The figure below shows a shaded rectangular region inside a large rectangle:
1 answer:
Answer:
b. 58%
Step-by-step explanation:
Calculate the area of the entire rectangle using the formula A = lw.
The lowercase "L" is for length.
"w" is for width.
The lighter square is 10 units long by 5 inches wide.
A = lw
A = (10 in)(5 in) Multiply
A = 50 in²
Calculate the area for the shaded rectangle, 7 inches by 3 inches.
A = lw
A = (7 in)(3 in) Multiply
A = 21 in²
Calculate the area for the non-shaded region by subtracting the shaded area from the total area.
50 in² - 21 in² = 29 in²
The chance that a point in the large rectangle will NOT be in the shaded region is 29/50.
Convert this fraction to decimal form by using a calculator. Divide the top number by the bottom number.
29/50 = 0.58
0.58 is in decimal form. To convert it to a percentage, multiply the number by 100.
0.58 = 58%
Therefore the probability that a point chosen inside the large rectangle is not in the shaded region is 58%.
You might be interested in
Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that
We need to proof that by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
And if we take common factor we got:
And as we can see then we can conclude that
Answer:
Step-by-step explanation:
The problem could be simplified as following:
Given:
The radius of a circle O is 26 feet.
Solve for:
The length of arc on circle O that measures 13 radians
Solution:
Step 1: Let's find out the correct formula to apply:
The formula to calculate the length of an arc measuring x radians on a circle with radius r feet is:
L = r*x
Step 2: Let's put the data into formula to work out the length L of arc:
L = 26*13 = 338 (ft)
=> The distance that a horse does on the outer edge travel when the carousel rotates through 13 radians: L = 338 (ft)
Hope this helps!
:)