Answer:
Slope = 0.667/2.000 = 0.333
x-intercept = 36/-1 = -36.00000
y-intercept = 36/3 = 12
Step-by-step explanation:
Answer:
Null hypothesis is 
Alternative hypothesis is 
Test Statistics z = 2.65
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
P- value = 0.004025
Step-by-step explanation:
Given that:
Mean
= 960 hours
Sample size n = 36
Mean population
937
Standard deviation
= 52
Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours
Null hypothesis is 
Alternative hypothesis is 
Degree of freedom = n-1
Degree of freedom = 36-1
Degree of freedom = 35
The level of significance ∝ = 0.01
SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;
from t-table t(0.99,35), the critical value = 2.438
The test statistics is :



Z = 2.65
The decision rule is to reject null hypothesis if test statistics is greater than critical value.
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
The P-value can be calculated as follows:
find P(z < - 2.65) from normal distribution tables
= 1 - P (z ≤ 2.65)
= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))
= 0.004025
Answer:
12 3/8
Step-by-step explanation:
16 -3 5/8 =12 3/8
to check:
12+3=15,
3/8+5/8= 8/8 which =1
so, 15+1=16
The height of the kite is 4.89 feet
Explanation
The length of the line attached to the kite=7 feet
The length of the shadow that is cast on the ground=5 feet
the system forms a right angled triangle where the taught string of the kite is the hypotenuse, the shadow is the base and the height of the kite above the ground is the height.
H=7 feet
b=5 feet
using pythagoras theorem

The kite is 4.89 feet above the ground
<u><em>Answer:</em></u>
Area of rhombus = 126 m²
<u><em>Explanation:</em></u>
<u>We are given that the two diagonals of the rhombus are:</u>
D₁ = 14 meters and D₂ = 18 meters
<u>The area of the rhombus using its diagonals can be calculated using the following rule:</u>

<u>Substitute with the given values to get the area as follows:</u>

Hope this helps :)