what is 2^-3 as a fraction

D= {-2,0,1, 2,3,4}

1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state

- The lowest value for that is given by x=-2

- The highest value for that is x= 4

- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)

2) So, we can write the set, the Domain, after examining the options as:

D= {-2,0,1, 2,3,4}

Notice that we're considering the x-coordinates

3) So the answer is D= {-2,0,1, 2,3,4}

To eliminate the coefficient divide each side by 3

Now solve the two step equation

3g - 5 = 17

3g = 17 + 5 = 22

then g= 22/3

Now solve 9 = 4a + 13

9 -13 = 4a

-4 = 4a then -1= a

a= -1

Let

y ------> the amount earned

x ----> the number of hours worked

In this problem we have a direct variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality

k=y/x

In this problem the value of k is hourly rate

so

we have

For y=$90 -------> x=5 hours

substitute

k=90/5

k=$18 per hour

substitute in the linear equation

y=18x

so

Part 1) What is the meaning of the 18 that appears in the table?

18 is the hourly rate ( amount earned by a one hour of work)

Part 2) Explain how Lin used this table to solve the problem.

using the table

For x=8 hours

the value of y=$144

Verify with the equation

y=18x

y=18(8)=144 -----> is ok

Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.

For x=3 hours

substitute in the equation

y=18x

substitute the value of x

y=18(3)=$54

For x=2.1 hours

y=18(2.1)=$37.8

Solution:

Given the endpoints of the line;

The slope, m of the line is;

Thus;

CORRECT ANSWER:

We have a rectangular garden.

The length L is 8 feet more than 3 times its width.

3 times the width is 3w, so we will add 8 to it and equal it to the length L:

The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:

The perimeter has a value of P=16+8w.

We can draw the diagram as:

Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?

We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.

The width is 9.75 feet.

For the point 1)

- The domain will be: (note that this is not an interval, it is a set of two points)

-The range is the set R of all real numbers (since the line extends to infinite)

-The first graph is NOT a function

For the point 2)

-The domain will be the interval

-The range is the interval:

-The second graph is a function.

Answer

It will take 2 hours to fill the daily quota if all the machines are running.

Explanation

To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:

Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines

Given:

The dimension of square shape floor is 200 feet by 200 feet.

The area of the square is calculated as,

Now, given that the 1/2 bottle will cover approximately 2000 quare feet.

It gives,

So, the number of bottles required are,

Answer: option B)

Given:

Required:

To identify the horizontal and vertical asymptotes, and to point the graph.

Explanation:

Now the graph of the given function is

To find the horizontal asymptotes apply the limit

She walked 3 1/4 miles per day.

Given,

Jane walked 9 3/4 miles in the course of 3 days.

If we calculate this mixed number into a fraction,

We get:

9 3/4 miles = {(9×4)+3} / 4 miles

=39/4 miles.

So, Jane walks 39/4 miles in 3 days.

Therefore, in one day she walked:

(39/4 ÷ 3) miles

= 13/4 miles per day

Let's now convert this fraction into a mixed number:

when 13 is divided by 4 we get the remainder as 1 and the quotient as 3.

So, a mixed number is given by:

quotient remainder/divisor

Hence 13/4 = 3 1/4.

So, Jane walked 3 1/4 miles per day.

Learn more about mixed number at

https://brainly.com/question/21610929

From the given data, the cost per pound of apple, CP=$1.89≈$2.

We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.

The cost of n=3 lb of apple can be calculated as,

Therefore, the cost of 3. pounds of apples is about $6.048.

s = 28π/3

The radius, r = 8

The angle, θ = 7π/6 radian

The length of the arc, s = rθ

s = 8 x 7π/6

s = 28π/3

2+7x=15

Explanation

Step 1

Let

x represents the number

seven times a number = 7x

two more = +2 or 2+, you need to add 2

is = "="

Step 2

replace,

"Two more than seven times a number is fifteen"

I hope this helps you

For this problem, we are given the dimensions of a rectangular prism and are asked to determine its volume.

The volume of a rectangular prism is given by the product of the three dimensions, therefore we have:

The correct answer is 328.02 cubic centimeters.

Given data:

The weight of man and daughter = 90

The weight of man and cat is = 70

The weight of cat and daughter = 40 .

The man weights 60 kg.

then daughter weight = 90-60 = 30.

Thus the daughter weight is 30kg.

therefore the cat weight iwith daughter, 40-30 = 10 .

also with father, 70-60 = 10 .

Thus, the father weight is 60 kg.

The daughter weight is 30 kg and

The cat weight is 10 kg.

SOLUTION:

We want to know the scale factor of the transformation from;

We do this by taking ratios of corresponding sides, they should be the same in either case;

Thus , the scale factor is;

Thus, the scale factor is 2.

We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).

You borrowed a principal amount of:

The time duration for which we have borrowed the money for is:

The annual interest rate coumpounded each year is:

Step 1: Determine the simple interest that accumulated at the end of ( t ) years.

The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.

The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).

Use the above simple interest formula ( I ) by plugging in the respective values as follows:

Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.

Step 2: Determine the total amount that is to be returned/paid to the lender

The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).

Therefore, the amount that you need to pay altogether is:

Solution

We have the following:

5!= 5*4*3*2= 20*3*2= 60*2= 120

Answer:

Explanation:

To solve compound inequalities, we do the same as in an equation or inequality: we need to do the same operation in all places.

We want to solve for x:

And that's the answer

INFORMATION:

We have the following options

And we must select the one that represents the explicit formula for a compound interest geometric sequence

STEP BY STEP EXPLANATION:

To select the correct one, we need to know that:

Finally, the correct one would be option A

ANSWER:

C. 6

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so

Step 1

given

a)let

b) now, replace and calculate

therefore, the answer is

C. 6

I hope this helps you

For the function, f(x) =0, we have x = -6 and x =4

The given function is  f(x) = x² + 2x - 24

For f(x) = 0

f(x) = x² + 2x - 24 =0

x² + 2x - 24 =0

Middle Term Splitting is a method to solve quadratic equations of the form ax² + bx +c, In middle-term splitting, we split the middle term into the factors of the constant terms, then we take common multiples from the terms and then convert the equation into factors, we equate each factor to zero and we get the desired results.

By splitting the middle term, we have:

x² + 6x -4x - 24 =0

x( x + 6) -4(x+6) =0

( x + 6 ) ( x - 4 ) = 0

( x + 6 ) = 0 and ( x - 4 ) = 0

x = -6 and x = 4

Hence, for f(x) =0, we have x = -6 and x =4

To read more about functions, visit https://brainly.com/question/21145944

#SPJ9

Given the numbers:

355, 382, 383, 427, 500, 572, 601, 638, 669

Total numbers = 9

a) We find the mean:

Change 669 to 606:

Then:

Answer: It decreases by 7

b) We find median

Median: 355, 382, 383, 427, 500, 572, 601, 638, 669

Median = 500

669 changed to 606

Median: 355, 382, 383, 427, 500, 572, 601, 606, 638

Median = 500

Answer: It stays the same

A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

Now, the equation passes through (2, 0)

y = ax² + bx + c

0 = 4a + 2b + c  ----------------(1)

The equation passes through (6, -4)

y = ax² + bx + c

-4= 36a + 6b + c ----------------(2)

The equation passes through (10, 0)

y = ax² + bx + c

0 = 100a + 10b + c ----------------(3)

Using the Gauss elimination method to solve the system of equations we get,

a = 1/4, b = -3, and c = 5

The quadratic equation will be:

y = ax² + bx + c

y = (1/4) x² - 3x + 5

Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

Learn more about quadratic function here:

brainly.com/question/5428105.

#SPJ1

We have to find the vertical and horizontal lines that passes through the point (3,6).

A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.

The same goes for horizontal lines, but in this case the line is defined as y = constant.

For a point (x1,y1), the horizontal line that pass through the point will be y = y1.

Then, for point (x,y)=(3,6), the vertical and horizontal lines as:

x=3 and y=6.

Answer:

Vertical line: x = 3

Horizontal line: y = 6.

the expression is

(a+b)^2=a+b^2

substitute a=1 and b=1

(1+1)^2 = 1+1^2

4=2

that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.

now substitute a=0, b=1

(0+1)^2 = 0+1^2

1=1

so this is true for the above expression.

now for a=-1, b=1

(-1+1)^2 = -1+1^2

0=0

this is true.

now for a=-1, b=2

(-1+2)^2 = -1+2^2

1=3

that is not possible

so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.

ANSWER :

49f and 7(f + 6f)

EXPLANATION :

From the problem, we have :

When multiplied, it will be 49f

When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)

The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.

So the only expressions that are equivalent to the given expression are 1 and 2

The Solution:

Let's solve with the Factoring Method:

Solving by the Completing the Square:

Take the square root of both sides.

Therefore, the answers is:

Answer:

Expected value = 2.21

Explanation:

The formula to obtain the expected value is given by:

We will proceed to calculate the given scenario as given below:

Therefore, the expected value of this scenario is 2.21