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3 years ago

A line contains the points R (-1, 8) S (1, 4) and T (6, y). Solve for y. Be sure to show and explain all work.

Mathematics

1 answer:

Nikitich [7]3 years ago

3 0

Given:

A line contains the points R(-1, 8), S(1, 4) and T(6, y).

To find:

The value of y.

Solution:

Three points are collinear if:

$x_1(y_2-y_3)+x_2(y_3-y_2)+x_3(y_1-y_2)=0$

A line contains the points R(-1, 8), S(1, 4) and T(6, y). It means, these points are collinear.

$-1(4-y)+1(y-8)+6(8-4)=0$

$-4+y+y-8+48-24=0$

$2y+12=0$

Subtract 12 from both sides.

$2y=-12$

Divide both sides by 2.

$y=\dfrac{-12}{2}$

$y=-6$

Therefore, the value of y is -6.

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The student body of 115 students want to elect a president and a vice president. How many different ways can they do that

Hitman42 [59]

The different ways that the students can elect a president and a vice president will be 13110.

<h3>What is probability?</h3>

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students = 115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

To learn more about probability, refer to the link;

brainly.com/question/11234923

#SPJ1

4 0

1 year ago

Let X denote the time from the present until the stock market hits 25,000. If X ≤ 1, you win $10, 000X. If X > 1, you win not

const2013 [10]

Answer: $6321

Step-by-step explanation:

Expected value is given as exactly what you might think it means intuitively, the return you can expect for some type of action.

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens:(P(x) * n).

he formula for the Expected Value for a binomial random variable is:

P(x) * X.

X is the number of trials and P(x) is the probability of success.

The formula for calculating the Expected Value where there are multiple probabilities is:

E(X) = ∑X * P(X)

The equation is basically the same, but here you are adding the sum of all the gains multiplied by their individual probabilities instead of just one probability.

Calculating the expected value of winning as follows:

Given,

Fx= e^-x, x is greater or equal to 0

Now, P less than or equal to zero =

[-e^-x] ^1

e^-0 - e^-1

= 1 - e^-1

= 0.6321

and P(x>1) = 1-0.6321= 0.3679

Therefore,Let y= amount of winnings.

Based on the above given information,

y= $10000 0

P(y)= 0.6321 0.3679

The expected value of winning:

E(y) = ΣyP(y)

E(y) = 10000 × 0.6321 + 0 × 0.3679

E(y) = $6321

Therefore, the expected value of winning is $6321

5 0

3 years ago

The weight, in pounds, of a newborn baby tt months after birth can be modeled by the function W(t)=1.25t+6.W(t)=1.25t+6. What is

ollegr [7]

Answer:

$6$

Step-by-step explanation:

GIVEN: The weight, in pounds, of a newborn baby $t$ months after birth can be modeled by the function $W(t)=1.25t+6$ .

TO FIND: What is the y-intercept of the function and what is its interpretation in the context of the problem.

SOLUTION:

in $W(t)=1.25t+6$

if $t=0$

$W(0)=6$

Hence y-intercept is $6$

the y-intercept in this represents the weight of baby just after he is born.

8 0

3 years ago

Help plsssssss i need explanation or not just give anser pls

alekssr [168]

Answer:

true

Step-by-step explanation:

4 0

3 years ago

Suzie made a mistake in the following problem. The mistake was made in Line ___. Only input the number of the first incorrect li

zalisa [80]

Answer:

Mistake in Line 2

Step-by-step explanation:

Line 1

7(6) ÷ 5 + 42

Line 2

7(6) ÷ 5 + 16

Line 3

42 ÷ 5 + 16

Line 4

42 ÷ 21

Line 5

To simplify any expression we use order of operation

Line 1 is 7(6) ÷ 5 + 42

Order of operation is PEMDAS

First we start with parenthesis

so we multiply 7(6) in line 2

7*6- 42

So Line 2 is 42 ÷ 5 + 42

Hence there is a mistake in Line 2

3 0

3 years ago