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2 years ago

Which of the following is equivalent to 25x2+16−40x−64y2? Select two.

Mathematics

1 answer:

Marat540 [252]2 years ago

3 0

The equivalent expression to the given expression 25x²+16−40x−64y² are; (5x-4)²−64y² and (5x−4−8y)(5x+4+8y)

<h3>Difference of two squares</h3>

According to the question:

We are required to determine the equivalent expression.

When we try to factorise the given expression systematically; we have;

25x²+16−40x−64y² = (25x²+16−40x)−64y²

By the difference of two squares concept;

(25x²+16−40x) = (5x-4)²

Therefore, an equivalent expression is; (5x-4)²−64y²

Similarly, (5x-4)²−64y² is the difference of two squares and can be rewritten as; (5x−4−8y)(5x+4+8y)

Hence, we have the suggested expressions as equivalent expressions.

Learn more about equivalent expression:

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3 years ago

A very large batch of parts (assume a normal distrbution0 from a manufacturer has a mean weight = 43g and a standard deviation =

AVprozaik [17]

Answer:

5.44% probability that exactly 8 of the 16 parts you selected will have weights exceeding 45g

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.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Percentage of parts with weights exceeding 45g?

1 subtracted by the pvalue of Z when X = 45. So

We have $\mu = 43, \sigma = 4$

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

$Z = \frac{45 - 43}{4}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

1 - 0.6915 = 0.3075

If you slect 16 parts at random form that batch, what is the probability that exactly 8 of the 16 parts you selected will have weights exceeding 45g?

This is P(X = 8) when n = 16, p = 0.3075. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{16,8}.(0.3075)^{8}.(0.6915)^{8} = 0.0544$

5.44% probability that exactly 8 of the 16 parts you selected will have weights exceeding 45g

4 0

3 years ago

sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of t

Fiesta28 [93]

Answer:

Amie should have multiplied 54 by 2/3

Step-by-step explanation:

The formula of the volume of a sphere is given by

$\frac{4}{3}\pi r^3$ , where r is the radius of the sphere.

to find the volume of the sphere, we must find $r^3$

We know that the formula of a cylinder of height h and radius r is given by

$\pi r^2h$

So $54 = \pi r^2 h$

We know that the sphere and the cylinder have the same height. Recall that the height of the sphere of radius r, is the diameter of a circle that passes through the heighest and lowest points of the sphere. Then, h=2r. This means that

$54 = 2\pi r^3$

From here, we know that $\pi r^3 = \frac{54}{2}$ .

So the volume of the sphere is $\frac{4}{3}\frac{54}{2} = \frac{2}{3}\cdot54$ .

So Amie should have multiplied 54 by 2/3.

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4 years ago

Read 2 more answers

I need help on number 10 , number 9 and number 11 thank you

Illusion [34]

9.
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10.
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3*6+3= 21
3*8+4= 28
11. you cannot see enough to do the problem so what ever the problem is you take the numbers and replace x with them 2 for the first one= x then do the problem to get the answer.

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3 years ago

Please help. I am trying to solve for x and i can't remember how.

Black_prince [1.1K]

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