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FinnZ [79.3K]
3 years ago
10

A triangle has side lengths of (8d – 3) centimeters, (6d + 2) centimeters, and

Mathematics
1 answer:
alisha [4.7K]3 years ago
3 0

The perimeter of a triangle is the sum of its side lengths.

The perimeter of the triangle is: 14d + 7f +7

<u>The sides of the triangle are:</u>

Side 1 = (8d - 3) cm

Side 2 = (6d + 2) cm

Side 3 = (7f + 8) cm

The perimeter (P) is calculated as:

P = Side 1 + Side 2 + Side 3

So, we have:

P = (8d - 3) + (6d + 2) + (7f + 8)

Remove brackets

P = 8d - 3 + 6d + 2 + 7f + 8

Collect like terms

P = 8d  + 6d + 7f - 3 + 2 + 8

P = 14d + 7f +7

Hence, the perimeter of the triangle is: 14d + 7f +7

Read more about perimeters at:

brainly.com/question/6465134

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The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum
Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

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 normally distributed samples are 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.

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 problem, we have that:

\mu = 26, \sigma = 6, n = 62, s = \frac{6}{\sqrt{62}} = 0.762

(a)

What is the likelihood the sample mean is at least $27.00?

This is 1 subtracted by the pvalue of Z when X = 27. So

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

By the Central Limit Theorem

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

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

1 - 0.9049 = 0.0951

(b)

What is the likelihood the sample mean is greater than $25.00 but less than $27.00?

This is the pvalue of Z when X = 27 subtracted by the pvalue of Z when X = 25. So

X = 27

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

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

X = 25

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

Z = \frac{25 - 26}{0.762}

Z = -1.31

Z = -1.31 has a pvalue of 0.0951

0.9049 - 0.0951 = 0.8098

c)Within what limits will 90 percent of the sample means occur?

50 - 90/2 = 5

50 + 90/2 = 95

Between the 5th and the 95th percentile.

5th percentile

X when Z has a pvalue of 0.05. So X when Z = -1.645

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

-1.645 = \frac{X - 26}{0.762}

X - 26 = -1.645*0.762

X = 24.75

95th percentile

X when Z has a pvalue of 0.95. So X when Z = 1.645

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

1.645 = \frac{X - 26}{0.762}

X - 26 = 1.645*0.762

X = 27.25

Between $24.75 and $27.25.

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3 years ago
If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq<br><br>​
Butoxors [25]

By way of example, suppose <em>A</em> = {1, 2, 3} and <em>B</em> = {<em>a</em>, <em>b</em>, <em>c</em>}. Then the Cartesian product of <em>A</em> and <em>B</em> is

<em>A</em> × <em>B</em> = {{1, <em>a</em>}, {1, <em>b</em>}, {1, <em>c</em>}, {2, <em>a</em>}, {2, <em>b</em>}, {2, <em>c</em>}, {3, <em>a</em>}, {3, <em>b</em>}, {3, <em>c</em>}}

That is, each element in <em>A</em> gets a pairing with each element in <em>B</em>, and for each pairing you have <em>n(A)</em> choices for the first element and <em>n(B)</em> choices for the second element.

So if <em>n(A)</em> = <em>p</em> and <em>n(B)</em> = <em>q</em>, then <em>n(A</em> × <em>B)</em> = <em>pq</em>.

6 0
3 years ago
Find the volume of a right circular cone that has a height of 14.3 ft and a base with a diameter of 17.2 ft. Round your answer t
saveliy_v [14]

Answer:

Volume of the given cone is 1107.6 cubic feet.

Step-by-step explanation:

Formula to get the volume of a right circular cone is,

V = \frac{1}{3}\pi r^{2}h

Here r = radius of the circular base

h = height of the cone

Now we put the values in the given formula

Volume = \frac{1}{3}\pi (8.6)^2(14.3)  [ radius = \frac{17.2}{2}=8.6 ]

             = \frac{1057.628\pi }{3}

             = 1107.55

             ≈ 1107.6 cubic feet

Therefore, volume of the given cone is 1107.6 cubic feet.

6 0
3 years ago
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