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Greeley [361]
3 years ago
11

Solve the system by substitution. y = 4x + 3 y = 72

Mathematics
1 answer:
Sever21 [200]3 years ago
4 0

Answer:

17.25

Step-by-step explanation:

You already know y = 72, so you could rewrite the equation to 72 = 4x + 3. To get to the answer, you need to find what X is. What you should do is subtract 3 from both sides, get 69, divide by 4 on both sides and get 17.25

I'm not sure if this is correct, but I hope this helped.

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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

5 0
3 years ago
The nth term of a sequence is given by 3n² + 11 Calculate the difference between the 6th term and the 9th term of the sequence.​
katovenus [111]

The difference between the 6th term and the 9th term of the sequence is 135

<h3>How to determine the difference</h3>

Given that the nth term is;

3n² + 11

For the 6th term, the value of n is 6

Let's solve for the 6th term

= 3( 6)^2 + 11

= 3 × 36 + 11

= 108 + 11

= 119

For the 9th term, n = 9

= 3 (9)^2 + 11

= 3( 81) + 11

= 243 + 11

= 254

The difference between the 6th and 9th term

= 254 - 119

= 135

Thus, the difference between the 6th term and the 9th term of the sequence is 135

Learn more about algebraic expressions here:

brainly.com/question/4344214

#SPJ1

4 0
2 years ago
What is 8 1/2 x 3 = <br>please help​
ludmilkaskok [199]

Answer:

C

Step-by-step explanation:

Convert 8 1/2 to 17/2 and this multiplied by 3 is 51/2. Convert it back to mixed fraction to get 25 1/2.

4 0
3 years ago
What is the best estimate for the product of 289 and 7
navik [9.2K]
The answer is 296 hope it helps
5 0
3 years ago
Evaluate: -8 over 9 + 4 over 9 - 2 over 9
stepan [7]
The answer is -2/3 from the solution above

4 0
3 years ago
Read 2 more answers
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