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yKpoI14uk [10]
2 years ago
9

Suppose you always eat a particular brand of cookies out of the standard sized package it comes in from the store. You notice th

at when you eat 3 at a time, there's always 1 cookie left over. You decide when you purchase the next package, you'll eat 5 at a time, but still, there's always 1 cookie left over. Since it really isn't helpful to always have a leftover cookie, you decide to eat 7 at a time, and there are no cookies leftover. If you know there are less than 100 cookies in the package, how many cookies are there?
Mathematics
1 answer:
Blababa [14]2 years ago
3 0

Answer:

There are 91 cookies in the package of cookies

Step-by-step explanation:

The given parameter for the number of cookies are;

The number of cookies left when eating 3 at a time = 1 cookie

The number of cookies left when eating 5 at a time = 1 cookie

The number of cookies left when eating 7 cookies at a time = No cookie leftover

Let 'n' represent the number of cookies in the pack, let 'a', 'b', and 'c' be the multiples of 3s, 5s, and 7s in 'n', respectively, we have;

The number of cookies in the pack, n < 100

Therefore, we have;

3·a = n - 1

5·b = n - 1

7·c = n

∴ n - 1 is a multiples of 3 and 5 less than 100 which are;

15, 30, 45, 60, 75, and 90

Therefore, the possible values of 'n' are'

n = n - 1 + 1 = 15 + 1 = 16, 30 + 1 = 31, 45 + 1 = 46, 60 + 1 = 61, 75 + 1 = 75, 90 + 1 = 91

Multiples of 7 includes;

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98

Therefore, n = 91 which is the number that appear simultaneously in both search

The number of cookies in a package = 91 cookies

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The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding
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Answer:

We conclude that the mean wedding cost is less than $30,000 as advertised.

Step-by-step explanation:

We are given the following data set:(in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{236100}{8} = 29512.5

Sum of squares of differences = 3408750

S.D = \sqrt{\frac{3408750}{7}} = 697.82

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Sample standard deviation, s = $ 697.82

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Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975

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t_{stat} < t_{critical}

We fail to accept the null hypothesis and reject it.

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