Which student evaluated the power correctly?
Anna's Work
99 = 9x9x9x9x9
- 59.049
O Hailey's Work
99 = 9x5
= 45
O Cameron's Work
9% = 9+9+9+9+9
=45
Jerry's Work
95 = 5x5x5x5x5x5x5x5x5
= 1,953.125

Answer:

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

The formula for the polynomial is

y = c( x- a1)( x- a2) ( x-a3)  where c is a constant and a1,a2,a3 are the zeros

We have zeros -5,-4 and 1

y = c( x- -5)( x- -4) ( x-1)

y = c( x+5)( x+4) ( x-1)

We have a y intercept of -15

That means x=0 and y = -15

-15 = c ( 0+5)( 0+4) ( 0-1)

-15 = c( 5) ( 4) (-1)

-15 = c( -20)

Divide each side by -20

-15/-20 = c

3/4 =c

The equation is

y = 3/4( x+5)( x+4) ( x-1)

Answer:

A.

Step-by-step explanation:

Anwer A has the following equation:

[tex]g(x)=\frac{3}{5}x^2-3[/tex]

In this equation, we can calculated the intercept replacing x by 0, as:

[tex]g(x)=\frac{3}{5}0^2-3=-3[/tex]

if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.

Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:

[tex]0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236[/tex]

It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.

So, the answer is A, [tex]g(x)=\frac{3}{5}x^2-3[/tex]

Step-by-step explanation:

If the line is parallel to y=2/3x+4 then,

m=m

slope of eqn y=2/3x+4

m=2/3(On comparing with y= mx + c)

the passing point is (3,7) then,

y-y1 = m(x-x1)

y-7=2/3(x-3)

y-7=2/3x -2

y-7= -4x/3

3y-7= -4x

4x + 3y - 7=0

So, The reqd eqn is 4x + 3y - 7 = 0

==================================================

Explanation:

Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.

Through similar reasoning, Paul's rate is 1/6 of a job per hour.

Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.

Combining the three individual rates gives

1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)

1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)

1/5 + 1/6 + 1/x = (11x+30)/(30x)

The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.

Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x

(11x+30)/(30x) = 1/2

2(11x+30) = 30x*1 .... cross multiply

22x+60 = 30x

60 = 30x-22x

60 = 8x

8x = 60

x = 60/8

x = 7.5

It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.

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

Here's another equation to solve though its fairly the same idea as above

1/5 + 1/6 + 1/x = 1/2

30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD

30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)

6x + 5x + 30 = 15x

11x + 30 = 15x

30 = 15x-11x

30 = 4x

4x = 30

x = 30/4

x = 7.5

We get the same answer

Answer:  7 . 5 hrs

Step-by-step explanation:

It takes Jane 5 hours to finish the fence so she can get  [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.

It takes Paul 6 hours to finish the fence so he can get  [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.

It takes Peter x hours to finish the fence so he can get  [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.

Together, it takes them 2 hours to finish the fence so they can get  [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.

Jane + Paul + Peter = Together

[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]

Multiply everything by 30x to eliminate the denominator:

[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]

Simplify and solve for x:

6x + 5x + 30 = 15x

      11x + 30 = 15x

              30 = 4x

              [tex]\dfrac{30}{4}=x[/tex]

              7.5 = x

Answer:

96

Step-by-step explanation:

800*0.12=96

Answer:

96

Step-by-step explanation:

12% of 800 is 96

Step-by-step explanation:

The probability that either Jack or Jill will be selected on the first draw is 2/30.

The probability that the other person will be selected on the second draw is 1/29.

The probability of both events is (2/30) (1/29), which simplifies to 1/435.

Answer:

55 games

Step-by-step explanation:

What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation [tex]g = 11/20[/tex]%. We solve this accordingly: [tex]g = (11/20) *100[/tex]; [tex]g = (.55)*100[/tex]; [tex]g = 55[/tex].

Answer:

[tex]\boxed{\sf Option \ 4}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x-3} +x=3[/tex]

Subtract x from both sides.

[tex]\sqrt{2x-3} +x-x=-x+3[/tex]

[tex]\sqrt{2x-3}=-x+3[/tex]

Square both sides.

[tex]( \sqrt{2x-3})^2 =(-x+3)^2[/tex]

[tex]2x-3=x^2-6x+9[/tex]

Subtract x²-6x+9 from both sides.

[tex]2x-3-(x^2-6x+9 )=x^2-6x+9-(x^2-6x+9)[/tex]

[tex]-x^2 +8x-12=0[/tex]

Factor left side of the equation.

[tex](-x+2)(x-6)=0[/tex]

Set factors equal to 0.

[tex]-x+2=0\\-x=-2\\x=2[/tex]

[tex]x-6=0\\x=6[/tex]

Check if the solutions are extraneous or not.

Plug x as 2.

[tex]\sqrt{2(2)-3} +2=3\\ \sqrt{4-3} +2=3\\\sqrt{1} +2=3\\3=3[/tex]

x = 2 works in the equation.

Plug x as 6.

[tex]\sqrt{2(6)-3} +6=3\\ \sqrt{12-3} +6=3\\\sqrt{9} +6=3\\3+6=3\\9=3[/tex]

x = 6 does not work in the equation.

Answer:

option d

Step-by-step explanation:

[tex]\sqrt{2x-3}+x = 3\\\\\sqrt{2x-3} = 3 -x\\[/tex]

Square both sides

[tex](\sqrt{2x-3})^{2}=(3-x)^{2}\\\\\\2x-3=9-6x+x^{2}\\\\0=x^{2}-6x + 9 - 2x + 3\\[/tex]   {Add like terms}

[tex]x^{2} - 8x + 12 = 0[/tex]

Sum = -8

Product = 12

Factors =  -2 , - 6

x² - 2x - 6x + (-2) * (-6) = 0

x(x -2) - 6(x -2) = 0

(x -2) (x - 6) = 0

x - 2 =0   ; x - 6 = 0

x = 2      ; x = 6

roots of the equation : 2  , 6

But when we put x = 6, it doesn't satisfies the equation.

When x = 6,

[tex]\sqrt{2x-3} + x = 3\\\\\sqrt{2*6-3}+6 = 3\\\\\sqrt{12-3}+6=3\\\\\sqrt{9}+6=3\\\\[/tex]

3 + 6≠ 3

Therefore, x = 2  but x = 6 is extraneous

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Answer:

Congressman Stevens will win the race

Step-by-step explanation:

Considering the margin of error, the possible outcomes for each candidate would be:

Congressman Stevens: from (54 - 3)% to (54+3)%

Challenger Jones: from (44 - 3)% to (44+3)%

Congressman Stevens: from 51% to 57%

Challenger Jones: from 41% to 47%

Therefore, even considering the margin of error, the pollster would be able to safely predict that Congressman Stevens will win the race.

Answer:

-28.

Step-by-step explanation:

(x^2 + 3) / (x + 6)

x = -9

[(-9)^2 + 3] / (-9 + 6)

= (81 + 3) / (-3)

= 84 / (-3)

= -28

Hope this helps!

Answer:  the value of the expression is 80

Step-by-step explanation:

[tex]x^2 +3/ x+6[/tex]

(-9)² + 3 / (-9 + 6) .  PEMDAS: figure  parentheses and exponents  first

81 + 3/-3    division   3/-3  = –1

81 + (–1) .adding a negative is the same as subtracting

81 –1

80

Answer:

La Tasha has 27 rabbit stickers. She splits the stickers

evenly among 3 pieces of paper. How many stickers

did La Tasha put on each piece of paper?​

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have f(x) and g(x). We are to evaluate each of these functions at the domain values given (1, 2, 3, 4, 5, and 6) and see where the output is the same.

[tex]f(1)=-(1)^2+4(1)+12[/tex] and f(1) = 15

[tex]f(2)=-(2)^2+4(2)+12[/tex] and f(2) = 16

[tex]f(3)=-(3)^2+4(3)+12[/tex] and f(3) = 15

[tex]f(4)=-(4)^2+4(4)+12[/tex] and f(4) = 12

[tex]f(5)=-(5)^2+4(5)+12[/tex] and f(5) = 7

[tex]f(6)=-(6)^2+4(6)+12[/tex] and f(6) = 0

Now for g(x) at each of these domain values:

g(1) = 1 + 2 and g(1) = 3

g(2) = 2 + 2 and g(2) = 4

g(3) = 3 + 2 and g(3) = 5

g(4) = 4 = 2 and g(4) = 6

g(5) = 5 + 2 and g(5) = 7

g(6) = 6 + 2 and g(6) = 8

It looks like the outputs are the same at f(5) and g(5). Actually, the domains are the same as well! f(5) = g(5)

Answer:

A = 55

B = 60

Step-by-step explanation:

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180 interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Answer:

[tex]\boxed{A = 55\°}[/tex]

[tex]\boxed{B = 60\°}[/tex]

Step-by-step explanation:

Exterior Angle with A = 180 - 55 = 125 degrees  (Angles on a straight line)

The measure of exterior angle is equal to the sum of non-adjacent interior angles.

So,

125° = B + 65°

B = 125 - 65

B = 60°

Now,

A = 180 - 60 - 65     (Interior angles of a triangle add up to 180 degrees)

A = 55°

Answer:

The answer is below

Step-by-step explanation:

Since they are two green balls, x cannot assume value of 0 and 1. The minimum number of red balls must be two since there are only two green balls and we need to select 4 balls

For x = 2 (select two red balls from 4 red balls and 2 green balls from 2 green balls):

P(x = 2) = [tex]\frac{C(4,2)*C(2,2)}{C(6,2)} =\frac{6}{15}[/tex]

For x = 3 (select 3 red balls from 4 red balls and 1 green balls from 2 green balls):

P(x = 3) = [tex]\frac{C(4,3)*C(2,1)}{C(6,2)} =\frac{8}{15}[/tex]

For x = 4 (select 4 red balls from 4 red balls and 0 green balls from 2 green balls):

P(x = 4) = [tex]\frac{C(4,4)*C(2,0)}{C(6,2)} =\frac{1}{15}[/tex]

Expected value = E(x) = ΣxP(x) = (2×6/15) + (3×8/15) + (4×1/15) = 40/15 = 2.67

Variance =  Σx²P(x) - [E(x)]² = (2²×6/15) + (3²×8/15) + (4²×1/15) - (40/15)² = 80/225 = 0.36

Standard deviation = √variance = √0.36 =  0.6

Using the hypergeometric distribution, it is found that:

The marbles are chosen without replacement, hence, the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

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

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

The expected value is:

[tex]E(X) = \frac{nk}{N}[/tex]

Hence:

[tex]E(X) = \frac{4(4)}{6} = 2.67[/tex]

The expected value is of 2.67.

The variance is:

[tex]V(X) = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]

Hence:

[tex]V(X) = \frac{4(4)(2)(2)}{6^2(6-1)} = 0.356[/tex]

The standard deviation is the square root of the variance, hence:

[tex]\sqrt{V(X)} = \sqrt{0.356} = 0.596[/tex]

A similar problem is given at https://brainly.com/question/19426305

Answer: There are 19 cats and  38 dogs.

Step-by-step explanation:

Given, A veterinarian clinic, there are twice as many dogs as there cats.

Let x = Number of cats

then, number of dogs = 2x

Since , total number of dogs and cats = 57

So, x+ 2x= 57

[tex]\Rightarrow\ 3x= 57[/tex]

Divide both sides by 3 , we get

[tex]x=\dfrac{57}{3}=19[/tex]

[tex]\Rightarrow\ x= 19[/tex]

Number of cats =19

then, number of dogs  = 2(19) = 38

hence, there are 19 cats and  38 dogs.

Answer: 19 cats and 38 dogs

Step-by-step explanation:

hope this helps

Answer:

15 miles

Step-by-step explanation:

Speed is the ratio of distance traveled to the time taken to reach the distance. The formula for speed is given by:

Speed = distance / time

Distance = speed × time

Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. At time t = 45 minutes = 45/ 60 hour = 0.75 hour, the distance traveled by Claire and Han is given as:

For Claire:

Distance = speed × time = 12 miles / hour × 0.75 hour = 9 miles

For Han:

Distance = speed × time = 8 miles / hour × 0.75 hour = 6 miles

Since both Han and Claire are traveling in opposite directions, the distance between them after 45 minutes = 9 miles + 6 miles = 15 miles

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

The most precise name of the quadrilateral will be rectangle .

Given,

Point A : (2,3) .

Here,

If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

So, graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

Know more about rectangle,

https://brainly.com/question/15019502

#SPJ6

Answer:

A

Step-by-step explanation:

Given

f(x) = [tex]\frac{3+x}{x-3}[/tex]

To evaluate f(a + 2), substitute x = a + 2 into f(x)

f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A

Answer: A y = -(2x+8)

Step-by-step explanation:

The first line is y=-2x-8

Thus, the answer that simplifies to y = -2x-8 is the answer.  

a) y=-(2x+8)

Distribute

y=-2x-8

Because it works, no need to try the others.

Hope it helps <3

Answer:

[tex]\boxed{y = -(2x + 8)}[/tex]

Step-by-step explanation:

For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.

First equation : y = -2x - 8

A. y = -(2x + 8)

   y = -2x - 8 correct

B. y = -2(x - 8)

   y = -2x + 16 incorrect

C. y = -2(x - 4)

   y = -2x + 8 incorrect

D. y = -(-2x+8)

    y = 2x - 8 incorrect

y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.

Answer:

B

Step-by-step explanation:

A nice way to remember the normal trig functions and what they stand for is with SOH CAH TOA, where S represents the Sin, C represents the Cos, and T represents tan. Note: those are only abbreviations of the actual words.

I don't know a way to remember the names of the inverse trig functions, but they are Csc, sec, and cot.

Looking at all of the options, only TON does not fit the bill, so that's the answer.

Answer:

A

Step-by-step explanation:

[tex] \frac{ {6}^{3}. {2}^{6} }{ {2}^{3 } } = \frac{ {2}^{3}. {3}^{3}. {2}^{6} } { {2}^{3} } = {2}^{6} . {3}^{3} [/tex]

Answer:

combinations = 10 * 10 * 26

combinations = 2,600

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The rate of change between two points a and b(a<b) for a fynction f is given by the formula:

so our rate of change is

Answer:

Age of teacher = 32 years

Step-by-step explanation:

Average age of 15 students = 16 years

Sum of age of 15 students = 16 * 15 = 240 years

Average of age 15 students and a teacher = 17 years

Sum of age  15 students and a teacher = 17 * 16 =  272 years

Age of teacher = 272 - 240 = 32 years

Answer:

Age of teacher = 32 years

Therefore, the correct answer is (b)

Step-by-step explanation:

We know that average is given by

Average age = Sum of ages /no. of students

We are given that the average age of 15 students is 16 years.

16 = Sum of ages/15

Sum of ages = 16×15

Sum of ages = 240

We are given that If teacher’s age is included the average increases by 1.

16 + 1 = New sum of ages/15 + 1

17 = New sum of ages/16

New sum of ages = 17×16

New sum of ages = 272

So the age of the teacher is found by

Age of teacher = New sum of ages - Sum of ages

Age of teacher = 272 - 240

Age of teacher = 32 years

Therefore, the correct answer is (b)

Answer:

y= 1

Step-by-step explanation:

A circle forms a sphere only when it goes around a straight line throughout the center so y= 1 because it's (1,0).

The y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.

It is given that the circle is on a coordinate plane with the centre at 1 on the y-axis.

It is required to find around which line would the following cross-section need to be revolved to create a sphere.

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the centre of a circle).

We have a circle on the coordinate plane the centre of the circle lies on the y-axis at 1.

On y=axis the value of x is zero ie. x= 0

The centre of the circle = (0,1)

If a half-circle revovle around the axis which is dividing the circle into two halves.

As we can see in the graph the y-axis and y=1 divide the circle into two halves.

Thus, the line y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.

Learn more about circle here:

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Answer:

−67b + 6 ≤ 9b + 43

Group like terms

That's

- 67b - 9b ≤ 43 - 6

Simplify

- 76b ≤ 37

Divide both sides by - 76

Hope this helps you

Answer:

No.

Step-by-Step Explanation:

When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.

See the triangle below in which two lines are parallel to each other.

Answer:

The airplane can fly up to 240 miles in a hour

Step-by-step explanation:

Cross multiply

(12)(60)=3x

720=3x

Divide 3 on both sides

x=240

There are 60 minutes in 1 hour.

60 ÷ 3 = 20

12 × 20 = 240

In one hour, the airplane could fly at 240 miles.

Answer:

76.9

Step-by-step explanation:

tan(α) = opposite leg/adjacent leg

tan(70°) = x/28

x = 28* tan(70°) = 76.9

Answer:

76.9  or 77

Step-by-step explanation:

tan(α) = opposite leg/adjacent leg

tan(70°) = x/28

x = 28* tan(70°) = 76.9