Ai bought three books for 8.71, 14.12, and 21.92 dollars. What is the best estimate for the total cost of the books?

Answer:

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1\)

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Answer:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

Step-by-step explanation:

Information given

\(\bar X=2.9\) represent the sample mean

\(\mu\) population mean

\(\sigma =1.4\) represent the population standard deviation

n=2092 represent the sample size  

Confidence interval

The confidence interval is given by:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Since the Confidence interval is 0.95 or 95%, the significance is \(\alpha=0.05\) and \(\alpha/2 =0.025\), and the critical value would be \(z_{\alpha/2}=1.96\)

Replacing the info we got:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

Answer:

Step-by-step explanation:

given:

Ann, Ben, and Cindy were eating strawberries.

The ratio of the numbers of berries they ate is 5:5:7.

If Cindy ate 30 strawberries less than Ann and Ben together,

find:

what is the total number of strawberries the three of them ate?

solution:

add the ratios 5 +5+7 = 17

since Cindy ate 30, less than Ann and Ben together so, the factor is

7x = 5x + 5x - 30

7x - 10x = -30

x = 30/3

x = 10

ann 5 x 10 = 50

ben 5 x 10 = 50

cindy 7 x 10 = 70  

total            = 170

Answer: x = 41

For x in the equation

5/25=9/(x+4)

5(x+4) =9(25)

5x + 20 = 225

5x = 205

x = 41

Therefore, the value of x for the equation 5/25=9/(x+4) is x = 41

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The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Diameter = 3 in

Radius r = diameter/2 = 3/2 = 1.5 in

Height h = 8 in

Mass m = 1250 g

Find the volume:

V = π × r² × h

V = 3.14 × (1.5 in )² × 8in

V = 56.52 in³

Find the density:

p = m / v

p = 1250g / 56.52 in³

p = 22.12 g/in³

Therefore, the density is 22.12 g/in³.

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\(\begin{aligned}\rm\frac{1}{5x-3}&=\rm\frac{1}{6x}\\\rm 6x&=\rm 5x-3\\\rm 6x-5x&=-3\\\bf x&=\boxed{\bf -3}\end{aligned}\)

Answer:

I don't know maybe it's 3

The limit of the given function is 0.

Given the following sum function expressed as:

The nth term of the series will be expressed as:

This can also be expressed as \(\lim_{n \to \infty} \(\frac{3}{k^2+2k}\)

Divide the resulting nth term of the function by k²

\(\lim_{n \to \infty} \(\frac{\frac{3}{n^2} }{\frac{n^2}{n^2} +\frac{2n}{n^2} }\\\lim_{n \to \infty} \(\frac{\frac{3}{n^2} }{1 +\frac{2}{n} }\\\)

Substitute the given value of n into the nth term to have:

\(=\(\frac{\frac{3}{\infty^2} }{1 +\frac{2}{\infty} }\\=\frac{0}{1+0}\\= 0\)

Hence the limit of the given function is 0.

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Therefore, integral specific function f(n) you're working with will determine which interval [a, b] you choose, and there may be several distinct methods for expressing the limit as a definite integral.

A definite integral is the area beneath a curve between two defined boundaries. An is the lower limit and b is the upper bound, and baf(x)dx represents the definite integral that is the function of two variables, defined to reference the x-axis.

Here,

lim n → ∞ f (n)

You can define this limit as a definite integral over the interval [a, b], where a and b are some constants that rely on n, where f(n) is a function of n, by saying:

For , f(x) = lim n → ∞ f(n) for a ≤ x ≤ b

The maximum can then be stated as follows:

=> lim n → ∞ f(n) = ∫a^b f(x) d

The specific function f(n) you're working with will determine which interval [a, b] you choose, and there may be several distinct methods for expressing the limit as a definite integral.

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Answer:

Step-by-step explanation:

First find the airithmatic mean

(-3-5+8+11+13)/5= 4.8

\(\frac{(-3-4.8)^2+(-5-4.8)^2+(8-4.8)^2+(11-4.8)^2+(13-4.8)^2}{5}= 54.56\)

The variance of this population data set is 69.45.

To find the variance of the set of data we first need to calculate the mean of the set.

mean = sum of each element / number of elements

mean = (-3 -5 + 8 + 11 + 13)/5 = 3.8

Now, using the formula for variance

s² = (X - mean)²/ (n- 1)

s² = (-3 - 3.8)² + (-5 - 3.8)² + (8 - 3.8)² + (11 - 3.8)² + (13 - 3.8)²   / (5- 1)

s² = 46.24 + 77.44 + 17.64 + 51.84 + 84.64 / 4

s² = 277.8/4

s² = 69.45

Hence, the variance of the data is 69.45.

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The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

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Answer:

The proposed equation is solved as follows:

2X + 7 = 21

2X = 21 - 7

2X = 14

X = 14 / 2

X = 7

The value of X is 7.

A first degree equation is an algebraic equation in which each term is either a constant or a product of a fixed term on a single variable. Therefore, this equation is a first degree one, since it only has a single variable, which is X.

The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer:

25% is your answer

Step-by-step explanation:

2/8 = 25%

Answer:

20% strawberries

Step-by-step explanation:

Since percentages can be found using fractions, we can turn the amounts of strawberries into a fraction. First, we determine the denominator by determining what the whole is or what the two numbers equal together. In this case: 8+2 is 10 meaning we will make our fractions with a denominator of ten. As we are determining the percentage of strawberries, we put 2 over 10 to get: \(\frac{2}{10\\}\) which, when converted to a percentage, equals 20%.

Answer:

The answer is D

Step-by-step explanation:

It should be the only one to fit the sequence

-1.2, earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X

Given that two machines, X and Y, produce earbuds

Let X represent the diameter of an earbud produced by machine X, and

let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm

Y has a mean of 15.2 mm with a standard deviation of 0.2 mm.

The mean of the difference, D = X - Y, can be calculated as:

mean(D) = mean(X) - mean(Y)

= 14 - 15.2

= -1.2

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

9.16

Step-by-step explanation:

by using pythagorean theorem,

given that PQ=4 and NQ = 2×5 = 10

NP²= NQ²-PQ²

= 10²-4²

= 100-16

= 84

NP = √84 = 9.16

The value of the expression 28 - {15 (3+2)} is -47.

To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the expression step by step:

First, we solve the expression inside the parentheses:

3 + 2 = 5

Now, we substitute the result back into the original expression:

28 - {15 * 5}

Next, we perform the multiplication:

15 * 5 = 75

Now, we substitute the result back into the expression:

28 - 75

Finally, we perform the subtraction:

28 - 75 = -47

Therefore, the value of the expression 28 - {15 (3+2)} is -47.

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Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

Answer:

The midpoint is (3, 3).

Step-by-step explanation:

We are given the two points A(9, 11) and B(-3, -5).

The midpoint is given by:

\(\displaystyle M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\Big)\)

So:

\(\displaystyle M = \Big( \frac{9+(-3) }{2}, \frac{ 11+(-5) }{2} \Big) = (3,3)\)

The midpoint is (3, 3).

We want to show that AM = MB.

We can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

The distance between A(9, 11) and M(3, 3) will then be:

\(AM=\sqrt{(9-3)^2+(11-3)^2}=\sqrt{6^2+8^2}=\sqrt{100}=10\)

And the distance between B(-3, -5) and M(3, 3) will be:

\(MB = \sqrt{ (3-(-3))^2 + (3-(-5))^2 } = \sqrt{(6)^2+(8)^2} = \sqrt{ 100 } = 10\)

So, AM = MB = 10.

Since AM = MB = 10, AM + MB = 10 + 10 = 20.

So, we want to prove that AB = 20.

By the distance formula:

\(AB=\sqrt{(9-(-3))^2+(11-(-5))^2}=\sqrt{12^2+16^2}}=\sqrt{400}=20\stackrel{\checkmark}{=}20\)

Answer:

c is the right answer

Step-by-step explanation:

okk how are u ?

The statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

Long-term bonds keep an investor's money locked up for a longer period than a short-term bond, giving the bond's price more time to be impacted by changes in interest rates and inflation.

As we know,

The fact that short-term bonds offer lower interest rates than long-term bonds is a drawback.

Long-term bonds have a larger chance of receiving higher rates since there is a bigger likelihood that interest rates will rise over time.

Bonds with a long term are often those that investors hold for almost ten years.

Thus, the statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

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Answer:

A. whether a woman took hormones.

B. whether to woman in the study had a heart attack.

D. access to health care

Step-by-step explanation:

The study conducted to observe the menopausal woman must be supported with their health history. Some woman may have menopause at an early age while other go towards this at a later age. This can be due to smoking, hormone intake, severe diseases like heart attack or cancer and their routine health checkup details. There variables must be observed and included in experiment to reach a conclusion.

There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

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

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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Mr. Cho received 3840 eggs in the beginning.

Let's assume that Mr. Cho received x eggs in the beginning.

In the morning, he sold 1/3 of the eggs, so he had 2/3 of the eggs left. Therefore, he had 2/3 x eggs left after the morning sales.

In the afternoon, he sold 320 eggs, so he had 2/3 × x - 320 eggs left at the end of the afternoon.

At the end of the day, he found that 1/4 of the eggs were not sold, which means that he had 3/4 of the eggs left. Therefore, we have:

3/4 × x = 2/3 × x - 320

Multiplying both sides by 12, we get:

9x = 8x - 3840

Simplifying, we get:

x = 3840

Therefore, Mr. Cho received 3840 eggs in the beginning.

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Answer:

40

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - 4 = -7(x - 0)

y = -7x + 4

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

True

Step-by-step explanation:

Answer:

-Picture attached-

Step-by-step explanation:

The gradient would be 4, with a rising graph and the y-intercept would be 1. I attached a picture of the graph, hope it helps.

Answer:

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%

Step-by-step explanation:

To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755

To convert this decimal to a percentage, we simply multiply by 100:

0.0755 * 100 = 7.55%