On average, Cody runs 4 miles in 38 minutes. How fast should he plan to run a 10-mile race if he maintains this pace?

1. Find the inverse of the one-to-one function f(x)= 6x-7 / 5

Elenna [48]

Rewrite it as y=6x-7/5

Flip the x and y
x=6y-7/5

Solve
5x=6y-7
5x+7=6y
5/6x+7/6=y

f^-1(x)=5/6x+7/6

4 0

3 years ago

Cesar had a part-time job last year. He worked every week for the year and made $23 an hour. He worked 28 hours each week. Cesar

Naddika [18.5K]

Answer:

D. $2,511

Step-by-step explanation:

First off, we need to write down the facts we know.

There are about 52.177 weeks in a year

Cesar works 28 hours each week

Cesar makes $23 an hour

There are 12 months in a year

Cesar has $3,360 after his monthly expenses

To figure out how many hours are in a "work year," multiply the number of work hours in a week by the number of weeks in a year. In other words, multiply Cesar's 28 hour work week by about 52.177 weeks. That makes 1,456 hours in his work year. That means he makes $33,492 a year. If you multiply $2,511 by the months in a year (12), you get $30132. Finally, subtract his annual salary by $30132 to get $3,360, which is what was left of Cesar's earnings after paying all of his monthly expenses.

5 0

3 years ago

Read 2 more answers

5-year Treasury bonds yield 5%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-year bonds is 0.4%.

Eddi Din [679]

Answer:

real risk-free rate = 2.7 %

Step-by-step explanation:

Given data

Treasury bonds yield r = 5%

time = 5 year

(IP) = 1.9%

MRP = 0.4%

to find out

real risk-free rate r*

solution

we will find real risk-free rate r* by the given formula that is

Treasury bonds yield = real risk-free rate + IP + MRP + default risk premium + liquidity premium

so here default risk premium and liquidity premium both are zero

put all the other value we get real risk-free rate

real risk-free rate = 5% - 1.9 % - 0.4%

real risk-free rate = 2.7 %

3 0

4 years ago

Jamie runs a math-tutoring program. For each student, she charges an enrollment fee of $63.00 plus $18.00 per hour of tutoring.

Tamiku [17]

Answer:

The best and most correct answer among the choices provided by your question is the third choice or letter C. The total number of hours is 17.

For h>7

C=210+20(h-7)

C=210+20h-140

C=20h+70, h>7

410=20h+70

20h=340

h=17 hours

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7 0

2 years ago

The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74. 32 inches2, w

Lelu [443]

The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

<h3>How can we interpret volume of a solid?</h3>

Volume of a solid is usually expressed in cubic units, or units cube.

Suppose that the volume was expressed in x cubic units. Then you can say that the considered solid takes same space as the volume occupied by x cubes of 1 unit as their side lengths.

<h3>What are similar objects?</h3>

They're like zoomed version of each other(might be non-zoomed, zoomed in, or zoomed out). Their sides can be obtained by multiplying one object's sides by a single constant(by single constant, we mean constant which will be same for obtaining any corresponding side).

For the given case, we're given that:

Volume of first solid = 729 cubic inches.
Volume of second solid = 125 cubic inches.

Both solids are similar.

Thus, let the scale factor by which their sides change be 'f'.

Then, we get:

Side of first solid = f × side of second solid

Surface area of first solid(a square piece chosen on its surface) = f × f × surface area of second solid

(as two times sides multiplied, so two times f got multiplied).

Similarly,

volume of first solid = f × f × f × volume of second solid.

Or

$729 = f^3 \times 125\\f = \: ^3\sqrt{\dfrac{729}{125}} = \dfrac{9}{5} = 1.8$

As surface area of smaller solid(second solid is smaller as its volume is less) is 74.32 sq. inches, and f = 1.8, thus, we get:

$S_{\text{larger solid}} = f^2 \times S_{\text{smaller solid}} = (1.8)^2 \times 74.32\\S_{\text{larger solid}} = 240.7968 \approx 240.80 \: \rm inch^3$

Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

Learn more about volume and surface area here:

brainly.com/question/2952465

8 0

2 years ago