-6(-12) = A —72 B 18 C 0.5 D 72​

\(Critical value $=Z_{\alpha / 2}=Z_{0.02 / 2}=2.33$Standard\\ Error $=\sqrt{((\hat{P} 1\times \hat{q} 1) / n 1)+((\hat{P} 2 \times \hat{q} 2) / n 2)}=0.028$\)

\((\hat{P} 1-\hat{P} 2) \pm Z_{\alpha / 2} \times \sqrt{((\hat{P} 1 \times \hat{q} 1) / n 1)+((\hat{P} 2 \times \hat{q} 2) / n 2)}\)

\(Z_{\alpha / 2}=Z_{0.02 / 2}=2.33\)

\(\begin{aligned}&\text { Lower Limit }=(0.4-0.12)-Z_{0.02 / 2} \times \sqrt{((0.12 \times0.88) / 596)+((0.4 \times 0.6) / 395)}=0.2148 \\&\text { upper Limit }=(0.4-0.12)+Z_{0.02 / 2} \times \sqrt{((0.12 \times 0.88) / 596)+((0.4 \times 0.6) / 395)}=0.3452\end{aligned}\)

\(98 \%\) Confidence interval is

\((0.215,0.345)$\\(0.215) (\mathrm{P} 2-\mathrm{P} 1) < 0.345)$$\)

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25 tablets are needed to dispense to fill the prescription order.

A prescription is a legally binding document or order prepared by a certified healthcare provider to diagnose, prevent, or treat a specific patient's ailment. It is authored by a licensed professional, it is written in the context of genuine doctor-patient interaction and it is a legal document that can be used as "prima facie" evidence in a court of law.

It was most likely intended for the pharmacist, who needs a certain amount of each component to mix the medicine (rather than the patient, who must take/consume" it).

So, a prescription for 10 days = 21/2

Tablets required for 10 days = 25

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Rose's interest rate when she bought the vehicle was 2.45%.

So, the correct option is (C)

An interest rate is that the quantity of interest that's collectable every amount explicit as a proportion of the number Lent, deposited, or borrowed (called the principal sum).The principal, interest rate, frequency of change of integrity, and length of the loan, deposit, or borrowing square measure all factors that have an effect on the ultimate quantity of interest charged on a total Lent or borrowed.

The interest rate that's determined over a year is that the annual charge per unit. different interest rates, that square measure usually annualized, square measure applicable over shorter time periods, such daily or a month.

The interest rate has been represented as associate index of the preference for a dollar of gift [income] over a dollar of future [income].

Calculation:

We have been given that the

Simple interest = $2,462.25

Principal =  $16,750

Time = 6 years

We know that, Simple interest × 100 = Principal × Rate × Time

$2,462.25 × 100 =  $16,750 × Rate × 6

246225 = 100500 × Rate

Rate =  2.45%

Hence, the correct option is (C).

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The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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The prime costs per unit (rounded to the nearest cent) for September were  $7.05 per unit.

In economics, total cost is the sum of all costs a company incurs in generating a certain output level.

Now, as per the question;

Prime cost = (cost of direct material + cost of direct labour)/number of units.

Cost of direct materials used = $66,000

Cost of direct labour = $75,000

Number of units = 20,000

Substituting the values;

= ($66,000 + $75,000) / 20,000 units

= $141,000 / 20,000 units

= $7.05 per unit

Thus, the prime cost per unit in September is found to be $7.05 per unit.

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Answer:

-3, -3

Step-by-step explanation:

Answer: The answer is 13,841,287,201

Step-by-step explanation:

You start with the equation that's in the parenthese which is  7^6, and the answer is 117,649. Then you're left with 117,649^2, so you solve for that which is 13,841,287,201. I'm not sure if this is what you're looking for but I hope this can help you.

There are 4 integers between 20 and 30 that have a prime factorization with exactly 3 factors that are not necessarily unique.

To find the integers with a prime factorization having exactly 3 factors, we need to look for numbers that can be expressed as the product of two distinct prime numbers.

Step 1: Identify the prime numbers between 20 and 30. The prime numbers in this range are 23, 29.
Step 2: Determine all possible pairs of distinct prime numbers. In this case, we have only one pair: (23, 29).
Step 3: Calculate the products of these pairs. The products of (23, 29) are 667 and 667.
Step 4: Count the integers between 20 and 30 that match these products. We have two integers that match, which are 21 and 27.
Step 5: Check if these integers have exactly 3 factors. The factors of 21 are 1, 3, 7, and 21 (a total of 4 factors), so it does not meet the criteria. The factors of 27 are 1, 3, 9, and 27 (a total of 4 factors), so it also does not meet the criteria.

Therefore, there are no integers between 20 and 30 with a prime factorization having exactly 3 factors that are not necessarily unique.

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The store owner's profit is 25% of the selling price of grapes, which corresponds to option B.

The store owner buys the grapes for 80 cents and sells it for 100 cents, so the profit is 100-80 = 20 cents.

The percentage of the profit is (profit/cost) x 100%. In this case, the profit is 20 cents and the cost is 80 cents, so the percentage of profit is (20/80) x 100% = 25%.

Therefore, the store owner's profit is 25% of the selling price of grapes, which corresponds to option B.

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Answer:

For 90 students, 12 adult chaperones are required.

Step-by-step explanation:

90 (students) divided by 15 gives us a proportion to multiple the amount of adults by.

90/15 = 6

Since there are 6 times as many students as the question provided, we will multiply the amount of adults in the question by 6.

2 x 6 = 12

An equation of the tangent line to curve [y = e⁶ˣ cos x] at the given point  (0, 1) is y = x + 6.

At a given point, the tangent line of a curve is a line that really just contacts the curve (function). In calculus, the tangent line may connect the curve at any other point(s), and it may also cross the graph at any other point(s).

Now, as per the given question;

Because of this, point (0,1) is a tangent point;

y = f((0) = e⁰cos0 = 1.

We differentiate to get the slope of the tangent line m. Tangent line equation:

y' = 6e⁶ˣcosx - e⁶ˣ sinx;

Thus, the slope of the curve becomes;

m = f'(0) = 6.

Substituting the values of slope and coordinates (0, 1).

y = 6 + 1(x - 0),

Simplifying the equation.

y = x + 6

Thus, the equation of the tangent line to the given curve is y = x + 6.

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Answer:

8.164

Step-by-step explanation:

The circumference of the ball is 8.164 inches.

Since the diameter of the tennis ball is 2.6 inches

So here the radius should be half i.e. 1.3 inches

Now we know that

Circumference = \(2\pi r\\\\\)

= 2(3.14)(1.3)

= 8.164 inches

Therefore, we can conclude that The circumference of the ball is 8.164 inches.

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Based on the information given about the exponent, the value of A is 24 and the value of n is 8.

In order to solve this problem, we can use the following steps:

Identify the exponents of x and y in the term 13440x6y4.

Write the term in the form (Ax + y)^n, where A and n are unknown.

Set the exponents of x and y in the term equal to the exponents of x and y in the expression (Ax + y)^n.

Solve the resulting equation for A and n.

Following these steps, we get the following:

The exponent of x in the term 13440x6y4 is 6.

The exponent of y in the term 13440x6y4 is 4.

The term 13440x6y4 can be written as (24x + y)^8.

Solving the equation (24x + y)^8 = 13440x6y4, we get A = 24 and n = 8.

Therefore, the value of A is 24 and the value of n is 8.

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The number of students whose favorite color is blue will be 40 students is the best prediction of the favorite colors by the 120 students based on the survey results given.

Here are the reasons why the other options are incorrect as follows: The number of students whose favorite color is green will be 12 more than the number of students who choose purple as their favorite color:

This statement cannot be a good prediction of the 120 students' favorite color.

It is possible that only two students chose purple, so if only two students choose purple as their favorite color, then the number of students whose favorite color is green would be 14, which does not make sense.

The number of students whose favorite color is red will be twice the number of students who choose purple as their favorite color:

This statement cannot be the best prediction of the 120 students' favorite color.

Even though 4 students chose red as their favorite color, only two students chose purple as their favorite color.

If the statement were accurate, then the number of students who chose red as their favorite color would be 4 × 2 = 8, which does not seem like a reasonable prediction.

The number of students whose favorite color is blue will be 12 less than the number of students who choose green: The statement cannot be the best prediction of the 120 students' favorite color.

Because according to the survey results, 8 students choose blue, but if this statement were accurate, the number of students who choose green would be 8 + 12 = 20.

This implies that the total number of students who choose blue is 20 - 12 = 8 students.

This is contradictory because the number of students who choose  is already given in the survey results. Therefore, this statement cannot be the best prediction.

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a. Beta of operation A = 1.16 * (1 / 4) = 0.29, Beta of B = 1.16 * (2 / 4) = 0.58, Beta of C = 1.16 * (1 / 4) = 0.29 b. Beta of D = 0.87 c. Weighted Average Beta of Potter = 0.29 d. Cost of Capital for D = 31.75%

(a) To calculate the betas of the assets for divisions A, B, and C of Potter plc, we need to use the following formulas:

Beta of A = Beta of Potter * (Market Value of A / Market Value of Potter)

Beta of B = Beta of Potter * (Market Value of B / Market Value of Potter)

Beta of C = Beta of Potter * (Market Value of C / Market Value of Potter)

Given that the beta of Potter is 1.16 and the market value ratios are:

Market Value of A : Market Value of B : Market Value of C = 1 : 2 : 1

Using these values, we can calculate the betas:

Beta of A = 1.16 * (1 / 4) = 0.29

Beta of B = 1.16 * (2 / 4) = 0.58

Beta of C = 1.16 * (1 / 4) = 0.29

The assumptions behind this calculation are that the betas of the assets are proportional to their market values within the portfolio and that the beta of the portfolio (Potter plc) is known.

(b) To calculate the beta for asset D, we need to use the formula:

Beta of D = Beta of B * (Revenue Sensitivity of D / Revenue Sensitivity of B)

Given that the revenue sensitivity of D is 1.5 times that of B, we have:

Beta of D = 0.58 * 1.5 = 0.87

(c) To find out the beta for Potter plc after the sale of assets and purchase, we need to consider the weighted average beta of the remaining assets.

Weighted Average Beta of Potter = (Beta of A * Market Value of A + Beta of C * Market Value of C) / Total Market Value of Potter

Given that the market value ratios are:

Market Value of A : Market Value of B : Market Value of C = 1 : 0 : 1

Using these values, we can calculate the weighted average beta:

Weighted Average Beta of Potter = (0.29 * 1 + 0.29 * 1) / (1 + 1) = 0.29

(d) The cost of capital for the new projects in division D can be estimated using the Capital Asset Pricing Model (CAPM) formula:

Cost of Capital for D = Risk-Free Rate + Beta of D * (Market Portfolio Return - Risk-Free Rate)

Given that the risk-free rate is 10%, the beta of D is 0.87, and the market portfolio return is 35%, we have:

Cost of Capital for D = 10% + 0.87 * (35% - 10%) = 10% + 0.87 * 25% = 10% + 21.75% = 31.75%

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Answer:

Step-by-step explanation:

If Susana runs 2 3/4 miles per 1/4 hour

in one hour

2 3/4=11/4

1h=11/4 *4=11 miles

11 miles/hour

The grocery store chain should rent 2 type A trucks and 233 type B trucks to achieve the minimum total cost.

In order to transport 3000 m of refrigerated goods and 4000 m of non-refrigerated goods, a grocery store chain is looking to rent trucks. To transport these goods, the company is planning to hire two types of trucks:

type A and type B. Each type A truck has a 20 m refrigerated goods section and a 40 m non-refrigerated goods section, while each type B truck has both sections with the same volume of 30 m.

The cost per cubic meter is $30 for a type A truck and $40 for a type B truck. How many trucks of each type should the grocery store chain rent to achieve the minimum total cost?

Assuming that we have x type A trucks and y type B trucks, then we can write the following equations:

20x ≤ 300030y ≤ 4000 40x + 30y > 3000 + 4000 30x + 30y > 3000x > 100Since x must be an integer, we must round x up to 2.Now we need to figure out the number of type B trucks we need

. Using the equations,

we can write the following:

30x + 30y = 3000 + 4000 30x + 30y

= 700030y

= 7000 - 30x y

= (7000 - 30x)/30 y

= 233.33 - x/3

Since y must be an integer, we must round y down to 233.

Now we have x = 2 and y = 233, so we need to rent 2 type A trucks and 233 type B trucks. The total cost will be:2 * 20 * 30 + 233 * 30 * 40 = $608,400

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

20705.875

Step-by-step explanation:

Area of a pentagon is 1/2 * P * A  p being the perimeter of the pentagon and a being the apothem.  1/2 * 548.5 * 75.5 equals 20705.875.  I'm almost positive this is correct.  So sorry if it's not.  Have a good day/night!

Answer:

66

Step-by-step explanation:

multiply both sides by 6 and get x=11x6=66

Answer:D

Step-by-step explanation:  3 over 9 = .333 repeating which is greater then .22 and lower then 33

Answer:

5040 inches long

Step-by-step explanation:

how to solve the area for something you do the length times the width. so 84 times 60 is 5040.

Answer:

The answer to your problem is, 5040

Step-by-step explanation:

We can do this formula:

L x W = A

By using this formula we can find the answer.

Lets substitute some of the letters.

L = 84

W = 60

A = ? ( We are trying to find that )

Lets do the problem:

84 x 60 = ?

? = 5040. Which is our answer

Thus the answer to your problem is, 5040

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Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

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

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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9x - 2y = 19, 7x = 21

7x = 21

=> x = 21/7

= x = 3 —————(1)

9x - 2y = 19

=> 9(3) - 2y = 19 [From (1)]

=> 27 - 2y = 19

=> -2y = 19 - 27

=> -2y = -8

=> y = -8/-2

=> y = 8/2

=> y = 4

So, x = 3 and y = 4.

If the columns of B do not span ℝ^4, it means that there are certain vectors y in ℝ^4 for which the equation Bx = dy does not have a solution. In this case, the system of equations is inconsistent, and there may not be a solution for some y.

To determine whether the columns of matrix B span ℝ^4, we need to check if the columns are linearly independent and if they span the entire space.

Let's assume matrix B is an m × n matrix, where m is the number of rows and n is the number of columns.

If the columns of B are linearly independent and there are n columns (n ≤ m), then the columns span ℝ^m. In this case, if B is a 4 × n matrix, the columns would span ℝ^4.

On the other hand, if the columns of B are linearly dependent or there are fewer than n columns (n > m), then the columns do not span the full space.

Regarding the equation Bx = dy, where y is a vector in ℝ^4, we can determine if there is a solution for each y by considering the consistency of the system of equations.

If the columns of B span ℝ^4, it means that for every vector y in ℝ^4, there exists a solution to the equation Bx = dy. In this case, the system of equations is consistent, and there is a solution for each y.

However, if the columns of B do not span ℝ^4, it means that there are certain vectors y in ℝ^4 for which the equation Bx = dy does not have a solution. In this case, the system of equations is inconsistent, and there may not be a solution for some y.

To conclusively determine whether the columns of B span ℝ^4 and whether the equation Bx = dy has a solution for each y in ℝ^4, we would need more information about the specific matrix B and its dimensions.

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Answer:

So There will be 2 congruent angle