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MatroZZZ [7]
3 years ago
12

A contractor can spend at most $250 a day on operating costs and payroll. It costs $45 each day to operate the forklift and $60

a day for each crew member. Write an inequality to represent the contractor's budget for the day.
Mathematics
2 answers:
GREYUIT [131]3 years ago
8 0

Answer:

Step-by-step explanation:

The answer is B. His budget is $250 so it has to be less than or equal to. $60 a crew member (x = the crew members) and $45 to use the forklift, so $60x + $45 is less than or equal to $250

OLga [1]3 years ago
5 0

Answer:

B is the correct answer.

Step-by-step explanation:

According to the problem, the contractor can spend AT MOST $250 a day, meaning $250 is the limit. Therefore, that gives you less than or equal too, or ≤. Next, it costs $45 a day, including $60, which you would add to get the final amount, or +.

Therefore, 60x + 45 ≤ 250

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jolli1 [7]

Answer:

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

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When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.

This means that:

p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247

Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.

This means that:

p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234

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s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034

Confidence interval:

The confidence interval is:

p \pm zs

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z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower bound is 0.45 - 1.96(0.034) = 0.3834

The upper bound is 0.45 + 1.96(0.034) = 0.5166

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

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