Answer:

And we can use the z scoe formula given by:

And if we find the z score for the limits we got:


And this probability is equivalent to:

Step-by-step explanation:
For this case we can define the random variable X as "number of miles between services" and we know the following info given:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean
is given by:
We select a random sample size of n =44. And we want to find this probability:

And we can use the z scoe formula given by:

And if we find the z score for the limits we got:


And this probability is equivalent to:

Step-by-step explanation:
H0: u = 44.3
Hi : u# 44.3
Z1-0.05/2
Z1-0.025
Z0.975 = 1.96
Z = x-u/s.d/√n
Z= 44.4 -44.3/2.6/√130
Z = (0.1×11.4018)/2.6
Z=0.44
Since the calcalculated value is less than the table value and does not fall in the rejection region we fail to reject the null hypothesis
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,

a = 33 cm, b = 37 cm and C is 120°
So,

So, the length of the third side of the triangle is 60.65 cm.
Answer:
x = -6
Step-by-step explanation:
Let the number be x
<u>Condition:</u>
=> 10-3x = x+22
<u><em>Let's Solve it:</em></u>
=> -3x-x = 22-10
=> -2x = 12
<em>Dividing both sides by -2</em>
=> x = -6
Answer:
a^2-b^2=(a+b)(a-b) where a=4x and b=5. (4x+5)(4x-5)
Step-by-step explanation:
Since both terms are perfect squares,factor using the difference of squares formula