Answer is 42, hope this helps
Answer:
The condition are
The Null hypothesis is 
The Alternative hypothesis is
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n = 20
The sample mean is 
The standard deviation is 
The Null hypothesis is 
The Alternative hypothesis is
So i will be making use of
level of significance to test this claim
The critical value of
from the normal distribution table is 
Generally the test statistics is mathematically evaluated as

substituting values


Looking at the value of t and
we see that
so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
Answer:
In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.
The full correct process is:
(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15
= 4m - 6m + 9 + 15
= -2m + 24
The two quadrilaterals are given similar .
In any similar figure sides are in proportion.The second largest side of quadrilateral ABCD is 16 ft .Let the second longest side of quadrilateral EFGH be x ft. These sides will be in proportion to each other .
The second shortest side of quadrilateral EFGH that is GF will be proportional to the third longest side of quadrilateral ABCD that is BC
We can form a proportion with the proportional sides:

To solve for x we cross multiply
12x=(16)(18)
12x=288
Dividing both sides by 12 we get
x=24.
The second longest side of quadrilateral EFGH is 24 ft.
Answer:

Step-by-step explanation:
<u>Use identities to set the equation up as a quadratic</u>

<u>Make the substitution u=cos(x) and solve the quadratic</u>
<u />


Hence, 