Answer:
Step-by-step explanation:
That is not a parallelogram. It has more than four sides.
Area of the white part of the figure is 4×20 = 80 m²
If you expand the figure to include the white part, its area is 9×23 = 207 m².
Green area = 207-80 = 127 m²
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that
Value of the test statistic:
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Answer: 40.
Answer:
There are a 25% probability that Christine fails the course.
Step-by-step explanation:
We have these following probabilities:
A 50% probability that Christine finds a tutor.
With a tutor, she has a 10% probability of failling.
A 50% probability that Christine does not find a tutor.
Without a tutor, she has a 40% probability of failing.
Probability that she fails:
10% of 50%(fail with a tutor) plus 40% of 50%(fail without a tutor). So
There are a 25% probability that Christine fails the course.
Answer:
Given expression : ......[1]
Using distributive property:
[1]⇒
Simplify:
Like terms are those terms which are same variables.
Combine like terms: we get;
......[2]
Simplify:
or
we can write equation [2] as;
Combine like terms of x variables;
Therefore, the expressions which are equivalent to the Given expression are: