The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a standard deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a standard deviation of 27 feet.

Noah says the second lake is generally deeper than the first lake. Do you agree with Noah? Why?

If the value exceeds\($0.200$\) by the tolerance of \($0.020$\) on either side, a repair cost of \($\$150$\)is incurred.

\($L(x) = 150(x - T)$\) option b.

The Taguchi loss function measures the cost or loss associated with deviations from a target value in a quality characteristic.

In this case, the specification for the quality characteristic is \($0.200 \pm 0.020$\).

If the value exceeds \($0.200$\) by the tolerance of \($0.020$\)on either side, a repair cost of $\$150$ is incurred.

Based on this information, the Taguchi loss function for this example is given by:

b.\($L(x) = 150(x - T)$\)

In the given options, option b represents the correct Taguchi loss function. The loss function is a linear function where the loss increases linearly with the deviation from the target value.

The coefficient of \($150$\) represents the cost of repair per unit deviation.

This loss function is appropriate for the given scenario as it accurately captures the cost associated with deviations from the target value.

The Taguchi loss function provides a quantitative measure to assess the impact of variations in the quality characteristic and helps in making decisions regarding process improvement and optimization.

In this case, it allows for evaluating the cost implications of exceeding the specified tolerance and guides decision-making on whether repairs are necessary based on the associated costs.

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The probability that exactly 4 of the workers interviewed are union members is 0.41

The probability that exactly 4 of the workers interviewed are union members can be calculated using the binomial probability formula.

Given that there are two possible outcomes in each trial (worker being a union member or non-union member), the probability of selecting a union member is P(U) = 0.80, and the probability of selecting a non-union member is P(U') = 0.20.

The TV station interviews a total of n = 5 workers at the university. We want to find the probability that exactly 4 of the workers interviewed are union members, denoted as P(X = 4).

Using the binomial probability formula, we have:

P(X = 4) = C(5, 4) * (0.80)^4 * (0.20)^1

C(5, 4) = 5! / (4! * (5-4)!) = 5

where C(5, 4) represents the number of ways to choose 4 workers out of 5.

Substituting the values:

P(X = 4) = 5 * (0.80)^4 * (0.20)^1

= 5 * 0.4096 * 0.20

= 0.4096

Therefore, the probability that exactly 4 workers interviewed are union members is 0.4096, or approximately 0.41.

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Answer:

Part A:

(0.20)(10) = (0.05)(x) + (0.40)(10 - x)

Part B:

5.7 litres of 5% and 4.3 litres of 40%

Step-by-step explanation:

Let's assume she will stick with 10 litres in total for her mixture. (Maybe that's the size of her container.)

Let the volume of 5% by x litres.

Therefore the volume of 40% will equal 10 - x.

Reason: 10 litres total, if we use 2 litres of the one, we'll use 8 litres of the other. Get it?

Moving along...

So:

(0.20)(10) = (0.05)(x) + (0.40)(10 - x)

Now we solve the equation...

2 = 0.05x + 4 - 0.4x

2 - 4 = - 0.35x

-2 = -0.35x

let's multiply both sides by 100 to get rid of the decimal

-200 = -35x

x = 200/35

x = 5.7 litres (volume of 5% solution needed)

volume of 40% = 10 - 5.7 = 4.3 litres

Therefore, the value that needs to be added to (-5)/8 in order to get 5/9 is -5/72.

To get 5/9, what number should be added to (-5)/8?

We can begin the solution by adding "x" to (-5)/8. Then, we will have:((-5)/8) + x = 5/9

The next step is to isolate the variable x, which is accomplished by subtracting (-5)/8 from both sides. The equation becomes:(-5/8) + (5/9) = x

We'll need to find a common denominator for this expression:

((-45)/72) + (40/72) = xSimplifying, we get:

((-45) + 40)/72 = x(-5)/72 = x

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A spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a spherical astroid has a radius of approximately 8.5 x 10^2 m.

we know,

the volume =  4/3 π r^3

so, by calculating, we get.

volume = 2.57 x 10^9 m^3

Hence, a spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

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\(\frac{3}{1}\)Answer:

Step-by-step explanation:

3x-y = 2

2x+y =4

put them into slope intercept form

y=3x-2

y=-2x+4

Now, you can either graph it or use substitution

3x-2 = -2x+4

+2x +2x

5x -2 = 4

+2 +2

5x = 6

5x/5 = 6/5

x = 6/5

3x -2 = y

3(6/5) -2 = y

3 x 6 / 1 x 5 = 18/5

3 3/5 -2 = 1 3/5

Let me know if it's wrong.

Hope this helps

Answer:

125

An exponent is the number written as a superscript above a number. This is used commonly in mathematics to signify multiplication, or the amount to multiply the number by.

If we look at \(5^{3}\) (Five to the power of 3), we can use this expression to solve for the answer.

Therefore, the answer to \(5^{3}\) is 125.

The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.

To find the average rate, follow these steps:

Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\)  is 24.

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Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

Answer: y = 5x - 1 ( look at the image  for the solution )

Step-by-step explanation:

Answer:

I don't see anything but Perimeter is Length + Width × 2

Answer:

$8

Step-by-step explanation:

25% is .25, also known as 1/4. So if you think of it that way, $2 is 1/4 of the entire payment that was added to it. 2*4 is 8, so the price of the tacos was $8 before any tip was added. Andrea paid $10 in total if you include the tip.

Answer:

42

Step-by-step explanation:

so since both the triangles attached to the rectangles are 4 feet tall:

cut one of them off on the dotted line, and you can actually put them together to form a rectangle

14x3=42

Answer:

g(x)

Step-by-step explanation:

y-intersect for h(x) is -11 as shown in the table, where the x value is 0

y-intersect for f(x) you find out by subbing 0 in the place of x and get the y intersect value of 2.99

y-intersect of g(x) is 3 as shown in the drawing

as seen across the three y-intersects, the value of g(x) y-intesect is the greatest

Answer:

Proof given by contradiction.

Step-by-step explanation:

Given that:

\(n \geq 2\)

To prove:

\(n\) is prime if and only if no positive integer > 1 and \(\leq\) \(\sqrt n\) divides \(n\).

Solution:

First of all, let \(n\) is a composite number i.e. not a prime number such that:

\(n =a\times b\)

and \(a\) and \(b\) are prime and \(a\) divides \(n\) and \(b\) also divides \(n\).

Let \(\sqrt n = p\)

or \(n = p\times p\)

1. \(\underline{a < p}\):

\(a\) is prime and is a divisor of \(n\).

2. \(\underline{a>p}\):

\(n = a\times b = p\times p\)

We have assumed that \(a > p \Rightarrow b <p\)

\(b\) is a prime number and is a divisor of \(n\).

But we are given that no prime number \(\leq \sqrt n\) divides \(n\) but we have proved that \(b < \sqrt n\) divides \(n\).

So, it is a contradiction to our assumption.

Therefore, our assumption is wrong that  \(n\) is a composite number.

Hence, proved that \(n\) is a prime number.

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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The probability of running out of anchovies before the evening is over is approximately 0.058, or 5.8%. We must presume that the number of pizzas ordered with anchovies follows a binomial distribution with parameters n = 60 (the total number of pizzas) and p = 0.08 in order to answer this issue using the normal approximation for the binomial distribution. (the probability of ordering anchovies on a pizza). 

The standard deviation of this binomial distribution is given by = sqrt(np(1-p)) = sqrt(60 x 0.08 x 0.92) = 2.03, and the mean is given by = np = 60 x 0.08 = 4.8.

Now, we need to determine the likelihood that we will need to prepare more than eight anchovy-topped pies before the evening is through in order to determine the likelihood that we will run out of anchovies. (since we only have enough anchovies for 8 pizzas).

This is equivalent to finding the probability that the number of pizzas with anchovies is greater than 8, or P(X > 8), where X is the number of pizzas with anchovies.

To use the normal approximation for the binomial distribution, we need to standardize the variable X using the standard normal distribution. This gives us:

z = (X - μ) / σ = (8 - 4.8) / 2.03 = 1.57

Using a standard normal table or calculator, we can find the probability that z is greater than 1.57, which is approximately 0.058. Therefore, the probability of running out of anchovies before the evening is over is approximately 0.058, or 5.8%.

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Step-by-step explanation:

Q5. Let the cost of 28subscriptions be $s.

Words: 1subscription/28subscription = $21/$28

Numbers: 1/28 = 21/s

Cross multiply and solve: 1 x s = 21 x 28

s = 588

Answer with label: $588

Q6.

Words: 2inches/3.6inches = 2.5hours/bhours

Numbers: 2/3.6 = 2.5/b

Cross multiply and solve:

2 x b = 2.5 x 3.6

2b = 9

b = 4.5

Answer with label: 4.5hours

The tail length of an alligator whose body length is 4.2 feet will be 3 feet.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. Mathematically, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is an alligator's tail length [T] varies directly as its body length [B]. An alligator with a body length of 2.8 feet has a tail length of 2 feet.

We can write as -

tail length [T]  \(\alpha\)  body length [B].

Therefore -

T/B = K    [Constant]

We can write -

T₁/B₁ = T₂/B₂

2/2.8 = T₂/4.2

T₂ = (2 x 4.2)/2.8

T₂ = 3 ft

Therefore, the tail length of an alligator whose body length is 4.2 feet will be 3 feet.

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If the correlation between two variables is .496, 75.4%. much of the variance has not been accounted for.

What is variable?

In the context of statistics and mathematics, a variable is a characteristic or quantity that can vary or take different values.

The correlation coefficient, which ranges from -1 to 1, measures the strength and direction of the linear relationship between two variables. If the correlation between two variables is 0.496, it indicates a moderate positive correlation.

The coefficient of determination, also known as R-squared, represents the proportion of the variance in one variable that can be explained by the other variable. In this case, if the correlation is 0.496, then the coefficient of determination is \((0.496)^2 = 0.246.\)

Therefore, 24.6% of the variance has been accounted for by the correlation, and the remaining 75.4% of the variance has not been accounted for.

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The fact that k≥4≥1 is used in the base case of the inductive proof, not in the inductive step.

In the base case, we need to show that the statement holds for k=4. Since 4≥1, this satisfies the condition. The inductive step assumes that the statement holds for some arbitrary k≥4 and then shows that it holds for k+1. The inductive step of an inductive proof aims to show that if a statement holds true for a certain value, it also holds true for the next value. In the given problem, we need to demonstrate that for k≥4, if 2k≥3k, then 2(k+1)≥3(k+1). The fact that k≥4≥1 is utilized in the base case step of the proof. The base case ensures that the initial condition (k=4) satisfies the given inequality. By showing that the inequality holds true for k=4, we establish a starting point for the inductive step. This allows us to apply the inductive step and generalize the result to all values of k greater than or equal to 4.

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The surface area of the right rectangular prism is 652 ft²

The surface area of a right rectangular prism is expressed as;

SA = 2( wl + hl + hw )

From the diagram;

Plug the values into the above formula and solve for the surface area.

SA = 2( wl + hl + hw )

SA = 2( (7×8) + (18×8) + 18×7 )

Simplify

SA = 2( 56 + 144 + 126 )

SA = 2( 326 )

SA = 652 ft²

Therefore, the surface area of the prsim is 652 ft².

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Answer:

10 inches

Step-by-step explanation:

Surface Area = π R² + π R L [ L is Slant Height ]

200 π = π (10)² + π (10) L

200 π = π (100) + π (10) L

200 π - 100 π = 10 π L

100 π = 10 π L

100 π / 10 π = L

10 = L

L = 10 inches

Hope this Helps......

\(\huge{ \mathrm{  \underline{ Answer} \:  \:  ✓ }}\)

Given terms :

Now, we know

\( \large\boxed{\mathrm{surface \: \: area = \: \pi r(l + r) }}\)

(note : " l " represents slant height.)

Therefore, Measure of slant height (l) :

\( \huge \boxed{10 \: \: in \: }\)

_____________________________

\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the function is not given. However, the following explanation will guide you.

The average rate of change is calculated using;

\(A = \frac{f(b) - f(a)}{b - a}\)

Where

\((a,b) = (-1,5)\)

Take for instance;

The function is:

\(f(x) = 2x\)

We have to solve for f(-1) and f(5);

i.e.

\(f(-1) = 2 * -1 -2\)

\(f(5) = 2 * 5 = 10\)

Substitute -1 for a and 5 for b

\(A = \frac{f(b) - f(a)}{b - a}\)

\(A = \frac{f(5) - f(-1)}{5 - (-1)}\)

\(A = \frac{f(5) - f(-1)}{5 +1)}\)

\(A = \frac{f(5) - f(-1)}{6}\)

Substitute values for f(5) and f(-1)

\(A = \frac{10 - (-2)}{6}\)

\(A = \frac{10 +2}{6}\)

\(A = \frac{12}{6}\)

\(A = 2\)

Apply this steps in your work

The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

\(n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }\)

On submitting and solving using calculator

n = 93

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Answer:

3x²

= 3(10)²

= 3(100)

= 300

Step-by-step explanation:

Answer:

sum of x and y

x + y

1.5 + 3

4.5

hope it helps u

Thus, triangle obtained is right triangle. This triangle is will be unique and one side and angle is fixed.

In a right triangle, one of the three angles is 90 degrees, while the other two acute angles add up to 90 degrees.

Given data:

One side of triangle = 3 in (say BC)

Angle C = 50 degrees

Angle A = 90 degrees

Construct a triangle using the scale and compass.

The obtained figure is attached.

Thus, triangle obtained is right triangle. This triangle is will be unique and one side and angle is fixed.

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