Answer:
1st blank: substitution property of equality
2nd blank: linear pair theorem
3rd blank: substitution property of equality
Step-by-step explanation:
<u>1st blank</u>
∠EIJ ≅ ∠GJI (eq. 1)
∠EIJ ≅ ∠IKL (eq. 2)
∠GJI ≅ ∠JLK (eq. 3)
Substituting eq. 3 into eq. 1:
∠EIJ ≅ ∠JLK
and then, substituting eq. 2:
∠IKL ≅ ∠JLK
which means that m∠IKL = m∠JLK
<u>2nd blank</u>
The Linear Pair Theorem states that two angles that form a linear pair are supplementary
<u>3rd blank</u>
m∠JLK + m∠JLD = 180°
Substituting with the previous result:
m∠IKL + m∠JLD = 180°
Answer:
The standard deviation of car age is 2.17 years.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.5
(a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age?
This means that 1 is 3 standard deviations below the mean and 14 is 3 standard deviations above the mean.
So
I want to find 
The standard deviation of car age is 2.17 years.
The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm
Total number of students=50
Number of boys=2x
Number of girls=y
total will be:
2x+y=50
⇒y=50-2x
when (y-6) boys left the auditorium the new number of boys was:
2x-(y-6)
=2x-y+6
but y=50-2x
thus the new number will be:
2x-(50-2x)+6
=4x-44
when (2x-5) girls left the auditorium the remaining number will be:
y-(2x-5)
=y-2x+5
but
y=50-2x
thus the new number of girls will be:
50-2x-2x+5
=55-4x
new total number of students:
(55-4x)+(4x-44)
=11
probability of selecting a girl at random will be:
(55-4x)/11=9/13
13(55-4x)=9*11
715-52x=99
616=52x
x=12
thus
y=50-12=38
thus
x=12 and y=38
Given:
Spoilage rate of fruits = 9% = 0.09
To find:
Amount of fruits to be order to have 100 pounds of peaches and considering the spoilage rate.
Solution:
Let the required amount of fruits you should order be x.
So, spoiled fruits = 9% of x = 0.09x
He would like to have 100 pounds of peaches to sell.
Divide both sides by 0.91.
The required amount of fruits to be order is 110 lbs. Therefore, the correct option is D.
