Ask question

Ask question

All categories

1 year ago

6

Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the s

ame solutions as the one shown. 8x + 7y = 39 4x – 14y = –68

1 answer:

telo118 [61]1 year ago

3 0

Answer:

(1/2, 5)

Step-by-step explanation:

8x + 7y = 39

-2(4x - 14y = -68)

-8x + 28y = 136

8x + 7y = 39

add the two equations together

35y = 175

y = 5

8x + 7(5) = 39

8x = 4

x = 1/2

You might be interested in

Tatooine is a fictional desert planet that appears in the Star Wars franchise. It is home to many settlers, including humans. Le

Dovator [93]

Answer:

a) For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

$\bar X \sim N (\mu , \sqrt{\frac{\sigma}{\sqrt{n}}})$

With the following parameters:

$\mu_{\bar X}= 96$

$\sigma_{\bar X} = \frac{23.3}{\sqrt{9}} =7.767$

b) $P(95< \bar X < 100)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for the limit we got:

$z = \frac{95-96}{\frac{23.3}{\sqrt{9}}}= -0.129$

$z = \frac{100-96}{\frac{23.3}{\sqrt{9}}}= 0.515$

$P( -0.129 < Z< 0.515) = P(Z$

The sketch is on the figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(96,23.3)$

Where $\mu=96$ and $\sigma=23.3$

Part a

For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

$\bar X \sim N (\mu , \sqrt{\frac{\sigma}{\sqrt{n}}})$

With the following parameters:

$\mu_{\bar X}= 96$

$\sigma_{\bar X} = \frac{23.3}{\sqrt{9}} =7.767$

Part b

For this case we want this probability:

$P(95< \bar X < 100)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for the limit we got:

$z = \frac{95-96}{\frac{23.3}{\sqrt{9}}}= -0.129$

$z = \frac{100-96}{\frac{23.3}{\sqrt{9}}}= 0.515$

$P( -0.129 < Z< 0.515) = P(Z$

The sketch is on the figure attached

3 0

1 year ago

If 8 people can pick the apples from trees in 6 days, how long will it take12 people?

kakasveta [241]

4 days.
If it takes 6 days for 8 people to pick apples then it must take 48 days for 1 person to do it because 6•8=48.
So then it must take 12 people
48/12 days which is 4 to pick apples from trees.

4 0

2 years ago

Let X denote the number of bars of service on your cell phone whenever you are at an intersection with the following probabiliti

lorasvet [3.4K]

Answer:

Step-by-step explanation:

Hello!

Given the variable

X: number of bars of service on your cell phone.

The posible values of this variable are {0, 1, 2, 3, 4, 5}

a. F(X) is the cummulative distribution function P(X≤x₀) you can calculate it by adding all the point probabilities for each value:

X: 0; 1; 2; 3; 4; 5

P(X): 0.15; 0.25; 0.25; 0.15; 0.1; 0.1

F(X): 0.15; 0.4; 0.65; 0.8; 0.9; 1

The maximum cumulative probability of any F(X) is 1, knowing this, you can calculate the probability of X=5 as: 1 - F(4)= 1 - 0.9= 0.1

b.

The mean of the sample is:

E(X)= ∑Xi*Pi= (0*0.15)+(1*0.25)+(2*0.25)+(3*0.15)+(4*0.1)+(5*0.1)

E(X)= 2.1

V(X)= E(X²)-(E(X))²

V(X)= ∑Xi²*Pi- (∑Xi*Pi)²= 6.7- (2.1)²= 2.29

∑Xi²*Pi= (0²*0.15)+(1²*0.25)+(2²*0.25)+(3²*0.15)+(4²*0.1)+(5²*0.1)= 6.7

c.

P(X<2)

You can read this expression as the probability of having less than 2 bars of service. This means you can have either one or zero service bars, you can rewrite it as:

P(X<2)= P(X≤1)= F(1)= 0.4

d.

P(X≤3.5)

This expression means "the probability of having at most (or less or equal to) 3.5 service bars", this variable doesn't have the value 3.5 in its definition range so you have to look for the accumulated probability until the lesser whole number. This expression includes the probabilities of X=0, X=1, X=2, and X=3, you can express it as the accumulated probability until 3, F(3):

P(X≤3.5)= P(X≤3)= F(3)= 0.80

I hope it helps!

5 0

2 years ago

What is the greatest common divisor of $1665,$ $4554,$ $1683,$ and $4050$?

Tju [1.3M]

9 is the greatest common divisor

7 0

2 years ago

Read 2 more answers

Katya cut part of the jump rope off to make it shorter. The new length is 8 and StartFraction 1 over 6 EndFraction feet. The dif

maksim [4K]

Answer:

9 feet it is right

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers