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3 years ago

5

Ankit makes 74% of the free throws he takes in his basketball league. If he is fouled on a three-point shot and gets three free

throws, what is the approximate probability he will make all three shots?

1 answer:

meriva3 years ago

7 0

Answer: 40.5%

Step-by-step explanation:

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Beth is selling tickets for a dinner at her school.

iren [92.7K]

Answer:

D

Step-by-step explanation:

check each child answer and multiply by 4.50

check each adult answer and multiply by 6.00

add both answers up

and see which one it is

its not A, B, or C

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3 years ago

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A store buys a jacket for $20.00 and sells it to customers for 80% more than that. What is the selling price of the jacket

Tamiku [17]

38 because 80% of 20 is 18 and then add the 2

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3 years ago

Substitution to evaluate the indefinite integral

gregori [183]

Answer:

$\displaystyle \int {e^{5x}} \, dx = \boxed{ \frac{e^{5x}}{5} + C }$

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$
Derivative Rule [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 Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

$\displaystyle \int {e^{5x}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

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

Set <em>u</em>:
$\displaystyle u = 5x$
[<em>u</em>] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = 5 \ dx$

<u>Step 3: Integrate Pt. 2</u>

[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\\end{aligned}$
[Integral] Apply Integration Method [U-Substitution]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\\end{aligned}$
[Integral] Apply Exponential Integration:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\\end{aligned}$
[<em>u</em>] Back-substitute:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\& = \boxed{ \frac{e^{5x}}{5} + C } \\\end{aligned}$

∴ we have used substitution to <em>evaluate</em> the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27593180

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

Unit: Integration

3 0

2 years ago

Reflection followed by a dilation, congruent or similar?

ddd [48]

Answer:

<h2>similar</h2>

Step-by-step explanation:

it'll be a different size and that wouldn't matter because it would still have the same area

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3 years ago

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Which pair of triangles is Alessandra referring to, and which criterion should she use for establishing congruence?

Doss [256]

Answer:

△ABCtriangle and △CDAtriangle, by side-angle-side

Step-by-step explanation:

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3 years ago