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alukav5142 [94]
2 years ago
6

Deandre can paint a small room in 6 hours. Deandre and Casey together can paint the same room in 4 hours. How long would it take

for Casey to paint the room alone? Express your answer as a decimal. If necessary, round to the nearest tenth of hour.
Mathematics
1 answer:
Zanzabum2 years ago
5 0

Answer:

Step-by-step explanation:

If D can paint the room in 6 hours, in 1 hour she gets \frac{1}{6} of the room painted;

If C can paint the room in x hours, in 1 hour she gets \frac{1}{x} of the room painted.

It takes 4 hours to paint it together. Setting up the classic work equation gives us

\frac{1}{6}+\frac{1}{x}=\frac{1}{4} and we need to solve for x. Multiply everything through by the LCM which is 12x:

12x(\frac{1}{6}+\frac{1}{x}=\frac{1}{4}) making our equation simplify to

2x + 12 = 3x and solve for x:

12 = x

C can paint the room alone in 12 hours.

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What is 447 times 63.
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Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The
kifflom [539]

Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

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n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

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- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

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The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Hope this Helps!!!

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