Answer:
see explanation
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides are equal
(a)
= 
, substitute values
= 
( cross- multiply )
13.23AB = 111.132 ( divide both sides by 13.23 )
AB = 8.4
(b)
= 
, substitute values
= 
( cross- multiply )
6.3DF = 54.243 ( divide both sides by 6.3 )
DF = 8.61
N•2>8
then dive both sides 2n>8
and get n>4
9514 1404 393
Answer:
21x² +20x +100 = 0
Step-by-step explanation:
We know the sum of the roots of x² +bx +c = 0 is -b, and their product is c. If the roots are α and β, then ...
The sum of the roots of the new equation will be ...
-b' = (α+1/β)+(β+1/α) = (α+β) +(1/α +1/β) = (α+β)(1 +1/(αβ))
The product of the roots of the new equation will be ...
c' = (α+1/β)(β+1/α) = αβ +2 +1/(αβ)
Using the above relations for (α+β) and αβ, we find that ...
-b' = (-b)(1 +1/c)
c' = c + 2 + 1/c
For the given equation, our definition of b and c is ...
b = 2/3
c = 7/3
so the new equation has values ...
b' = (2/3)(1 + 1/(7/3) = (2/3)(10/7) = 20/21
c' = 7/3 + 2 + 1/(7/3) = 13/3 + 3/7 = 100/21
So, the equation with the roots of interest is ...
x² +20/21x +100/21 = 0
Multiplying by 21 gives ...
21x² +20x +100 = 0
Answer:
Step-by-step explanation:
Using the normal distribution, it is found that there is a 0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
The probability a randomly selected box has less than the 34 ounces of advertised weight is the <u>p-value of Z when X = 34</u>, hence:
Z = -1.5
Z = -1.5 has a p-value of 0.0668.
0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.
More can be learned about the normal distribution at brainly.com/question/24537145
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