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gayaneshka [121]
3 years ago
12

A line that passes through the points (2,1) and (k,5) is perpendicular to the line y=3x-9. Find the value of k

Mathematics
1 answer:
BartSMP [9]3 years ago
6 0
Since we know it is perpendicular to y=3x-9, we know the slope of the line is the opposite reciprocal of 3, or -\frac{1}{3}. Then we can use the two points in the slope formula to solve for k:
-\frac{1}{3}=\frac{5-1}{k-2}
-\frac{k-2}{3}=4
k-2=-12
k=-10
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The distribution of SAT II Math scores is approximately normal with mean 660 and standard deviation 90. The probability that 100
gayaneshka [121]

Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of 660, hence \mu = 660.
  • The standard deviation is of 90, hence \sigma = 90.
  • A sample of 100 is taken, hence n = 100, s = \frac{90}{\sqrt{100}} = 9.

The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{670 - 660}{9}

Z = 1.11

Z = 1.11 has a p-value of 0.8665.

1 - 0.8665 = 0.1335.

0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

7 0
2 years ago
Walt is mixing fruit punch for a party. He combines 1 gallon 2 quarts 3 pints of orange juice, 1 gallon 3 quarts 7 pints of pine
Soloha48 [4]
1 gal    2 qts    3 pts
1 gal    3 qts    7 pts
1 gal    3 qts    3 pts
---------------------------add
3 gal    8 qts    13 pts

1 pt = 0.5 qts...so 12 pts = 12* 0.5 = 6...so now we have :
3 gal   14 qts   1 pt

1 qt = 0.25 gal..so 12 qts = 12 * 0.25 = 3 gallons...so now we have :
6 gal   2 qts   1 pt <===
7 0
3 years ago
Mr.Henderson did not realize his checking account had a balance of $200 when he used his debit card for a $317.25 purchase. What
gulaghasi [49]

Answer:

His account balance would be -$117.25

Step-by-step explanation:

His purchase exceeded the amount of money in his checking account balance. He is now in the negative numbers.

6 0
3 years ago
Read 2 more answers
30. What is the solution to the system of equations? (1 point)
sesenic [268]

Answer:

Option B) (-1,7,5) is correct.

The solution to the given system of equation is (-1,7,5)

Step-by-step explanation:

Given system of equations are

-7x-2y+z=-2\hfill (1)

6x-y-z=-18\hfill (2)

5x+4y-z=18\hfill (3)

To find the solution of the given system of equations by using Elimination method:

Now adding equations (1) and (2)

-7x-2y+z=-2

6x-y-z=-18

_________________

-x-3y=-20

________________

-x-3y=-20

-(x+3y)=-20

x+3y=20\hfill (4)  (since "-" getting cancelled)

Now adding equations (1) and (3)

-7x-2y+z=-2

5x+4y-z=18

_________________

-2x+2y=16

________________

-2x+2y=16

2(-x+y)=16

-x+y=8\hfill (5)

Now adding equations (4) and (5)

x+3y=20

-x+y=8

_________________

4y=28

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y=\frac{28}{4}

Therefore y=7

Substituting y=7 in equation (4)

x+3y=20

x+3(7)=20

x+21=20

x=20-21

Therefore x=-1

Now substituting the values x=-1 and y=7 in equation (1) we get

-7x-2y+z=-2

-7(-1)-2(7)+z=-2

7-14+z=-2

z=-2+7

Therefore z=5

Therefore the solution to the given system of equation is (-1,7,5)

Therefore Option B) (-1,7,5) is correct.

8 0
3 years ago
The table shows the pricing for four different types of gasoline. Type Cost A $20.20 for 10 gal B $26.04 for 12 gal C $28.14 for
Sever21 [200]
Type A: $20.20 ÷ 10 gal = $2.02 per gal
Type B: $$26.04 ÷ 12 gal = $2.17 per gal
Type C: $ 28.14 ÷ 14 gal = $2.01 per gal
Type D: $30.45 ÷ 15 gal = $2.03 per gal

Type B costs less per gallon.
Hope this helps!!
7 0
3 years ago
Read 2 more answers
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