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2 years ago

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Kerry invited 23 friends to his pool party. They played a game where everyone had to separate into groups. Each group had the sa

me number of children. The game could not be played with all 24 children in one group, and each group had to have more than 2 children.
Which of the following are ways that they could divide into groups? Select all that apply.

A.
They can form 4 groups of 6.

B.
They can form 12 groups of 2.

C.
They can form 8 groups of 3.

D.
They can form 4 groups of 9.

E.
They can form 2 groups of 12.

1 answer:

Alex17521 [72]2 years ago

6 0

Answer:

A, C, and E are the answers

Step-by-step explanation:

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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

How many solutions does this equation have 3x-2x+4=2+x+2

ch4aika [34]

If you simply it down you get
$x + 4 = x + 4$
so X can technically be any number

8 0

3 years ago

Solve 6^x+2 = 10 for x using the change of base formula

pashok25 [27]

Answer:

$x\approx-0.7149$

Step-by-step explanation:

$\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149$

Recall that the change of base formula is $\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}$

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2 years ago

Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles

Bas_tet [7]

Answer:

a) We reject H₀ We find difference between the mean of the two groups

b) we accept H₀ : There is no statistical difference ( in the scale of pain) when the difference in samples means is 1

Step-by-step explanation:

Group 1: Only with educational material

Sample size n₁ = 42

Sample mean x₁ = 3,2

Sample standard deviation s₁ = 2,3

Group 2: With exercises with the treatment of individuals

Sample size n₂ = 42

Sample mean x₂ = 5,2

Sample standard deviation s₂ = 2,3

Test Hypothesis

Null Hypothesis H₀ x₂ - x₁ = 0 or x₁ = x₂

Alternative Hypothesis Hₐ x₂ - x ₁ > 0 or x₂ > x₁

Significance level α = 0,01

Sample sizes are n₁ = n₂ > 30

We use z-test

for α = 0,01 z(c) ≈ 2,32

To calculate z(s)

z(s) = ( x₂ - x₁ ) / √ (2,3)²/42 + (2,3)²/42

z(s) = ( 5,2 - 3,2 )/ √0,2519

z(s) = 2 / 0,5

z(s) = 4

Comparing z(s) and z(c)

z(s) > z(c)

z(s) is in the rejection region. We reject H₀ the true average pain level for the control condition exceeds that for the treatment condition.

b) Does the true average pain level for the control condition exceed that for the treatment condition by more than 1.

In this case

z( s) = x₂ - x₁ / 0,5

z(s) = 1 /0,5

z(s) = 2

Comparing z(s) and z(c) now

z(s) < z(c) 2 < 2,32

And z(s) is in the acceptance region ( for the same significance level) and we should accept H₀ equivalent to say that the two groups statistical have the same mean

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3 years ago

In the scale drawing, what will the length of the east, south, west, and north side of the backyard be?

Y_Kistochka [10]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers