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3 years ago

Find the equation of the line through (0,-2) and (4, 18).

Mathematics

1 answer:

Montano1993 [528]3 years ago

3 0

Let me = slope

m = (18 - (-2))/(4 - 0)

m = 20/4

m = 5

We now plug slope 5 and one of the given points into the point-slope formula.

y - y_1 = m(x - x_1)

y - 18 = 5(x - 4)

y - 18 = 5x - 20

y = 5x - 20 + 18

y = 5x - 2

Done!

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34 is added to x, the result is 98 . What is the value of x? Enter your answer in the box as a fraction in simplest form

KonstantinChe [14]

Not sure why it needs to be a fraction, if I am missing something please tell me. 64 or 64/1

4 0

3 years ago

Read 2 more answers

One-Half the difference of a number and 15

slega [8]

Answer:

x - 15 ÷ 2

Step-by-step explanation:

Since it wants you to find the half of your answer after you find the difference, be sure to leave the two at the end of your equation. With that said, let's move into finding out what "the difference of a number and fifteen is". Whenever they tell you 'a number', it means they want you to put a variable, such as x, since you do not know the number and it could be any number. Now, the "difference" of something usually means...you guessed it, subtraction! Now that you've decoded your equation, you now know it means that x - 15 is the first part, and you can now put the one half right after it.

If this is confusing, I can explain further. :D

5 0

3 years ago

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A game of chance involves rolling a standard, six-sided die. The amount of money the player wins depends on the result of the di

Sloan [31]

Answer:

If you play this game once (and it costs you nothing to play), the expected amount of money you will win is:

$8.

Step-by-step explanation:

a) Data and Calculations:

The probability for the result to be 1 or 2 = 33.33% (100/6 * 2)

The probability for the result to be 3, 4, or 5 = 50% (100/6 * 3)

The probability for the result to be 6 = 16.67% (100/6 * 1)

Data Table:

Event Probability Value Won

The result is 1 or 2 33.33% $0

The result is 3, 4 or 5 50.00% $4.00

The result is 6 16.67% $36.00

Expected Value:

Event Probability Value Expected Value

The result is 1 or 2 33.33% $0 $0 ($0 * 33.33%)

The result is 3, 4 or 5 50.00% $4.00 $2.00 ($4 * 50%)

The result is 6 16.67% $36.00 $6.00 ($36 * 16.67%)

Total expected amount of money = $8.00

8 0

2 years ago

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probab

LiRa [457]

Answer:

a) 0.0082

b) 0.9987

c) 0.9192

d) 0.5000

e) 1

Step-by-step explanation:

The question is concerned with the mean of a sample.

From the central limit theorem we have the formula:

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

a) $z=\frac{1224-1200}{\frac{60}{\sqrt{36} } }=2.40$

The area to the left of z=2.40 is 0.9918

The area to the right of z=2.40 is 1-0.9918=0.0082

$\therefore P(\bar X\:>\:1224)=0.0082$

b) $z=\frac{1230-1200}{\frac{60}{\sqrt{36} } }=3.00$

The area to the left of z=3.00 is 0.9987

$\therefore P(\bar X\:$

c) The z-value of 1200 is 0

The area to the left of 0 is 0.5

$z=\frac{1214-1200}{\frac{60}{\sqrt{36} } }=1.40$

The area to the left of z=1.40 is 0.9192

The probability that the sample mean is between 1200 and 1214 is

$P(1200\:$

d) From c) the probability that the sample mean will be greater than 1200 is 1-0.5000=0.5000

e) $z=\frac{73.46-1200}{\frac{60}{\sqrt{36} } }=-112.65$

The area to the left of z=-112.65 is 0.

The area to the right of z=-112.65 is 1-0=1

5 0

3 years ago

A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum

galina1969 [7]

Answer:

Original number of sixes = 6

Original number of nines = 10

Step-by-step explanation:

We are told in the question that:

A certain number of sixes and nines is added to give a sum of 126

Let us represent originally

the number of sixes = a

the number of nines = b

Hence:

6 × a + 9 × b = 126

6a + 9b = 126.....Equation 1

If the number of sixes and nines is interchanged, the new sum is 114.

For this second part, because it is interchanged,

Let us represent

the number of sixes = b

the number of nines = a

6 × b + 9 × a = 114

6b + 9a = 114.......Equation 2

9a + 6b = 114 .......Equation 2

6a + 9b = 126.....Equation 1

9a + 6b = 114 .......Equation 2

We solve using Elimination method

Multiply Equation 1 by the coefficient of a in Equation 2

Multiply Equation 2 by the coefficient of a in Equation 1

6a + 9b = 126.....Equation 1 × 9

9a + 6b = 114 .......Equation 2 × 6

54a + 81b = 1134 ........ Equation 3

54a + 36b = 684.........Equation 4

Subtract Equation 4 from Equation 3

= 45b = 450

divide both sides by b

45b/45 = 450/45

b = 10

Therefore, since the original the number of nines = b,

Original number of nines = 10

Also, to find the original number of sixes = a

We substitute 10 for b in Equation 1

6a + 9b = 126.....Equation 1

6a + 9 × 10 = 126

6a + 90 = 126

6a = 126 - 90

6a = 36

a = 36/6

a = 6

Therefore, the original number of sixes is 6

7 0

3 years ago