Suppose a basketball player has made 217 out of 302 free throws. If the player makes the next 3 free throws, I will pay you $23.
1 answer:
Answer:
-$0.90
Step-by-step explanation:
There are only two possible outcomes, winning $23 (W) or losing $15 (L). Therefore:
The probability of the player making his next 3 free throws (P(W)) is:
The probability of the player NOT making his next 3 free throws (P(L)) is:
Expected value (EV) is given by the payoff of each outcome multiplied by its probability:
The expected value of the proposition is -$0.90
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Answer:
(1) 256 inches
(2) 5 feet
(3) 400 inches
(4) 10 feet
Step-by-step explanation:
(1) The function that gives the height in inches of the spray of water at a distance <em>x</em> from the sprinkler head is given as follows;
h(x) = 160·x - 16·x²
At x = 2 feet, we have;
h(2) = 160 × 2 - 16 × 2² = 256
Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches
(2) The x-coordinate, , of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;
= -b/(2·a)
The x-coordinate, , of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;
= -160/(2 × (-16)) = 5
Therefore, the number of feet along the way, the function will reach maximum height, = 5 feet
(3) The function, h(x) = 160·x - 16·x², will reach maximum height, , at x = 5, therefore;
= h(5) = 160 × 5 - 16 × 5² = 400
The maximum height of the spray, = 400 inches
(4) The water is at ground level where h(x) = 0, therefore;
At ground level, h(x) = 0 = 160·x - 16·x²
160·x - 16·x² = 0
∴ 16·x × (10 - x) = 0
By zero product rule, we 16·x = 0, or (10 - x) = 0, from which we have;
x = 0, or x = 10
The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.
Avani wrote the linear equation y = 5x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5x+ 4 and that passes through (15,–2). If her new equation is in the form , what is the value of b?
- m is the slope
- b is the y-intercept
The equation of a line that is perpendicular to another line always has the opposite reciprocal slope. In the original equation, the slope is 5. The opposite of 5, which refers to the sign, is -5. The reciprocal of -5 is -1/5. That means the slope of the new line is -1/5.
The perpendicular line:
- Has a slope of
- Passes through the point (15, -2)
To find the equation of a line that passes through a specific point, you need to use slope-intercept form.
- y₁ is the y-value of the point
- m is the slope
- x₁ is the x-value of the point
y₁ is -2, m is -1/5, and x₁ is 15.
Substitute the known values into the equation:
Open the parentheses and distribute:
The new equation will be:
Lastly, you need to move the positive 2 to the other side to keep it in y = mx + b form.
The equation of the perpendicular line is:
The value of b is 1.