college gpa and salary. do students with higher college grade point averages (gpas) earn more than those graduates with lower gpas (civicscience)? consider the college gpa and salary data (10 years after graduation) provided in the file gpasalary. a. develop a scatter diagram for these data with college gpa as the independent variable. what does the scatter diagram indicate about the relationship between the two variables? b. use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college gpa. c. at the .05 level of significance, does there appear to be a significant statistical relationship between the two variables?

Step-by-step explanation:

inversely means

y = k/x

therefore

30 = k/4

120 = k

y = 120/10 = 12

FYI :

directly would mean

y = kx

The value of y will be 12 when x is equal to 10.

The relationship between two variables known as "inverse variation" occurs when the value of one variable increases while the value of the other variable decreases.

Given that, y varies inversely with x.

Here, y∝1/x

y=k/x

xy=k

When x is 4, y is equal to 30, we get

k=4×30

k=120

When x=10, we get

10y=120

y=12

Therefore, the value of y will be 12 when x is equal to 10.

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The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

The binomial distribution table is a table of values that shows the probability of getting a certain number of successes (x) in a certain number of trials (n). In this case, the probability is 0.75, so we need to look for the column that has a value of 0.75. We can see that this column corresponds to x = 5, so that is the column we should use.

The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

the complete question is :

on the table for the binomial distribution, if you have a probability of 0.75, which vertical column for x do you use?

Table :

n x P(x)

5 0 0.23730

5 1 0.39615

5 2 0.26335

5 3 0.08789

5 4 0.01801

5 5 0.00152

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The given value 4.1 x 10^-4 can be written in standard form as 0.00041

The standard form can be done by following the format of multiplying a *10^b where b is the power and a is the digit.

A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.

Hence 4.1 x 10^-4 = 0.00041

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At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.

(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:

f'(t) = 400 + 200cos(πt/12).

At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.

(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:

g'(t) = 200 - 200cos(πt/12).

At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.

the complete question is :

both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?

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The expression that is equivalent to x² +7x+12 ÷ x²+8x+15 is (x + 4) ÷ (x + 5)

From the question, we have the following parameters that can be used in our computation:

x² +7x+12

÷

x+8x+15

Express properly

So, we have

x² +7x+12 ÷ x²+8x+15

Factorize each expression

This gives

(x + 4)(x + 3) ÷ (x + 5)(x + 3)

Cancel out the common factor

(x + 4) ÷ (x + 5)

Hence, the expression is (x + 4) ÷ (x + 5)

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Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

The percentage of people who took less than 30 seconds to complete

the task 84.4%.

The diagram shows us how many people finished the task in what time.

40 people finished in 5-10 seconds.

40 people finished in 10-15 seconds.

30 people finished in 15-20 seconds.

30 people finished in 20-25 seconds.

25 people finished in 25-30 seconds.

25 people finished in 30-35 seconds.

25 people finished in 35-40 seconds.

25 people finished in 40-45 seconds.

15 people finished in 45-50 seconds.

That is what the diagram is telling us, and what "frequency" means in this case.

Therefore,

In total, 255 people participated.

only the last 2 groups took longer than 40 seconds.

Therefore,

The estimate of how many took less than 40 seconds is

255 - 25 - 15 = 215 people.

215 people are how many % of 255 :

100% = 255

1%  = 100%/100

     = 255/100

     = 2.55

215 is a many % as how often 1% fits into these 215 :

215 / 2.55 = 84.31372549%

                 ≈ 84.4%

Complete Question:

Times taken to complete a task. Here is a histogram showing the times taken to complete a task.

40- Estimate the percentage of 35 people who took less than 40 seconds to complete the task.

Give your answer to 1 decimal place.

Frequency Density : 1 5 0 5

Time (Density) :

10 15 20 25 30 35 40 45 50

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The area of a rectangle is 35x^2 + 12x  - 36

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

To determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given that the length of the rectangle is (7x − 6) and the width is (5x + 6).

Thus the width be (5x + 6).

So, the length = (7x − 6)

So,

Area of rectangle = (7x − 6) (5x + 6).

= 35x^2 + 42x -30x - 36

= 35x^2 + 12x  - 36

So, The area is 35x^2 + 12x  - 36

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Answer:

1

Step-by-step explanation:

6 is tenths and after is 1 which is hundredths

Answer: If a ball is chosen at random 80 times, with replacement, and there are an equal number of blue, green, pink, and red balls, then the probability of choosing a green ball each time is 1/4. Over many trials, the number of times a green ball is chosen would be roughly proportional to the probability of choosing a green ball, so we would expect the green ball to be chosen about 80 * (1/4) = 20 times.

However, since this is a random process, it is unlikely that the green ball will be chosen exactly 20 times. It is more likely that the actual number of green balls chosen will be slightly different, possibly higher or lower, than 20. So the answer is C: The color green would be chosen roughly 20 times, but probably not exactly 20 times.

Step-by-step explanation:

The sum of the geometric sequence for this problem is given as follows:

S = 665.

The sum of the first n terms of a geometric sequence of first term [tex]a_1[/tex] and common ratio q is given by the equation presented as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

The parameters for this problem are given as follows:

[tex]a_1 = 32, n = 6, r = 1.5[/tex]

Hence the sum is obtained as follows:

S = 32 x (1 - 1.5^6)/(1 - 1.5)

S = 665.

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Answer: $14.20

Step-by-step explanation:

the 42.60 has to be given to three people equally, (two makers and yourself).

42.60/3 = $14.20/person

Answer: $14.20

Step-by-step explanation:

Since you share with 2 other people, there are 3 people (including yourself) that are entitled to the tip.

∴ $42.60/3= $14.20 each.

You get $14.20

Hope this helps :)

If the length of the rectangular plot  is 180m , then the width of the rectangular plot is 51.2 m .

The Area of square plot is ⇒ Area = (Side) × (Side),

In this case, Side is = 96m,

So , the area of the square plot is : A = 96m x 96m = 9216 m² .

The Area of  Rectangular Plot is ⇒ A = (Length) × (Width) ;

We know that the area of the rectangular plot is the same as that of the square plot,

that means ⇒ Length × Width = 9216 m² ;

We also know that Length = 180m, so we substitute this value in the equation above ;

⇒ 180m × Width = 9216 m² ;

Dividing  both sides by 180m ;

we get ;

⇒ Width = 9216/180 ;

⇒ Width = 51.2 m ;

Therefore, the width of the rectangular plot is 51.2 meters.

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The given question is incomplete , the complete question is

In exchange of a square plot of side 96 m, a man wants to acquire a rectangular plot of 180m long and of the same area of the square plot .

Find the width of the rectangular plot .

The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

We need to make some assumptions in order to calculate the probability that the time intervals between manufacturing production line breakdowns will be shorter than two days. Assume that the intervals between breakdowns have an exponential distribution with a mean of 3.5 days (1/2 times per week).

The probability that an interarrival time is fewer than two days can be calculated using the exponential distribution formula as follows:

P(X < 2) = 1 - e(-2/3.5)

where "X" stands for the duration in between breakdowns.

When we condense the expression, we get:

P(X < 2) = 0.553

Therefore, The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

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Angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let the triangle be ABC.

The angle A is 27 degrees.

The angle B is 75 degrees,

We need to find the angle of C

From Angle sum property the sum of three angles is 180 degrees.

∠A+∠B+∠C=180

27+75+∠C=180

102+∠C=180

∠C=78 degrees.

Hence, angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

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Complete Question below:

In Triangle ABC, angle A is 27 degrees, angle B is 75 degrees then the angle C?.

The solution is, Right answer: C) -7 is a solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

We have the equation 2x² +5x -63 = 0

First, let's find the coefficients a, b and c as ax² +bx +c = 0:

• a = 2

• b = 5,

• c = -63

Now, we will use the formula below to solve this equation:

x = -b ±√b²-4ac/2a

Let's replace the coefficients with the values that we already found:

putting the values we get,

x = -5±23/4

Now, let's divide it into two solutions, look:

x1 = 9/2

x2 = -7

Right answer: C) -7 is a solution.

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The two point baskets are 16 and the three point basket is 1.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a basketball player scored 50 points.

Let the two point baskets be x and the three point baskets be y.

The total number of baskets made was 17.

Here, x+y=17 -------(i)

During last nights game all two point and three point baskets.

Now, 2x+3y=50 -------(ii)

Substitute x=17-y in the equation (ii), we get

2(17-y)+3y=50

34-2y+3y=50

y=16

Substitute y=16 in equation (i), we get

x=1

Therefore, the two point baskets are 16 and the three point basket is 1.

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Answer:

(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b

Step-by-step explanation:

Add like terms

6a^2 + 12b

Answer:

Step-by-step explanation:

Let's say that after the break, the group of friends watches m minutes of the movie.

We know that they watched 42 minutes before the break, so the total time they have watched before and after the break is 42 + m minutes.

Since the movie is 115 minutes long, the inequality that represents the number of minutes they will watch after the break is:

42 + m < 115

So, the inequality that represents the number of minutes, m, they will watch after the break is:

m < 115 - 42 = 73

This means that m has to be less than 73 for the group of friends to finish watching the movie.

Yes, it is possible for a system of linear equations with fewer equations than variables to have no solution. For example, consider the system of linear equations: x + y = 1, x + 2y = 3, x + 3y = 4.

The system of linear equations given is:

x + y = 1

x + 2y = 3

x + 3y = 4

This system has two variables (x and y) but only three equations. We can add and subtract the equations to see that the first two equations imply that y = 2, but the third equation implies that y = 1. This is a contradiction, so there is no solution to the system.

To solve this system, we can use techniques such as elimination or substitution. For example, we can subtract the first equation from the second equation to eliminate x, and get:

[tex]x + 2y - (x + y) = 3 - 1[/tex]

[tex]y = 2[/tex]

Similarly, we can subtract the first equation from the third equation to eliminate x, and get:

[tex]x + 3y - (x + y) = 4 - 1[/tex]

[tex]2y = 3[/tex]

[tex]y = 3/2[/tex]

However, we obtained two different values for y, which is a contradiction. As a result, the equation system cannot be solved. In other words, there is no pair of values of x and y that satisfy all three equations simultaneously.

Geometrically, this means that the system of equations represents three planes in three-dimensional space. However, these planes do not intersect at a common point, so there is no solution to the system.

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According to the above, we can infer that the value of FE is: 10 cm

To find the value of FE we must analyze the image of this triangle. Additionally, we must take into account the information we know, that is, the length of two sides (5 cm) and the height (4 cm), the area (20cm²).

So we must use the formula for the area of a triangle and isolate the values that we do know to find the value of the base.

According to the above, the value of segment FE is 10 cm.

Note: This question is incomplete. Here is the complete information:

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The linear function giving the amount remaining after buying x cups of coffee is given as follows:

A(x) = -3x + 15.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Each cup of coffee costs $3, hence the slope m is given as follows:

m = -3.

(for each cup purchased, the balance decays by $3).

Hence:

A(x) = -3x + b.

Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:

3 = -3(4) + b

b = 15.

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The area of the triangle PQR is 12 square units

From the question, we have the following parameters that can be used in our computation:

J(–2, 2), K(–2, 6), and L(–8, 2),

Reflection and rotation are rigid transformation

This means that

Area of PQR = Area of JKL

So, we have

Area = 1/2 * |x1y2 - x2y1 + x2y3 - x3y2 + x3y1 - x1y3|

So, we have

Area = 1/2 * |-2 * 6 + 2 * 2 + -2 * 2 + 8 * 6 - 8 * 2 + 2 * 2|

Evaluate

Area = 1/2 * |24|

So, we have

Area = 12

Hence, the area is 12 square units

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Answer:

37.437

Step-by-step explanation:

Answer:

37.437

Hope it helps

Answer:

2 × 3 × 3 × 5 = 2 × 3 × 3 × 5

Step-by-step explanation:

The prime factorization of 90 is 2 × 3 × 3 × 5, so the prime factors are 2, 3, 3, and 5. Ordering the factors from least to greatest, we have:

2 × 3 × 3 × 5 = 2 × 3 × 3 × 5.

Answer: 19x+24

Step-by-step explanation: 12x−8+7x+3212−8+7+32 x12+24+7

Answer: 19x +24

Step-by-step explanation:

The population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.

To calculate the population of McKinney after 2 years with an average growth rate of 8.4%, we can use the formula for compound interest:

[tex]P = P_0 * (1 + r/100)^t[/tex]

Where P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 = 180,000, r = 8.4, and t = 2. Plugging these values into the formula, we get:

[tex]P = 180,000 * (1 + 8.4/100)^2[/tex]

[tex]P = 180,000 * 1.084^2[/tex]

[tex]P = 180,000 * 1.174996[/tex]

[tex]P = 210,099.76[/tex]

So, the population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.

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The complete question is :

The population of McKinney is about 180,000. The population is increasing at an average rate of 8.4% . It's population after 2 years will be.

Answer:

Step-by-step explanation:

go up to the 85 on the grade track that over until you meet the dot.

that dot says it would be 3 hours

B .The value of f(x) is increasing for each unit decrease in x  about the graph is correct.

What is the graph of exponential function?

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines

Exponential function f(x) is given

According to given graph, The value of f(x) is increasing for each unit decrease in x

Therefore, The statement, The value of f(x) is increasing for each unit decrease in x about the graph is correct.

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