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2 years ago

Help with problems 1 & 3

Mathematics

1 answer:

vlabodo [156]2 years ago

5 0

One side of the rectangle is x=2, the other side is 2x-5
Add up all the four sides: (x+2) +(x+2)+(2x-5)+(2x-5)=54
6x-6=54
x=10

#3: suppose the first integer is x, then the second one is x+2
x(x+2)=255
x^2 +2x -255 =0
factor the quadratic equation: (x+17)(x-15)=0
x=-17, which is impossible, or x=15
so the two positive integers are 15 and 17

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E5 In (x + 1) Simplify

pentagon [3]

Answer:

e^ (5 ln (x + 1)) = (x + 1)^5

Step-by-step explanation:

e5 In (x + 1) or did you mean e^ (5 ln (x + 1))

because then this would simplify a lot

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5)

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5) = (x + 1)^5

or did you mean (e^5) ( ln (x + 1)) = ln [(x+1)^(e^5)]

But I think you meant:

e^ (5 ln (x + 1)) = e ^ (ln (x + 1)^5) = (x + 1)^5

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2 years ago

Factor the expression. = 28x– 14

Veseljchak [2.6K]

Answer:

14(2×-1) is the factorization of this expression

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2 years ago

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Lera25 [3.4K]

Answer:

Step-by-step explanation:

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2 years ago

Seven more than the product of a number and 8 is equal to 5

yuradex [85]

8x + 7 = 5

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3 years ago

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

garri49 [273]

Using the normal distribution and the central limit theorem, 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 between Z = -2 and Z = 2, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

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

By the Central Limit Theorem

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