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irga5000 [103]
3 years ago
12

A student has a savings account earning 3% simple interest. She must pay $1900 for first-semester tuition by September 1 and $19

00 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1900 between September 1 and January 1? (Round your answer to the nearest cent.)
Mathematics
1 answer:
Anastaziya [24]3 years ago
8 0

Answer:

$3781.19

Step-by-step explanation:

Let us assume that the student has to earn $(1900 + x) by September 1 so that he can pay the $1900 tuition fee by September 1 and the remaining $x will grow at 3% simple interest to make him able to pay another tuition fee of $1900 by January 1.

So, we can write x( 1 + \frac{4 \times 3}{12 \times 100}) = 1900

{Because September 1 to January 1 is 4 months and the monthly simple interest rate is \frac{3}{12}%}

⇒ 1.01x = 1900

⇒ x = $1881.19 (Rounded to the nearest cents)

Therefore, the student has to earn $(1900 + 1881.19) = $3781.19 (Answer)

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a+b+c=68

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3 years ago
A university with a high water bill is interested in estimating the mean amount of time that students spend in the shower each d
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Answer: (4.0845,\ 6.5755)

Step-by-step explanation:

As per given , we have

n = 11

\overline{x}=5.33\\\\ s=1.33

Since population standard deviation is missing, so we use t-test.

Critical t-value for 99% confidence :

t_{\alpha/2,\ n-1}=3.106   [using two-tailed t-value table]

Confidence interval :

\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}\\\\= 5.33\pm (3.1060)\dfrac{1.33}{\sqrt{11}}\\\\\approx5.33\pm1.2455\\\\=(5.33-1.2455,\ 5.33+1.2455)\\\\=(4.0845,\ 6.5755)

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Step-by-step explanation:

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In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system
Contact [7]

Answer:

n=206

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

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The margin of error for the proportion interval is given by this formula:  

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n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.09}{2.58})^2}=205.44  

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