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2 months ago

12

Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount

of money in the account after x years.
A 2-column table with 5 rows. The first column is labeled years with entries 0, 10, 20, 30, 40. The second column is labeled amount (dollar sign) with entries 10,000; 16,000; 27,000; 43,000; 70,000.
What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?

f(x) =
(
)x

2 answers:

Leona [12.6K]2 months ago

7 0

Response:f(x)= 9,974.73 (1.05)x

babunello [11.8K]2 months ago

3 0

Response:f(x)= 9,974.73 (1.05)x

Step-by-step clarification:

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To reduce wear and tear on the family vehicle, you decide to rent a car. Happy Harry’s Rentals has a $500 fee for any rental up

Inessa [12570]

Assuming a maximum rental duration of 8 days, if we apply this to the equation, Happy Harry's Rentals costs $500, while Smilin' Sam's charges $600. Therefore, for the 7th and 8th days, Happy Harry's Rentals is a better option, while Smilin' Sam's is preferable for the first six days.

8 0

2 months ago

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs

PIT_PIT [12445]

Answer:

The formula to determine the distance Jane's trainer bikes is $x=\sqrt{16^2+12^2}$ .

Detailed explanation:

A diagram has been included for clarity.

Known values:

Distance biked to the south = 16 miles

Distance ran west = 12 miles

We need to determine the distance covered by Jane's trainer.

Solution:

Let the biking distance be represented by 'x'.

We will assume it forms a right-angled triangle.

According to the Pythagorean theorem, it states that;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides."

When set in equation form, this gives us;

$x^2=16^2+12^2\\\\x=\sqrt{16^2+12^2}$

Thus, the equation representing the distance biked by Jane's trainer is $x=\sqrt{16^2+12^2}$ .

Upon solving, we find;

$x=\sqrt{16^2+12^2}\\\\x= \sqrt{256+144}\\ \\x=\sqrt{400} \\\\x=20\ miles$

Consequently, Jane's trainer covers a distance of 20 miles.

7 0

1 month ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

Inessa [12570]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

5 0

3 months ago

Read 2 more answers

Josh needs to cover a rectangular opening of 12 inches × 18 inches with plywood. how much will he need, in square feet, if he wa

tester [12383]

We understand that

1 foot corresponds to 12 inches.

Step 1

Dimensions of the plywood needed are

(12+3+3) x (18+3+3)------> 18 inches x 24 inches.

Step 2

Convert inches into feet:

18 in-------> 18/12=1.5 ft.

24 in------> 24/12=2 ft.

Step 3

To calculate the area of plywood needed:

A=b*h------> 1.5*2------> A=3 ft².

The final result is

3 ft²

5 0

3 months ago