All categories

2 years ago

Please help me with this question.

Mathematics

1 answer:

Arturiano [62]2 years ago

7 0

Answer:

Monica = 48.50

Samuel = 24.25

Kara = 17.25

Step-by-step explanation:

First you write equations as you are reading the text:

m = 2s ("Monica earned twice as much as Samuel")

s = k+7 ("Samual earned 7 more than Kara")

m = 48.50

Next, you convert these equations to solve for s and k respectively.

So, if m=2s, then s=m/2:

s = m/2 = 24.25

Likewise, if s=k+7, then k=s-7

k = s-7 = 17.25

The difference between greatest and least is 48.50 - 17.25 = 31.25

You might be interested in

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 1

Nuetrik [128]

Answer:

attached

Step-by-step explanation:

attached

Download docx

8 0

2 years ago

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

2 years ago

You deposit $3000 into a bank account that pays 1.25% annual interest, compounded semi-annually. What is the final balance after

mojhsa [17]

Answer:

$3,153.32

Step-by-step explanation:

Given that

The deposited amount is $3,000

The annual interest rate is 1.25%

So, the semi-annual interest rate is 1.25% ÷2 = 0.625%

And, the time period = 4 × 2 = 8

We need to find out the final balance

So,

As we know that

Future value = Present value × (1 + rate of interest)^number of years

= $3,000 × (1 + 0.625%)^8

= $3,153.32

8 0

3 years ago

You rode your bike 27 miles during the last month. Your total travel time was 3 hours. What was your average speed in miles per

JulsSmile [24]

You divide 27 by 3 which equal 9

27÷3=9

5 0

3 years ago

Read 2 more answers

Solve the following equation: -2|3-4x|=10x

max2010maxim [7]

Answer:

I have to get the answer above hope it helps

5 0

2 years ago

Please help me with this question.​

Please help me with this question.