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kupik [55]
3 years ago
13

The sum of 2 numbers is 50. the second number is 5 times the first. what is the number.

Mathematics
2 answers:
grandymaker [24]3 years ago
7 0
Let the first number be x, and the second 5x. The second is five times the first, so thats why it is 5x. Now, add x+5x=50. Simplify the equation to be 6x=50, because x+5x is 6x. Do the opposite of multiplyig because 6x is the same as 6 times x. Divide 6 on both sides. 50 divided by six is your first number (x). Now multiply your quotient by 5 to find the second number, and those are your two numbers.
sp2606 [1]3 years ago
3 0

Let the first and smaller number be x. Since the second number is 5 times the first, the second number is 5x. We also know both of these numbers must add to 50; thus, we can create the following equation.

x+5x=50

Combine like terms

6x = 50

Divide both sides by 6

x = 50/6 = 25/3 \approx 8.333

This is the value of the first number. The number you're looking for isn't specified in the question description, so I'll just provide the value of the second number. The second number has to be 5 times the first.

Thus, we just multiply 5 to x.

5x = 5(25/3) = 125/3 \approx 41.667

That's the value of the second number.

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Point A' has been rotated 90° CCW about point B.

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there are 225 wolves in a state park the population is increasing at the rate of 15% per year you want to make a prediction for
erastova [34]
Well, here is how i would do it.

We start with 225, at a rate of 15% per year. Assuming your answers are in years and not months, we will increase by this increment; years.

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So after one year, we would have a total of 258.75, or about 259 wolves.

after two years, we would have about 298 (we cant have a half of a wolf!)

after 3 years, we would have about 343 wolves.

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How do you find out the mean?
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Read 2 more answers
A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is tr
vesna_86 [32]

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

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 proportion p in a sample of size n, we have that \mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}

In this question:

p = 0.8, n = 100

So

\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

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

By the Central Limit Theorem

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

Z = \frac{0.85 - 0.8}{0.04}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944.

X = 0.75

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

Z = \frac{0.75 - 0.8}{0.04}

Z = -1.25

Z = -1.25 has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

6 0
3 years ago
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