Answer:

Step-by-step explanation:
Given

Required
Determine the roots
To get the root of the function, then f(b) must be 0;
i.e. f(b) = 0
So, the expression becomes

Add 75 to both sides


Take square roots of both sides


Reorder

Expand 75 as a product of 25 and 3

Split the expression




The options are not clear enough; however the roots of the equation are 
Using the normal distribution, it is found that the probability is 0.16.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:

- It 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, which is the percentile of X.
In this problem, the mean and the standard deviation are given by, respectively,
.
The proportion of students between 45 and 67 inches is the p-value of Z when <u>X = 67 subtracted by the p-value of Z when X = 45</u>, hence:
X = 67:


Z = -1
Z = -1 has a p-value of 0.16.
X = 45:


Z = -8.3
Z = -8.3 has a p-value of 0.
0.16 - 0 = 0.16
The probability is 0.16.
More can be learned about the normal distribution at brainly.com/question/24663213
Answer:
(2, -4.5)
Step-by-step explanation:
Used midpoint formula
First, let's establish a ratio between these two values. We'll use that as a starting point. I personally find it easiest to work with ratios as fractions, so we'll set that up:

To find the distance <em>per year</em>, we'll need to find the <em>unit rate</em> of this ratio in terms of years. The word <em>unit</em> refers to the number 1 (coming from the Latin root <em>uni-</em> ); a <em>unit rate</em> involves bringing the number we're interested in down to 1 while preserving the ratio. Since we're looking for the distance the fault line moves every one year, we'll have to bring that 175 down to one, which we can do by dividing it by 175. To preserve our ratio, we also have to divide the top by 175:

We have our answer: approximately
0.14 cm or
1.4 mm per year
Answer:
b=
−3
/x
Step-by-step explanation:
Step 1: Add -10 to both sides.
−2bx+10+−10=16+−10
−2bx=6
Step 2: Divide both sides by -2x.
−2bx
−2x
=
6
−2x
b=
−3
/x