The mean weight of a group of dogs in a dog show is 38 pounds. If a certain dog in the show
has a z-score of 0, how much does it weigh?

1) Therefore, the approximate mean of the circle is 125 feet. 2) Therefore, the approximate variance of the circle is 0.1 ft².

To approximate the mean and variance of the circle to first order, we need to use the concept of linear approximation.

The linear approximation formula is as follows:
f(x) ≈ f(a) + f'(a)(x - a)

In this case, the mean and variance of the circle can be approximated using the linear approximation formula.

1. Approximating the mean:
The mean of the circle is given as the random variable with a mean of 125 feet.

Since the linear approximation formula uses a first-order approximation, we can approximate the mean of the circle as the mean of the random variable itself, which is 125 feet.

Therefore, the approximate mean of the circle is 125 feet.

2. Approximating the variance:
The variance of the circle is given as the random variable with a variance of 0.1 ft² (standard deviation = 0.32 ft).

To approximate the variance to first order, we need to use the formula:

Var(X) ≈ Var(a) + 2a * Cov(X, Y) + a² * Var(Y)

Since the radius of the circle is a random variable with a variance of 0.1 ft², we can approximate the variance of the circle to first order as the variance of the random variable itself, which is 0.1 ft².

Therefore, the approximate variance of the circle is 0.1 ft².

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Answer:

34

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

2+2 = 4

5+5+5+5+5+5 = 5 x 6 = 30          [ as their are 6 5s]

2+2+5+5+5+5+5+5= 34!!

The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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Answer:

x = \(\frac{5}{2}\) + \(\sqrt[i]{55}\)/2

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

Answer:

f(2) = sqrt(4 - 2 ^ 2)

f(2) = sqrt(4 - 4)

f(2) = sqrt(0)

f(2) = 0

Answer: 0

Step-by-step explanation:

Give me Brainliest if that helped! :)

Answer:

36

Step-by-step explanation:

180-126=54 Since two angles are supplimentary if they both add up to 180, and 90-54=36 since two angles are complementary if they add up to 90.

Step-by-step explanation:

To make your answer concrete, suppose there will be 30 guests and the genie will tell you either x-bar= 5 cans or M=3 cans. Which of these two measures would best help you determine how many can you should have on hand?

Answer: f(x) = (1/8)(x + 5)3

Step-by-Step:

f(x) = a(x + 5)3

f(3) = a(3 + 5)3 = 64

a = 64 / 83 = 82 / 83 = 1/8

Answer:

C

Step-by-step explanation:

V = lwh

v = 60 x 15 x 34

v = 30,600

Helping in the name of Jesus.

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Rachel's personal loan of $4,500 with a 12% annual interest rate for 36 months will have a finance charge of $6,230.16, meaning that she will need to pay a total of $10,730.16 to pay off the loan amount.

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months).

Finance Charge = (Loan Amount x Interest Rate x Loan Term)

Finance Charge = ($4,500 x 0.12 x 36 months)

Finance Charge = $6,230.16

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months). In this case, Rachel took out a $4,500 loan with a 12% annual interest rate for 36 months. The total finance charge for this loan can be calculated as follows: Finance Charge = ($4,500 x 0.12 x 36 months) = $6,230.16. This means Rachel will need to pay a total of $10,730.16 to pay off the loan, including the finance charge. This also means that Rachel's monthly payments of $173.06 will go towards the principle balance of the loan and the interest accrued during each month.

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The statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

What are integers?

Integers are a set of numbers that include whole numbers (positive, negative, or zero) as well as their opposites.

We will use mathematical induction to prove the statement.

Base case: Let n=1. Then the left-hand side of the equation is 1·1!=1 and the right-hand side is (1+1)!=2!-1=1. Therefore, the statement holds for n=1.

Induction hypothesis: Assume that the statement holds for some positive integer k, i.e., 1·1!+2·2!+···+k·k!=(k+1)!−1.

Inductive step: We need to show that the statement also holds for k+1, i.e., 1·1!+2·2!+···+(k+1)·(k+1)!=(k+2)!−1.

We have:

1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+(k+1)!−1+(k+1)·(k+1)!=k!(k+1+1)+(k+2)!−1=(k+1)!(k+2)−1=(k+2)!−1,

where we have used the induction hypothesis in the second step and simplified in the fourth step.

Therefore, the statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

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Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer: \(\Large\boxed{-30x^2+40x}\)

Step-by-step explanation:

Given expression

10x (4 - 3x)

Expand the parenthesis by distributive property

= 10x · 4 - 10x · 3x

= (10 × 4)x - (10 × 3) (x × x)

\(\Large\boxed{=-30x^2+40x}\)

Hope this helps!! :)

Please let me know if you have any questions

Hi :)

We'll use distributive property to solve this

\(\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}\)

Thus

\(\large\boldsymbol{10x\cdot4-3x\cdot10x}\)

Simplify

\(\Large\boldsymbol{40x-30x^2}\)

\(\tt{Learn~More;Work~Harder}\)

:)

If $550 is deposited in an acount paying 8.6% annual interest, compounded semiannually the account will take approximately 5.2 years to increase to $850.

To calculate the time it takes for the account to increase to $850, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)\)

Where:

A is the final amount ($850),

P is the initial deposit ($550),

r is the annual interest rate (8.6% or 0.086),

n is the number of times the interest is compounded per year (semiannually, so n = 2),

and t is the time in years.

Rearranging the formula to solve for t, we have:

t = (1/n) * log(A/P) / log(1 + r/n)

Plugging in the values, we get:

t = (1/2) * log(850/550) / log(1 + 0.086/2)

Calculating this expression gives us approximately 5.2 years, rounded to the nearest tenth. Therefore, it will take around 5.2 years for the account to increase to $850.

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Answer:

Hello,

Please, see the attached file.

Thanks.

Step-by-step explanation:

The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.

Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.

The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:

These steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.

Thus, this can be the match for the given scenario.

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

The difference between 5 and a certain number is divided by 3. find the number if is equal to 7.

The number line for the set of jump distances to make a new record.

Option B is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

The school record in the long jump = 518 cm

Now,

To make a new record the set of jump distances should be greater than 518 cm.

To represent the set of jump distances on a number line we can not have a black dot on 513 on the number line.

The dot should be an open dot.

Thus,

Option B is the number line for the set of jump distances to make a new record.

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Answer:

Supplementary angles add up to 180°

180=7x-9+4x+3

180=7x+4x-9+3

180=11x-7

180+7=11x

187=11x

11x=187

x=187/11

x=17

Therefore x = 17

Solution:

The word problem needs to be developed into mathematical expressions.

Developing the statements given;

Substituting equations (2) and (3) into equation (1);

Substituting the value of j in equation (2) and equation (3) to get l and a respectively ;

Therefore,

Latoya sent 24 messages

Austin sent 51 messages

Jim sent 17 messages.

Answer: 1406.25 or 1406 1/4

Step-by-step explanation:

From the question, we are informed that a soccer field at a park is 9000 square yards and that the soccer field takes up 6 2/5 square inches on the map of the park.

To calculate how many square yards does 1 square inch on the map represent, we divide 9000 by 6 2/5. This will be:

= 9000 ÷ 6 2/5

= 9000 ÷ 6.4

= 1406.25 or 1406 1/4

1 square inch on the map represents 1406.25 square yards.

Answer: 45,000 / 32 or 1,406 and 1/4

I dont feel like doing the work all over again

The measure of two angles are 39 degree and 69 degree. By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree, so the final angle is 72 degree. Therefore, the largest angle in the triangle is 72 degree.

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

Given:

\(The\;sum\;of\;two\;angles\;in\;a\;triangle\;is\;\frac{6}{5}\;of\;a\;right\;angle\;is,\;\frac{6}{5} \times 90^{\circ} = 108^{\circ}\)

\(let\;x\;is\;the\;measure\;of\;the\;first\;angle\)

\(one\;of\;these\;two\;angles\;is\;30\;larger\;than\;the\;other,\;is\;x+30=108\)

We know that sum of two angles is 108

\(x+x+30=108^{\circ}\)

\(2x+30=108\)

\(2x=108-30\)

\(2x=78\)

\(x=39^{\circ}\)

Second angle y is,

\(y=x+30\)

\(y=39+30\)

\(y=69^{\circ}\)

By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree,

Third angle z is,

\(x+y+z=180\)

\(39+69+z=180\)

\(108+z=180\)

\(z=180-108\)

\(z=72^{\circ}\)

\(By\;comparing\;the\;angles\;39^{\circ},\;69^{\circ}\;and\;72^{\circ}, 72^{\circ}\; is\;greater\)

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

The definition of the given piecewise function is:

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x until 2, the function is the cube function shifted down 3 units, hence the definition is:

\(y = x^3  - 3, x \leq 2\)

For x greater than 2, the function is the square function shifted up 6 units, hence the definition is:

\(y = x^2 + 6, x > 2\)

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The complete question is:

Fred's Donuts is installing new equipment in its bakery. Many employees are fearful they will not be able to operate it. Which of the following courses of action is best for Fred to use to overcome this employee resistance?

A) threaten the employees who resist the change

B) present distorted facts to the employees

C) terminate employees who resist the change

D) educate employees and communicate with them

The answer is option D) educate employees and communicate with them.

Threatening employees (option A) is not a productive or ethical approach. It can create a negative and hostile work environment, leading to decreased morale and potential legal consequences.

Presenting distorted facts (option B) is dishonest and can lead to mistrust among employees. Providing accurate and transparent information is crucial for building trust and gaining employee support.

Terminating employees (option C) solely based on their resistance to change is not an effective solution. It is important to engage with employees and understand their concerns before considering any drastic actions such as termination.

Educating employees and communicating with them (option D) is the recommended approach. This involves providing thorough training on how to operate the new equipment, addressing any concerns or fears employees may have, and ensuring open lines of communication throughout the process. By involving employees in the decision-making and change implementation, they are more likely to feel valued and willing to adapt to the new equipment.

Overall, a collaborative and supportive approach that focuses on education, communication, and addressing employee concerns is the most effective way to overcome resistance to change in this scenario.

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