is approximately 39.9997.

The question states that the sum of three numbers is 20. Let's call the first number x, the second number y, and the third number z.

According to the given information, we have three equations:
1. x + y + z = 20 (sum of three numbers is 20)
2. x = 4(y + z) (the first number is four times the sum of the other two)
3. y = 7z (the second number is seven times the third)

To solve this system of equations, we can substitute the values of x and y from equations 2 and 3 into equation 1:
4(y + z) + 7z + z = 20
4y + 5z = 20

Now, we can substitute the value of y from equation 3 into the updated equation:
4(7z) + 5z = 20
28z + 5z = 20
33z = 20
z ≈ 0.6061

Now, we can substitute the value of z back into equation 3 to find y:
y = 7(0.6061)
y ≈ 4.2424

Finally, we can substitute the values of y and z into equation 1 to find x:
x + 4.2424 + 0.6061 = 20
x ≈ 15.1515

The three numbers are approximately x ≈ 15.1515, y ≈ 4.2424, and z ≈ 0.6061.

To find the product of all three numbers, we multiply them together:
15.1515 * 4.2424 * 0.6061 ≈ 39.9997

Therefore, the product of all three numbers is approximately 39.9997.

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Complete question: The sum of three numbers is 20. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three?

Answer:

Step-by-step explanation:

To find the unknown angle in this geometry, you must make use of several facts.

__

The long arc intercepted by the inscribed 130° angle will measure 2×130° = 260°. The sum of arcs of a circle is 360°, so the short arc intercepted by the 130° angle (and by x°) is ...

  x° = 360° -260° = 100°

The measure of angle x is 100°.

Answer:

w<1,800

Explanation: W stands for weight. So the weight must be under 1,800 pounds. And B clearly shows the answer because the smaller side is facing how much weight you have on the elevator and the smaller side of math symbol means how much weight you have on the elevator is less than 1,800 pounds.

Hope that helps! :)

Answer: Probably W > 1,800

( ">" has a line under it)

The value of (ΣX)² for the scores 1, 5, 2 is:  

64

It is the representation of the sum of infinite or many values. And it is represented by the following symbol:

∑xi

The value of (ΣX)² for the scores 1, 5, 2 can be found by first finding the summation of the scores and then squaring the result.

Steps to follow:

Step 1: Find the summation of the scores.
            ΣX = 1 + 5 + 2 = 8

Step 2: Square the summation.
            (ΣX)² = 82 = 64

Therefore, the value of (ΣX)² for the scores 1, 5, 2 is 64.

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Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

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Answer:

the answer is n=17

Step-by-step explanation:

1/5= 8-5/n-2

Answer:

The mathematical problem that forms the basis of most modern cryptographic algorithms is the difficulty of factoring large prime numbers.

Step-by-step explanation:

The problem that forms the basis of most modern cryptographic algorithms is the difficulty of factoring large integers into their prime factors. This is known as the integer factorization problem. It is believed to be a computationally hard problem, meaning that it would take an impractically long time to factor very large integers using classical computers. Many cryptographic algorithms, such as RSA, rely on this problem for their security.

Michelle rode an altogether distance of 810 kilometers from her home to school and back, riding her bike.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have been given that Michelle lives 2.7 km from school, Last year she made 150 round trips from her home to school and back, riding her bike.

According to the given condition, the required solution would be as:

Total distance rode by her =  150 × 2 × 2.7

Total distance rode by her =  300 × 2.7

Apply the multiplication operation, we get

Total distance rode by her =  810 kilometers

Therefore, Michelle rode an altogether distance of 810 kilometers.

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=================================================

Explanation:

2 freshmen + 3 sophomores + 2 juniors + 2 seniors = 9 students total.

Let's consider the cases where we have the same number of juniors and seniors. We'll then take the complement of this to get the final answer.

-----------

Case A: There is 1 junior and 1 senior

There are 2 ways to pick a junior and 2 ways to pick a senior. That's 2*2 = 4 ways so far.

Then we have 9-4 = 5 students left to pick from (i.e. 2 freshmen+3 sophomores = 5 students left) and we have 5-2 = 3 seats to fill. Order doesn't matter on the committee since each person has equal rank.

We use the nCr combination formula.

n = 5 students

r = 3 seats to fill

n C r = (n!)/(r!(n-r)!)

5 C 3 = (5!)/(3!*(5-3)!)

5 C 3 = (5!)/(3!*2!)

5 C 3 = (5*4*3!)/(3!*2!)

5 C 3 = (5*4)/(2!)

5 C 3 = (5*4)/(2*1)

5 C 3 = (20)/(2)

5 C 3 = 10

There are 10 ways to fill the remaining 3 seats when we pick from the freshmen and sophomores only.

To recap everything so far:

Therefore, we have 4*10 = 40 different combinations possible for case A. We'll refer to this value later.

-----------

Case B: We pick 2 juniors and 2 seniors

Since there 2 juniors to pick from, and 2 junior seats to fill, there's only 1 way to do this. Likewise, there's only 1 way to pick the 2 seniors to fill the 2 seats.

In total so far there is 1*1 = 1 way to pick the 2 juniors and 2 seniors in any order you like.

Then we have 9-4 = 5 students left that are freshmen or sophomores. This is the number of choices we have for the final 5th seat.

We have 1*5 = 5 ways to have case B happen.

----------

Summary so far:

There are 45 ways to have the same number of juniors as seniors (either 1 of each or 2 of each).

Now we must calculate the number of total combinations possible on this committee. We'll turn to the nCr formula again.

n = 9 students

r = 5 seats

n C r = (n!)/(r!(n-r)!)

9 C 5 = (9!)/(5!*(9-5)!)

9 C 5 = (9!)/(5!*4!)

9 C 5 = (9*8*7*6*5!)/(5!*4!)

9 C 5 = (9*8*7*6)/(4!)

9 C 5 = (9*8*7*6)/(4*3*2*1)

9 C 5 = (3024)/(24)

9 C 5 = 126

There are 126 different five-person committees possible.

Of those 126 committees, 45 of them consist of cases where we have the same number of juniors and seniors.

That must mean there are 126-45 = 81 combinations where we do not have the same number of juniors and seniors. This is where the concept of "complement" comes in.

1) The process is 3-sigma capable but not 6-sigma capable because the process variation is smaller than the tolerance .

2) The process is not 3-sigma capable.

3) The process is not 6-sigma capable.

To determine whether the process is 3-sigma capable, we need to calculate the process capability index, also known as Cpk, which measures how well the process fits the design specifications.

Cpk is calculated as the minimum of two ratios: the ratio of the difference between the target value and the nearest specification limit to three times the standard deviation (Cpk = (USL - mean)/(3stdev) or (mean - LSL)/(3stdev)), and the ratio of the difference between the mean and the target value to three times the standard deviation (Cpk = (target - mean)/(3*stdev)).

For ABC's screw manufacturing process, the upper specification limit (USL) is 0.808 cm, and the lower specification limit (LSL) is 0.792 cm. With a mean of 0.8 cm and a standard deviation of 0.002 cm, the process capability index is:

Cpk = min((0.808 - 0.8)/(30.002), (0.8 - 0.792)/(30.002)) = 1.33

Since Cpk > 1, the process is 3-sigma capable. To determine if the process is 6-sigma capable, we need to calculate the process sigma level, which is the number of standard deviations between the mean and the nearest specification limit multiplied by two. The process sigma level can be calculated using the formula: Process Sigma = (USL - LSL)/(6*stdev).

For ABC's screw manufacturing process, the process sigma level is:

Process Sigma = (0.808 - 0.792)/(6*0.002) = 3.33

Since the process sigma level is greater than 6, the process is 6-sigma capable.

If the ABC process mean is now 0.803 cm, it is no longer 3-sigma capable since the mean is outside the target value range. To improve the mean to make it 3-sigma capable, ABC would need to adjust the production process to shift the mean towards the target value of 0.8 cm. This could involve changing the manufacturing process, adjusting the machinery, or modifying the materials used to manufacture the screws.

Assuming the standard deviation is fixed at 0.002 cm, we can calculate the new process capability index required to achieve 3-sigma capability. Using the formula for Cpk, we get:

Cpk = (0.8 - 0.803)/(3*0.002) = -0.5

To achieve 3-sigma capability, the process capability index needs to be greater than or equal to 1. Since -0.5 is less than 1, ABC would need to improve the mean diameter of the screws to make the process 3-sigma capable.

To improve the standard deviation to make the process 3-sigma capable, assuming the mean is fixed at 0.803 cm, ABC would need to reduce the amount of variation in the manufacturing process. This could involve improving the quality of the raw materials, enhancing the precision of the machinery, or adjusting the manufacturing process to reduce variability. If the standard deviation is reduced to 0.001 cm, the new process capability index would be:

Cpk = min((0.808 - 0.803)/(30.001), (0.803 - 0.792)/(30.001)) = 1.67

Since 1.67 is greater than 1, the process would be 3-sigma capable.

If the ABC process mean is now 0.803 cm, it is still 6-sigma capable since

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Answer:

x = 1

Step-by-step explanation:

5 - 5 + 3x = 8 - 5

3x = 3

3x/3 = 3/3

x = 1

In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

So, the wrong step will be:

Then, the next step should be:

But, the steps it is given as:

Which makes the error.

Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).

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Answer:

9 degrees and 81 degrees.

Step-by-step explanation:

Complementary angles sum to 90 degrees.

Let one angle be x degrees the the other = 9x.

So we have the equation

x + 9x = 90

10x = 90

x = 9 degrees

and the other angle = 9*9 = 81 degrees.

Answer:

1/2 or 0.5

Step-by-step explanation:

Your previous results don't change the probability of the next time.

Answer:

yes

Step-by-step explanation:

y's can have the same x

Answer:

yes because the line does not cross vertically

2x^2 + 7x + 3 factors into (2x + 1)(x + 3).

What is factoring?

The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:

Look for two numbers that add up to b and multiply to c.

With these numbers, rewrite the quadratic polynomial as the sum of two terms.

Choose the term that has the most in common with each group of terms.

Remove the common binomial factor between the two groups.

Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:

2x² + 3x + 4x + 3

Then, for each collection of terms, we factor out the term with the highest common factor:

x(2x + 3) + 1(4x + 3)

Lastly, we remove the common binomial factor between the two groups:

(2x + 1)(x + 3)

As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).

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Answer:

-1/8

Step-by-step explanation:

Answer:

No less than 42 lessons

Step-by-step explanation:

To find the total numbers of hours needed to teach, divide the total amount of money needed by the amount of money made an hour.

$894.60/$21.30 = 42

There are 15 different 2-member committees that can be formed from the 6 members of the high school student council as per combination.

In mathematics, a combination is a way of selecting objects from a larger group without considering the order in which they are chosen. A combination is also known as a binomial coefficient or a choose function, and is denoted by the symbol "n choose k", where n is the total number of objects and k is the number of objects to be selected.

In mathematics, a permutation is an arrangement of objects in a specific order. The number of possible permutations of a set of n distinct objects is given by n!, which is the product of all positive integers up to n.

The number of different 2-member committees that can be formed from a group of 6 members is given by the combination formula:

C(6, 2) = 6! / (2! * (6 - 2)!) = 15

where C(n, r) represents the number of combinations of r items that can be selected from a group of n items.

Therefore, there are 15 different 2-member committees that can be formed from the 6 members of the high school student council to attend the rally in Washington D.C.

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Step-by-step explanation:

2x+3y=13..........(I)

2x-3y=5.….........(II)

Subtract equation II from equation I

0+6y=8

6y=8

y=8/6=4/3

Substitute 4/3 for y in 2x-3y=5

2x-3×(4/3)=5

2x-4=5

Collect like terms

2x=4+5

2x=9

x=9/2

Therefore,y=4/3,x=9/2

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{4}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{7} }}\)

so we're really looking for the equation of a line whose slope is -4/7 and it passes through (2 , -2)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{4}{7}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{4}{7} ( x -2) \\\\\\ y+2=- \cfrac{4}{7}x+\cfrac{8}{7}\implies y=- \cfrac{4}{7}x+\cfrac{8}{7}-2\implies {\Large \begin{array}{llll} y=- \cfrac{4}{7}x-\cfrac{6}{7} \end{array}}\)

Answer:

7x

Step-by-step explanation:

You add the two numbers and bring over your variable.

The long-run cost function is C(q) = 2w(sqrt[rw(q^3)]). The profit-maximizing output can be found by minimizing this cost function with respect to q.

Part a: Deriving the long-run cost function C(q):

To derive the long-run cost function, we need to find the minimum cost of producing a given output level q using the given production function.

Given the production function q = F(L, K) = (KL)^(1/3), we can rewrite it as K = (q^3)/L.

Now, let's express the cost function C(q) in terms of q. We have the cost function as C(q) = wL + rK, where w is the wage rate and r is the rental rate.

Substituting the expression for K in terms of q, we get C(q) = wL + r[(q^3)/L].

To minimize the cost function, we can take the derivative of C(q) with respect to L and set it equal to zero:

dC(q)/dL = w - r[(q^3)/(L^2)] = 0.

Simplifying the equation, we have w = r[(q^3)/(L^2)].

Solving for L, we get L^2 = r(q^3)/w.

Taking the square root, we have L = sqrt[(r(q^3))/w].

Substituting this value of L back into the cost function equation, we get:

C(q) = w(sqrt[(r(q^3))/w]) + r[(q^3)/sqrt[(r(q^3))/w]].

Simplifying further, we have:

C(q) = 2w(sqrt[rw(q^3)]).

So, the long-run cost function C(q) is given by C(q) = 2w(sqrt[rw(q^3)]).

Part b: Solving the long-run profit maximization problem directly:

To solve the profit maximization problem directly, we need to maximize the expression:

max K, L [F(L, K) - wL - rK].

Taking the derivative of the expression with respect to L and K, and setting them equal to zero, we can solve for the optimal values of L and K.

The first-order conditions are:

dF(L, K)/dL - w = 0, and

dF(L, K)/dK - r = 0.

Differentiating the production function F(L, K) = (KL)^(1/3) with respect to L and K, we get:

(1/3)(KL)^(-2/3)K - w = 0, and

(1/3)(KL)^(-2/3)L - r = 0.

Simplifying the equations, we have:

K^(-2/3)L^(1/3) - (3/2)w = 0, and

K^(1/3)L^(-2/3) - (3/2)r = 0.

Solving these two equations simultaneously will give us the optimal values of L and K.

Part c: Using the derived long-run cost function:

In Part a, we derived the long-run cost function as C(q) = 2w(sqrt[rw(q^3)]).

To find the profit-maximizing output, we can minimize the long-run cost function C(q) with respect to q.

Taking the derivative of C(q) with respect to q and setting it equal to zero, we can solve for the optimal value of q.

dC(q)/dq = w(sqrt[rw(q^3)]) + (3/2)w(q^2)/(sqrt[rw(q^3)]) = 0.

Simplifying the equation, we have:

(sqrt[rw(q^3)])^2 + (3/2)(q^2) =

0.

Solving this equation will give us the profit-maximizing output q.

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Answer:

I think it's D because my mind said so

A)  annual percentage increase in the winner's check over this period is approximately 11595652.17%.

B)   if the winner's prize increases at the same rate, it will be approximately $3,651,682,684.48 in 2055.

a. To find the annual percentage increase in the winner's check over this period, we can use the formula:

Annual Percentage Increase = ((Final Value - Initial Value) / Initial Value) * 100

First, let's calculate the annual percentage increase in the winner's check from 1899 to 2020:

Initial Value = $23
Final Value = $2,670,000

Annual Percentage Increase = (($2,670,000 - $23) / $23) * 100

Now, we can calculate this value using the given formula:

Annual Percentage Increase = ((2670000 - 23) / 23) * 100 = 11595652.17%

Therefore, the annual percentage increase in the winner's check over this period is approximately 11595652.17%.

b. If the winner's prize increases at the same rate, we can use the annual percentage increase to calculate the prize money in 2055. Since we know the prize money in 2020 ($2,670,000), we can use the formula:

Future Value = Initial Value * (1 + (Annual Percentage Increase / 100))^n

Where:
Initial Value = $2,670,000
Annual Percentage Increase = 11595652.17%
n = number of years between 2020 and 2055 (2055 - 2020 = 35)

Now, let's calculate the prize money in 2055 using the given formula:

Future Value = $2,670,000 * (1 + (11595652.17 / 100))^35

Calculating this value, we find:

Future Value = $2,670,000 * (1 + 11595652.17 / 100)^35 ≈ $3,651,682,684.48

Therefore, if the winner's prize increases at the same rate, it will be approximately $3,651,682,684.48 in 2055.

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m=-4

you are subtracting all the numbers by 4 therefore they are all changing by -4

The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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Answer:

hahaha I stole your points lololoooooooooooollllllllllolololol

Step-by-step explanation:

JK, if you are asking how many hours it would take to make 242 dolla then the answer is 11

Answer:

11 hours

Step-by-step explanation:

$396 per hour / 18 hours = 22 per 1 hour of work

$242 / $22 per hour = 11 hours total work to make $242

Answer:

x=0 and y= -2

Step-by-step explanation:

−5x+y=−2for y:

−5x+y=−2

−5x+y+5x=−2+5x(Add 5x to both sides)

y=5x−2

5x−2foryin−3x+6y=−12:

−3x+6y=−12

−3x+6(5x−2)=−12

27x−12=−12(Simplify both sides of the equation)

27x−12+12=−12+12(Add 12 to both sides)

27x=0

x=0

Substitute0 for X in y=5x−2:

y=5x−2

y=(5)(0)−2

y=−2(Simplify both sides of the equation)