In a study of job satisfaction, we surveyed 30 faculty members
at a local university. Faculty rated their job satisfaction on a
scale of 1-10, with 1 = "not at all satisfied" and 10 = "totally
satisfi

Answer:

Step-by-step explanation:

5b-5-9b+8+4b=

=0+3=3

The expression that represents the discount price of the shirt is (option a) 0.95x

Discount:

Discount causes the product's selling price to drop, which increases its allure for the consumer. Price reduction has a psychological effect on the buyer, influencing them to make the purchase. The two discounts available are trade discounts and cash discounts.

Given,

The discount percentage of the shirt in a store = 5%

Original price of the shirt = x

We have to find the expression that represents the discount price of the shirt:

Discount price = (Original price × (100 - Discount percentage) / 100

Discount price = (x × (100 - 5)) / 100

Discount price = (x × 95) / 100

Discount price = 0.95x

That is, the expression that represents the discount price of the shirt is (option a) 0.95x.

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The question is incomplete. Completed question is given below:

A shirt at the store is being offered at a 5% discount. If the original price of the shirt is x, which answer choice shows an expression that represents the discounted price of the shirt?

1. 0.95x

2. 1.05x

3. 0.05x

4. x + 0.05

Answer:

Value of x = 5

Step-by-step explanation:

Given:

x + 4 = 3(x - 2)

Find:

Value of x

Computation:

x + 4 = 3(x - 2)

⇒ x + 4 = 3x - 6

⇒ x = 3x -6 - 4

⇒ x - 3x = -10

⇒-2x = - 10

⇒ x = -10 / - 2

Value of x = 5

Answer:

67,900

Step-by-step explanation:

Answer: Her net income is less than $120.

Step-by-step explanation:

Based on the information given, the gross income for Amy will be:

= 15 × $8

= $120

Net income is the income that an individual has left after tax and every other necessary deductions have been removed. Therefore when this is done, the net income for Amy will be less than $120

A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is

Information from the problem

You have made 160 duct tape wallets to sell

If you sell 3 each day

From the information we can deduce that

assuming amount left is y and the number of days x the  we have

y = 160 - 3x

Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is  y = 160 - 3x

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The x-component of the cross product \(\vec a\) × \(\vec b\) is 4.

The cross product of two vectors \(\vec a\) and \(\vec b\), denoted as \(\vec a\) × \(\vec b\), can be calculated using their components. Given that vector \(\vec a\) = \(2\hat{i} + 1 \hat{j}\) and vector \(\vec b\) = \(4\hat{i} - 5 \hat{j}+4\hat{k}\), let's find the cross product \(\vec a\) × \(\vec b\) and its x-component.
The cross product is determined by using the following formula:
\(\vec a\) × \(\vec b\) = \((a_{2} b_3 - a_3b_2)\hat{i} - (a_1b_3 - a_3b_1)\hat{j} + (a_1b_2 - a_2b_1)\hat{k}\)
where \(a_1\), \(a_2\), and \(a_3\) are the components of vector \(\vec a\), and \(b_1\), \(b_2\), and \(b_3\) are the components of vector \(\vec b\).
Substitute the given components into the formula:
\(\vec a\) × \(\vec b\) = \(((1)(4) - (0)(-5))\hat{i} - ((2)(4) - (0)(4))\hat{j} + ((2)(-5) - (1)(4))\hat{k}\)
\(\vec a\) × \(\vec b\) = \((4)\hat{i} - (8)\hat{j} + (-14)\hat{k}\)
The x-component of the cross product \(\vec a\) × \(\vec b\) is 4, which is an integer.

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Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Answer:

6 2/9

Step-by-step explanation:

56 divided by 9 is 6.22 and 2/9 is .22

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

The probability exactly two of the appeals were successful is 0.9536

We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012), and suppose ten first-round appeals have just been received by a Medicare appeals office.

This situation can be represented through Binomial distribution as;

\(P(X=r)={}^{n}C_{r}(p)^r(1-p)^r\) where \(x=0,1,2,3.....\)

where,  n = number of trials (samples) taken = 10

            r = number of success

            p = probability of success which in our question is % of first-round

                  appeals that were successful, i.e.; 40%

So, here X ~ Binom(n=10 , p=0.40

Probability that at least two of the appeals will be successful = P(X>=2)

   P(X >= 2) = 1 - P(X = 0) - P(X = 1)

                    = 1 - \(^{10}C_{0}(0.40)^0(1-0.40)^{10-0}-^{10}C_{1}(0.40)^1(1-0.40)^{10-1}\)

                     = 1 - 0.00605 - 0.0403

                     = 0.9536

Hence, the probability exactly two of the appeals were successful is 0.9536

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Answer:

\(\sqrt{5}\)

Step-by-step explanation:

to simplify use the rule of radicals

\(\frac{\sqrt{x} }{\sqrt{y} }\) ⇔ \(\sqrt{\frac{x}{y} }\) , then

\(\frac{\sqrt{15} }{\sqrt{3} }\) = \(\sqrt{\frac{15}{3} }\) = \(\sqrt{5}\)

The law of large numbers is a fundamental concept in probability theory that describes the behavior of the average of a large number of independent random variables.

It states that as the sample size increases, the sample mean will converge to the true population mean, and the sample proportion will converge to the true population proportion.

In other words, the larger the sample size, the more reliable the sample mean and proportion will be as an estimate of the true population mean and proportion. This is because the variation in the sample mean and proportion decreases as the sample size increases, and the sample becomes more representative of the population. This principle is widely used in statistics, and it underpins many statistical methods and techniques.

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We can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

Now, We can use a bar model to represent the total number of cans and the number of stacks that can be formed.

First, let's find the total number of cans:

7 boxes x 48 cans/box = 336 cans

Now, let's use a bar model to represent this total:

| 336 cans of food  |

Next, we want to find how many stacks of 8 cans we can form. We can use a separate bar model to represent the size of each stack:

| 42 stacks of 8 cans each |

Hence, The number of stacks that can be formed, we need to divide the total number of cans by the number of cans in each stack:

336 cans ÷ 8 cans/stack = 42 stacks

So the final bar model looks like this:

| 336 cans of food  | = | 42 stacks of 8 cans each |

Therefore, we can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

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After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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Multiplying the entire expression by 100 gives us the percentage of peanut concentration in the final mix.

To find the percentage of peanut concentration in the final mix after Marshall adds x ounces of peanuts, we can use the following expression:

((0.3 * 32) + x) / (32 + x) * 100

Let's break down the expression:

0.3 * 32 represents the number of ounces of peanuts initially present in the mixed nuts. Since the mixed nuts are estimated to be 30% peanuts, multiplying 0.3 by the total weight of 32 ounces gives us the initial amount of peanuts

Adding x to this expression represents the additional ounces of peanuts that Marshall adds to the mix.

The denominator (32 + x) represents the total weight of the final mix, which includes both the initial mixed nuts (32 ounces) and the additional x ounces of peanuts.

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Answer:

5/64

Step-by-step explanation:

5/8 divided by 8

5/8 * 1/8 = 5/64

So, the system of equations representing this situation is: n + d + q = 95; 0.05n + 0.10d + 0.25q = 13.70; q = d + 11.

To represent this situation with a system of equations, we can use the following equations:

The total number of coins: n + d + q = 95

The total value of the coins in dollars: 0.05n + 0.10d + 0.25q = 13.70

The relationship between the number of quarters and dimes: q = d + 11

The first equation represents the total number of coins, which is given as 95.

The second equation represents the total value of the coins in dollars, which is given as $13.70. The values of each coin (nickel, dime, quarter) are multiplied by their respective quantities (n, d, q) and summed up to obtain the total value.

The third equation represents the relationship between the number of quarters (q) and dimes (d), which states that there are 11 more quarters than dimes.

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Answer:

 (a)  A and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

 A and B are similar, but not congruent.

Answer:

2. 7 + 4

3. 21 - 27

4. 8 - 28

Step-by-step explanation:

2. 1 (7+4) = 1×7 + 1×4 = 7 + 4

3. 3 (7-9) = 3×7 - 3×9 = 21 - 27

4. 4 (2-7) = 4×2 - 4×7 = 8 - 28

hope this helps :)

Answer:

1. the answer is 7+4

2. the answer is 21-9.

3. the answer is 8-7.

Hope this helps, have a great day/night, and stay safe!

The total amount of water deposited at the research site whenever an inch of rainfall occurs is 14400 cubic inches.

The first thing to do is to determine the volume of water deposited per square foot of surface area with 1 inch of rainfall.

This is given as 144 cubic inches (0.623 gallons).

To find the total amount of water that will be deposited at the research site whenever an inch of rainfall occurs, the surface area must first be determined.

All research sites are 100 square feet in area.

Now, multiply the volume of water deposited per square foot of surface area with 1 inch of rainfall by the surface area to obtain the total amount of water deposited at the research site with 1 inch of rainfall.

Volume of water deposited per square foot of surface area with 1 inch of rainfall

= 144 cubic inches (0.623 gallons)

Total surface area of all research sites

= 100 square feet

Total amount of water deposited at the research site with 1 inch of rainfall

= 144 cubic inches x 100 sq feet
= 14400 cubic inches

Therefore, the total amount of water deposited at the research site whenever an inch of rainfall occurs is 14400 cubic inches.

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Step-by-step explanation:

\( = \lim \limits_{x \to0}x \cot(2x) \)

\( = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \)

\( = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \times \frac{2x}{2x} \)

\( = \lim \limits_{x \to0} \frac{2x}{ \tan(2x) } \times \lim \limits_{x \to0} \frac{x}{2x} \)

\( = \lim \limits_{u \to0} \frac{u}{ \tan(u) } \times \frac{1}{2} \)

\( = \frac{1}{2} \)

Answer:

2x + 11

Step-by-step explanation:

We are given

6 - 2x + 5 + 4x

Combining like terms with x, we have

6 + 5 + 2x

Combine like terms again, this time constants

11 + 2x

Answer:

-23

Step-by-step explanation:

h+11.5=-11.5

h=-11.5-11.5

h=-23

you will subtract -11.5 on both sides which leaves h alone on one side

Step-by-step explanation:

subtract 11.5 from both side of equation

h + 11.5 = -11.5

h + 11.5 - 11.5 = -11.5 - 11.5

h + 0 = -23

h = -23

Answer:

300 jumping jacks

Step-by-step explanation:

120 ÷ 2 = 60 jumping jacks per minute

60 × 5 = 300 jumping jacks

Sam can do 300 jumping jacks in 5 minutes.

Hope that helps.

Answer:

60

Step-by-step explanation:

120 / 2 = 60 (jumping jacks per minute)

60 * 5 = 300

Best of Luck!

We have the following:

Now,

replacing:

Therefore, the answer is 6 units

We need to first identify the center of the circle.

We see that the coordinate point of the center of the circle is (-1, -2).

The equation of a circle is given with the equation

where h is x, k is y, and r is the radius of the circle.

Therefore, we can plug in the coordinates first to find the h and k of the equation.

Then, we need to determine r.

The circle intersects points (-6, -2) and (4, -2). We can simply subtract the x-coordinates from each other to find the diameter of the circle.

Finally, we know the radius is half of the diameter:

We can plug in the radius into the equation.

Therefore, our final equation is Choice D:

The statistics are as follows:

- Test Statistic: The calculated test statistic is approximately 1.02.

- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.

- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.

To solve the problem completely, let's go through each step in detail:

1. Test Statistic:

The test statistic can be calculated using the formula:

z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

Substituting these values into the formula, we get:

z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

z ≈ 0.02 / √(0.0001386 + 0.0002493)

z ≈ 0.02 / √0.0003879

z ≈ 0.02 / 0.0197

z ≈ 1.02 (rounded to two decimal places)

Therefore, the test statistic is approximately 1.02.

2. P-value:

To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.

The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.

3. Confidence Interval:

To estimate the difference in proportions with a 95% confidence interval, we can use the formula:

(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

z = 1.96 (for a 95% confidence interval)

Substituting these values into the formula, we get:

(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

0.02 ± 1.96 * √(0.0001386 + 0.0002493)

0.02 ± 1.96 * √0.0003879

0.02 ± 1.96 * 0.0197

0.02 ± 0.0386

The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).

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Answer:

35

Step-by-step explanation:

10 - (-20) turns into 10+20 and 8+(-3) is just 8-3

Answer:

Step-by-step explanation:

remove brackets

8-3+10+20=35