3y×2x+5 if x=3 and y=4

Dillion divided a 3 1/3 pound bag of pears among his 5 friends. How many pounds of pears does did each friend revive?

IgorLugansk [536]

Your answer is .6 repeating or 2/3 per person.

8 0

3 years ago

A simple impact crater on the moon has a diameter of 15 kilometers. a complex impact crater has a radius of 30 kilometers. how m

timurjin [86]

The general equation for computing the circumference of a circle is $C=\pi d$ , where C is the circumference, and d is the diameter. (You might also see the equation as $C=2 \pi r$ where r is the radius, because $d=2r$ )

Computing the circumferences of the two circles, we get:
$C_{d=15}=\pi (15)=15\pi$
$C_{d=30}=\pi (30)=30\pi$ .

To calculate the ratio of two numbers, we can divide one by the other. You can look at this as "How many times does the denominator fit in the numerator?"
$\frac{C_{d=30}}{C_{d=15}}=\frac{30\pi}{15\pi}=2$
So the circumference of the complex impact crater is 2 times greater than the circumference of the simple impact crater.

7 0

4 years ago

Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs. What is the probability th

Lubov Fominskaja [6]

Answer:

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

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:

$\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34$

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?

pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So

X = 990

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

By the Central Limit Theorem

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

$Z = \frac{990 - 975}{9.34}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463

X = 960

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

$Z = \frac{960 - 975}{9.34}$

$Z = -1.61$

$Z = -1.61$ has a pvalue of 0.0537

0.9463 - 0.0537 = 0.8926

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

7 0

3 years ago

What is the probability of tossing a penny and landing on heads three times in a row

lesantik [10]

$|\Omega|=2^3=8\\|A|=1\\\\P(A)=\dfrac{1}{8}=12.5\%$