Mr. Dylan asks his students throughout the year to record the number of hours per week they spend practicing math at home. At the end of the year, he creates a scatter plot that models the relationship between exam score and time spent practicing. Which line of best fit will give Mr. Dylan the most accurate linear equation in order to make predictions about this relationship?

Answer:

a = 6

b = 3

c = 64

d= 64

Step-by-step explanation:

1. Apply the quotient of powers:

[tex](-2)^a / 4^b[/tex]

In the given expression:

[tex]4^5(-2)^9/4^8(-2)^3[/tex]

base same then the powers are subtracting if the bases are in numerator and denominator

i.e [tex]a^m/a^n = a^{m-n}[/tex]

Solving:

[tex]=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3[/tex]

therefore, the values of a and b are: a = 6

b = 3

2. Evaluate Powers

c/d

We have

[tex](-2)^6/4^3[/tex]

When power is even negative sign changes into plus sign

64/64

Therefore, we get the values of c and d

c = 64

d= 64

Answer:

a = 6

b = 3

c = 64

d= 64

Step-by-step explanation: i got it right

Answer:

[tex]\frac{-73}{40}[/tex]

[tex]\frac{-29}{132}[/tex]

Step-by-step explanation:

[tex]-\frac{2}{1}+\frac{3}{8}-\frac{1}{5}[/tex]

[tex]-\frac{80}{40}+\frac{15}{40}-\frac{8}{40}[/tex]

[tex]\frac{-80+15-8}{40}[/tex]

[tex]\frac{-73}{40}[/tex]

[tex]\frac{2}{3}-\frac{7}{11}-\frac{1}{4}[/tex]

[tex]\frac{88}{132}-\frac{84}{132}-\frac{33}{132}[/tex]

[tex]\frac{88-84-33}{132}[/tex]

[tex]\frac{-29}{132}[/tex]

Answer:

-1 33/40

- 29/132

Step-by-step explanation:

i) -2 + ( 3 / 8 ) + ( - 1 / 5 ) = -2 + 3/8 - 1/5=

- 2 + 15/40- 8/40=  -2 + 7/40= -1 33/40

ii) (2/3) + ( -7/11) + (-1/4 ) = 2/3 - 7/11 - 1/4=

2/3 - (28+11)/44=  2/3 - 39/44=  (2*44- 3*39) /3*44= - 29/132

Answer:

A.

Step-by-step explanation:

There are 3 ft in a yd. That means if we have 1 ft left over, then we have 1/3 yd left over. Add that to our 1 yd and we get 1 1/3 yds

Answer:

-4n³ - 8n² - 4n

Step-by-step explanation:

Answer: The line is AB and the plane is ABD, the first option is the correct one.

Step-by-step explanation:

Ok, first some definitions.

A line is any line that crosses two colinear points. Particularly, you can see in the graph that the line crosses through A and B, so the line is AB.

A plane needs 3 non-colinear points (if the points where colinear, then the points may define a line). Other definition of plane is "a line and a point that is not in the line"

So, if our line is AB, then the possible planes are:

ABC and ABD.

then the correct option is:

Line AB and plane ABD, so the correct option is the first one.

Answer:

A shift to the right 8 units

Step-by-step explanation:

Remember to take the opposite of the sign when you are moving horizontally. The -8 signifies that it will be moving right 8 units instead of left.

Answer:

Meena's is 5 and her father is 30

Step-by-step explanation:

x+5+6x+5=2x+6x+5

x+6x-2x-6x=5-5-5

-x =-5

x =5 Meena

6*5

=30 Her father's age

Have a good day and stay safe!

Answer:

x(x+2)^2

Step-by-step explanation:

x^-3 +2x^2 +x

Taking x as common

x(x^2+2x+1)

x[(x)^2+2(x)(1)+(1)^2]

x(x+2)^2

I hope it will help you

Answer: A. (x,y)→(−y,x)

Step-by-step explanation:

For rotating a point about the origin at 90° in the counterclockwise direction, the x and y coordinate values are interchanged with the interchanged y value also given a negative sign.

For clarity :

Given the coordinate (2, 5)

Rotating (2, 5) about the origin at an angle of 90° in the counterclockwise direction:

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

(2, 5) - - - - - - - - - - - > (-5, 2)

Answer:

78

Step-by-step explanation:

ur boi got it right

Answer:

Step-by-step explanation:

A. 2x-4

B. x+y

C. x+6 ≤20

Answer:

x = 155

Step-by-step explanation:

155 and x are alternate exterior angles and alternate exterior angles are equal when a and b are parallel

x = 155

Answer:

Options (1), (3), and (5)

Step-by-step explanation:

In the figure attached,

An inequality has been graphed and the shaded region shows its solutions.

Inequality : y < 0.5x + 2

If the given points in the options lie in the shaded region, point will satisfy the inequality.

For (3, -2)

-2 < 0.5(3) + 2

-2 < 3.5 [True]

Therefore, (3, -2) point is the solution.

For (-2, 1)

1 < 0.5(-2) + 2

1 < -1 + 2

1 < 1 [Not true]

Therefore, (-2, 1) is not the solution.

For (-1, -2)

-2 < 0.5(-1) + 2

-2 < 1.5 [True]

Therefore, (-1, -2) is the solution.

For (-1, 2)

2 < 0.5(-1) +2

2 < 1.5 [Not True]

Therefore, (-1, 2) is not the solution.

For (1, -2)

-2 < 0.5(1) + 2

-2 < 2.5 [True]

Therefore, (1, -2) is the solution.

Options (1), (3) and (5) will be the answer.

Answer:

A, C, and E

Step-by-step explanation: Rate it 5 stars and give it a thanks. I took the test you can comment a question i will answer back.

Answer:

D. -√3/2

Step-by-step explanation:

Remember your unit circle.

Alternatively, you can plug in cos(7π/6) into your calc (Put it in rad mode) and calculate your answer.

Answer:

D. -√3/2

Step-by-step explanation:

Answer:

x = 5.25

Step-by-step explanation:

width = x

length = (x + 8)

length that overlaps with width = (x + 8) - x = 8

perimeter (clockwise)

= 90

= x + 8 + (x + 8) + x + (x + 8) + x + 8 + (x + 8) + x + (x + 8)

= 8x + 6(8)

= 8x + 48

8x + 48 = 90

8x = 42

x = 5.25

Answer:

Option C is correct.

The standard deviation of B is greater.

Step-by-step explanation:

Distribution A is given

A = {91, 94, 89, 93, 87, 92, 86, 87, 92, 91}

Then distribution B is all of distribution A including the percentage for the package where the least kernels popped

B = {74, 91, 94, 89, 93, 87, 92, 86, 87, 92, 91}

Taking the statements one at a time

- The mean of A is the same as the mean of B.

Mean = (sum of variables)/(sample size)

It is evident that most of the percentages in distribution A hover around a consistent spot, hence, the mean too will land around that consistent spot. The mean of distribution A as calculated = (902/10) = 90.2

Mean of distribution B should hover around that spot too, but a new addition of 74 is expected to bring the mean down.

Mean of distribution B = (976/11) = 88 73

Hence, statement 1 is incorrect as the mean of A isn't the same as the mean of B.

- Including the percentage for the package where the least kernels popped causes the center of the data to increase.

The center of the data is synonymous with the mean and it is evident that this centre doesn't increase after including the percentage for the package where the least kernels popped causes the center of the data to increase, rather, it drops from 90.2 to 88.73.

Hence, this statement is false.

- The standard deviation of B is greater

Standard deviation measures how far away from the mean the variables of the distribution are. And since we've established that the variables of distribution A hover around a spot, hence, the stamdard deviation is expected to be small. But distribution B has all of the variables of distribution A plus a value that is very far away from the Mean (74), hence, it is easy to see that distribution B will have the greater standard deviation. Let us now calculate.

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean

N = Sample size

Standard deviation for distribution A = 2.638

Standard deviation for distribution B = 5.293

Hence we can conclude that this statement is true and the standard deviation of distibution B is greater.

Hope this Helps!!!

Answer:

C. G(x) is a negative number with a small absolute value

Step-by-step explanation:

As x increases, G(x) goes towards 0 from the a negative quadrant.

Answer:

2 events are mutually exclusive when they cannot both occur simultaneously. 2 events are mutually inclusive when they can both occur simultaneously. The possible results of 1 trial of a probability experiment. ... When everyone or everything in a population has an equal chance of being selected.

Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0.

Step-by-step explanation:

Answer:

The answer is b I believe

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Here we have to apply " combination and permutation. " It is given that the drama club had to choose three booths from a selection of 9, considering the possible ways to choose so. This is a perfect example of combination. In nCr, n corresponds to 9, respectively r corresponds to 3.

[tex]\mathrm{n\:choose\:r},\\nCr=\frac{n!}{r!\left(n-r\right)!},\\\\\frac{9!}{3!\left(9-3\right)!} =\\\frac{9!}{3!\cdot \:6!} =\\\\\frac{9\cdot \:8\cdot \:7}{3!} =\\\frac{504}{6} =\\\\84\\\\Solution = Option B[/tex]

Hope that helps!

Answer:

B. 84 is correct.

I did the quiz.

Answer:

y=25/6

Step-by-step explanation:

We can set up a proportion!

We know that y/x=y/x because they vary directly.

So, we have 5/6=y/5. We need to solve for y.

We cross multiply and get:

6y=25

y=25/6

When x equals 5, y will equal 25/6.

Hope this helps

Answer:

= 2y^2+18y+6/  y^3+8y^2+13y+6

Step-by-step explanation

Answer:

2(y^2+9y+3 / (y+1)^2(y+6)

Step-by-step explanation:

To solve this -->

Fraction --> Find the LCD -->

Combine all

Answer:

150°

Step-by-step explanation:

a complementary angle is 90°

so 60°+ 90°

is 150°

i hope this helps

Answer:

The correct answer is 15° and 75°.

Step-by-step explanation:

n  +  n  + 60°  = 90°

2n  + 60°  = 90°

2n  + 60°  − 60°  =  90° − 60°

2 n  = 30°

2n  ÷ 2  =  30° ÷ 2

n  = 15°

The first angle measures 15°. Now plug in n = 15° to find the measure of the other angle, n + 60°.

n  + 60°  =  15° + 60°  = 75°

So, the two angles measure 15° and 75°.

Answer:

y= -2/3x+490

slope: -2/3

y-intercept: 490

Step-by-step explanation:

Y-intercept form is y=mx+b, so you would first subtract 2x from both sides to get 3y= -2x+1,470. Then you divide both sides by 3, to get y= -2/3x+490. -2/3 is in the place of m, so it is the slope, and 490 is in the place of b, so it is the y-int.

Answer:

2x+3y =1470

slope intercept form

y=mx+b

2x+3y =1470

subtract 2x from each side

3y = -2x+1470

divide by 3

y = -2/3 x +1470/3

y = -2/3x +490

slope = -2/3

y intercept = 490

Answer:

The answer is 2 hours later.

Step-by-step explanation:

In order to find how many hours you and your friend meet, you have to solve the equation to find h :

[tex]50h = 190 - 45h[/tex]

[tex]50h + 45h = 190[/tex]

[tex]95h = 190[/tex]

[tex]h = 190 \div 95[/tex]

[tex]h = 2[/tex]

Answer:

No solution

Step-by-step explanation:

Either you set them equal to each other or use system of linear equations, the answer will be no solution. That is because these 2 lines are parallel.

If the question is 2x + 1 < 10

Step 1: Isolate x

2x < 9

Step 2: Divide both sides by 2

x < 9/2

x < 4.5

Answer:

The last option

Step-by-step explanation:

You can tell by looking at the title of the x-axis. The domain is all x-values. So, the domain are the number of months.

Answer:

0.07% probability of selecting all students

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the jury is selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability of selecting all students?

Desired outcomes:

8 students from a set of 12. So

[tex]D = C_{12,8} = \frac{12!}{8!4!} = 495[/tex]

Total outcomes:

8 people from a set of 12+12 = 24. So

[tex]T = C_{24,8} = \frac{24!}{8!16!} = 735471[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{495}{735471} = 0.0007[/tex]

0.07% probability of selecting all students