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Kay [80]
3 years ago
7

Match the graph with its equation.

Mathematics
1 answer:
hram777 [196]3 years ago
5 0
The equation to this is A 5X+4Y=-20
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The amount of potato chips an 18-ounce bag contains follows a normal distribution with a mean of 18.5 ounces and a standard devi
bekas [8.4K]

Answer:

100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces

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 question, we have that:

\mu = 18.5, \sigma = 0.2, n = 100, s = \frac{0.2}{\sqrt{100}} = 0.02

What is the probability that the sample mean weight of these 100 bags is less than 18.6 ounces

This is the pvalue of Z when X = 18.6. So

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

By the Central Limit Theorem

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

Z = \frac{18.6 - 18.5}{0.02}

Z = 5 has a pvalue of 1

100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces

7 0
3 years ago
Find the midpoint of the segment with the following endpoints.<br> (4,2) and (7,6)
Tema [17]

Answer:

The answer is

<h2>( \frac{11}{2} \: , \: 4)</h2>

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

M = (  \frac{x1 + x2}{2} , \:  \frac{y1 + y2}{2} )

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(4,2) and (7,6)

The midpoint is

M = ( \frac{4 + 7}{2}   \: , \:  \frac{2 + 6}{2} ) \\  = ( \frac{11}{2} \: , \:  \frac{8}{2} )

We have the final answer as

( \frac{11}{2} \: , \: 4)

Hope this helps you

4 0
3 years ago
What’s the common multiples for 12 and 30
jasenka [17]

Hi!

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 30: 1, 2, 3, 5, 6, 10, 30

Explanation: <u><em>This question is super super easy. This question should be the least common multiples. First find the prime factorization of 12. It gave us 2*2*3=12. Then the prime factorization of 30. It gave us 2*3*5=30. You can also multiply each factors the greater number of times and it occurs to in steps 1 or step 2  and it gave us LCM=2*2*3*5=60. The least common multiple factors is 60 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie</em></u>

6 0
3 years ago
Read 2 more answers
What is the solution to log (9x)-log 3 = 3?
xeze [42]

Answer:

The solution x = \frac{e^{3} }{3}

Step-by-step explanation:

<u>Step 1</u>:-

Given log(9 x) -log 3 =3

we have to use formula  log a-log b=log\frac{a}{b}

log(9 x)- log 3 = log(\frac{9 x}{3} ) =3

Again by using formula log a =b

                                       a = e^{b}

so \frac{9 x}{3} =e^{3}

<u>step 2:</u>-

   3 x = e^{3}

  x = \frac{e^{3} }{3}

The solution of given problem is x=\frac{e^3}{3}

5 0
3 years ago
Complete the two-column the proof.
Serga [27]
1. ∠1 is complementary to ∠2. 1. givem

2.  m∠1 + m∠2.  2. Definition of complementary

3.BD bisects ∠ADC. 3. Given

4.  4. Definition of bisect

5. m∠2 = m∠3 5.  

6. m∠1 + m∠3 = 90° 6.  sunsitution

7. 7.
5 0
3 years ago
Read 2 more answers
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