Answer:
Smaller number: 12
Greater number: 31
Step-by-step explanation:
Hi there!
Let x equal to the smaller number.
Let y be equal to the greater number.
<u>1) Translate the information into equations</u>
"One is 7 more than twice the other"
⇒ 
"The sum of the numbers is 43"
⇒ 
<u>2) Use substitution to solve for the smaller number</u>
Plug the equation into the above equation
Subtract both sides by 7
Divide both sides by 3 to isolate x
Therefore, the smaller number equates to 12.
<u>3) Use substitution to solve for the greater number</u>
Plug in x as 12
Subtract both sides by 12 to isolate y
Therefore, the greater number equates to 31.
I hope this helps!
Speed = distance/ time
Car : 450m/1min
Train: 69km/45 min
Answer:
a) The approximate probability that more than 25 chips are defective is 0.1075.
b) The approximate probability of having between 20 and 30 defecitve chips is 0.44.
Step-by-step explanation:
Lets call X the total amount of defective chips. X has Binomial distribution with parameters n=1000, p =0.02. Using the Central Limit Theorem, we can compute approximate probabilities for X using a normal variable with equal mean and standard deviation.
The mean of X is np = 1000*0.2 = 20, and the standard deviation is √np(1-p) = √(20*0.98) = 4.427
We will work with a random variable Y with parameters μ=20, σ=4.427. We will take the standarization of Y, W, given by
The values of the cummmulative distribution function of the standard normal random variable W, which we will denote 
, can be found in the attached file. Now we can compute both probabilities. In order to avoid trouble with integer values, we will correct Y from continuity.
a)
Hence the approximate probability that more than 25 chips are defective is 0.1075.
b)
As a result, the approximate probability of having between 20 and 30 defecitve chips is 0.44.
the answer is B. 72 mm^2 because
9x4.5=40.5
then
7x4.5=31.5
then
40.5+31.5=72.0 mm^2
