Answer:
Each goal gives 5 points and a penalty costs 7 points.
Step-by-step explanation:
Let a penalty cost = x points
And a goal gives = y points
Ben makes 7 goals and 2 penalties ending the game with 21 points,
7y - 2x = 21 --------(1)
Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,
10y - 8x = -6
5y - 4x = -3 --------(2)
Equation (1) multiplied by 2, then subtracted from equation (2),
(5y - 4x) - 2(7y - 2x) = -3 - 2(21)
5y - 4x - 14y + 4x = -3 - 42
-9y = -45
y = 5
From equation (1)
7(5) - 2x = 21
35 - 2x = 21
2x = 35 - 21
2x = 14
x = 7
Therefore, each goal gives 5 points and a penalty costs 7 points.
Answer:
x = 12
m(QS) = 52°
m(PD) = 152°
Step-by-step explanation:
Recall: Angle formed by two secants outside a circle = ½(the difference of the intercepted arcs)
Thus:
m<R = ½[m(PD) - m(QS)]
50° = ½[(12x + 8) - (4x + 4)] => substitution
Solve for x
Multiply both sides by 2
2*50 = (12x + 8) - (4x + 4)
100 = (12x + 8) - (4x + 4)
100 = 12x + 8 - 4x - 4 (distributive property)
Add like terms
100 = 8x + 4
100 - 4 = 8x
96 = 8x
96/8 = x
12 = x
x = 12
✔️m(QS) = 4x + 4 = 4(12) + 4 = 52°
✔️m(PD) = 12x + 8 = 12(12) + 8 = 152°
Answer:
The line passing through the points (2, -14) and (4, -24)
Step-by-step explanation:
The answer is 12 because the linear equation is mx+b,where m is the slope and b is the y-intercept.
Let X be a discrete random variable with geometric distribution.
Let x be the number of tests and p the probability of success in each trial, then the probability distribution is:
P (X = x) = p * (1-p) ^ (x-1). With x = (1, 2, 3 ... n).
This function measures the probability P of obtaining the first success at the x attempt.
We need to know the probability of obtaining the first success at the third trial.
Where a success is defined as a customer buying online.
The probability of success in each trial is p = 0.3.
So:
P (X = 3) = 0.3 * (1-0.3) ^ (3-1)
P (X = 3) = 0.147
The probability of obtaining the first success at the third trial is 14.7%
