In a recent​ study, volunteers who had 8 hours of sleep were three times more likely to correctly on a math test than were​ sleep-deprived participants.
1) Identify the sample used in the study.
A) The sample is the math questions in the study.
B) The sample is the responses of the volunteers in the study.
C) The sample is the amount of sleep the volunteers got in the study.
D) The sample is the​ sleep-deprived participants in the study. ​
2) What is the​ sample's population?
A) The population is the collection of all the math questions from the math test.
B) The population is the collection of the responses of all individuals who completed the math test.
C) The population is the collection of all the individuals who completed the math test. ​
3) Which part of the study represents the descriptive branch of​ statistics?

Answer:

3z/4

Step-by-step explanation:

Here, we start by calculating the 50% of z

mathematically, that would be 50/100 * z = 50z/100 = z/2

Now we want to calculate the 150% of this.

That would be 150/100 * z/2 = 150z/200 = 3z/4

Answer:

a. 4r² b. 2r c. 6 cm

Step-by-step explanation:

The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.

Now, equating both expressions, 6L² = 24r²

dividing both sides by 6, we have

6L²/6 = 24r²/6

L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².

b.  Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have

√L² = √4r²

L = 2r

So, the polynomial that represents the length of an edge of the cube is L = 2r

c. The length of an edge of the cube is L = 2r. When r = 3 cm.

L = 2r = 2 × 3 cm = 6 cm

So, the length of an edge of the cube is 6 cm.

Answer:

Because the triangle is isosceles, the base angles are congruent. Since the sum of angles in a triangle is 180° we can write:

24 + x + x = 180

24 + 2x = 180

2x = 156

x = 78°

Answer:

[tex]\boxed{x=78}[/tex]

Step-by-step explanation:

The triangle is an isosceles triangle.

The two base angles are equal.

Angles in a triangle add up to 180 degrees.

x + x + 24 = 180

Combine like terms.

2x + 24 = 180

Subtract 24 on both sides.

2x = 156

Divide both sides by 2.

x = 78

Answer:

[tex]\boxed{\mathrm{C.}\:\: g(x)=(x-4)^2-3(x-4)-2}[/tex]

Step-by-step explanation:

The function is shifted 4 units right.

The value of x in the function is subtracted from 4, because this is a horizontal translation.

[tex]f(x)=x^2-3x-2[/tex]

[tex]g(x)=(x-4)^2-3(x-4)-2[/tex]

Answer:

c

Step-by-step explanation:

if you shift to the right funnily enough, you have to "compensate" for that by SUBTRACTING the number of units.

EXTRA

To check, use a simple function f(x)= x²

The top of this parabola is at (0,0).

We want to check if g(x) = (x-4)² is the right function....

Now if f(x) is shifted 4 units right than all variables with x in them, need to be compensated for. The question is do you need to add or subtract...

We know that the result is g(x), and we know that the top of g(x) would end up at (4,0).

For that to happen you need to compensate with g(x) = (x-4)²

Now check if (4,0) is on g(x) by substituting x=4. if the result turns out to be 0, then you know it is ok...

Substituting x=4 indeed results to

4-4 = 0, so (4,0) is on g(x).

Conclusion, by checking this one special value, you now know you have found the correct compensation factor!

Answer:   [tex]\dfrac{27}{65}[/tex]

Step-by-step explanation:

There are 130 students.

There are 58 boys --> 72 girls

A) 49 chose football: 27 are girls --> 22 are boys

B) 72 girls: 24 chose running, 27 chose football --> 21 girls chose tennis

C) 27 students chose tennis: 21 are girls --> 6 are boys.

D) 58 boys: 22 chose football, 6 chose tennis --> 30 boys chose running.

[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&22&27&49\\Tennis&6&21&27\\\underline{Running}&\underline{\quad 30\quad}&\underline{\quad 24\quad}&\underline{\quad 54\quad}\\Total&58&72&130\end{array}}[/tex]

Total running = 30 boys + 24 girls = 54

Total students = 130

[tex]\dfrac{\text{Total running}}{\text{Total students}}=\dfrac{54}{130}\quad \rightarrow \large\boxed{\dfrac{27}{65}}[/tex]

Answer:

Length L = 51.88 feet

Step-by-step explanation:

From the given information,

The length of the pendulum can be determined by using the Formula for the period T which  is the time of one full oscillation of a simple pendulum.

[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]

where;

T = period of the time of one full oscillation = 8 seconds

L = length in feet

g = acceleration due to gravity in  feet = 32 ft/s²

π = 22/7

[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]

[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]

[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]

[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]

[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]

[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]

[tex]7.2012= {\sqrt L}[/tex]

L = 7.2012²

L = 51.88 feet

Answer:

Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99

Step-by-step explanation:

Cost of k key chain=$2.49

Cost of p photo frames=$2.49

Cost of a T-shirt=$5.99

Total cost of all items=cost of k key chain + cost of p photo frame + cost of The shirt

=2.49k + 2.49p + 5.99

Factorise

2.49 is common to both k and p

=2.49(k + p) + 5.99

Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99

Answer:

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)

The slope of BC is ...

  mBC = (q -1)/(9 -6) = (q -1)/3

We want the product of these slopes to be -1:

  mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)

  -(q-1)/(6 -p) = -1 . . . . cancel factors of 3

  q -1 = 6 -p . . . . . multiply by -(6 -p)

  q + p = 7 . . . . . matches choice D

Answer:

C p+q=7

Step-by-step explanation:

I did it on plato and it was right

Answer:

Step-by-step explanation:

[tex]5x + y = 28[/tex]

[tex]x + y = 8[/tex]

Solve the equation for y by moving 'x' to R.H.S and changing its sign

[tex]5x + y = 28[/tex]

[tex]y = 2 - x[/tex]

Substitute the given value of y into the equation 5x + y = 28

[tex]5x + 2 - x = 28[/tex]

Solve the equation for x

Collect like terms

[tex]4x + 2 = 28[/tex]

Move constant to R.H.S and change its sign

[tex]4x = 28 - 2[/tex]

Subtract the numbers

[tex]4x = 26[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{26}{4} [/tex]

Calculate

[tex]x = \frac{26}{4} [/tex]

Reduce the numbers with 2

[tex]x = \frac{13}{2} [/tex]

Now, substitute the given value of x into the equation y = 2 - x

[tex]y = 2 - \frac{13}{2} [/tex]

Solve the equation for y

[tex]y = - \frac{9}{2} [/tex]

The possible solution of the system is the ordered pair ( x , y )

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

Let's check if the given ordered pair is the solution of the system of equation:

plug the value of x and y in both equation

[tex]5 \times \frac{13}{2} - \frac{9}{2} = 28[/tex]

[tex] \frac{13}{2} - \frac{9}{2} = 2[/tex]

Simplify the equalities

[tex]28 = 28[/tex]

[tex]2 = 2[/tex]

Since , all of the equalities are true, the ordered pair is the solution of the system.

[tex](x \:, y \: ) = ( \frac{13}{2} \: , - \frac{9}{2}) [/tex]

Hope this helps....

Best regards!!

Answer:

[tex]\boxed{x=6.5} \\ \boxed{y=-4.5}[/tex]

Step-by-step explanation:

5x + y = 28

x + y = 2

Subtract both equations. (eliminating y variable)

4x + 0 = 26

4x = 26

Divide both sides by 4.

x = [tex]\frac{26}{4}[/tex]

x = 6.5

Plug x as 6.5 in the second equation and solve for y.

6.5 + y = 2

Subtract 6.5 on both sides.

6.5 - 6.5 + y = 2 - 6.5

y = -4.5

Answer:

  2^(x-1)  -5x +12

Step-by-step explanation:

f(x) = 2^(x-1) + 3

g(x) = 5x - 9

(f-g) (x) =  2^(x-1) + 3 - ( 5x-9)

Distribute the minus sign

             2^(x-1) + 3 -  5x+9

Combine like terms

             2^(x-1)  -5x +12

Answer:

a. 63 °F

b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.

Step-by-step explanation:

a. To model this situation, we assume the temperature varies inversely as elevation decreases since at elevation 6288 ft the temperature is 56 °F and at elevation 2041 ft, the temperature is 87 °F

So, we model this as a straight line.

Let m be the gradient of the line.

Let the (6288 ft, 56 F) represent a point on the line and (2041 ft, 87 °F) represent another point on the line.

So m = (6288 ft - 2041 ft)/(56 °F - 87 °F) = 4247 ft/-31 °F = -137 ft/°F

At elevation 5376 ft, let the temperature be T and (5376 ft, T) represent another point on the line.

Since it is a straight line, any of the other two points matched with this point should also give our gradient. Since in the gradient, we took the point (6288 ft, 56 °F) first, we will also take it first in this instant.

So m = -137 ft/ °F = (6288 ft - 5376 ft)/(56 °F - T)

-137 ft/°F = 912 ft/(56 °F - T)

(56 °F - T)/912 ft = -1/(137 ft/ °F)

56 °F - T = -912 ft/(137 ft/°F)

56 °F - T = 6.66 °F

T = 56 °F + 6.66 °F

T = 62.66 °F

T ≅ 62.7 °F

T ≅ 63 °F to the nearest degree

b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.

Answer:

Step-by-step explanation:

Given,

Area of square ground = 42025

Now, let's find the length of square ground

Area of square = [tex] = {l}^{2} [/tex]

plug the values

[tex]42025 = {l}^{2} [/tex]

Swipe the sides of the equation

[tex] {l}^{2} = 42025[/tex]

Squaring on both sides

[tex] \sqrt{ {l}^{2} } = \sqrt{42025} [/tex]

Calculate

[tex]l = 205[/tex] meters

The length of square ground = 205 meters

Now,Let's find the perimeter of square

Perimeter of square [tex] = 4l[/tex]

plug the value of length

[tex] = 4 \times 205[/tex]

Multiply the numbers

[tex] = 820[/tex] meters

Hope I helped.

Best regards!!

Answer:

Rest of the part will be = x - 5x/10- x/10

solution will be 4x/10 i.e 4/10 part of the garden

Step-by-step explanation:

Let the sum total of parts of garden be x

If it is divided into 10 equal parts then

one part will be equal to x/10

Given carrots are planted on 5/10 of the garden

parts on which garden is planted = 5/10 * total part of garden = 5x/10

Given peas are planted on 1/10 of the garden

parts on which peas are is planted = 1/10 * total part of garden = x/10

On rest of the part corn is planted.

Rest of the part will be = total parts of garden - part on which carrots are planted - part on which carrots are planted

Rest of the part will be = x - 5x/10- x/10 = (10x-5x-x)/10 = 4x/10

Model will be

Rest of the part will be = x - 5x/10- x/10

solution will be 4x/10 i.e 4/10 part of the garden

Answer:

1/6

Step-by-step explanation:

Each roll is independent.  So the probability of rolling a six is 1/6, regardless of the previous rolls.

Answer:

7^11 / 4^11

Step-by-step explanation:

( 7/4) ^ 11

We know that ( a/b) ^c = a^c / b^c

7^11 / 4^11

Answer: B. [tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]

Step-by-step explanation:

There is exponent rule that states [tex](\frac{a}{b})^{x} = \frac{a^x}{b^x}[/tex]

So we can apply this rule to this problem.

[tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]

Answer:

The Answer is 180

Step-by-step explanation:

First, let's find the area of the triangle:

[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}\times3\times4=6[/tex]

Now, we multiply this area by the length of the prism, which is 20

[tex]20\times6=120[/tex]

All 3 answers have 120. However, since we're calculating volume, it will be represented by [tex]\text{units}^3[/tex]. Since no specific unit (such as cm or in) is specified, it will be left at that.

Thus, the answer is answer choice D.

Let me know if you need any clarifications, thanks!

The volume of prism is 120 unit³.

The correct option is D.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.

First, Area of Triangle

= 1/2 x b x h

= 1/2 x 3 x 4

= 3 x 2

= 6

So, the volume of prism is

= 6 x 20

= 120 unit³

Thus, the volume of prism is 120 unit³.

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Answer: 169

Step-by-step explanation:

13 squared = 13*13

Simply plug this into a calculator to get 169

Hope it helps <3

Answer:

169

Step-by-step explanation:

the answer is 169 because u will square the 13

Answer:

x = - [tex]\frac{96}{23}[/tex]     or   x=  4.1739

Step-by-step explanation:

[tex]\frac{3x}{8}[/tex]  -  [tex]\frac{4x}{3}[/tex]  =  4

I will show  two methods  of solving this equation

First method

We will follow the steps below:

First find the LCM of 8 and 3

The LCM of 8 and 3 is 24

Next is to multiply through by 24

Our equation becomes

24 ×[tex]\frac{3x}{8}[/tex]  - 24× [tex]\frac{4x}{3}[/tex]  = 24× 4

3×3x    -  8×4x    =24×4

9x  -  32x   = 96

-23x = 96

Divide both-side of the equation by - 23

-23x/-23= 96/-23

x=-[tex]\frac{96}{23}[/tex]        or      x=4.1739

second method

[tex]\frac{3x}{8}[/tex]  -  [tex]\frac{4x}{3}[/tex]  =  4

[tex]\frac{9x - 32x}{24}[/tex]   =   4

multiply both-side of the equation by 24   or cross multiply

9x - 32x = 96

-23x = 96

divide both-side of the equation by -23

x = - [tex]\frac{96}{23}[/tex]     or   x=  4.1739

Answer:  Annual Gross Income = $55,489.20

               Annual Net Income = $46,439.72

Step-by-step explanation:

Total hours worked per week = 3(10) + 5 + 11 = 46

Regular hours worked = 3(8) + 5 + 8 = 37

Overtime hours worked = 3(2) + 0 + 3 = 9

Weekly Tips at 20% of $60 for 46 hours:

0.2(60)(46) = $552.00

Annual tips = $552.00 x 52 weeks = $28,704.00

Weekly Regular pay at $10.20 per hour for 37 hours:

10.20(37) = $377.40

Annual regular pay = $377.40 x 52 weeks = $19,624.80

Weekly Overtime pay at time and a half for 9 hours:

10.20(1.5)(9) = $137.70

Annual overtime = $137.70 x 52 weeks = $7,160.40

Total Annual Gross Income = Tips + Regular Pay + Overtime

$28,704.00 + $19,624.80 + $7,160.40 = $55,489.20

****************************************************************************************

Deductions (per question 5):

a) Pension at 5% = $55,489.20(0.05) = $2,774.46

b) Employee Insurance at 2.4% = $55,489.20(0.024) = $1,331.74

c) Income Tax at 0% for $0-$11,000 = $11,000(0) = 0

   Income Tax at 8% for $11,000-$25,000 = $14,000(0.08) = $1,120.00

   Income Tax at 12% for $25,000-$50,000 = $25,000(0.12) = $3,000.00

   Income Tax at 15% for $50,000-$100,000 = $5,489.2(0.15) =$823.38

Total Income Tax = $4,943.28

Annual Net Income = Gross - Pension - Employee Insurance - Income Tax:

$55,489.20 - $2,774.46 - $1,331.74 - $4,943.28 = $46,439.72

Answer:

a) Multiplied by 1.04

b)160(1.06)=169.6

Step-by-step explanation:

Its increasing so (1+4%) will be what it multiplied to.

Hope it helps u

160(1+6%)=169.6

Answer:

20 hours

Step-by-step explanation:

If your computer can download a movie in 5 hours, then it downloads [tex]\frac{1}{5}[/tex] of a movie in 1 hour.

The extra processor in 1 hour, reduces the time down to 5 hours, so it downloads [tex]\frac{1}{4}[/tex] of the movie in 1 hour.

The time that the extra processor will spend to download a whole movie added to  [tex]\frac{1}{5}[/tex] will equal [tex]\frac{1}{4}[/tex] .

So our equation is [tex]\frac{1}{5} + \frac{1}{x} = \frac{1}{4}[/tex].

To simplify this, lets multiply all sides by 20x.

[tex](\frac{1}{5}+\frac{1}{x} \cdot 20x) = \frac{1}{4}\cdot20x\\ 4x + 20 = 5x[/tex]

Now we can simplify this equation.

[tex]20 = 5x-4x\\\\20 = x\\x = 20[/tex]

So the extra processor alone would take 20 hours to download the movie.

Hope this helped!

Answer:

997

Step-by-step explanation:

Well let's find the square root of 2011 because Paul and his wife are about the same age.

[tex]\sqrt{2011}[/tex]

= 44.8

Paul is 45 and his wife is 44.

44 + 45 = 1980.

2011 - 1980

= 31

So the children are 15 and 16.

45 + 44 + 15 + 16

= 997

Paul and wife - 45 and 44

Children - 15 and 16

Thus,

13 years ago they would be 997.

Hope this helps :)

Answer:

T1he values for x and y of the equations is y = 11, and x = -19/5.

Step-by-step explanation:

To solve this question, we need to rearrange the expression:

5x+4y=25 - (5x+2y=3)

Look, if we subtract one equation to the other, then:

5x+4y=25 [1]

-(5x+2y=3) [2]

Which is the same as:

5x+4y=25

-5x-2y=-3

Subtract them:

5x+4y=25

-5x-2y=-3

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

      2y =22

y = 22/2 = 11

Then, y = 11.

To find x, we can substitute y in either equation [1] or [2].

Let us use [1]

5x+4y=25

5x+4(11)=25

5x+44=25

5x=25-44

5x=-19

x = -19/5

Then, the values for x and y of the equations is y = 11, and x = -19/5.

Answer:

The answer is 0.133

Step-by-step explanation:

All you have to do is take 2/3 as if it was a whole number and divide it by 5, or if you are able to use a calculator, you can just but it in as 2 divided by 3 and then divide 5 by whatever answer you get.

Answer:

Hello! 2/3 divided by 5 in fraction will be 2/15

Step-by-step explanation:

Since we have a 5 we need to change that into a fraction

5 would turn into 1/5

Now you have to multiply both of the fractions to get your answer.

2/3 x 1/5

= 2/15

(So 2/15 will be your answer.)

Hope this helps! :)

Answer: [tex]h(x)=10(0.4)^x[/tex]

Step-by-step explanation:

The exponential function h, represented in the table, can be written as [tex]h(x)=ab^x[/tex]

From table, at x=0, h(x) =10

Put theses values in equation,, we get

[tex]10=a.b^0\\\\\Rightarrow\ 10= a (1)\\\\\Rightarrow\ a= 10[/tex]

Also, for x= 1 , h(x) = 4, so put these values and a=10 in the equation , we get

[tex]4=10b^1\\\\\Rightarrow\ b=\dfrac{4}{10}\\\\\Rightarrow\ b= 0.4[/tex]

Put value of a and b in the equation ,

[tex]h(x)=10(0.4)^x[/tex]  →  Required equation.

Answer:

the answer is option A one graph

and I think or am sure it is correct ans.

Answer:

(-4, 6), (0, 2), (4, -2)

Step-by-step explanation:

You just need to guess and check.

(-4,6) → -4 + 6 = 2 ✔

(0,2) → 0+2 = 2 ✔

(4,2) → 4 + 2 = 6

(4, -2) → 4 - 2 = 2 ✔

(-4,-6) → -4 - 6 = -10

The correct answer is the second list (-4, 6), (0, 2), (4, -2)

Explanation:

By definition, i = sqrt(-1)

Which means,

sqrt(-64) = sqrt(-1*64)

sqrt(-64) = sqrt(-1)*sqrt(64)

sqrt(-64) = i*sqrt(8^2)

sqrt(-64) = i*8

sqrt(-64) = 8i

On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.

Answer:

Click 8i for Correct Answer

Step-by-step explanation:

The graph of the given linear equation can be seen at the end.

Here we have the linear equation:

3x - 4y = 8

Isolating, y, we can rewrite:

-3x + 4y = -8

4y = -8 + 3x

y = (-8 + 3x)/4

y = (3/4)*x - 2

Now, we can evaluate the line in two values of x, so we can get two points on the line.

Evaluating in x = 0 and x = 4 we get:

if x = 0

y = (3/4)*0 - 2 = -2

So we have the point (0, -2)

If x = 4 we get:

y = (3/4)*4 - 2 = 1

Then we have the point (4, 1).

Now we can graph these two points and connect them with a line, that is the graph of the linear equation.

The graph can be seen below.

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