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UkoKoshka [18]
3 years ago
7

T a linen sale Mrs. Earle bought twice as many pillowcases for $2 each as sheets for $5 each. If she spent less than $40, not in

cluding tax, what is the maximum number of pillowcases she could have purchased?
Mathematics
1 answer:
Anettt [7]3 years ago
3 0
For this case, the first thing we must do is define variables:
 x: number of pillowcases
 y: number of sheets
 We now write the system of equations:
 2x + 5y = 40
 x = 2y
 Solving the system we have:
 x = 8.9
 y = 4.4
 Answer:
 
The maximum number of pillowcases she could have purchased is:
 
x = 8 (spent less than $ 40)
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A research study investigated differences between male and female students. Based on the study results, we can assume the popula
garri49 [273]

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of \mu = 3.5.
  • The standard deviation is of \sigma = 0.5.
  • Sample of 100, hence n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-2 = \frac{X - 3.5}{0.05}

X - 3.5 = -0.1

X = 3.4

Z = 2:

Z = \frac{X - \mu}{s}

2 = \frac{X - 3.5}{0.05}

X - 3.5 = 0.1

X = 3.6

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

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Round 0.581 to the nearest tenth.
Furkat [3]
The answer is 0.6, 5 or higher add one more, 4 or less stays the same
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nalin [4]

Answer:

78.53975

Find area of circle using radius, divide that by four

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Nikola buys a bouquet of 8 sunflowers for $18<br> What is the cost of 1 sunflower?
Umnica [9.8K]
1 sunflower = $?
8 sunflowers = $18

Divide $18 by 8 = 2.25

1 sunflower is $2.25.
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3 years ago
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For which values of a the system has at least one solution: x≤7 x≥a urgent pls help now
allochka39001 [22]

Answer:

We have the system:

x ≤ 7

x ≥ a

Now we want to find the possible values of a such that the system has, at least, one solution.

First, we should look at the value of a where the system has only one solution:

We can write the 2 sets as:

a ≤ x

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So, writing both together:

a ≤ x ≤ 7

if a is larger than 7, we do not have solutions.

then a = 7 gives:

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Here the only solution is 7.

Now, if a is smaller than 7, for example 5, we have:

5 ≤ x ≤ 7

Now x can take different values, so we have a lot of solutions.

Then the restrictions for a, such that the system has at least one solution, is:

a ≤ 7.

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