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babunello [35]
3 years ago
5

George is 4 times Dorothy's age. If George is 56, how old is Dorothy? Let d = Dorothy's age.

Mathematics
2 answers:
Over [174]3 years ago
5 0
D = 56/4
d = 14, because that is one fourth of George's age
Verification:
56 = d x 4
56 = 14 x 4
56 = 56
True
Yuri [45]3 years ago
3 0
4d=56
d=14. Ad a result, Dorothy is 14 years old. Hope it help!
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iren [92.7K]

Answer: 32 room

Step-by-step explanation:

7\frac{3}{4} =\frac{4(7)+3}{4} =\frac{28+3}{4} =\frac{31}{4}=7.75

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Use proportions & cross-multiply to solve:

\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258

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2 years ago
Rita deposits $800 into an account that pays simple interest at a rate of 3% per yearHow much interest will she be paid in the f
grin007 [14]

Answer: $72

Step-by-step explanation:

Simple interest (I) is calculated as Principal × Rate × Time.

From the question, Principal = $800

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2 years ago
In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91
Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that n = 3900, \pi = \frac{1911}{3900} = 0.49

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

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Answer:

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Answer:

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Step-by-step explanation:

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