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2 years ago

5

An ellipse has a vertex at (4, 0), a co-vertex at (0, 2), and a center at the origin. Which is the equation of the ellipse in st

andard form?

1 answer:

Korolek [52]2 years ago

7 0

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable. It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

You might be interested in

Jennifer began an exercise program in which she ran 4 blocks the first day and then two blocks more than the previous day for ea

Andrews [41]

Answer:

84 blocks.

Step-by-step explanation:

If you are adding 2 to each day (which already has 4) in a 2 week period (14 days) than you would have to time 2(14) and 4(14) and add them. Thus would make the answer 84 blocks.

5 0

2 years ago

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

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 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 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:

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

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

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

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

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

Help!!!! Plssss!!! ASAP

zimovet [89]

Answer:

The y-intercept is (0,-26)

Step-by-step explanation:

Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression

$\displaystyle y-b=\frac{d-b}{c-a}(x-a)$

We'll take the first two points P(34,-52) and Q(51,-65) to find

$y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26$

Let's verify if the third point is on the line:

$y=-\frac{13}{17}68-26=-52-26=-78$

It belongs to the line. To find the y-intercept of the line, we set x to 0

$y=-\frac{13}{17}(0)-26=-26$

The y-intercept is (0,-26)

5 0

2 years ago

Select the description that is true of the equation y=-5x+5 .

gladu [14]

In y = mx + b form, the slope is in the m position and the y intercept is in the b position.

y = (m)x + (b)
y = -5 x + 5.....slope (m position) = -5....y int (b position) = 5

3 0

3 years ago

Find the value of x A. does not exist B. -7 C. 26 D. 35

alexandr1967 [171]

Answer:

A-does not exist

Step-by-step explanation:

The pythagorian theorem :

12²+x²= (x-2)²
144+x²= x²-4x+4
144-4+x²-x²= -4x
140 = -4x
x = 140/-4
x= -35

That's absurd . A side cannot be negative since it's a distance

It was obvious from the beginning since one of the sides is greater than the hypotenus wich is impossible x≥x-2

8 0

3 years ago

Read 2 more answers