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skad [1K]
3 years ago
15

Find an equation for the line with slope m through the point (a,c).

Mathematics
1 answer:
lidiya [134]3 years ago
4 0
If you want the answer in point slope form then,

y-y1 = m(x-x1)
y-c = m(x-a)

---------------------------------------

If you want the answer in slope intercept form, then solve for y

y-c = m(x-a)
y-c = mx-ma
y-c+c = mx-ma+c
y = mx-ma+c
y = mx+c-ma
y = mx+(c-ma)

For this answer in slope intercept form the slope is m and the y intercept is c-ma

---------------------------------------

If you want the answer in standard form, then get the variable terms to the left side. Have the constant terms on the right side.

y = mx+c-ma
y-mx = mx+c-ma-mx
-mx+y = c-ma

Optionally you can multiply both sides by -1 to get mx-y = -c+ma but it will depend on your book if this step is carried out or not.

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Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It c
aksik [14]

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The <em>expected value</em> is given by the <u>sum of each outcome multiplied by it's respective probability.</u>

In this problem:

  • The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is \frac{1}{6} \times \frac{1}{12} = \frac{1}{72}.
  • The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is \frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}
  • In the other cases, Ayo wins £1.40, with 1 - \frac{18}{72} = \frac{54}{72} probability.

Hence, his expected profit for a single game is:

E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583

For 216 games, the expected value is:

E = 216(0.2583) = 55.8

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at brainly.com/question/24855677

6 0
2 years ago
The perimeter of a rectangle is 50 centimeters. If the width of the rectangle is 9 centimeters
nordsb [41]

Answer:

Length = 17 cm

Width = 8 cm

Step-by-step explanation:

Let the length be x cm

Therefore, Width = (x - 9) cm

Perimeter of rectangle = 2(l +w)

50 = 2[x + (x - 9)]

50/2 = 2x - 9

25 = 2x - 9

25+ 9 = 2x

2x = 34

x = 34/2

x = 17 cm

x - 9 = 17 - 9 = 8 cm

Therefore,

Length = 17 cm

Width = 8 cm

Thus, the dimensions of the rectangle are 17 cm and 8 cm.

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The total would be $2.73.
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Answer:

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