Answer:
Part a) 
Part b) When Jenny divides the square root of her favorite positive integer by
, she gets an integer
Step-by-step explanation:
Let
x-------> the favorite positive integer
Part a)
1) For 
-----> the product is an integer
so
The number
could be Jenny favorite positive integer
2) For 
-----> the product is an integer
so
The number
could be Jenny favorite positive integer
3) For 
-----> the product is an integer
so
The number
could be Jenny favorite positive integer
Part B)
1) For 
-----> the result is an integer
2) For 
-----> the result is an integer
3) For 
-----> the result is an integer
Therefore
When Jenny divides the square root of her favorite positive integer by
, she gets an integer
Answer:
Q1. x= 18, y=59
Q2. m∠J= 56°
Step-by-step explanation:
Q1. (3x +5)°= y° (base ∠s of isos. △)
y= 3x +5 -----(1)
(3x +5)° +y° +(4x -10)°= 180° (∠ sum of △)
3x +5 +y +4x -10= 180
7x +y -5= 180
7x +y= 180 +5
7x +y= 185 -----(2)
Substitute (1) into (2):
7x +3x +5= 185
10x= 185 -5
10x= 180
x= 180 ÷10
x= 18
Substitute x= 18 into (1):
y= 3(18) +5
y= 59
Q2. (5x -13)°= (3x +17)° (base ∠s of isos. △)
5x -13= 3x +17
5x -3x= 17 +13
2x= 30
x= 30 ÷2
x= 15
∠LKJ
= 3(15) +17
= 62°
∠KLJ= 62° (base ∠s of isos. △)
m∠J
= 180° -62° -62° (∠ sum of △JKL)
= 56°
Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.
For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of <u>exactly x successes on n repeated trials, with p probability</u>, and has variance given by:

In this problem:
- 95% pass final inspection, hence

- 120 components are inspected in one day, hence
.
The variance is given by:

The variance of the number that pass inspection in one day is 5.7.
To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377
The area of a rhombus is half of the product of the lengths of the diagonals.
area = (7.5 yd + 7.5 yd)(13 yd + 13 yd)/2
area = (15 yd)(26 yd)/2
area = 390 yd^2/2
area = 195 yd^2
Answer: 195
Answer:
Step-by-step explanation: