Answer:
g(1) = 2
Step-by-step explanation:
g(x) = x^2 + 1
if x=1
g(1) = 1^2 + 1
g(1) = 1 + 1
g(1) = 2
Hope this helps!
Answer:
X = 2
Step-by-step explanation:
44 + 104 + (18+7x) = 180
Simplify
Answer:
Correct answer: t₇ - a₇ = 2 · 7⁶, t₂₀ - a₂₀ = 2 · 7¹⁹
Step-by-step explanation:
Given:
Geometric sequence 2, 14, 98, 686, ......
First term is a₁ = 2
Second term a₂ = 14
Third term a₃ = 98
The quotient ( ratio) is obtained as follows:
r = 14 / 2 = 98 / 14 = 7
r = 7
n-th term is obtained as follows:
aₙ = a₁ · rⁿ⁻¹
according to this:
a₇ = 2 · 7⁶ = 2 · 117,649 = 235,298
a₂₀ = 2 · 7¹⁹ = 2 · 11,398,895,185,373,143 = 22,797,790,370,746,286
God is with you!!!
Answer:
The first quartile of the strengths of this alloy is 9.055 GPa.
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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.
The strength of an aluminum alloy is normally distributed with mean 10 gigapascals (GPa) and standard deviation 1.4 GPa.
This means that ![\mu = 10, \sigma = 1.4](https://tex.z-dn.net/?f=%5Cmu%20%3D%2010%2C%20%5Csigma%20%3D%201.4)
What is the first [lower] quartile of the strengths of this alloy?
This is the 100/4 = 25th percentile, which is X when Z has a pvalue of 0.25, so X when Z = -0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-0.675 = \frac{X - 10}{1.4}](https://tex.z-dn.net/?f=-0.675%20%3D%20%5Cfrac%7BX%20-%2010%7D%7B1.4%7D)
![X - 10 = -0.675*1.4](https://tex.z-dn.net/?f=X%20-%2010%20%3D%20-0.675%2A1.4)
![X = 9.055](https://tex.z-dn.net/?f=X%20%3D%209.055)
The first quartile of the strengths of this alloy is 9.055 GPa.
Answer:
y = -4x + 1
Step-by-step explanation:
Slope intercept form is y = mx + b.
The slope can be found by using the formula (y2-y1)/(x2-x1)
So (5-(-3))/(-1-1) which equals 8/-2 which can be simplified to -4.
Also this problem only has one answer with a slope of -4.