the following data was collected to explore how the average number of hours a student studies per night and the student's gpa affect their act score. the dependent variable is the act score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's gpa. effects on act scores study hours gpa act score 6 2 30 4 4 25 3 4 25 2 2 19 1 4 27 step 1 of 2: find the p-value for the regression equation that fits the given data. round your answer to four decimal places.

The equivalent expression to the given expressions after using distributive property is [tex]6(13+7)[/tex]

As per the question statement, we are supposed to find the expression equivalent to the given expression [tex]6*13 + 6*7[/tex] after using the distributive property. Before solving this problem, we should know about the distributive property, which states that [tex]a(b+c) = a*b + a*c[/tex].

Therefore, [tex]6*13 + 6*7[/tex]

[tex]=6(13+7)[/tex], as per the definition of the distributive property.

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Answer:

a. 3 units

Step-by-step explanation:

The length of BC can be found in 3 main steps, namely the formation of equations, solving for x and substitution.

Let's rewrite the given lengths:

AB= 4x +1 -----(1)

BC= 2x -7 -----(2)

AC= 24 -----(3)

Form an equation which relates the 3 lengths:

Given that B is between A and C,

AC= AB +BC -----(4)

Substituting equations (1) to (3) to equation (4):

24= 4x +1 +2x -7

Simplify:

24= 6x -6

Add 6 to both sides:

6x= 24 +6

6x= 30

Divide both sides by 6:

x= 5

Substitute x= 5 into (2):

BC

= 2x -7

= 2(5) -7

= 10 -7

= 3 units

Thus, option a is correct.

Additional:

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Answer:

1:

Step-by-step explanation:

5 divided by 5 is 1, and 35 divided by 5 is

Step-by-step explanation:

this just means

q = k×p

and we need to find k.

the sum of both q values when p = 6 and p = 11 is then

k×6 + k×11 = 51

17k = 51

k = 51/17 = 3

so, our equation is

q = 3p

and when q = 72

72 = 3p

p = 72/3 = 24

The second vector that's perpendicular to the line we want (call it L) is missing; I'll denote it by ⟨a, b, c⟩.

The cross product of ⟨1, 1, 0⟩ and ⟨a, b, c⟩ is perpendicular to both of these vectors. The direction vector of L will be parallel to this cross product.

Compute the cross product.

⟨1, 1, 0⟩ × ⟨a, b, c⟩ = ⟨1•c - 0•b, 0•a - 1•c, 1•b - 1•a⟩ = ⟨c, -c, b - a⟩

Then the vector equation of L is

L(t) = ⟨c, -c, b - a⟩ t + ⟨-3, 3, -1⟩

As parametric equations, we write

x(t) = ct - 3

y(t) = -ct + 3

z(t) = (b - a) t - 1

Eliminating the parameter above, we get

x + y = (ct - 3) + (-ct + 3) = 0   ⇒   x = -y

and substituting

x = ct - 3   ⇒   t = (x + 3)/c

into z(t), we get

z = (b - a) (x + 3)/c - 1   ⇒   x = c (z + 1)/(b - a) - 3

As symmetric equations, then, we write

x = -y = c (z + 1)/(b - a) - 3

Based on the vertices of point B, the image point of point A before the translation is (-5, 5)

To find the original image point, you need to move in reverse from the point that was created by the translation.

In order to find point A,  from point B you should move left 4 units and down 3 units.

This means that the x-axis point would be:

= -1 - 4

= -5

The y-axis point:
= 8 - 3

= 5

The image point of A is (-5, 5)

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The values of x and y in the lines are x = 13 and y = 54

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

The lines m and n are parallel lines

This means that the following angles are congruent by the corresponding angle theorem

7x - 31 + 5x - 8 + 63 = 180

4y + 27 - 180 = 63  

Solving the equation 4y + 27 - 180 = 63  

We have the following representation

4y + 27 - 180 = 63  

Evaluate the like terms

4y = 216

Divide by 4

y = 54

Recall that

7x - 31 + 5x - 8 + 63 = 180

Evaluate the like terms

12x = 156

Divide by 12

x = 13

Hence, the values are x = 13 and y = 54

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The probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

According to the given question.

Total number of cards in a deck is 52.

As we know that total number of red cards in a well shuffled deck is 26.

Since, Eric first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. Which means there is a replacement of cards.

So, the probability of drawing the first card is red = 26/52 = 1/2

And the probability of drawing the another card is red = 26/52 = 1/2

Therefore,

The probability of drawing a red card, placing it back in the deck, and drawing another red card

= 1/2  × 1/2

= 1/4

Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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The circumference of the Canadian $1 coin is 83.21 mm

For given question,

We have been given the Canadian $1 coin has a diameter of 26.5 mm.

We need to find the circumference of the coin.

We know that circumference of a circle of radius r is,

c = 2πr

The Canadian $1 coin has a diameter of 26.5 mm.

So, the radius of the coin would be,

r = 26.5 /2

r = 13.25

Using the formula of circumference, the circumference of the coin would be,

⇒ c = 2πr

⇒ c = 2 × π × r

⇒ c = 2 × 3.14 × 13.25

⇒ c = 83.21 mm

Therefore, the circumference of the Canadian $1 coin is 83.21 mm

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The missing points are listed below:

The picture attached aside shows us a right-angled parallelepiped and the Euclidean geometry indicates that a plane is generated by three non-colinear points, that is, three points that cannot be contained by a line.

Therefore, coplanar points are points that can be contained by one and same plane. Parallelepipeds are solids with eight vertices and twelve sides, each of them corresponding to a plane.

In this problem we must determine what fourth point is contained by the same plane that comprises the other three. Now we show the corresponding answers:

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The graph can be viewed at the conclusion of the response. We want to graph a number line and certain points on it.

Let A denote the truck stop and then it is 0 miles away from the truck stop.

Let us take the north side of the truck stop as the negative side.

Then the south side of the truck stop is the positive side.

We are asked to represent the following positions on the number line:

a. The truck stop

b. 5 miles to the north of the truck stop

c. 3.5 miles to the south of the truck stop

Point A refers to the truck stop.

Let B denote the point 5 miles away from A towards the north side of the truck stop.

And let C denote the point 3.5 miles away from A towards the south side of the truck stop.

Refer to the attached image for the required number line.

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Answer:

(x, y) --> (x, - y)

Step-by-step explanation:

.......

Answer:

3/10

Step-by-step explanation:

4/5 * 3/8

We can rewrite the fractions as

4/8 * 3/5

4/8 simplifies to 1/2

1/2 * 3/5

Multiply the numerators

1*3 = 3

Multiply the denominators

2*5 = 10

Numerator over denominator

3/10

Answer:non terminating

Step-by-step explanation:

The ratio of blue hats to red hats IS 3:2 , the ratio of the blue hats all hats is 3:5 and If the store purchased 45 hats, 27 hats were blue

The ratio of blue hats to red hats is 9:6, which can be simplified to 3:2

Therefore the ratio of blue hats to red hats is 3: 2

The total number of hats is the summation of blue hats and red hats = 9+6= 15

So, The ratio of blue hats to all hats is 9:15, which can be simplified to 3:5

Therefore the ratio of blue hats to red hats is 3: 5

If the store purchased 45 hats, and we need to find out the number of blue hats

We have to assume the number of blue hats be x

Then the ratio becomes x: 45::3:5

We can also write this as

X= 3a and 45= 5a

The value of a comes out to be 9

So the number of blue hats purchased in the lot is 3a= 3 9 = 27

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Answer:

14x

Step-by-step explanation:

2x*7=

2*7=14x

Answer:

8x - 4y

Step-by-step explanation:

First: solve the parentheses

8x - 7y - (3-6y)

Second: combine like terms (terms that both have y or x, or other variable)

8x - 7y - (-3y)

Third: there are no more like terms, so you are left with this as your answer

8x - 4y

Cost of pen = 20x  when x< 10

                              and

                      =10x when x>10

Let the number of pens bought be x.

So the total pen cost is 20x when the number of the pen is less than 10.

Now let's take that the number of pens bought is more than 10

So the pen will cost a 50% discount  

    50% of 20x

  = 20/100 × 20x

  = 10x

So the cost of the pen will be 10x when the number of the pen is greater than 10.

From this, we get to know that

Cost of pen = 20x when x<10

                              and

                       = 10x when x>10

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Answer:

Step-by-step explanation:

x < 0

Answer : x is less than or equal to 0

First, the direction of the number line in the graph is the negative number side, so it has to be 0 or less.

If it is less than 0, the dot that starts at the point 0 must have a hollowed out part in the middle. If it is 0 or less, the dot that starts at the point 0 is completely filled with no hollowed middle part.

Since the dot is completely blacked out, the answer is the second option.

The value of ∠ F L H  is 3x-6°

∠FLG and ∠FLH are adjacent angles with L being the common vertex  and both the angles form the ∠HLG

As ∠FLG is given as 14x + 5° and  ∠ H L G is given as 17 x − 1 °

We need to find the value of ∠ F L H

We can write that ∠FLG +∠FLH = ∠ H L G

by putting the values given

14 x + 5 ° + ∠ F L H  = 17 x − 1 °

∠ F L H = 17x-1 - (14x + 50

Here we got a linear equation in one variable and by solving the equation we will get the value of ∠ F L H

∠ F L H = 17x - 1 - 14x -5

∠ F L H  = 3x-6

Hence, the value of ∠ F L H  is 3x-6°

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Answer: K(8,6)

Step-by-step explanation:

M(8,3) - the midpoint of KL    L(8,0)    K(x,y)=?

[tex]\displaystyle\\Mx=\frac{Kx+Lx}{2}[/tex]

Multiply both parts of the equation by 2:

[tex]2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)[/tex]

According to the question, a region is bounded by semicircular arcs on the side of the squares. Therefore, the side of the square is the diameter of the circle.

And the side of the square is [tex]\frac{2}{\pi }[/tex].

Now, the radius of the semicircle is [tex]\frac{1}{2} \frac{2}{\pi } =\frac{1}{\pi }[/tex]

The length of the semicircular arc is equal to half the circumference of the corresponding circle.

Therefore, the length of the arc is [tex]\frac{1}{2} (2)(\pi)\frac{1}{\pi } =1[/tex]

Now, the desired parameters of the region made by these arcs is [tex](4)(1)=4[/tex]

What are semicircular arcs and circumference of the circle?

Semicircular arcs is another name for the semicircle. It divides the circle into two parts. And the endpoints on a circle defines the minor arc or major arc. Similarly, circumference is the perimeter of the circle.

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Answer:

x2 + 8x + 15

Step-by-step explanation:

First - take the first terms of the brackets (so, x and x) and multiply them together: for this example that gives x2.

Outside - take the two outermost terms of the brackets (x and 5) and multiply them together: for this example that gives 5x.

Inside - take the two innermost terms of the brackets (3 and x) and multiply them together: for this example that gives 3x.

Some people may draw lines between terms when doing this (as seen in the diagram above) leaving you with a “crab claw” around the brackets.

Write down everything you have worked out as one long expression:

x2 + 5x + 3x + 15

Then, we will simplify this expression by grouping any “like” terms (this just means adding together any bits with x where they have the same power).

This leaves us with our final answer, which is:           

x2 + 8x + 15

Answer: 48

Step-by-step explanation: 48 is the highest mileages

Answer:

3.1.1.  A(-4, 0)   B(0, -2)   E(4, 0)

3.1.2.  k = -16

3.1.3.  (-∞, ∞)

3.1.4.  [-16, ∞)

3.1.5.  [-6, 4]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+k\\g(x)=-2x+8\\h(x)=\dfrac{6}{x-2}+1\end{cases}[/tex]

Points A and B are the x-intercept and y-intercept of function h(x).

Point E is the x-intercept of function g(x).

The x-intercept of function h(x) is when h(x) = 0:

[tex]\begin{aligned}h(x) & = 0\\\implies \dfrac{6}{x-2}+1 & = 0\\\dfrac{6}{x-2} & = -1\\6 & = -1(x-2)\\6 & = -x+2\\4 & = -x\\x & = -4\end{aligned}[/tex]

Therefore, the coordinates of point A are (-4, 0).

The y-intercept of function h(x) is when x = 0:

[tex]\begin{aligned}h(x) & = \dfrac{6}{x-2}+1\\\implies h(0) & = \dfrac{6}{0-2}+1\\ & = -3+1\\& = -2\end{aligned}[/tex]

Therefore, the coordinates of point B are (0, -2).

The x-intercept of function g(x) is when g(x) = 0:

[tex]\begin{aligned}g(x) & = 0\\\implies -2x+8 & = 0\\-2x & = -8\\x & = 4\end{aligned}[/tex]

Therefore, the coordinates of point E are (4, 0).

As function f(x) passes through point C (-6, 20), substitute the point into the equation of the function to find the value of k:

[tex]\begin{aligned}f(-6) & = 20\\\implies (-6)^2 + k & = 20\\36 + k & = 20\\k & = 20 - 36\\k & = -16\end{aligned}[/tex]

Hence, proving that the value of k is -16.

The domain is the set of all possible input values (x-values).

The domain of function f(x) is unrestricted, therefore its domain is:

The range is the set of all possible output values (y-values).

The range of function f(x) is restricted, since the minimum point of the parabola is at (0, -16).  Therefore its range is:

[tex]\begin{aligned}g(x) - f(x) & \geq 0\\\implies g(x) &\geq 0+f(x)\\ \implies g(x) & \geq f(x)\end{aligned}[/tex]

Therefore, find the interval for which g(x) is greater than or equal to f(x).

From inspection of the given graph this is between points C and E:

Answer: 24x² + 20x + 4

Step-by-step explanation:

       Area of a rectangle can be found with A = L * W;

               A = L * W

               A = (8x + 4) * (3x + 1)

       Now we can use the "FOIL" method, which is used to multiply binomials.

[F] First ➜ 8x * 3x = 24x²

[O] Outside ➜ 8x * 1 = 8x

[I] Inside ➜ 4 * 3x = 12x

[L] Last ➜ 4 * 1 = 4

       Lastly, we add it all together for our final answer.

24x² + 8x + 12x + 4 = 24x² + 20x + 4

Answer:

24x^2+20x+4

Step-by-step explanation:

Area is length times width.

The length is (8x+4) and the width is (3x+1).

If we follow the formula for the area of a rectangle, then it would be

(8x+4)(3x+1).

Next, you would foil.

Take the first and multiply it by the second equation as follows

8x*3x+8x*1 which would give you

24x^2+8x

Then, you would take the second from the first equation and multiply it with the second equation as well.

4*3x+4*1 which would give you

12x+4

Combine all of it together

24x^2+8x+12x+4

Combine like terms

24x^2+20x+4

That's the area.

Hope this helps.