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andrew11 [14]
3 years ago
7

Fred has 36 strawberries and 42 blueberries. He wants to use them to garnish desserts so that each dessert has the same number o

f berries, but only one type of berry. He wants as much fruit as possible on each dessert. How many berries will be on each dessert? How many desserts with each type of fruit will he have?
Mathematics
2 answers:
Andreyy893 years ago
7 0
6 berries on each dessert, 6 desserts of strawberries, 7 desserts of blueberries
timurjin [86]3 years ago
5 0

Answer:

There are 6 fruits in each dessert,

6 strawberry desserts and 7 blueberry desserts.

Step-by-step explanation:

Given,

The number of strawberries = 36,

Blueberries = 42,

∵ Each desserts of berries has the same number of berries but only one type of berries,

So, the number of fruits( either strawberry or blueberry ) in each dessert = HCF(36, 42)

= 6,

Now, the number of strawberry desserts

=\frac{\text{Total strawberries}}{\text{strawberries in each dessert}}

=\frac{36}{6}

= 6,

Similarly, the number of blueberries desserts = \frac{42}{6} = 7.

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Veronika [31]

Answer:

99% of the sample means will fall between 0.93288 and 0.94112.

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

The true mean is .9370 with a standard deviation of 0.0090

This means that \mu = 0.9370, \sigma = 0.0090

Sample of 32:

This means that n = 32, s = \frac{0.009}{32} = 0.0016

Within what interval will 99 percent of the sample means fall?

Between the 50 - (99/2) = 0.5th percentile and the 50 + (99/2) = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

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

By the Central Limit Theorem

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

-2.575 = \frac{X - 0.9370}{0.0016}

X - 0.9370 = -2.575*0.0016

X = 0.93288

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

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

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X - 0.9370 = 2.575*0.0016

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99% of the sample means will fall between 0.93288 and 0.94112.

6 0
3 years ago
3 solutions for equation <br> y=7x
vodomira [7]
<span>y=7x

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5 0
4 years ago
A tuter promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tuto
creativ13 [48]

Answer:

t48 = 1.7500

Step-by-step explanation:

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

x=test value before , y = test value after  

The system of hypothesis for this case are:

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Alternative hypothesis: \mu_y -\mu_x >50

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And the sample standard deviation for the differences, is:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =12

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t=\frac{\bar d -\Delta}{\frac{s_d}{\sqrt{n}}}=\frac{53 -50}{\frac{12}{\sqrt{49}}}=1.75

Since we don't have the population standard deviaition we need to use the t distribution and we can calculate the degrees of freedom given by:

df=n-1=49-1=48

Now we can calculate the p value, since we have a right tailed test the p value is given by:

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3 years ago
There are 24 men and 36 women in a choir.
Molodets [167]

Answer:

Step-by-step explanation:

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Percentage of women = (100 - 42.5)% = 57.5%

6 0
3 years ago
Read 2 more answers
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