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Sidana [21]
3 years ago
8

The perimeter of the rectangle below is 112 units. Find the length of side VW . Write your answer without variables. Top YX: 4z

Left YV: 5z + 2 Right XW: (blank) Bottom VW: (blank)
Mathematics
1 answer:
dimaraw [331]3 years ago
4 0

Answer:

VW = 33

Step-by-step explanation:

<em>See attachment for complete question</em>

Given

VY = 4x - 1

VW = 5x + 3

Perimeter = 112

Required

Determine the length of VW

Perimeter is calculated as:

Perimeter = 2 * (Width + Length)

This gives:

Perimeter = 2 * (VW + VY)

Substitute values for VW, VY and Perimeter

112 =  2 * (4x - 1 + 5x + 3)

Collect Like Terms

112 = 2 * (4x + 5x -1 +3)

112 = 2 * (9x +2)

Divide through by 2

56 = 9x + 2

Collect Like Terms

9x = 56 - 2

9x = 54

x = 54/9

x = 6

Substitute 6 for x in VW = 5x + 3

VW = 5 * 6 + 3

VW = 30 + 3

VW = 33

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Step-by-step explanation:

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The general form of an parabola is 2x2−12x−3y+12=0 .
Murljashka [212]

Answer:

The standard form of the parabola is (x-3)^2=4*\frac{3}{8}(y+2)

Step-by-step explanation:

The standard form of a parabola is

(x-h)^2=4p(y-k).

In order to convert 2x^2-12x-3y+12=0 into the standard form, we first separate the variables:

2x^2-12x+3y+12=0\\\\2x^2-12x+12=3y

we now divided both sides by 2 to remove the coefficient from 2x^2 and get:

x^2-6x+6=\frac{3}{2}y.

We complete the square on the left side by adding 3 to both sides:

x^2-6x+6+3=\frac{3}{2}y+3

x^2-6x+9=\frac{3}{2}y+3

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now we bring the right side into the form 4p(y-k) by first multiplying the equation by \frac{2}{3}:

\frac{2}{3} *(x-3)^2=\frac{2}{3} *(\frac{3}{2}y+3)\\\\\frac{2}{3} *(x-3)^2=y+2

and then we multiplying both sides by \frac{3}{2} to get

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Here we see that

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\boxed{(x-3)^2=4*\frac{3}{8}(y+2)}

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3 years ago
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Step-by-step explanation:

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In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. In addition, there
lesya692 [45]

Answer:

15.87% probability that a random sample of 16 people will exceed the weight limit

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.

For sums, the theorem can be applied, with mean n*\mu and standard deviation s = \sqrt{n}*\sigma

In this problem, we have that:

n = 16, \mu = 16*150 = 2400, s = \sqrt{16}*27 = 108

If a random sample of 16 persons from the campus is to be taken, what is the chance that a random sample of 16 people will exceed the weight limit

This is 1 subtracted by the pvalue of Z when X = 2508. So

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

By the Central Limit Theorem

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

Z = \frac{2508 - 2400}{108}

Z = 1

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that a random sample of 16 people will exceed the weight limit

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3 years ago
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