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Dominik [7]
3 years ago
9

Tyger is trying to eat less sugar in his diet.He reduces his sugar intake from 15 spoons a day to 9 1/2 spoons a day. What is th

e percentage reduction in his sugar intake.
Mathematics
1 answer:
seraphim [82]3 years ago
8 0

Answer:the percentage decrease is 36.67%

Step-by-step explanation:

Initial amount of sugar in his diet is 15 spoons in a day. Currently, the amount of sugar in his diet is 9 1/2 spoons in a day. Converting to decimal, it becomes 9.5 spoon in a day. The amount by which he reduced his sugar intake is 15 - 9.5 = 5.5 spoons.

Percentage decrease would be expressed as

Amount by which the intake decreased/ initial intake × 100

It becomes

5.5/15 × 100 = 36.67%

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The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var
Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

Z = \frac{3765 - 3639}{59.5}

Z = 2.12

Z = 2.12 has a pvalue of 0.983

X = 3513

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

Z = \frac{3513 - 3639}{59.5}

Z = -2.12

Z = -2.12 has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0
3 years ago
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such tha
natita [175]

Answer:

Step-by-step explanation:

Given that:

Population Mean = 7.1

sample size = 24

Sample mean = 7.3

Standard deviation = 1.0

Level of significance = 0.025

The null hypothesis:

H_o: \mu = 7.1

The alternative hypothesis:

H_a: \mu > 7.1

This test is right-tailed.

degree \ of \  freedom=  n - 1 \\ \\ degree \  of \  freedom  =  24 - 1 \\ \\ degree \ of \  freedom   = 23

Rejection region: at ∝ = 0.025 and df of 23, the critical value of the right-tailed test t_c = 2.069

The test statistics can be computed as:

t = \dfrac{ \hat X - \mu_o}{\dfrac{s}{\sqrt{n}}}

t = \dfrac{ 7.3-7.1}{\dfrac{1}{\sqrt{24}}}

t = \dfrac{0.2}{0.204}

t = 0.980

Decision rule:

Since the calculated value of t is lesser than, i.e t = 0.980 < t_c = 2.069, then we do not reject the null hypothesis.

Conclusion:

We conclude that there is insufficient evidence to claim that the population mean is greater than 7.1 at 0.025 level of significance.

6 0
3 years ago
What is the length of the hypotenuse of the triangle?
igor_vitrenko [27]

Answer:

The answer is 37.

Step-by-step explanation:

#Hope it helps uh.......

8 0
3 years ago
Which function is an example of exponential growth? y = 2(0.3)x y = 1.5(0.4)x y = 3(8)x y = 2(0.7)x
4vir4ik [10]
Exponential equation is
y=a(b)ˣ

when b>1, it is growth
when 0>b>1, it is decay

so

we want the 2nd number to be more than 1
that would be the 3rd one, y=3(8)ˣ
7 0
3 years ago
4. 150 men working in a factory produce 6000 articles in 15 working days. How long will it take, a. 50 men to produce the 6000 a
sergiy2304 [10]
<h2><u><em>Answer:</em></u></h2><h2><u><em></em></u></h2><h2><u><em>work done by 150 men on 1 day=6000/15.</em></u></h2><h2><u><em></em></u></h2><h2><u><em>work done by 1 man on 1 day=6000/(15*150).</em></u></h2><h2><u><em></em></u></h2><h2><u><em>work done by 50 men on 1 day=(6000*50)/(15*150).</em></u></h2><h2><u><em></em></u></h2><h2><u><em>let X days taken to produce 6000 articles by them, then</em></u></h2><h2><u><em></em></u></h2><h2><u><em>((6000*50)/(15*150))X=6000.</em></u></h2><h2><u><em></em></u></h2><h2><u><em>on solving X=45 days.</em></u></h2><h2><u><em></em></u></h2><h2><u><em>So 45 days will take for 50 men to produce 6000 articles.</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Please mark me Brainliest</em></u></h2>
6 0
2 years ago
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