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3 years ago

3. What three numbers are the Pythagorean triple generated by using 4 for x and 1 for y. Remember to use the formulas:

Mathematics

1 answer:

Doss [256]3 years ago

8 0

Given:

Consider the three number are given by:

$a=x^2-y^2$

$b=2xy$

$c=x^2+y^2$

To find:

The three numbers are the Pythagorean triple generated by using 4 for x and 1 for y.

Solution:

We have,

$a=x^2-y^2$

$b=2xy$

$c=x^2+y^2$

Substituting 4 for x and 1 for y, we get

$a=4^2-1^2$

$a=16-1$

$a=15$

Similarly,

$b=2(4)(1)$

$b=8$

And,

$c=4^2+1^2$

$c=16+1$

$c=17$

The three three numbers are the Pythagorean triple are 8,15 and 17.

Therefore, the correct option is C.

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3 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

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3 years ago

Jake's water bottle has a capacity of 1.43 L. What is the bottle's capacity in milliliters?

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Answer:

1430 milliliters

Step-by-step explanation:

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3 years ago

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Tyler is packing lunches for a local youth program. He has 36 sandwiches, 72 apples, and 108 granola bars. What is the greatest

lys-0071 [83]

Answer:

The greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.

Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars

Step-by-step explanation:

The greatest common divisor (GCD) of two or more numbers is the largest number by which these numbers can be divided, that is, it is the largest number that divides them all exactly.

In other words, the greatest common divisor of two numbers a and b is the largest number that divides a and divides b.

To find the greatest common divisor of two or more numbers, you start by breaking those numbers down into prime factors. In this case:

36=2²*3²

72 = 2³*3²

108 = 2²*3

The greatest common divisor is obtained by choosing only the prime factors common to the numbers, raised to the smallest exponent. That is, you choose only the common factors and those that are repeated must be raised to the minimum exponent.

The 2 appears as a prime factor in the three decompositions, whose minimum exponent is 2.

3 also appears as a common factor, whose minimum exponent is 1.

By doing the multiplication to get the greatest common divisor, you get:

2²*3=12

So the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.

To calculate how many lunches each item will contain, you simply divide the amount you have of each item by the most lunches Tyler can pack, 12.

Sandwiches: 36÷12= 3

Apples: 72÷12= 6

Granola bars: 108÷12= 9

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3 years ago

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dsp73

Answer: B, Equivalent 0.4(k+3) = 0.4k +1.2

Step-by-step explanation:

when you distribute the 0.4 across k and 3, you multiply 0.4 by k and 3, getting you 0.4k+1.2 which is equivalent.

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1 year ago

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