Answer:
-3
Step-by-step explanation:
p(x) = x^2-6x+5
Let x= 4
p(4) = 4^2-6(4)+5
Exponents first
= 16 -6(4) +5
Multiply
= 16 -24 +5
Add and subtract
= -8+5
= -3
Answer: the probability that a selected cup will be overfilled is 0.16
Step-by-step explanation:
Since amount of hot chocolate dispensed by a hot chocolate machine is normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = amount of hot chocolate dispensed by a hot chocolate machine.
µ = mean
σ = standard deviation
From the information given,
µ = 16.0 oz
σ = 2 oz
We want to find the probability that a selected cup will be overfilled. Since the cup can hold 18.0 oz, the expression would be
P(x > 18) = 1 - P(x ≤ 18)
For x = 18,
z = (18 - 16)/2 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
P(x > 18) = 1 - 0.84 = 0.16
See attached photo for solution
Step-by-step explanation:
step 1. let's call the line in the middle y.
step 2. y = sqrt(5^2 + 7^2) = sqrt(74). pythagorean theorem.
step 3. x^2 + y^2 =100 (pythagorean theorem))
step 4. x^2 + (sqrt(74))^2 = 100.
step 5. x^2 = 100 - 74
step 6. x^2 = 26
step 7. x = sqrt(26). note: sqrt is the square root.
The above is the equation of the parabola and the steps to solve it.
