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Natasha2012 [34]

3 years ago

14

Bill earns $12 per hour and works at most 40 hours per week. Identify the independent and dependent quantity in the situation, a

nd find reasonable domain and range values.

2 answers:

inessss [21]3 years ago

8 0

hours worked; amount of money earned; 0 to 40; $0 to $480

sesenic [268]3 years ago

3 0

Independent: number of hours worked
Dependent: income earned
Domain: between 0 and 40 hours
Range: between 0 and 480$

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Yolanda is planning out her square vegetable garden. One side 7 feet. How

Elan Coil [88]

Well if it’s a square all sides are equal, so all sides are 7ft.

Perimeter=
7+7+7+7=28ft
Or
7•4=28

Hope this helps!!!

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The number of people contacted at each level of a phone tree can be represented by f(x) = 3x, where x represents the level.What

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4 years ago

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Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at

Anna007 [38]

Answer:

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

Step-by-step explanation:

Loan payment per month=Amount to pay÷discount factor

Mathematically P=A÷D

where D is the discount factor calculated using the formula;

$\frac{(1+i)^n-1}{i(1+i)^n}$

where i=periodic interest rate=annual rate divided by number of payment periods

A is the amount to pay after downpayment

P is the loan monthly payment amount

n=number of periodic payments=payments per year times number of years

⇒In this question you find the discount factor then divide the amount remaining to pay with the discount factor to get monthly payments

Given;

Cost of boat=$32000

Down payment=$14000

Loan to pay=$32000-$14000=$18000

Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458

Periodic payments, n=4×12=48

Finding the discount factor D;

$D=\frac{(1+i)^n-1}{i(1+i)^n} \\\\\\D=\frac{(1+0.00458)^{48} -1}{0.00458(1+0.00458)^{48} } \\\\\\D=\frac{1.2455-1}{0.005703} \\\\\\D=\frac{0.2455}{0.005703} =43.05$

To get the amount to pay monthly divide the loan to pay with the discount factor

$=\frac{18000}{43.05} =418.14$

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

8 0

3 years ago

If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

<u>Step 2: Differentiate</u>

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

3 years ago

What percent of the first 10 natural numbers are prime numbers? Answer in a percent please.<br> :)

saul85 [17]

So the first 10 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Since a prime number is only divisible by 1 and itself and greater than 1, our answers are 2, 3, 5, and 7. That's 4 numbers, or 4/10=0.4 of the 10. Since percentage is based out of 1, we can multiply 0.4 by 100 to get 40%. I hope that Helped :)

6 0

3 years ago