Find the slope that passes through each pair of points

(-3,2), (7,2)

We know that the population proportion of instructors who are satisfied with their careers is 0.73, according to the national educational association.

The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is 0.73 in this case. The standard deviation of the sampling distribution is calculated as:
σ = sqrt(p*(1-p)/n) = sqrt(0.73*(1-0.73)/900) = 0.024
Now, we want to find the probability that 650 or fewer instructors were satisfied with their careers. We need to calculate the z-score associated with this value:
z = (650 - 0.73*900) / sqrt(900*0.73*(1-0.73)) = -5.43
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -5.43 or lower is very close to 0. Therefore, the probability that 650 or fewer instructors were satisfied with their careers is essentially 0.
In conclusion, it is highly unlikely that only 650 or fewer instructors out of a sample of 900 would be satisfied with their careers, given the national educational association's estimate of a 73% satisfaction rate among all instructors.

According to the National Educational Association, it is estimated that 73% of all instructors are satisfied with their careers. You want to find the probability that 650 or fewer instructors were satisfied with their careers in a random sample of 900 instructors.
To solve this, we will use the following steps:
1. Calculate the mean and standard deviation of the sample distribution of the proportion of satisfied instructors.
2. Convert the number of instructors (650) to a proportion (p) by dividing by the sample size (900).
3. Use the z-score formula to calculate the z-score for the given proportion.
4. Use the z-score to find the probability.
Step 1: Mean (μ) and standard deviation (σ) of the sample distribution:
μ = P * Q = 0.73 * 0.27 = 0.1971
σ = sqrt(P * Q / n) = sqrt(0.1971 / 900) = 0.0147
Step 2: Convert the number of instructors (650) to a proportion (p):
p = 650 / 900 = 0.7222
Step 3: Calculate the z-score using the formula:
z = (p - μ) / σ = (0.7222 - 0.73) / 0.0147 = -0.5306
Step 4: Use the z-score to find the probability:
The probability of having 650 or fewer satisfied instructors is the area to the left of z = -0.5306. Using a z-table or calculator, we find that this probability is approximately 0.2981.
So, in a random sample of 900 instructors, the probability that 650 or fewer instructors were satisfied with their careers is approximately 0.2981.

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Using the profit function, the maximum profit for the given constraints is $960.

To find the maximum for the profit function P = 3x + 12y subject to the given constraints, we need to solve the linear programming problem.

The constraints are as follows:

1. x + y ≤ 80

2. x - 2y ≥ 15

3. x ≥ 0

4. y ≥ 0

To solve this problem, we can graph the feasible region determined by these constraints and then find the vertex or vertices that maximize the profit function within that region.

1. x + y ≤ 80:

This constraint represents a line with a slope of -1 passing through the point (0, 80). Shade the area below this line.

2. x - 2y ≥ 15:

This constraint represents a line with a slope of 1/2 passing through the point (15, 0). Shade the area above this line.

3. x ≥ 0:

This constraint represents the x-axis. Shade the area to the right of the y-axis.

4. y ≥ 0:

This constraint represents the y-axis. Shade the area above the x-axis.

The shaded feasible region is the intersection of all these shaded areas.

Now, we need to evaluate the profit function P = 3x + 12y at the vertices of the feasible region to find the maximum.

By analyzing the graph, we can see that the vertices of the feasible region are:

A: (0, 0)

B: (15, 0)

C: (15, 65)

D: (0, 80)

We calculate the profit at each vertex:

P(A) = 3(0) + 12(0) = 0

P(B) = 3(15) + 12(0) = 45

P(C) = 3(15) + 12(65) = 855

P(D) = 3(0) + 12(80) = 960

The maximum profit is achieved at point D with P = $960.

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Answer:

hamburger = h = $0.22

Fries = f = $0.96

Cola = c = $0.82

Step-by-step explanation:

Let

last year's price for each item be hamburger = h

Fries = f

Cola = c

h + f + c = 2.00 (1)

The price of a hamburger has increased by 10%

New price of hamburger = 1.10h

The price of fries has increased by 30%

New price of fries = 1.30f

The price of cola has increased by 40%

New price of cola = 1.40c

The same meal now costs $2.58.

1.1h + 1.3f + 1.4c = 2.58 (2)

If the price of a cola is now 9 cents more than that of a hamburger

1.4c = 1.1h + .09

1.4c - 1.1h = .09

Multiply (1) by 1.4

h + f + c = 2.00 × 1.4

1.4h + 1.4f + 1.4c = 2.8 (3)

1.1h + 1.3f + 1.4c = 2.58 (2)

subtract the new equation:

0.3h + 0.1f = 0.22

Multiply by 10

3h + f = 2.2

Recall,

1.4c - 1.1h = .09

1.4h + 1.4f + 1.4c = 2.8 (3)

- 1.1h + 0.0f + 1.4c = .09

Subtract

2.5h + 1.4f = 2.71

multiply by 10

25h + 14f = 27.1

Recall

3h + f = 2.2

Multiply by 14

42h + 14f = 30.8

25h + 14f = 27.1

Subtract to eliminate f

17h = 3.7

Divide both sides by 17

h = 3.7 / 17

= 0.22

h = 0.22

Substitute h into

1.4c - 1.1h = .09

1.4c - 1.1(0.22) = .09

1.4c - 0.242 = .09

1.4c = .09 + 0.242

1.4c = 1.142

Divide both sides by 1.4

c = 1.142 / 1.4

= 0.82

c = 0.82

Substitute values of c and h into

h + f + c = 2.00

0.22 + f + 0.82 = 2.00

1.04 + f = 2.00

f = 2.00 - 1.04

f = 0.96

Therefore, the price of each item last year was

hamburger = h = $0.22

Fries = f = $0.96

Cola = c = $0.82

Answer:

ready-steady paint

Step-by-step explanation:

if he needs 12 tins, and purchased from paint -O  mine, he would spend (12/3) X 7.50 = 4 x 7.50 = £30

from ready steady, he can buy 4 for £11. he needs 12.

so he will spend (12/4) X 11 = 3 X 11 = £33. but he can get 15% off. 15% off is the same as multiplying by 0.85.

33 X 0.85 = £28.05.

so he his better purchasing from ready steady paint

Answer:

Profit = $6

Step-by-step explanation:

The box of apple that the man bought contained 100 apples.

These 100 apples were gotten for $44

Then he sold the 100 apples for $0.5 each.

So sales price = 0.5 * 100 = $50

To know if he made profit or loss.

Sales price - cost price

$50 - $44

= $6

This man made profit of $6 from the sales of the apples from the calculation above.

There are total 720 ways that Canesha and her friend sit in these six seats.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

For the first seat, Canesha and 5 of her friends can all sit in. So there are a possible of 6 different persons.

For the second seat, because one has already sat down, there are a possible of 5 different persons sitting in the second seat.

Continuing on, the total number of different ways Canesha and her friends can sit in those 6 seats are:

= 6*5*4*3*2*1

= 720

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Answer:

x=40

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

180-130=50

180-90-50=40

Technological advances and war maintained continuity by reinforcing traditional gender roles, while also fostering change by opening up new opportunities and expanding women's roles in various sectors such as employment, education, and activism.

Let's explore these aspects in more detail:

Continuity,

Domestic Technologies, Advancements in household technologies such as washing machines, vacuum cleaners, and kitchen appliances reduced the amount of time and effort required for household chores. This allowed women to be more efficient in managing domestic responsibilities, although the burden of unpaid domestic labor still primarily fell on them.

Gender Roles, Traditional gender roles and societal expectations placed women primarily in the role of caregivers and homemakers. Despite technological advancements, these gender norms persisted, and women faced barriers to entering male-dominated fields or pursuing higher education.

Change,

Employment Opportunities, Technological advancements and wars created new employment opportunities for women. During World War I and World War II, women entered the workforce in large numbers to replace male workers who had gone to war. They worked in factories, industries, and offices, breaking barriers in traditionally male-dominated sectors.

Changing Perceptions, The experiences of women working outside the home during wartime challenged traditional notions of gender roles. Women proved their capabilities and contributions in various roles, leading to a shift in societal perceptions of women's capabilities and their roles in society.

Technological Advancements in Communication, The advent of telephone systems, radio, and later television created new opportunities for women to express their voices, share their ideas, and participate in public discourse. This allowed women to advocate for social and political change, advancing the feminist movement and women's rights.

Reproductive Technologies, The development of contraception methods and advances in reproductive health technologies, such as the birth control pill, gave women greater control over their reproductive choices. This had a profound impact on women's ability to pursue education, careers, and engage in society on their terms.

Technological Advances in Medicine, Medical advancements, including improved healthcare and access to prenatal care, helped reduce maternal and infant mortality rates. This contributed to better health outcomes for women and increased their life expectancy, allowing them to participate more fully in societal advancements.

In summary, technology advances and war both maintained continuity and fostered change in the lives of women in the United States during the twentieth century. While traditional gender roles and expectations persisted to some extent, new employment opportunities, changing perceptions, and technological advancements provided women with greater opportunities for education, work, and personal autonomy. These changes played a vital role in advancing the rights and status of women in society.

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a) A department manager receiving an allocation of costs will care about management's methodology of overhead allocation because the overhead costs allocated to their department will have a direct impact on the department's profitability and cost efficiency.

b) The allocation base is the measure used to determine how much of the overhead costs should be allocated to a particular department or product, while the allocation rate is the amount of overhead costs allocated to each unit of the allocation base

c) Budgets are an important tool for cost planning, but their effectiveness depends on how well they are developed and implemented.

a) If the allocation method used by management is not accurate or fair, it could result in the department being burdened with more costs than they actually incur, which could affect their ability to meet their targets and objectives. It is, therefore, important for department managers to ensure that the allocation of costs is done fairly and accurately.

b) The allocation base and rate are important because they determine how the overhead costs are allocated to different departments or products.

Different allocation bases and rates can result in significantly different amounts of overhead costs being allocated to different departments or products, which can impact their profitability. While all of the overhead costs eventually make their way to the income statement, the allocation of these costs can have a significant impact on the accuracy of the income statement and the ability of the organization to make informed decisions.

c) Budgets can be helpful in providing a roadmap for achieving the organization's goals and objectives, but they need to be flexible enough to adapt to changing circumstances and priorities.

The budget(s) that are most important to the organization's success will depend on the nature of the organization and its objectives. However, typically the operating budget, capital budget, and cash budget are the most important budgets for most organizations.

The government's budget process is similar to the operating budgeting process described in the chapter in that it involves the development of a budget to allocate resources and achieve goals. However, the government's budget process is more complex and involves additional considerations such as political priorities and public opinion. Additionally, the government's budget process involves a more detailed review and approval process than the operating budgeting process.

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The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.

THE MATCHING LAW

Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.

After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.

Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.

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Answer: -2

Step-by-step

y = k*x

3 = k*-1

So k = -3

6 = -3 * x

6/-3 = -2

x = -2

solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.

Let x = the width of the rectangle

Then, the length = 3x + 4

Perimeter = 2(3x + 4) + 2x = 48

2(3x + 4) + 2x = 48

6x + 8 = 48

6x = 40

x = 40/6

x = 6.67 feet

The width of the rectangle = 6.67 feet

The length of the rectangle = 3(6.67) + 4 = 22.67 feet

To solve for the length and width of the rectangle, an equation was set up using the perimeter of 48 feet. The length was represented by 3x + 4, where x is the width. After solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.

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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:

(-2, 3)

Step-by-step explanation:

not sure

Answer:

x > 6

{7, 8, 9, 10...}

Step-by-step explanation:

\(3<3x-15\\\\3x-15>3\\\\3x-15+15>3+15\\\\3x>18\\\\\frac{3x>18}{3}\\\\\boxed{x>6}\)

Any number will be a solution if it's value is greater than 6.

Hope this helps.

Finding the area of the circle of spilled juice as a function of time is: j(t) = πr(t)²

An equation is mathematical statement that asserts  equality of two expressions. It contains one or more variables, and typically consists of terms on either side of equals sign.

Part A:

Let the radius of the circular pattern be r at time t. Then, we have:

j = πr²

Taking the derivative of both sides with respect to time, we get:

dj/dt = 2πr(dr/dt)

Since the rate of change of the radius is unknown, we can express it in terms of the rate of change of j:

dr/dt = (1/2πr)(dj/dt)

Substituting this expression for dr/dt back into our original equation, we get:

j = πr²

dj/dt = π(2r)(dr/dt)

dj/dt = 2πr(dr/dt)

dj/dt = 2πr(1/2πr)(dj/dt)

dj/dt = dj/dt

Therefore, the area of the spilled juice as a function of time is:

j(t) = πr(t)²

Part B:

If we assume that the rate of change of the radius is constant over the first 2 minutes, we can use the formula for the area of a circle to find the area of the spilled juice after 2 minutes:

j(2) = πr(2)²

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Answer:1.21x

Step-by-step explanation:

Let the initial population was x

(1.1x)*1.1=1.21x

Answer:

8 seconds if tyres took 1 second each tyre as 2.5/2.5 =1

The question did specify 2 1/2 secs to fll them all up which is 1 second each x 8 = 8 sec total.

Step-by-step explanation:

2  1/2 litres = number of tyres

2 1/2 seconds taken

= if each tyre took 2 1/2 seconds the quetsion should say clear but would be

2 1/2 tyres x 2 1/2 seconds = 6.26 seconds every 2 1/2 tyres

so 8 tyres x 2 1/2 seconds = 20 seconds every 8 tyres

If the 2 1/2 seconds applied to all 2 1/2

then we need to find a multiplier for 1 tyre

Here we divide

2 1/2 / 2  1/2 = 1

8 x 1 = 8 seconds.

The height of the triangular prism is 22 meters, having a total surface area of 1192 square meters.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let h represent the height of the triangular prism.

The base are right triangles with side lengths 12 meters, 15 meters, and 19 meters. Hence:

Total surface area = 2 * Area of base + sum of remaining area of surface

Total surface area = 2(1/2 * 15 * 12) + 12*h + 15*h + 19*h

The total surface area of the triangle prism is 1192 square meters. therefore:

1192 = 180 + 46h

46h = 1012

h = 22

The height is 22 meters

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The percentage occupied by fresh water on Earth is 47%. The pH of the solution with H+ concentration 0.08606951774271 M is 1.1.

To calculate the percentage of fresh water on Earth, we can subtract the percentage of water in the oceans (53%) from 100%. This gives us 47%, which represents the percentage occupied by fresh water.

The pH of a solution is a measure of its acidity or alkalinity. It is determined by the concentration of hydrogen ions (H+) in the solution. In this case, the H+ concentration is given as 0.08606951774271 M. The pH scale ranges from 0 to 14, with values below 7 indicating acidity and values above 7 indicating alkalinity. By calculating the negative logarithm (base 10) of the H+ concentration, we find that the pH of the solution is approximately 1.1.

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Answer:

Step-by-step explanation:

From the question, we are informed that Michael and Tyler both ran a half marathon and that Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 97 minutes and 49 seconds.

First, we should know that 60 minutes makes 1 hour, therefore we need to change Tyler's time taken to finish the marathon appropriately. Since Tyler finished in 97 minutes and 49 seconds, this will be converted to 97 minutes equals 1 hour 37 minutes. Therefore, Tyler used 1 hour, 37 minutes and 49 seconds.

Since Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 1 hour, 37 minutes and 49 seconds. We can see that Tyler is faster than Michael.

To know how much faster Tyler was, we subtract Tyler's time from Michael's. This will be:

= (1 hour, 42 minutes 13 seconds) - (1 hour, 37 minutes, 49 seconds)

= 4 minutes, 24 seconds.

Tyler was faster by 4 minutes, 24 seconds.

In hypothesis testing, the null hypothesis (H0) and the alternative hypothesis (Ha) are used to assess the validity of a claim or statement about a population parameter.

Here are the answers to the given questions:

12. The null and alternative hypotheses divide all possibilities into:

b. Two non-overlapping sets

The null hypothesis and the alternative hypothesis are mutually exclusive and collectively exhaustive.

They represent two distinct possibilities or explanations regarding the population parameter being tested.

These sets do not overlap, meaning that an observation or outcome can only fall into one of these two categories.

13. Which of the following is true of the null and alternative hypotheses?

d. It is possible for neither hypothesis to be true

In hypothesis testing, the null hypothesis represents the default position or the status quo. It assumes that there is no significant difference or effect present in the population.

The alternative hypothesis, on the other hand, contradicts the null hypothesis and suggests that there is a significant difference or effect.

It is important to note that the null hypothesis is either rejected or failed to be rejected based on the evidence provided by the data.

The alternative hypothesis is not proven or accepted; instead, it is typically accepted by default when the null hypothesis is rejected.

Therefore, it is possible for neither hypothesis to be true if there is insufficient evidence to support the rejection of the null hypothesis. In such cases, no strong conclusion can be made based on the available evidence.

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Answer:

terminal side of theta means a line passes through the origin and a point. in this situation, (7,2). this then forms a triangle:

Step-by-step explanation:

then us the values to find sin, sec, and tan

(im assuming you know how to do this)

The correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that:-

We have the data from the question that the temperature of Bangkok is hotter than cape town.

Bangkok > Cape town

And the temperature of Cape town is hotter than Moscow.

Cape town > Moscow

Now for both the statements, the inequality will be given as:-

Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

Therefore the correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

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Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15