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3 years ago

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You have 2 bags of brightly colored gumballs. The first bag contains 9 balls, and the second bag contains 5 balls. How many poss

ible ways can you draw 2 gumballs at random, 1 from each bag?

1 answer:

lapo4ka [179]3 years ago

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Arlene is showing her work in simplifying −7.9 + 8.2 − 3.4 + 2.1. Identify any errors in her work or in her reasoning. Write fee

NemiM [27]

Step 1 it says Additive inverse, that is not additive inverse. Additive inverse is the opposite of a number. There is no opposite number in the problem. And step 5 is the answer, it shouldn't be simplify. Hope that helps! <span />

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2 years ago

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What is 17728272×93738383?

Olegator [25]

Answer:

1.6618196e+15

Step-by-step explanation:

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2 years ago

Graph the line y = 6

Eva8 [605]

Horizontal line through 6 on the y-axis

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2 years ago

Please help<br><br> In which table does y vary directly with x?

grigory [225]

Answer:

Table D

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

<em>Table A</em>

For x=1, y=3

Find the value of k

$k=y/x$ -----> $k=3/1=3$

For x=2, y=9

Find the value of k

$k=y/x$ -----> $k=9/2=4.5$

the values of k are different

therefore

The table A not represent a direct variation

<em>Table B</em>

For x=1, y=-5

Find the value of k

$k=y/x$ -----> $k=-5/1=-5$

For x=2, y=5

Find the value of k

$k=y/x$ -----> $k=5/2=2.5$

the values of k are different

therefore

The table B not represent a direct variation

<em>Table C</em>

For x=1, y=-18

Find the value of k

$k=y/x$ -----> $k=-18/1=-18$

For x=2, y=-9

Find the value of k

$k=y/x$ -----> $k=-9/2=-4.5$

the values of k are different

therefore

The table A not represent a direct variation

<em>Table D</em>

For x=1, y=4

Find the value of k

$k=y/x$ -----> $k=4/1=4$

For x=2, y=8

Find the value of k

$k=y/x$ -----> $k=8/2=4$

For x=3, y=12

Find the value of k

$k=y/x$ -----> $k=12/3=4$

All the values of k are equal

therefore

The table D represent a direct variation or proportional relationship

The linear equation is $y=4x$

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3 years ago

Read 2 more answers

If the gradient of the tangent to

Marizza181 [45]

Answer:

Point A(9, 3)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

<u>Algebra I</u>

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em /> $\displaystyle y = \sqrt{x}$ <em />

<em /> $\displaystyle y' = \frac{1}{6}$ <em />

<em />

<u>Step 2: Differentiate</u>

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{2}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}$
Simplify: $\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x}}$

<u>Step 3: Solve</u>

<em>Find coordinates of A.</em>

<em />

<em>x-coordinate</em>

Substitute in <em>y'</em> [Derivative]: $\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}$
[Multiplication Property of Equality] Cross-multiply: $\displaystyle \sqrt{x} = 3$
[Equality Property] Square both sides: $\displaystyle x = 9$

<em>y-coordinate</em>

Substitute in <em>x</em> [Function]: $\displaystyle y = \sqrt{9}$
[√Radical] Evaluate: $\displaystyle y = 3$

∴ Coordinates of A is (9, 3).

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

Unit: Derivatives

Book: College Calculus 10e

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3 years ago