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sladkih [1.3K]
3 years ago
12

Peter and Flopsy are Mairies pet bunnies. Peter is one year older than four times Flopsy's age. The sum of their ages is 19. How

old is each bunny ?
Mathematics
1 answer:
amm18123 years ago
5 0

Answer: See explanation

Step-by-step explanation:

Let Flopsy's age be represented by x.

Therefore, since Peter is one year older than four times Flopsy's age. Peter's age will be:

= (4 × x) + 1

= 4x + 1

We are further told that the sum of their ages is 19. This will be:

x + 4x + 1 = 19

5x + 1 = 19

5x = 19 - 1

5x = 18

x = 18/5

x = 3.6 years

Flopsy's age = 3.6 years

y = 4x + 1

= 4(3.6) + 1

= 14.4 + 1

= 15.4 years

Peter's age = 15.4 years

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Now, we will determine the mass of the object

F = 15 N

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Putting the parameters into the formula, we get

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The mass of the object is 5 kg.

Now, to determine the force the same object will exert if it accelerates at a rate of 7 m/s²

That is,

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and

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Learn more here: brainly.com/question/13590154

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How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has l
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Answer:

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - <em>α</em>) % confidence interval for population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The margin of error in this interval is:

MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

The formula to compute the sample size is:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}

(1)

Given:

\hat p = 0.50\\MOE=0.1\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.1^{2}}\\=96.04\\\approx97

Thus, the minimum sample size required is 97.

(2)

Given:

\hat p = 0.50\\MOE=0.05\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.05^{2}}\\=384.16\\\approx385

Thus, the minimum sample size required is 385.

(3)

Given:

\hat p = 0.50\\MOE=0.01\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use the <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.01^{2}}\\=9604

Thus, the minimum sample size required is 9604.

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