A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than theorange.By what percentage is the grapefruit heavi
er than the apple?
2 answers:
<h2>Answer:</h2>
Hence, the grapefruit is 20% heavier than the apple.
<h2>Step-by-step explanation:</h2>Let the weight of orange be x.
This means that the weight of grapefruit is:
1.08x
( Since grapefruit is: 8% heavier than orange )
Also, the weight of apple is 10% lighter than apple.
This means that the weight of apple is: 0.90 x
Hence, the percent change in the weight of grapefruit as compared to apple is calculated by:
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Answer:
The claim that all ages have purchase rates proportional to their driving rates is false.
Step-by-step explanation:
The complete question is:
A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic used to test the claim that all ages have crash rates proportional to their driving rates.
Age >26 26-45 46-65 45<
Drivers 66 39 25 30
A) 95.431
B)101.324
C)85.123
D)75.101
Solution:
In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that all ages have crash rates proportional to their driving rates.
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
<em>H₀</em>: The observed frequencies are same as the expected frequencies.
<em>Hₐ</em>: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
The values are computed in the table.
The test statistic value is 75.10.
The degrees of freedom of the test is:
n - 1 = 4 - 1 = 3
Compute the p-value of the test as follows:
p-value < 0.00001
*Use a Chi-square table.
p-value < 0.00001 < α = 0.05.
So, the null hypothesis will be rejected at any significance level.
Thus, there is sufficient evidence to warrant rejection of the claim that ages have crash rates proportional to their driving rates.
Answer:
length of the photograph will be 4.2 in. after pressing the button 5 times.
Step-by-step explanation:
By pressing the button, every time size of the photograph gets reduced by 12%.
Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,
L =
Where l = Actual length of the photograph
L = length of the reduced image
n = Number of times the button has been pressed
For l = 8 in. and n = 5
L =
=
= 4.22 in
L ≈ 4.2 in.
Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.