I need to find the values of the variable. Then find the angle measures if the polygon

The 99% confidence interval estimate for the difference between the percentages of married elderly men and women is (0.0741, 0.2659).

To determine a 99% confidence interval estimate for the difference between the percentages of elderly men and women who were married, we can use the formula for the confidence interval of two proportions:

CI = (p1 - p2) ± Z * √[(p1 * (1-p1) / n1) + (p2 * (1-p2) / n2)]

Where p1 and p2 are the proportions of married elderly men and women, n1 and n2 are the sample sizes, and Z is the Z-score for a 99% confidence level (which is 2.576).

First, convert the percentages to proportions:
p1 = 0.65 (65% married elderly men)
p2 = 0.48 (48% married elderly women)
n1 = 300 (sample size of elderly men)
n2 = 400 (sample size of elderly women)

Now, plug the values into the formula:

CI = (0.65 - 0.48) ± 2.576 * √[((0.65 * 0.35) / 300) + ((0.48 * 0.52) / 400)]
CI = 0.17 ± 2.576 * √[(0.2275 / 300) + (0.2496 / 400)]
CI = 0.17 ± 2.576 * √(0.00075833 + 0.000624)
CI = 0.17 ± 2.576 * √(0.00138233)
CI = 0.17 ± 2.576 * 0.0372
CI = 0.17 ± 0.0959

Thus, the 99% confidence interval estimate for the difference between the percentages of married elderly men and women is (0.0741, 0.2659).

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Answer:

The third one

Step-by-step explanation:

Answer:

decrease

Step-by-step explanation:

The reason is 6 is bigger than 10 in fraction form

Answer:

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Step-by-step explanation:

The amount of profit y made by the company from selling each widget at x price is modeled by the equation:

\(y=-x^2+72x-458\)

Since this is a quadratic with a negative leading coefficient, its maximum will occur at its vertex point. We want to find the price that the widget should be sold to make the maximum profit. So, we want to find the x-coordinate of the vertex. This is given by the formula:

\(\displaystyle x=-\frac{b}{2a}\)

In this case, a = -1, b = 72, and c = -458. Substitute and evaluate:

\(\displaystyle x=-\frac{72}{2(-1)}=36\)

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Answer:

$3.00 per person $8.00 per vehicle

Step-by-step explanation:

2x3=6    6+8=14

4x3=12   12+8=20

8x3=24  24+8=32

Hope this helps

Answer:

so it 15

Step-by-step explanation:

Step-by-step explanation:

part (a) - you plug 25 into the given function they give you and that'll be your answer

part (b) - 200 is your original amount given by the function so what is half of 200? 100. So set 100 on the right side of your function and solve for t to find the year

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

The variance of the bonus received by the risk manager is $1.3456 \times 10^2.$

Given that X is a loss random variable with density function exponential with θ = 60.

If X < 50, a risk manager is paid a bonus equal to 65% of the difference between X and 50.

We need to find variance of the bonus received by the risk manager.

We know that the mean of the exponential distribution is given as $E(X) = \frac{1}{\theta }$

The density function for the exponential distribution with parameter $θ$ is

                 $f(x) = \frac{1}{θ} \times e^{-\frac{x}{θ}}, x ≥ 0$If $X$ is an exponential random variable with parameter $θ$, then $E(X^k) = k! θ^k$

The bonus received by the risk manager when $X < 50$ is given as $B = 0.65 \times (50 - X)$

Thus, the bonus received by the risk manager is given as$B = 0.65 \times (50 - X) = 32.5 - 0.65 X$As $X$ is an exponential distribution with parameter $\theta = 60$, then $E(X) = \frac{1}{60} = 0.0167$

By linearity of expectation, the mean of the bonus is given by:

                        $E(B) = 0.65(50 - E(X)) = 0.65(50 - 0.0167) = 32.46$

Variance of the bonus can be found as follows:

                $Var(B) = E(B^2) - [E(B)]^2$To find $E(B^2)$,

we can use $E(B^2) = E[0.65^2 (50 - X)^2]$

We can now substitute the density function for $X$ as follows:

                    $E(B^2) = 0.65^2 \int_0^{50} (50 - x)^2 \cdot \frac{1}{60} \cdot e^{-\frac{x}{60}}dx$$

                                          = 114.3235$

Thus,$Var(B) = E(B^2) - [E(B)]^2$$= 114.3235 - 32.46^2$$= 1.3456 \times 10^2$

Therefore, the variance of the bonus received by the risk manager is $1.3456 \times 10^2.

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B. 72

1st. 60/130

= .461538462 or 6/13

2nd. Multiply by 156. (Use decimal or fraction)

= 72

Answer:

245

Step-by-step explanation:

4242/12=3.5

70×3.5=245

Answer:

7 slices

Step-by-step explanation:

1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)

By.. 4m exponent 2, I'm going to assume that you meant this ⇨ 4m². If so, then here's how you should solve your question. I've included 2 ways of solving the question. You can choose your method. I'd suggest the 2nd one since it's a whole lot easier than the first method.

\( \tt \: 4m ^ { 2 } +5m \\ \)

Quadratic polynomial can be factored using the transformation \(\tt\: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)\), where \(\tt\:x_{1} and x_{2}\) are the solutions of the quadratic equation ax²+bx+c=0.

\( \tt \: 4m^{2}+5m=0 \)

All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: \(\tt\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \). The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

\( \tt \: m=\frac{-5±\sqrt{5^{2}}}{2\times 4} \\ \)

Take the square root of 5².

\( \tt \: m=\frac{-5±5}{2\times 4} \\ \)

Multiply 2 times 4.

\( \tt \: m=\frac{-5±5}{8} \\ \)

Now solve the equation m=\(\tt\frac{-5±5}{8}\) when ± is plus. Add -5 to 5.

\( \tt \: m=\frac{0}{8} \\ \\ \tt \: m = 0\)

Now solve the equation m=\(\tt\frac{-5±5}{8} \) when ± is minus. Subtract 5 from -5.

\( \tt \: m=\frac{-10}{8} \\ \)

Reduce the fraction -10/8 to its lowest terms by extracting and cancelling out 2.

Factor the original expression using \(\tt\:ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)\). Substitute 0 for \(\tt\:x_{1} \:and \:-\frac{5}{4} \:for\: x_{2}\).

\( \tt \: 4m^{2}+5m=4m\left(m-\left(-\frac{5}{4}\right)\right) \\ \)

Simplify all of the expressions of the form \(\tt\:p-\left(-q\right)\) to p+q.

\( \tt \: 4m^{2}+5m=4m\left(m+\frac{5}{4}\right) \\ \)

Add 5/4 to m by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

\( \tt \: 4m^{2}+5m=4m\times \left(\frac{4m+5}{4}\right) \\ \)

Cancel out 4, the greatest common factor in 4 and 4.

\( \tt \: 4m^{2}+5m= \boxed{\boxed{\bf \: m\left(4m+5\right) }}\)

Don't worry. If this process seems long & wears you out or if you haven't learned the biquadratic formula yet, you can just use the simple method of factoring out the common term (m). Here's how you do that \(\downarrow\)

\( \tt \: 4m ^ { 2 } +5m\)

Factor out m.

\( = \boxed{ \boxed{ \bf \: m\left(4m+5\right) }}\)

See, the second method is easier. But, if your question comes for a lot of marks then you might prefer using the first method.

Answer:

When four dice are rolled, there are 6 x 6 x 6 x 6 = 1296 possible outcomes, since each die has 6 possible outcomes and the rolls are independent.

To find the probability that each of the four numbers that appear will be different, we need to count the number of outcomes where each die shows a different number. We can do this by breaking it down into cases:

Case 1: The first die shows any number. The second die must show a different number than the first, so there are 5 possible outcomes. The third die must show a different number than the first two, so there are 4 possible outcomes. The fourth die must show a different number than the first three, so there are 3 possible outcomes. Therefore, there are 5 x 4 x 3 = 60 outcomes in this case.

Case 2: The first die shows any number. The second die shows the same number as the first. There is only 1 possible outcome in this case. The third die must show a different number than the first two, so there are 5 possible outcomes. The fourth die must show a different number than the first three, so there are 4 possible outcomes. Therefore, there are 1 x 5 x 4 = 20 outcomes in this case.

Case 3: The first die shows any number. The second die shows a different number than the first. The third die shows the same number as either the first or the second. There are 2 possible outcomes in this case. The fourth die must show a different number than the first three, so there are 4 possible outcomes. Therefore, there are 2 x 4 = 8 outcomes in this case.

To get the total number of outcomes where each die shows a different number, we add up the outcomes from each case:

60 + 20 + 8 = 88

Therefore, the probability that each of the four numbers that appear will be different is:

88 / 1296 = 0.0679, or approximately 6.79%.

Answer:

\(inrease \: = 900 - 250 = 650 \\ persent = \frac{650}{250} \times 100 \\ = 65 \times 4 = 260\)

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer: Your answer for the question would be 0.75 or 3/4

Step-by-step explanation: You would have make the denominators the same in order to divide them

The set {p, q, r, s} is linearly dependent if `a = -31` is found for the given linear combination of functions.

A set of functions is said to be linearly dependent if one or more functions can be expressed as a linear combination of the other functions.

Consider the given functions:

`p(x) = x³x²+2x+3,

q(x) = 3x³ + x²-x-1,

r(x) = x³ + 2x + 2`, and

`s(x) = 7x³ + ax² + 5`.

To show that these functions are linearly dependent, we need to find constants `c₁, c₂, c₃, and c₄`, not all zero, such that

`c₁p(x) + c₂q(x) + c₃r(x) + c₄

s(x) = 0`.

Let `c₁p(x) + c₂q(x) + c₃r(x) + c₄s(x) = 0`... (1)

We can substitute the given functions in this equation and obtain the following:

`c₁(x³x²+2x+3) + c₂(3x³ + x²-x-1) + c₃(x³ + 2x + 2) + c₄(7x³ + ax² + 5) = 0`... (2)

Let's simplify and rearrange the above equation to obtain a cubic equation in terms of `a`.

This is because we need to find the value of `a` for which there are non-zero values of `c₁, c₂, c₃, and c₄` that satisfy this equation.

`(c₁ + c₂ + c₃ + 7c₄)x³ + (c₁ + c₂ + 2c₄)x² + (2c₁ - c₂ + 2c₃ + ac₄)x + (3c₁ - c₂ + 5c₄) = 0`

The coefficients of this cubic equation should be zero for all `x` in the domain.

So, we have:

`c₁ + c₂ + c₃ + 7c₄ = 0` ...(3)

`c₁ + c₂ + 2c₄ = 0` ...(4)

`2c₁ - c₂ + 2c₃ + ac₄ = 0` ...(5)

`3c₁ - c₂ + 5c₄ = 0` ...(6)

Solving equations (3) to (6), we obtain:`

c₁ = -7c₄`

`c₂ = -2c₄`

`c₃ = -13c₄`

`a = -31`

Hence, the set {p, q, r, s} is linearly dependent if `a = -31`.

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Answer:

6 Hours and 20 minutes

Step-by-step explanation:

Answer:

6hrs and 20 mins

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0

To decrease the width of the confidence interval, the researcher can take the following steps:

1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.

2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.

Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.

The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.

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Answer:

a = 6 , b = 5

Step-by-step explanation:

using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) = \(\sqrt{ab}\)

then

\(\sqrt{180}\)

= \(\sqrt{36(5)}\)

= \(\sqrt{36}\) × \(\sqrt{5}\)

= 6\(\sqrt{5}\)

with a = 6 and b = 5

The radius of the planet is half the diameter, which is r = 1240/2 = 620 miles.

To find the volume of a sphere, we need to use the formula V = (4/3)πr^3, where r is the radius of the sphere. Since we are given the diameter of the planet, which is 1240 miles, we need to first find the radius by dividing the diameter by 2:

radius = diameter / 2 = 1240 / 2 = 620 miles

Now that we know the radius, we can plug it into the formula for the volume of a sphere:

V = (4/3)πr^3 = (4/3)π(620)^3 ≈ 672,508,160 cubic miles

Rounding to the nearest thousand, we get the volume of the planet to be approximately 672,508,000 cubic miles.

Therefore, the volume of the planet is approximately 672,508,000 cubic miles.

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The maximum probability that a photon with the polarization state will be transmitted through the A filter is 1/2

To solve this problem, we need to use Malus' law, which states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incoming light and the axis of the polarizer.

To find the overall probability that a photon will be transmitted through all three filters, we need to multiply the probabilities of each filter

P = 1/2 × cos²(θ) × 1

We are not given the angle θ, so we cannot calculate the exact value of P. However, we can calculate the maximum value of P, which occurs when the rotated filter is aligned with the A filter (i.e., θ = 0). In this case, P = 1/2.

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The given question is incomplete, the complete question is:

H filter Rotated filter Rotated filter followed by A filter An unpolarized photon beam is incident on a linear polarizing filter. The incoming photon flux is is 2.34 x 101 photons/m' /sec.  What is the probability that a photo with the polarization state be transmitted through a subsequent filter, that is aligned with the direction?

um you need to be more specific on the question bud

Answer: The prime factorization is 3*11*11.

The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.

Graph explain: What is it?

A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).

It will be a V-shape, with the vertex at x = 40 and y = 8.

On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.

On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

Key features of the graph in the context of the situation:

The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.

The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.

The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.

The y-intercept is at 8, which means Tyra starts 8 miles away from home.

The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.

The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.

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Answer:

x = 21

Step-by-step explanation:

Angle 1 and angle 2 are supplementary because they make a straight line

so their sum is equal to 180:

m<1 + m<2 = 180

x + 96 + 3x = 180 add like terms

4x + 96 = 180 subtract 96 from both sides

4x = 84 divide both sides by 4

x = 21 to fins the angle measure replace x with the value we found