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3 years ago

Which choice is equivalent to the expression below?

Mathematics

1 answer:

eimsori [14]3 years ago

6 0

Answer:

Step-by-step explanation:

We have the expression:

$\sqrt{-100}$

Rewriting this yields:

$=\sqrt{-1\cdot100}=\sqrt{-1}\cdot\sqrt{100}=i\sqrt{100}=10i$

Therefore, our answer is C.

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Hulk left home and walked 8 blocks west. Then he turned and walked 6 blocks north. If each block is 500 ft. long, how far is Hul

son4ous [18]

The answer is 5000 ft

His displacement is actually the hypotenuse (c) of the triangle with sides 6 blocks and 8 blocks.
According to the Pythagorean theoreme:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 blocks

Since 1 block is 500ft long, then 10 blocks are 5000 ft long:
1 : 500ft = 10 : x
x = 10 * 500ft / 1 = 5000 ft

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3 years ago

Is it possible for two numbers to have a difference of 5, and a sum of 12?

frozen [14]

Uhhh that doesn’t seem possible but then again i forgot simple math lol

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How to find the least common denominator with fractions?

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Find out what the lowest number is that each of the numbers on the bottom of the fractions can divide into evenly.

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Mrs. Backstrom built a small wooden box for her cat. The box has a length of one and one tenth feet, a width of 1.6 feet, and a

likoan [24]

Answer:

$\text{Volume of cat box}=3.52\text{ ft}^3$

Step-by-step explanation:

We have been given that Mrs. Backstrom built a small wooden box for her cat. The box has a length of one and one tenth feet, a width of 1.6 feet, and a height of 2 feet. We are asked to find the volume of the box.

Let us convert one and one tenth feet into decimal.

$1\frac{1}{10}=\frac{11}{10}=1.1$

Since the cat box is in form of cuboid, so its volume will be equal to the product of length, width and height as:

$\text{Volume of cat box}=1.10\text{ ft}\times 1.6\text{ ft}\times 2\text{ ft}$

$\text{Volume of cat box}=3.52\text{ ft}^3$

Therefore, the volume of the cat box is 3.53 cubic feet.

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3 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$