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2 years ago

A collection of quarters and nickels is worth $3.70. There are 22 coins in all. How many of each coin are there?

Mathematics

1 answer:

ladessa [460]2 years ago

3 0

9 numbers of nickels

13 numbers of quarters

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Find the z score that corresponds to P30 (the 30th percentile).

Leokris [45]

Answer:

Step-by-step explanation:

From the standard normal distribution tables it is -0.524.

7 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:

Calculus

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:

Step 1: Define

Identify

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

Step 2: Differentiate

[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

2 years ago

3(2x+6) Distributive Property

Ksivusya [100]

Answer:

6x+18

Step-by-step explanation:

Multiply 3 to all the numbers on the parenthesis

Hope this helps!

7 0

2 years ago

Read 2 more answers

write an equation for the amount of money, m that will be collected if b boxes of chocolate are sold.

Digiron [165]

Answer:

m = b(t)

t= the price per box

4 0

3 years ago

Read 2 more answers

What Is the area of the shaded part???

Aloiza [94]

Answer: The area of the shaded region is 27.74 centimeters squared

Step-by-step explanation: The diagram shows a two-in-one figure, a circle inscribed in a rectangle. The shaded region is the part of the rectangle not covered by the circle, hence we would have to subtract the area of the circle from that of the rectangle.

Area of Rectangle = L x W

Area of rectangle = 8 x 7

Area of rectangle = 56

Also,

Area of circle = Pi x r^2

Area of circle = 3.14 x 3^2

Area of circle = 3.14 x 9

Area of circle = 28.26

Area of shaded region is given as area of rectangle minus area of circle

Therefore, shaded region = 56 - 28.26

Area of shaded region = 27.74 centimeters squared

3 0

3 years ago