solution
1 inch = 2.54 centimeters
Therefore, to convert to cubic measurements
(1 in)³ = (2.54 cm)³
Thus;
1 in³ = 16.387 cm³
Hence 305 cubic inches will be equivalent to
305 × 16.387
= 4998.035 cm³
The two angles shown form a linear pair.
The angles are supplementary, which means their measures add to 180 deg.
Now we can write an equation and solve for x.
5x + 120 = 180
5x = 60
x = 12
Answer: x = 12
Answer:
we will fail to reject the null hypothesis and conclude that the return rate is less than 20%.
Step-by-step explanation:
We are given;
Sample size;n = 6970
Success rate;X = 1334/6970 = 0.1914
Now, we want to test the claim that the return rate is less than p = 0.2, hence the null and alternative hypothesis are respectively;
H0: μ < 0.2
Ha: μ ≥ 0.2
The standard deviation formula is;
σ = √(x(1 - x)/n)
σ = √(0.1914(1 - 0.1914)/6970)
σ = 0.004712
Now for the test statistic, formula is;
z = (x - μ)/σ
z = (0.1914 - 0.2)/0.004712
z = -1.825
From the a-distribution table attached, we have a value of 0.03362.
This p-value gotten from the z-table is more than the significance value of 0.01. Thus, we will fail to reject the null hypothesis and conclude that the return rate is less than 20%.
Answer:
H = 1/30
H = 0.0333
0.033
Step-by-step explanation:
The time spent waiting at a traffic light can be considered a random variable with values from 0 seconds,
it’s green when you approach and can go on through, to 30 seconds with the following distribution shape
The entire area under the distribution curve must be 1.
Let assume the Shape is rectangle
Given
Time taken from 0s to 30s = 30s - 0s = 30s
To find height of the distribution?
Let H = the height of the distribution
Based on the above assumption;.
H * 30 = 1 --- make H the subject of formula
H = 1/30
H = 0.0333
To three decimal places is 0.033
<h3>Hence, the calculated height of the distribution is 0.033</h3>
We are to identify the three integers (let x, y and z be the three integers) given the conditions stated in the problem such as:
the sum of the three numbers is 92 => x+y+z = 92
the second number is three times the first number => y = 3x
the third number is ten less than twice the first number => 2x - 10 =z
Solving the equation, we have it:
x + y + z = 92
x + (3x) + (2x-10) =92
6x -10 = 92
6x = 92 +10
6x = 102
x = 17
solving for y:
y = 3x
y = 3*17
y = 51
solving for z, we have:
z = 2x -10
z = 2*17 - 10
z = 34 - 10
z = 24
The answers are:
x = 17
y = 51
z = 24
