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3 years ago

Use the given points to answer the following questions.

Mathematics

2 answers:

zaharov [31]3 years ago

6 0

Answer:

1) C

2) B

Step-by-step explanation:

1) If a point lies ON the yz-plane, no matter what its coordinates are, one thing is for sure that its x-coordinate will always be zero! (this is helpful for visualization).

This information can guides us about which coordinate is responsible for how close or far we are to yz-plane!

The closest point to yz-plane would be the point the smallest value of x-coordinate. regardless of the the side.

here, among A,B, and C. C has the smallest x-coordinate, hence C is closest to the yz-plane.

2) If a point lies on xz plane, no matter what its coordinates are, its y-coordinate will always be zero.

Hence, among A,B, and C. A is the coordinate with y-coordinate as 0. Hence, B lies on the xz-plane.

Brums [2.3K]3 years ago

6 0

Answer:

1. C

2. A

Step-by-step explanation:

Given;

A(−4, 0, −8),

B(3, 3, −7),

C(1, 4, 9)

1. y,z plane lies on the that passes x = 0.

xy-plane = (0,y,z)

Therefore, the point closest to the yz is the point with the lowest absolute x (lowest |x|)

For;

A: |x| = |-4| = 4

B: |x| = |3| = 3

C: |x| = |1| = 1

The lowest |x| = 1 which is C

Therefore, the closest point to the yz axis is C

2. xz-plane is the plane passing through y=0.(xz plane = (x,0,z))

For a point to lie on the xz plane, it most be on y=0 (y coordinate must be equal to 0)

So,

For A: (-4,0,-8) = (x,y,z)

For A : y = 0

Therefore, A lies on the xz plane.

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tamaranim1 [39]

Step-by-step explanation:

$a)$

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Step-by-step explanation:

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Read 2 more answers

The amount of coffee that a filling machine puts into an 8 dash ounce 8-ounce jar is normally distributed with a mean of 8.2 oun

Inessa [10]

Answer:

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theore.

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 question, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

That is, probability of the sample mean between 8.2-0.02 = 8.18 and 8.2 + 0.02 = 8.22, which is the pvalue of Z when X = 8.22 subtracted by the pvalue of Z when X = 8.18.

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665.

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335.

0.8665 - 0.1335 = 0.7330

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

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3 years ago