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3 years ago

Which of the following expression is equal to -3x^2-12?

1 answer:

7 0

$i=\sqrt{-1}\to i^2=-1\\\\-3x^2-12=-3(x^2+4)=-3(x^2+2^2)=-3(x^2-(-2^2))\\\\=-3(x^2-(-1\cdot2^2))=-3(x^2-(i^2\cdot2^2))=-3(x^2-(2i)^2)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=-3(x-2i)(x+2i)\\\\\text{use distributive property}\\\\=\boxed{(-3x+6i)(x+2i)}\to\boxed{a.}$

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Solve for d. Help is appreciated thank u!!

crimeas [40]

Answer:

d = 16.88

Step-by-step explanation:

Start by simplifying both sides of the equation then isolate the variable

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3 years ago

Chip and dale are driving in a toy engine around the Christmas tree at a speed of 300 miles/hour. how many minutes will it take

Deffense [45]

Using proportions, it is found that it will take them 0.00248548 minutes to do one loop.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, according to their speed, in 60 minutes, they drive 300 miles. In how many minutes will they drive 20 m = 0,0124274 miles?

The rule of three is:

60 min - 300 miles

x min - 0.0124274 miles

Applying cross multiplication:

$300x = 60 \times 0.0124274$

$x = \frac{60 \times 0.0124274}{300}$

$x = 0.00248548$

It will take them 0.00248548 minutes to do one loop.

More can be learned about proportions at brainly.com/question/24372153

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2 years ago

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alexdok [17]

Answer:

......................

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3 years ago

. Exam scores for a large introductory statistics class follow an approximate normal distribution with an average score of 56 an

Andru [333]

Answer:

0.1% probability that the average score of a random sample of 20 students exceeds 59.5.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Normal probability distribution

Problems of normally distributed samples can be 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.

In this problem, we have that:

$\mu = 56, \sigma = 5, n = 20, s = \frac{5}{\sqrt{20}} = 1.12$