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:
Answer:
Step-by-step explanation:
Hope this helps u!!
First Problem:
angle R and angle S are complementary which means they add to 90 degrees. Think "C" for "Complementary" and "Corner" as in a sharp 90 degree corner. That's how I remember it.
Let's solve for x
(angle R) + (angle S) = 90
(12x-3) + (7x-2) = 90
12x-3 + 7x-2 = 90
(12x+7x)+(-3-2) = 90
19x-5 = 90
19x-5+5 = 90+5
19x = 95
19x/19 = 95/19
x = 5
Since x = 5, we can say
angle R = 12x - 3
angle R = 12*5 - 3
angle R = 60 - 3
angle R = 57 degrees
Final Answer: 57 degrees
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Second Problem:
Angle 1 and angle 2 "form a linear pair". This means they are adjacent and supplementary (add to 180 degrees). Put another way, they combine to form a single straight angle or line.
Let's make
x = measure of angle 1
y = measure of angle 2
We're also told that "the measure of angle 2 is six more than twice the measure of angle 1", which basically translates to
y = 2*x + 6
Because the angles (x and y) are supplementary, we can also say
x+y = 180
So we have this system of equations
y = 2x+6
x+y = 180
Start with equation (2). Plug in the equation (1) and solve for x
x+y = 180
x+2x+6 = 180 ... note how y has been replaced with 2x+6
3x+6 = 180
3x+6-6 = 180-6
3x = 174
3x/3 = 174/3
x = 58
Now that we know x, we can find y
y = 2x+6
y = 2*58+6
y = 116+6
y = 122
Final Answer: 122 degrees
Answer:
1) A profit of Rs 250 is made.
3) 11 marks
3) 14/15 kg
4) 15/28
Step-by-step explanation:
1) A profit of Rs.10 per bag of oranges and a loss of Rs.5 per bag of grapes sold. The total profit/loss from selling 200 bags of oranges and 350 bags of grapes is:
total profit/loss = 200 (10) - 5(350) = 2000 - 1750 = Rs 250
A profit of Rs 250 is made.
2) (+5) marks are given for every correct answer and (-3) marks are given for every incorrect answer and 0 for answer not attempted. If he answer 4 correct and 3 incorrect out of 7 questions. His score is:
Score = 5(4) - 3(3) = 20 - 9 = 11 marks
His score is 11 marks
3) An object weighs 28/5 kg on earth. Since its weight on moon is 1/6 its weight on Earth.
The weight on moon = 1/6 × 28/5 = 14/15 kg
4) 3/4 of 5/7 = 15/28
