Answer:
The product equality property allows an equation in one variable to be written as a system of equations
Step-by-step explanation:
We can express an equation in one variable as follows;
f(x) = g(x)
The properties of equality of products allows us to write an equation in one variable into a system of equations as follows;
(x - 3)×(x + 2) = 0
The zero product property gives;
x- 3 = 0 or x + 2 = 0
Also we have;
Product of two negatives = positive
Therefore when (x - 2)² = 25
x - 2 = ±5.
Answer:
8.06 is the correct answer
Answer:
112.249
I added more places after the decimal in case you need to round it.
The radius of the donut is 3.14
Answer:
a) 0.1003
b) 35.26
c) 21.92
d) Middle 80% smallest 10% and largest 10% = 20.02 and 39.98
Step-by-step explanation:
Given that: mean ц = 30 , standard deviation δ = 7.8
a) P(x ≤ 20)
= P [ (x - ц ) / δ ≤ ( 20 -30) / 7.8 ]
= P(z ≤ -1.28)
= 0.1003
probability = 0.1003
b) 75th percentile
P(Z < z) = 0.75
z = 0.674
Using z-score formula
x = z * δ + ц
x = 0.674 * 7.8 + 30
x = 35.26
c) 15th percentile
P(Z < z) = 0.15
z = -1.036
Using z-score formula
x = z * δ + ц
x = (-1.036) * 7.8 + 30
x = 21.92
d) Middle 80%
P(-z ≤ Z ≤ z) = 0.80
P(Z ≤ z) - P(Z ≤ -z) = 0.80
2P(Z ≤ z) - 1 = 0.80
2P(Z ≤ z) = 1 + 0.80 = 1.80
P(Z ≤ z) = 1.80 / 2 = 0.90
P(Z ≤ ± 1.28) = 0.90
z = -1.28, + 1.28
x = z * δ + ц
x = (-1.28) * 7.8 + 30
x = 20.02
x = z * δ + ц
x = 1.28 * 7.8 + 30
x = 39.98
Middle 80% two values = 20.02 and 39.98
smallest 10%
P(Z < z) = 0.10
z = -1.28
Using z-score formula
x = z * δ + ц
x = ( -1.28) * 7.8 + 30
x = 20.02
largest 10%
P(Z > z ) = 0.10
1 - P(z < z) = 0.10
P(z < z) = 1 - 0.10 = 0.90
z = 1.28
Using z-score formula
x = z * δ + ц
x = (1.28) * 7.8 + 30
x = 39.98