Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. The following is the amount ($000) earned per month by a sample of 15 Claiborne models:

$4.7 $3.8 $6.7 $3.8 $3.9 $4.2 $4.0 $4.0 $4.8 $3.1 3.1 5.5 3.4 6.1 4.9

The following is the amount ($000) earned by a sample of 12 Klein models.

$4.0 $3.8 $3.6 $2.5 $4.9 $5.2 $5.9 $4.9 $4.4 $3.6 5.1 4.7

Required:
a. Find the degrees of freedom for unequal variance test.
b. State the decision rule for 0.05 significance level: H0: μLC ≤ μCK; H1: μLC > μCK.
c. Compute the value of the test statistic.
d. Is it reasonable to conclude that Claiborne models earn more? Use the 0.05 significance level.

The simplified form of the rational expression \((7x)/(14x^6)\) is \(1/(2x^6).\)

To simplify the rational expression \((7x)/(14x^6)\), we can begin by simplifying the numerator and denominator separately.

In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.

In the denominator, \(14x^6\), we can see that both 14 and x^6 have a common factor of \(2x^6\).

So, we can rewrite the denominator as

\(14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.\)

Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:

\((7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)\)

Therefore, the simplified form of the rational expression\((7x)/(14x^6)\) is \(1/(2x^6).\)

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The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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Answer:

-22

Step-by-step explanation:

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Answer: B

Step-by-step explanation:

\((5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}\)

Answer:

650

Step-by-step explanation:

The number of packets of waffles is W

and the number of muffins are M

The weight of dough is 250 pounds and a pack of muffins requires 1 lb of dough whereas a pack of waffles uses 3/4 lb of dough.

3÷4W+M≤250

Multiplying both sides by 4

3W+4M≤1000

It takes bakers 6 minutes to make a packer of waffles and 3 minutes to make a pack of muffins, the total time available is 20 hours or 1200 minutes.

3M+6M≤1200

Minus the initial equation from the new equation:

(3M+6M≤1200)−(3W+4M≤1000)

2M≤200

Dividing equation by 2

M≤100

For M≤100

3W+4M≤1000

3W≤1000−4M

For the Maximum values of M

the least value of W is obtained

3W≥1000−4×100

3W≥600

Dividing the equation by 3

W≥300

For maximum profit, the number of waffles and muffins is taken as 300 and 100 respectively :

1.5∗300+2∗100

=650

Answer:

1.5 miles

Step-by-step explanation:

.3 miles/12 minutes x 5/5 = 1.5 miles/ 1 hour

Answer:

x=3

Step-by-step explanation:

make it equal 0 since 2x^2=4x+30

0=2x^2+4x+30 then you factor out the 2

2(x^2+2x+15) then you factor and get

2(x+5)(x-3)

So x=-5 or x=3 and x cannot be negative

Answer:

(a)

\(\mu=54\)    

The standard deviation is  

\(\sigma=6.6543\)

(b)

\(\mu=246\\\sigma=6.6543\)  

Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is  

\(z=-1.73\)

So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is  

\(P(Y\geq 235)=P(Y\geq 234.5)=P(z\geq -1.73)=0.9582\)

Step-by-step explanation:  

Let X is a random variable that shows the number of people who would drop out of the Rewards Program within four weeks. Here X has binomial distribution with parameters n = 300 and p = 0.18.

(a)  

The mean number of people who would drop out of the Rewards Program within four weeks in a sample of this size is  

\(\mu=np=300\cdot 0.18=54\)  

The standard deviation is  

\(\sigma=\sqrt{np(1-p)}=\sqrt{300\cdot 0.18\cdot 0.82}=6.6543\)  

(b)  

Let Y is a random variable that shows the number of people in the sample who will still be in the Rewards Program after the first four weeks. Here Y has a binomial distribution with parameters n= 300 and p=0.82. So mean of Y is  

\(\mu=np=300\cdot 0.82=246\\\sigma=\sqrt{np(1-p)}=\sqrt{300\cdot 0.18\cdot 0.82}=6.6543\)  

Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is

\(z=\frac{Y-\mu}{\sigma}=\frac{234.5-246}{6.6543}=-1.73\)  

So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is  

\(P(Y\geq 235)=P(Y\geq 234.5)=P(z\geq -1.73)=0.9582\)

We are asked to formulate an algebraic expression for the statement "The sum of 5 and three times a number is 23​", first a "sum" is mentioned and it says that the result is 23, let's say that we are adding two numbers a and b and we get 23, like this:

a + b = 23

From the statement we know that one of the numbers that is being added is 5, then by using 5 instead of a, we get:

5 + b = 23

And we are told that the other number that is being added is being multipliend by 3, by replacing 3x (three times a number "x") for b we get:

5 + 3x = 23

Then, the answer is 5 + 3x = 23

Answer:

No

Step-by-step explanation:

When you plug in (2,-2) into the equation, the solution does not equal 4. So the point (2,-2) does not lie on the line.

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

D

Step-by-step explanation:

The greatest common factor of 12 and 24 is 12. The only option which accounts for this is D.

Answer:

9100.09

Step-by-step explanation:

i did the math so this is it

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Option D is correct, the region above of the line y=x/2-3 that we can write as  y>x/2-3

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We know by reading the exercise that the company estimates same day delivery as a region of the miles.

y>x/2-3

We need to represent this region in a graph.

One way is to find the graph of y=x/2-3

This line will divide the plane into two regions. Then, using any point that verifies the original equation  we can find the graph.

y=x/2-3

If x=0

y=-3

The point (0, -3)  is the interception of the line with y-axis.

Now if y=0

0=x/2-3

3=x/2

6=x

The point (6, 0) is the interception of the line with x-axis.

We know that  y>x/2-3 will be the region above of or below of the line y=x/2-3

Now using an arbitrary point (0,0), for example  and replacing in the expression :

0>-3

The point  (0, 0) verifies the expression. Therefore, this point belongs to the region.

Finally, we conclude that the region is the region above of the line y=x/2-3 that we can write as  y>x/2-3 and the correct option is D.

Hence , option D is correct, the region above of the line y=x/2-3 that we can write as  y>x/2-3

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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Answer:

9^4

Step-by-step explanation:

There is 4 nines.

9*9*9*9 = 6561

9^4 = 6561

9^3 = 729

Answer:

$450.

Step-by-step explanation:

62% = 0.62.

Let yesterday's price be $x, then.

0.62x = 279

x = 279 / 0.62

= $450.

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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Answer:

D

Step-by-step explanation:

This graph doesn't show a function because if you draw a vertical line  for the vertical line test through almost anywhere, there would be two points with the same x-value, and that shows that it is not a function.

Length of hole digging for \(2\frac{1}{2}\) hours is 4.167 feet.

Given that;

Rate of digging hole by Abe = \(1\frac{2}{3}\) feet every hour

Find:

Length of hole digging for \(2\frac{1}{2}\) hours

Computation:

Rate of digging hole by Abe = \(1\frac{2}{3}\) feet every hour = 5/3 feet every hour

Time taken =  \(2\frac{1}{2}\) hours = 5/2 hours

Length of hole digging for \(2\frac{1}{2}\) hours = Rate of digging hole by Abe × Time taken

Length of hole digging for \(2\frac{1}{2}\) hours = (5/3)(5/2)

Length of hole digging for \(2\frac{1}{2}\) hours = 25 / 6

Length of hole digging for \(2\frac{1}{2}\) hours = 4.167 feet (Approx.)

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-4 1/6

Hope it's correct!

Answer:

afdgdfdf

Step-by-step explanation:

Answer:

its going up by 1 each time theres a new number so next youll multiply 4 by 120 which is 480

Step-by-step explanation:

Answer

1

Step-by-step explanation

Given the expression:

It has the form:

with a = 106° and b = -61°. Therefore, the first expression is equivalent to: