MATHEMATICS COLLEGE

I'm having trouble with finding the solutions.

Answers

Answer 1

Answer:

Answer:x=−8 and y=8

Step-by-step explanation: Do you want it solved step by step?

Answer 2

Answer:

Answer:

One solution, (-8,8)

x = -8

y = 8

Step-by-step explanation:

-6x + 3y = 72 then 3y = 72 + 6x, y = 24 + 2x

5x + 8y = 24

substitute for y:

5x + 8(24 + 2x) = 24

5x + 192 + 16x = 24

21x = -168

x = -8

y = 24 + 2(-8) = 8

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The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12. The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is:

Answers

The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is 0.0668.

Calculation of the probability:

Since The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12.

Here we need to find out the z score

= $78-75/ 12/ 36$

= 1.5

Here we considered normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

So, the average is less or equal to 78.

Now

Subtract from 1 to get the complement.

So,

P(x>78)=1-0.9332

=0.0668

Learn more about probability here: brainly.com/question/24613748

Answer:

0.0668

Step-by-step explanation:

Assuming the distribution is normally distributed with a mean of $75,

with a standard deviation of $12.

We can find the z-score of 78 using;

$z=(x-\mu)/((\sigma)/(√(n) ) )$

$\implies z=(78-75)/((12)/(36) ) =1.5$

Using our normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

This is the area corresponding to the probability that, the average is less or equal to 78.

Subtract from 1 to get the complement.

P(x>78)=1-0.9332=0.0668

Find the square root of 8-2√5

Answers

Answer:

The square root of 8 - 2√5 is

$\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }$

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

$\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }$

Hope this helps you.

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

A box contains 5 plain pencils and 5 pens. A second box contains 3 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected

Answers

The events 'select a plain pencil' and 'select a color pencil' are independent. therefore the probability of both occurring is the product of their probabilities:
$P(plain\ pencil\ and\ color\ pencil)=(5)/(10)*(3)/(10)=(3)/(20)$
The answer is 3/20 or 0.15.

You are on the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 17 domestic car makes and find an average fuel economy of 34.904 MPG with a standard deviation of 4.6729 MPG. For imports, you sample 15 cars and find an average MPG of 28.563 MPG with a standard deviation of 8.4988. Construct a 90% confidence interval for the difference between the true average fuel economies in question. Assume the difference will represent (domestic - import). You can also assume that the standard deviations are statistically the same between the two populations.

Answers

Answer:

Step-by-step explanation:

Hello!

The objective is to test if there is a difference between the fuel economy of mid-size domestic cars and mid-size import cars.

For this there are two samples taken:

X₁: Fuel economy of a domestic car.

Sample 1

n₁= 17 domestic cars

X[bar]₁= 34.904 MPG

S₁= 4.6729 MPG

X₂: Fuel economy of an import car.

Sample 2

n₂= 15 import cars

X[bar]₂= 28.563 MPG

S₂= 8.4988 MPG

To estimate the difference between the average economic fuel of domestic cars and import cars, assuming both variables have a normal distribution and both population variances are unknown but equal, the statistic to use is a t-test for two independent samples with pooled sample variance:

(X[bar]₁-X[bar]₂)± $t_(n_1+n_2-2;1-\alpha /2) * (Sa*\sqrt{(1)/(n_1) +(1)/(n_2) } )$

$Sa^2= ((n_1-1)S_1^2+(n_2-1)S^2_2)/(n_1+n_2-2)$

$Sa^2= (16*(4.6729)^2+14*(8.4988)^2_2)/(17+15-2)= 45.35$

Sa= 6.73

$t_(n_1+n_2-2;1-\alpha /2) = t_(30; 0.95)= 1.697$

(34.904-28.563)± $1.697* (6.73*\sqrt{(1)/(17) +(1)/(15) } )$

6.341±1.697*2.38

[2.30;10.38]

With a confidence level of 90%, you'd expect that the difference between the average economic fuel of domestic cars and import cars will be contained in the interval [2.30;10.38].

I hope it helps!

Which set of ordered pairs could represent the same function as y = x2 ?A (1, 1), (2, 4), (3,6)
B (1,1),(3,9), (7,49)
© (1,2), (4,16), (8, 64)
D (4,8), (5, 25), (6,36)

Answers

Answer:

B (1, 1),(3, 9), (7, 49)

Step-by-step explanation:

Given function:

y = x²

Let's verify which set of pairs are same with the given function:

A....................

(1, 1) - yes
(2, 4) - yes
(3, 6) - no, 6≠ 3²

B....................

(1, 1) - yes
(3, 9) - yes
(7, 49) - yes

C....................

(1, 2)- no, 2≠ 1²
(4, 16) - yes
(8, 64) - yes

D....................

(4, 8) - no, 8 ≠ 4²
(5, 25) - yes
(6, 36) - yes

-6n+5=59 can someone plz tell me what this is

Answers

Answer:

-6n + 5 = 59

-6n = 54

n = -9

Answer: n = -9

Step-by-step explanation: you subtract the 5 from both sides leaving the equation to -6n=54. then you divide both sides by -6 leaving it with n = -9

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