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2 years ago

26. A positive whole number is called stable if at least one of its digits has the same value

Mathematics

1 answer:

Kisachek [45]2 years ago

5 0

Answer:

Step-by-step explanation:

Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.

The following are the 3-digits stable numbers that appears in 78247

The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).

Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.

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Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° tria

Norma-Jean [14]

Answer:

(C)Determine the principal square root of both sides of the equation.

Step-by-step explanation:

Given: Isosceles right triangle XYZ (45°–45°–90° triangle)

To Prove: In a 45°–45°–90° triangle, the hypotenuse is $\sqrt{2}$ times the length of each leg.

Proof:

$\angle XYZ$ is 90^\circ$ and the other 2 angles are 45^\circ. \\\overline{XY} = a, \overline{YZ}= a, \overline{XZ}= c.\\$

Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, $a^2 + b^2 = c^2$

Since a=b in an isosceles triangle:

$a^2 + a^2 = c^2\\$Combining like terms\\2a^2 = c^2\\$Determine the principal square root of both sides of the equation.\\\sqrt{c^2}=\sqrt{2a^2} \\\\c=a\sqrt{2} \\$

Therefore, the next step is to Determine the principal square root of both sides of the equation.

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2 years ago

Read 2 more answers

A pack of paper costs $3.75 including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write

STALIN [3.7K]

If a pack of paper costs 3.75 including tax, and there is a $20 budget, then the equation to find out the answer would be 3.75p is greater or equal to $20. So the answer would be B. 3.75 would be multiplied by the tax and then applied up to $20.

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2 years ago

a school district requires all graduating seniors to take a mathematics test. This year, the rest scores were approximately norm

Klio2033 [76]

A score of 85 would be 1 standard deviation from the mean, 74. Using the 68-95-99.7 rule, we know that 68% of normally distributed data falls within 1 standard deviation of the mean. This means that 100%-68% = 32% of the data is either higher or lower. 32/2 = 16% of the data will be higher than 1 standard deviation from the mean and 16% of the data will be lower than 1 standard deviation from the mean. This means that 16% of the graduating seniors should have a score above 85%.

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2 years ago

A hospital finds that 22% of its accounts are at least 1 month in arrears. A random sample of 425 accounts was taken. What is th

GenaCL600 [577]

Answer:

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

Step-by-step explanation:

For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .