Answer:
B
Step-by-step explanation:
4x-5y=2 ...(1)
10x-21y=10 ...(2)
(1)+2(2) gives
24x-47y=22
Answer:
And we can find the individual probabilities using the probability mass function and we got:
And replacing we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
For this case we want this probability:
And we can use the complement rule and we got:
And we can find the individual probabilities using the probability mass function and we got:
And replacing we got:
5/8 - 1/8 = 4/8
4/8 in it's simplest form is 1/2
To find out what 1 and 3/4 times 2 is, we need to find out a way to make it much more simple and then answer it.
A quick way to answer this in a few steps is to:
1.) convert the fraction into decimal.
To do this, we need to divide 100 by our denominator (the number on the bottom of a fraction). Let's try it.
100 / 4 = 25.
For every 1/4, it adds 25.
Since we have 3/4, multiply 3 by 25.
You get 75, but it is not whole.
2.) Put your quotient into decimal form by putting it as 0.## (if we divided 100 by a smaller number).
Your number for 3/4 is 0.75.
Since we have a whole number (1), put it in the single-digit place.
(#.00)
1.75 is your fraction into decimal form.
Now, we need to multiply 1.75 by 2.00.
2.00 x 1.75 = 3.5
Your product is 3.5.
I hope this helps!
Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
