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3 years ago

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there is 90 5th grade students going on a field trip. each student gives the teacher $9.25 to cover admission to the theater and

for lunch. admission for all of the students will cost $315, and each student will get an equal amount to spend on lunch. how much will each fifth grader get to spend on lunch

1 answer:

Allisa [31]3 years ago

5 0

(9.25x90-315)/90
(832.5-315)/90
517.5/90
5.75

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Scores on a test have a mean of 78.2 and 8 percent of the scores are above 89. The scores have a distribution that is approximat

anyanavicka [17]

Answer:

The standard deviation is 7.7

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 78.2$

8 percent of the scores are above 89

This means that X = 89 has a pvalue of 1 - 0.08 = 0.92. So when Z = 89, Z = 1.405.

$Z = \frac{X - \mu}{\sigma}$

$1.405 = \frac{89 - 78.2}{\sigma}$

$1.405\sigma = 10.8$

$\sigma = \frac{10.8}{1.405}$

$\sigma = 7.7$

The standard deviation is 7.7

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4 years ago

A band expects to put 12 songs on their next CD. The band writes and records 25% more songs than they expect to put on the CD.

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4 years ago

Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.

scoray [572]

Answer:

6075

Step-by-step explanation:

Given series is: 25 + 30 + 35 + ⋯ + 245.

Here, first term (a) = 25
Common difference (d) = 5
Last term $(a_n) = 245$

First we find the number of terms that this series has by the following formula:

$a_n = a+(n-1)d$

Plugging the values of a, d and $a_n$ , we find.

$245 = 25+(n-1)5$

$\implies 245 - 25=(n-1)5$

$\implies 220=(n-1)5$

$\implies \frac{220}{5}=n-1$

$\implies 44=n-1$

$\implies 44+1=n$

$\implies\red{\bold{ n=45}}$

Thus, the given series contains 45 terms.

Next, we find the sum of the given series using the formula given below.

$S_n = \frac{n}{2}(a+a_n)$

$\implies S_{45}= \frac{45}{2}(25+245)$

$\implies S_{45}= \frac{45}{2}(270)$

$\implies S_{45}=45*135$

$\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}$

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