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bogdanovich [222]
3 years ago
7

(2/3) × (2/3) × (2/3)​

Mathematics
1 answer:
s2008m [1.1K]3 years ago
7 0

Answer:

8/27

Step-by-step explanation:

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Write 230% in simplest form
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230% in the simplest form is 2.3

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Which real-world scenario involves a right triangle?
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Putting a ladder up against a straight wall. The sides of the triangle are:
1: the ladder
2: the walls
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3 years ago
Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of
tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A                          Sample B

x_A = 30                              x_B = 50

n_A = 100                             n_B =250

Solving (a): Standard error using formula

First, calculate the proportion of A

p_A = \frac{x_A}{n_A}

p_A = \frac{30}{100}

p_A = 0.30

The proportion of B

p_B = \frac{x_B}{n_B}

p_B = \frac{50}{250}

p_B = 0.20

The standard error is:

SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}

SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}

SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}

SE_{p_A-p_B} = \sqrt{0.00274}

SE_{p_A-p_B} = 0.052

Solving (a): Standard error using bootstrapping.

Following the below steps.

  • Open Statkey
  • Under Randomization Hypothesis Tests, select Test for Difference in Proportions
  • Click on Edit data, enter the appropriate data
  • Click on ok to generate samples
  • Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A                          Sample B

x_A = 23                              x_B = 57

n_A = 100                             n_B =250

p_A = 0.230                          p_A = 0.228

So, we have:

SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}

SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}

SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}

SE_{p_A-p_B} = \sqrt{0.002475064}

SE_{p_A-p_B} = 0.050

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stiv31 [10]
(40-10)/7

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Mrs Herñàndez can take 4 children
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The factored form of 20x+35y would be 5(4x+7y). If you use the distributive property of multiplication, you can see that the expression has not changed. 
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