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3 years ago

13

Your parents allow you to have Internet access on your cell phone as long as you prepay the bill. If your bill is $17.50 per wee

k, how much would you have to save per day to pay the bill? Describe the step-by-step process you use to solve the problem

1 answer:

Darina [25.2K]3 years ago

5 0

Answer:

2.5 dollars a day

Step-by-step explanation:

17.5 /7 in calculator

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(7x-14)<br> (4x + 19)<br> What’s the value of x

erastovalidia [21]

Answer:

Step-by-step explanation:

( 7x - 14 ) ( 4x + 19 )

28x^2 - 133x - 56x - 416

= 28x^2 - 189x - 416

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4 years ago

6. April works as an emergency medical technician (EMT) and is a photographer. As an EMT she earns $19 per

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Answer: 19t +100

Step-by-step explanation:

19t +100 where t is the number of hours she worked and the extra 100 dollars is the money she got from her friend.

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4 years ago

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Luca has a box of dog toys. There are 3 bones, 5 balls, and a stuffed animal. What is the ratio of balls to stuffed animals?

Anna007 [38]

The answer would be D. 1:5 since there is 1 stuffed animal and 5 balls.

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3 years ago

Area of the bounded curves y=x^2, y=√(7+x)

N76 [4]

Answer:

$\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

U-Substitution

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

<u>Step 1: Define</u>

$\displaystyle \left \{ {{y = x^2} \atop {y = \sqrt{7 + x}}} \right.$

<u>Step 2: Identify</u>

<em>Graph the systems of equations - see attachment.</em>

Top Function: $\displaystyle y = \sqrt{7 + x}$

Bottom Function: $\displaystyle y = x^2$

Bounds of Integration: [-1.529, 1.718]

<u>Step 3: Integrate Pt. 1</u>

Substitute in variables [Area of a Region Formula]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \int\limits^{1.718}_{-1.529} {x^2} \, dx$
[Right Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \frac{x^3}{3} \bigg| \limits^{1.718}_{-1.529}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - 2.88176$

<u>Step 4: Integrate Pt. 2</u>

<em>Identify variables for u-substitution.</em>

Set <em>u</em>: $\displaystyle u = 7 + x$
[<em>u</em>] Basic Power Rule [Derivative Rule - Addition/Subtraction]: $\displaystyle du = dx$
[Limits] Switch: $\displaystyle \left \{ {{x = 1.718 ,\ u = 7 + 1.718 = 8.718} \atop {x = -1.529 ,\ u = 7 - 1.529 = 5.471}} \right.$

<u>Step 5: Integrate Pt. 3</u>

[Integral] U-Substitution: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{8.718}_{5.471} {\sqrt{u}} \, du - 2.88176$
[Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = \frac{2x^\Big{\frac{3}{2}}}{3} \bigg| \limits^{8.718}_{5.471} - 2.88176$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 8.62949 - 2.88176$
Simplify: $\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773$

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

Unit: Integration

5 0

3 years ago

A set of data has 50 observations. How many classes would you recommend?

nignag [31]

Answer:

6 classes

Step-by-step explanation:

If k is the number of classes and n is the number of observations, then for number of classes we should select the smallest k such that 2^k > n.

<u>We have n = 50 and:</u>

2^5 = 32 < 50
2^6 = 64 > 50

As per above described 2 to k rule, we are taking k = 6.

So 6 classes should be used.

6 0

3 years ago