Question 11

8 pts

11) Five students in a graduate program were rändomly selected. Their grade point average (GPAs)

when they entered the program were between 3.5 and 4.0. The following data were obtained

regarding their GPAs on entering the program versus their current GPAs. Find the equation of the

regression line.

Round the final answer to 3 decimals.

Entering GPA/ Current GPA

37

3.1

38

3.7

34

4.0

33

38

false :) thats ur answer

The set of integers that represents a debit of $10 and a credit of $6 would be  option 1. {-10, 6}.

An integer is a mathematical object that represents a whole number, either positive, negative or zero, without any decimal or fractional part. Integers include the natural numbers (1, 2, 3, ...), their negative counterparts (-1, -2, -3, ...) and the number zero (0).

In this case, a debit of $10 means that $10 has been spent or taken out of the account, which is represented by the negative integer -10. A credit of $6 means that $6 has been added to the account, which is represented by the positive integer 6.

Therefore, the set {-10, 6} represents a debit of $10 and a credit of $6.

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The complete question is:

Which set of integers represents a debit of $10 on a number line, and the credit of $6?

The equation x² + 2x = 2x + x² demonstrates the commutative property of addition.

The commutative property of addition states that the order of the terms does not affect the result when adding.

In this case, the terms x² and 2x on the left side of the equation are switched to 2x and x² on the right side of the equation, and the equation still holds true.

This shows that the terms can be rearranged without changing the sum.

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Answer:

(1.5,2.5) I think

Step-by-step explanation:

I put it into demos

An interval containing one period of y = 3tan x - π/6 is ( - π/2, π/2 ) and the two consecutive asymptotes occur at x = - π/2 and x = π/2. The complete explanation is given below:A period is the length it takes for a graph to repeat itself. One cycle of the graph is known as a period.

The formula y = a tan bx, where a and b are constants, is used to generate the tangent function. The graph of the tangent function has numerous characteristics that are critical for understanding the function. The period of the tangent function is π/b, which is determined by the variable b in the formula y = a tan bx. The function becomes periodic with this length. The graph of the tangent function is asymmetrical. The two types of asymptotes are horizontal and vertical asymptotes. To find the vertical asymptotes of a graph, equate the denominator to zero and solve for x. The points on the graph where the function approaches infinity are known as vertical asymptotes. For x = kπ/2, where k is an odd integer, the tangent function has a vertical asymptote. As a result, we have to equate tan x to ±∞, which occurs at x = kπ/2, where k is an odd integer.

The graph of y = 3 tan x - π/6 passes through the origin, that is, (0,0). The tangent function's period is π/b. So, in the formula y = 3tan x - π/6, the period will be π/b, which is equal to π/1, and the period of the function is π.The range of tan x is (-∞, ∞). Thus, the range of y = 3 tan x - π/6 will be (-∞, ∞).The domain of the function is all real numbers except for values that make the denominator zero. The denominator is 0 at x = kπ/2, where k is an odd integer, which generates the vertical asymptotes of the function. Hence, the domain of the function is the set of all real numbers except {kπ/2, where k is an odd integer}.To find the interval containing one period of the function, we will start with the interval ( - π/2, π/2 ) since the period of the function is π. Thus, one period of the function will be ( - π/2, π/2 ).The function has two types of asymptotes: vertical and horizontal. The vertical asymptotes of the function occur at x = kπ/2, where k is an odd integer. Since the period of the function is π, we will have the consecutive asymptotes at x = - π/2 and x = π/2. Therefore, two consecutive asymptotes occur at x = - π/2 and x = π/2.

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Answer:

8) 25.12

9) 15.07

10) 48.98

11) 1962.5

12) 20

13) r = 8.5

14) diameter: 72 radius: 36

Answer:

They Have The Same Y-Intercept.

Function 2's y-intercept is -5.

Function 1 y-intercept could be found by inputting 0 as r.

p=0-5

p=-5

Meaning, they're equal.

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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The correct statement is that if both individuals apply a discount rate of 7%, the present value of Caroline's award is higher than the present value of Jiexin's award.

To compare the present value of the awards that Caroline and Jiexin will receive, we need to discount the future amounts using a discount rate of 7%. The present value of an amount A to be received in n years, discounted at an annual rate r, is given by:

Present value = \(A / (1 + r)^n\)

For Caroline, A = $20,000 and n = 6, so the present value is:

Present value of Caroline's award = $20,000 / \((1 + 0.07)^6\) = $14,008.32

For Jiexin, A = $20,000 and n = 9, so the present value is:

Present value of Jiexin's award = $20,000 /\((1 + 0.07)^9\) = $12,043.60

Therefore, the correct statement is that if both individuals apply a discount rate of 7%, the present value of Caroline's award is higher than the present value of Jiexin's award. Caroline's award is worth $14,008.32 in today's dollars, while Jiexin's award is worth $12,043.60 in today's dollars.

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Complete question :

Caroline is going to receive a sword of $20.000 six years from now. Jiexin is going to receive en sward of $20,000 nine years from now. Which one of the following statements is correct if both individuels apply discount rete of 7 percent? Multiple Choice

The value of  f(-3) for the given function f(x) = 4x + 7 will be -5.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

f(x) = 4x + 7

At x = -3

f(-3) = 4(-3) + 7

f(-3) = -12 + 7 = -5

Hence "The value of  f(-3) for the given function f(x) = 4x + 7 will be -5".

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Answer: A

Step-by-step explanation:

A best represents the graph

The probability to get the numbers greater than 2 from the outcomes of  the event of rolling a single fair die is equal to P(A) = 2/3.

As given in the question,

Event is rolling a single fair die.

Number of fair die to be rolled = 1

Possible outcomes =  { 1, 2, 3, 4, 5, 6 }

Total number of possible outcomes = 6

Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }

Number of favourable outcomes = 4

Probability of getting a number greater than 2

= (Number of favourable outcomes) / (Total number of outcomes)

= 4 / 6

= 2 / 3

Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.

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A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician the odor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells.

The relative growth rate is k = 3 ln 2 hr -1

To find out the relative growth rate:

Let the exponential model is

A = \(Pe^{kt}\)

We have been given that

(a)Cell divides into two cells every 20 minutes

\(t = \frac{20}{60} = \frac{1}{3}hr\)

A = 2P

Thus, we have

2P= Pe\(\frac{k}{3}\)

In 2 = In(e\(\frac{k}{3}\))

In 2 = \(\frac{k}{3}\)

k = 3 ln 2 hr -1

Hence, the answer is k = 3 ln 2 hr -1 for the relative growth rate

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Answer: x = 56

It’s a supplementary angle

Step-by-step explanation:

It’s a supplementary angle if their measures add to 180 degrees

is the equation

2x + 68 = 180 degrees

2x = 180 -68

2x = 112

x = 112/2

x = 56

The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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Answer:

x=8.1 /hour during the week

y=10.4 /hour in  the weekend

Step-by-step explanation:

x=earnings during the week

y= earnings in the wekend

13x+14y=250.90  |*-4

15x+8y=204.70    |*7

-52x-56y=-1003.6

105x+56y=1432.9

---------------------------

53x=429.3

x=8.1 /hour during the week

15*8.1+8y=204.7

121.5+8y=204.7

-121.5        -121.5

8y=83.2

:8    :8

y=10.4 /hour in  the weekend

Answer:

B. The graph of the function starts high and ends low.

Step-by-step explanation:

Answer:

Step-by-step explanation:

p=15-4

p= 11

Answer:

less than 1yd²:

2/3x3/5= 2/5

1/4x5/3= 5/12

1/2x9/10= 9/20

equal to 1yd²

1/4x4/1= 1

4/3x6/8= 1

more than 1yd²

2/3x5/3= 1.1

Step-by-step explanation:

2/3x3/5= 2/5

1/4x4/1= 1

2/3x5/3= 1.1

1/4x5/3= 5/12

1/2x9/10= 9/20

4/3x6/8= 1

Answer:

2..........3

--- x ---

3............5

Step-by-step explanation:

goes to area less than 1square yard

The measure of the angle ∠A will be 12°. Then the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angle formed by two secants (lines cutting a circle at two places) intersecting outside the ring is half the distance between their arc minus the closest arc.

From the diagram, the equation is given as,

∠A = (arc DE - arc BC) / 2

∠A = (94° - 70°) / 2

∠A = 24° / 2

∠A = 12°

The measure of the angle ∠A will be 12°. Then the correct option is B.

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The sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

What is quadrilateral ?

A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" comes from the Latin words "quadri" meaning "four" and "latus" meaning "side". Quadrilaterals can have different shapes and properties, including rectangles, squares, parallelograms, trapezoids, and kites.

Since quadrilaterals HIJK and ABCD are congruent, we can map one onto the other using a sequence of transformations. We need to determine which of the given sequences of transformations maps HIJK to ABCD.

Sequence A involves a 270° rotation about point J, followed by a translation 9 units to the right and 8 units down.

Sequence B involves a reflection over the line HÌ, followed by a translation 6 units to the right and 3 units down.

To determine which sequence maps HIJK to ABCD, we can apply each sequence to the vertices of HIJK and see if the resulting image matches the vertices of ABCD.

Starting with sequence A, we apply the rotation and translation to the vertices of HIJK:

Vertex H(-2, 1) is rotated 270° about J(-2, 2) to get H'(0, 0). Then we translate 9 units to the right and 8 units down to get H''(9, -8).

Vertex I(-3, -1) is rotated 270° about J(-2, 2) to get I'(1, -3). Then we translate 9 units to the right and 8 units down to get I''(10, -11).

Vertex J(-2, 2) is fixed by the rotation and then translated 9 units to the right and 8 units down to get J''(7, -6).

Vertex K(0, 0) is rotated 270° about J(-2, 2) to get K'(-2, -2). Then we translate 9 units to the right and 8 units down to get K''(7, -10).

The resulting image of HIJK under sequence A has vertices H''(9, -8), I''(10, -11), J''(7, -6), and K''(7, -10). We can see that these vertices do not match the vertices of ABCD, so sequence A does not map HIJK to ABCD.

Next, we apply sequence B to the vertices of HIJK:

Vertex H(-2, 1) is reflected over line HÌ to get H'(-4, 3). Then we translate 6 units to the right and 3 units down to get H''(2, 0).

Vertex I(-3, -1) is reflected over line HÌ to get I'(-1, 1). Then we translate 6 units to the right and 3 units down to get I''(5, -2).

Vertex J(-2, 2) is reflected over line HÌ to get J'(-4, 4). Then we translate 6 units to the right and 3 units down to get J''(2, 1).

Vertex K(0, 0) is reflected over line HÌ to get K'(-2, 2). Then we translate 6 units to the right and 3 units down to get K''(4, -1).

The resulting image of HIJK under sequence B has vertices H''(2, 0), I''(5, -2), J''(2, 1), and K''(4, -1). We can see that these vertices match the vertices of ABCD, so sequence B maps HIJK to ABCD.

Therefore, the sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

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Answer:

504.

Step-by-step explanation:

multiplication is just repeated addition. so it would be 84+84+84+84+84+84. multiply all 6 80's first to get 480. then multiply all 6 4's to get 24. 480+24=504

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

For every 1 cup of banana you have to add 6 cups of apples. So it means there's six times as much apples as there is bananas. If there's 3 cups of apples, which is half of 6, it means the banana would now also have to be halved from 1 to half a cup.

Whatever you do to the bananas or the apples, you have to maintain the same ratio. Which is that apples is 6 times as much as bananas.

So 1 cup of apple would need to be divided by 6, to get banana. That would be approximately 1÷6= 0.167 cups

Answer:

SAS

Step-by-step explanation:

Sas states that if two sides and the angle of one triangle are congruent to two sides and the include angle of another triangle, then these two triangle are congruent.

Answer:

\(\displaystyle \frac{1}{3}\)

Step-by-step explanation:

Hi there!

\(\displaystyle \frac{x}{y}\)

We're given that x=4 and y=12. Plug these in:

\(=\displaystyle \frac{4}{12}\\\\=\displaystyle \frac{1}{3}\)

I hope this helps!

Answer:

R

Step-by-step explanation:

Answer:

D. 13

Step-by-step explanation:

54 ÷ 3 = 18 (your age in 5 years)

18 - 5 = 13 (your age now)

The number of markers that Stella has would be = 27 markers

The number of markers owned by Jerry = U

The number markers owned by Stella = t +16

If U = 43

t = X

That is, 43= t + 16

Make t the subject of formula;

t = 43-16

t = 27

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Complete question;

Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella. The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has. U = t + 16 If Jerry has 43 markers, how many markers does Stella have? Show your work