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3 years ago

Solve the linear system of equations using the linear combination method. {8a−4b=205a−8b=62

Mathematics

1 answer:

Nata [24]3 years ago

6 0

Step 1:

Line up respective variables in column.

$8a-4b=20$ .................(1)

$5a-8b=62$ .................................(2)

Step 2:

We need to multiply first equation with -2 so that the coefficient of b becomes equal and opposite of -8.

$8a-4b=20$ *2

$-16a + 8b=-40$ ...................(3)

Step 3:

Add equation (2) and (3)

$5a-8b=62$

$-16a+8b=-40$

The b terms will cancel out and we are left with only a terms.

-11a = 22

dividing both sides by -11

a=-2

Step 4:

plug this value of a in equation (1) to find value of b,

$8a-4b=20$

$8(-2)-4b=20$

$-16-4b=20$

b=-9

Answer : a=-2 and b =-9

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Assume that foot lengths of women are normally distributed with a mean of 9.6 in and a standard deviation of 0.5 in.a. Find the

Makovka662 [10]

Answer:

a) 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b) 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c) 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

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.

In this problem, we have that:

$\mu = 9.6, \sigma = 0.5$ .

a. Find the probability that a randomly selected woman has a foot length less than 10.0 in

This probability is the pvalue of Z when $X = 10$ .

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

$Z = \frac{10 - 9.6}{0.5}$

$Z = 0.8$

$Z = 0.8$ has a pvalue of 0.7881.

So there is a 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b. Find the probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 8.

When X = 10, Z has a pvalue of 0.7881.

For X = 8:

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

$Z = \frac{8 - 9.6}{0.5}$

$Z = -3.2$

$Z = -3.2$ has a pvalue of 0.0007.

So there is a 0.7881 - 0.0007 = 0.7874 = 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c. Find the probability that 25 women have foot lengths with a mean greater than 9.8 in.

Now we have $n = 25, s = \frac{0.5}{\sqrt{25}} = 0.1$ .

This probability is 1 subtracted by the pvalue of Z when $X = 9.8$ . So:

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

$Z = \frac{9.8 - 9.6}{0.1}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

There is a 1-0.9772 = 0.0228 = 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

5 0

3 years ago

Jug can type 128 words in 3 minutes. How many minutes will it take him to type 576 words

KATRIN_1 [288]

Answer:

13.5 minutes

Step-by-step explanation:

$\frac{3 min }{128 words} = \frac{xmin}{576 words}$

Cross multiply

3 × 576 = 128x

3 × 576 = 1,728

1,728 = 128x

1,728 ÷ 128 = x

13.5 = x

8 0

3 years ago

Read 2 more answers

What is the distance of BC?

Aliun [14]

Answer:

BC = 9 miles

Step-by-step explanation:

Here, we are given ΔABC ∼ ΔEDC, which means both triangles are similar and they tend to have the same dimensions and properties.

To find the length of BC, we are given the proportion:

$\frac{12}{8} = \frac{x}{6}$

Where x represents the length BC.

Solving further, let's cross multiply

$12 * 6 = 8x$

$72 = 8x$

Solving for x, we have:

$8x = 72$

Lets divide both sides by 8

$\frac{8x}{8} = \frac{72}{8}$

$x = 9$

Therefore the distance BC is 9 miles

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3 years ago

The formula V=R-N describes the variation V of the recorded temperature R from the normal temperature N. If the recorded tempera

katovenus [111]

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3 years ago

A model of a famous statue is 2 and one half inches tall. The actual statue is 6 and one fourth feet tall. What is the ratio of

mel-nik [20]

ratio is 75:2.5

30:1is the answer

8 0

3 years ago