The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?

Amount in Juanita’s Savings Account
Number of Months Working at Part-Time Job
0
2
4
6
8
Amount in Savings Account (in dollars)
$36
$60
$84
$108
$132

Answer:

[tex]y=\dfrac{10}{3}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac25\right)^{-3} \cdot\left(\dfrac52\right)^{-15} =\left(\dfrac25\right)^{2+3y}[/tex]

[tex]\textsf{Using exponent rule:}\left(\dfrac{a}{b}\right)^{-c} =\left(\dfrac{b}{a}\right)^{c}[/tex]

[tex]\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25\right)^{2+3y}[/tex]

[tex]\textsf{Using exponent rule: } a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}[/tex]

[tex]\implies \left(\dfrac25\right)^{12} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}[/tex]

[tex]\implies \left(\dfrac25\right)^{12} \div\left(\dfrac25}\right)^2 =\left(\dfrac25\right)^{3y}[/tex]

[tex]\textsf{Using exponent rule: } \dfrac{a^b}{a^c}=a^{b-c}[/tex]

[tex]\implies \left(\dfrac25\right)^{10} =\left(\dfrac25\right)^{3y}[/tex]

[tex]\textsf{Using exponent rule: } a^b=a^c \implies b=c[/tex]

[tex]\implies 10=3y[/tex]

[tex]\implies y=\dfrac{10}{3}[/tex]

Answer:

5 people

Step-by-step explanation:

1/10 meaning for every 10 people there will be 1 person with red hair.

50 people is 10×5=50

also do it to the 1: 1×5=5

then we get a ratio of 5/50

5/50 reduced is still 1/10

Answer: 5

Step-by-step explanation:

Answer:

26.6%

Step-by-step explanation:

total = 75 games

number of games won = 55

number of games lost = 75 - 55 = 20

75 — 100%

20 — x%

x = 20/75 * 100 = 26.6%

Answer:73.33%

Step-by-step explanation: If you do 55/75 you will get 0.73 repeating and you would move the decimal place 2 places to the right.

Answer:

8.7388

Step-by-step explanation:

square root of 5832=76.37

square root of 76.37= 8.73

8.7388 x 8.7388 x 8.7388 x 8.7388

Answer:

4 years

Step-by-step explanation:

Sara saved $16,000 for a new car that costs $10,500, plus $1200 each year for insurance.

Let the number of years she can pay for insurance be written as: x

$10,500 + $1200 × x = $16,000

$1200 × x = $16,000 - $10,500

x = $5,500/1200

x = 4.5833333333 years

Since the number of years is in decimal, we would pick the whole number there as the maximum number of years.

Therefore, the maximum number of years, x, she could pay insurance with her current savings is 4 years.

Answer:

[tex]\displaystyle 3x - y = 19\:or\:y = 3x - 19[/tex]

Step-by-step explanation:

Plug the information into the Slope-Intercept Formula:

[tex]\displaystyle 5 = 3[8] + b \hookrightarrow 5 = 24 + b; -19 = b \\ \\ y = 3x - 19[/tex]

Suppose you need to write this equation in standard form. You would follow these procedures:

y = 3x - 19

- 3x - 3x

__________

[tex]\displaystyle -3x + y = -19[/tex]

*Now, you can leave the standard equation like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

[tex]\displaystyle \boxed{3x - y = 19}[/tex]

I am joyous to assist you at any time.

Answer:

Its A women

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

I think combining like terms

Step-by-step explanation:

Answer: 8/9

Step-by-step explanation:

First, we can find a common denomiator.

The least common multiple of 2, 9, and 6 is 18.

Therefore, the lcd is 18.

1/2 = 1/2 * (9/9) = 9/18

2/9 = 2/9 * (2/2) = 4/18

1/6 = 1/6 * (3/3) = 3/18

Therefore, 1/2 + 2/9 + 1/6 = 9/18 + 4/18 + 3/18.

We can add the numerators together.

= 16/18

Divide the nuumerator and denominator by 2:

= 8/9

Answer:

I don't clearly understand your question pls can you rearrange it to a simpler form

Answer:

yo I'm looking for the same answer I need it ASAP before Friday

Answer:

g=7

Step-by-step explanation:

10g–7g–3=18

subtract 7g from 10 g

3g-3=18

add 3 to both sides

3g=21

divide each side by 3

g=7

Answer:

g=7

Step-by-step explanation:

We move all terms to the left:

10g-7g-3-(18)=0

We add all the numbers together and all the variables

3g-21=0

We move all the terms containing "g" to the left and all the other terms to the right

3g=21

g=27/3

which is the same as

g=3

Answer:

3 feet

Step-by-step explanation:

To begin, find the width of the first painting by dividing 32 by 4. You get 8 feet as the width. Since the second painting has a width of 8, divide 24 by 8 to get the length (area of a rectangle is length times width). You get that the length of the second painting is 3 feet.

Hopefully this helps- let me know if you have any questions!

Answer:

X = 10

Step-by-step explanation:

if we say 1/2 base = a

a² = 13² - 12²

a² = 25

a = √25

a = 5

if 1/2 base = 5 then x = a × 2

hence X = 5 × 2 = 10

The number is 6.4.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

Five Times the difference of a number and 3 is 17.

let the number be x

So,

5(x-3) = 17

5x - 15 = 17

5x = 32

x= 32/5

x= 6.4

Learn more about algebra here:

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Answer:

see below

Step-by-step explanation:

given function: [tex]Cos(x)=\frac{1}{3}[/tex]

Cosine - (In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.)

#1: Take the inverse cosine of both sides of the equation to extract [tex]x[/tex] from inside the cosine.

[tex]x=arccos\frac{1}{3}[/tex]

#2: Evaluate

[tex]x=1.23095941[/tex]

#3: The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from [tex]2[/tex]π to find the solution in the fourth quadrant.

[tex]x=2(3.14159265)-1.23095941[/tex]

#4: Simplify the equation above.

- Multiply [tex]2[/tex] by [tex]3.14159265[/tex]

[tex]x=6.2831853-1.23095941[/tex]

- Subtract [tex]1.23095941[/tex] from [tex]6.2831853[/tex]

[tex]x=5.05222588[/tex]

#5: Find the period.

- The period of the function can be calculated using [tex]\frac{2\pi }{|b|}[/tex].

[tex]\frac{2\pi }{|b|}[/tex]

- Replace [tex]b[/tex] with [tex]1[/tex]  in the formula for period.

[tex]\frac{2\pi }{|1|}[/tex]

#6: Solve the equation.

- The absolute value is the distance between a number and zero. The distance between [tex]0[/tex] and [tex]1[/tex] is [tex]1[/tex].

[tex]\frac{2\pi }{1}[/tex]

- Divide [tex]2\pi[/tex] by [tex]1.[/tex]

[tex]2\pi[/tex]

The period of the [tex]cos(x)[/tex] function is [tex]2\pi[/tex] so values will repeat every [tex]2\pi[/tex] radians in both directions.

[tex]x=1.23095941+2\pi n,5.05222588+2\pi n[/tex], for any integer [tex]n[/tex]

Answer:

I need help with mathematics please

Answer:

x = 24; x = 25

Step-by-step explanation:

Question 1

x/4 = 6

x = 24  *multiply both sides by the denominator to isolate the x value

Question 2

x/2 = 12.5

x = 25 *multiply both sides by the denominator to isolate x

Answer:

Z=1

Step-by-step explanation:

please mark me as brainlest

Answer:

z = 1

Step-by-step explanation:

Given :-

12 = 15(z - 1/5)

To Find :

z

Solving :-

12 = 15(z - 1/5)

12 = 15z - 3

15z = 15

Solution :-

z = 1

Answer:

i dont understand either

Step-by-step explanation:

A normally distributed set of data has been generated where 50% of the data lies below 97 and 70% lies below 104. Then, mean of the data is equal to 97 and standard deviation is equal to 13.358.

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that 50% of the data lies below 97, implies that median of the data is equal to 97. In a normal distribution, mean = median = mode, therefore, mean = 97.

Given the mean and value at 70th percentile, we can find the standard deviation.

Using the z score - percentile table, we find that the z score corresponding to the given percentile.

z score corresponding to 70th percentile = 0.524

[tex]0.524 = \frac{x - mean}{standard\ deviation}\\ \\0.524 = \frac{104 - 97}{standard\ deviation} \\\\standard\ deviation = \frac{7}{0.524} = 13.359[/tex]

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Answer: a=36pi

Step-by-step explanation:

We know that the formula for the area of a circle is a=(pi)(r)^2

Knowing that the diameter is 12 we can find the radius is 6 as the radius is half of the diameter. Now we can plug that into the equation. a=pi*6^2

Simplify

a=36pi

Answer:

F

Step-by-step explanation:

75.00-67.50 is 7.5

8-6 is 2

7.5/2 is 3.75

Answer:

x = 6

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle. Sum the 3 sides and equate to 51, that is

15 + 5x - 6 + 2x = 51

7x + 9 = 51 ( subtract 9 from both sides )

7x = 42 ( divide both sides by 7 )

x = 6

The circumference of the outer edge of the path around the pool is 113.04 ft.

The Circumference (or) perimeter of circle = 2πR. where, R is the radius of the circle.

Given

A circular swimming pool has a radius of 15 ft.

There is a path all the way around that pool that is three feet wide.

A circle has a radius of 15 feet.

A larger circle goes around the smaller circle that is 3 feet wide.

The radius of the outer edge of the path around the pool = Radius of circle + width of outer circle.

The radius of the outer edge of the path around the pool = 15 + 3

The radius of the outer edge of the path around the pool = 18ft

The circumference of the outer edge of the path around the pool is;

[tex]\rm Circumference=2\pi r\\\\Circumference = 2\times 3.14 \times 18\\\\Circumference=113.04 \ ft[/tex]

Hence, the circumference of the outer edge of the path around the pool is 113.04 ft.

To know more about circumference click the link given below.

https://brainly.com/question/5023328

Answer:

-10

Step-by-step explanation:

Hope that helps!!

Answer:

The answer is 41,472

Step-by-step explanation:

We know, that when you find the area of a quadrilateral(4 sided figure) we multiply all of the sides together.