Hello from MrBillDoesMath!
Answer:
Solutions: x = +\- 5i or x = +\- sqrt(5)
Discussion:
Factor x^4 - 25:
x^4 - 25 = (x^2+5) (x^2-5) => factor x^2 - 5
x^4 - 25 = (x^2+5)(x + sqrt(5)) (x - sqrt(5)) => factor x^2 + 5
x^4 = 25 = (x +5i)(x-5i) (x + sqrt(5)) (x - sqrt(5))
Hence the solutions are
x = +\- 5i and x = +\- sqrt(5)
Thank you,
MrB
Answer: -4
Explanation:
f(4) = 4(4) - 20
f(4) = 16 - 20
f(4) = -4
Answer:
0.62% probability that randomly chosen salary exceeds $40,000
Step-by-step explanation:
Problems of normally distributed distributions are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
What is the probability that randomly chosen salary exceeds $40,000
This is 1 subtracted by the pvalue of Z when X = 40000. So
has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that randomly chosen salary exceeds $40,000
2(3x - 4) = 2x + 12
6x - 8 = 2x + 12
4x = 20
x = 5
AB = 3(5) - 4 = 11
AC = 2(5) + 12 = 22
BC = 7(5) - 2 = 35 - 2 = 33
AC:BC = 22:33 = 2:3
Answer:
73.12 cm
Step-by-step explanation:
The perimeter of the square is 3 sides of the square (the 4th side is not included because of the semicircle)
P square = 3 s
=3 (16)
=48 cm
The perimeter of the semicircle is 1/2 of the circumference of a circle
P semicircle = 1/2 (pi *d)
=1/2 (pi* 16)
= 8 pi
= 8 (3.14)
=25.12 cm
The total perimeter is the sum of the square and the circle
P total = P square + P semicircle
=48+25.12
=73.12 cm
