Answer:
27
Step-by-step explanation:
Let the two numbers, smaller be x and larger be y.
As per statement, one number is 3 less than a second number.
x = y - 3…Eq..1
Twice the second number is 3 less than 3 times the first.
3x = 2y + 3…Eq..2
Now putting the value of x from Eq..1 to Eq…2
3x = 2y + 3
3 (y - 3) = 2y + 3
3y - 9 = 2y + 3
3y - 2y = 3 + 9
y = 12
The larger number is 12.
Now putting the value of y in Eq. 1 to get the value of x
x = y - 3
x = 12 - 3
x = 9
The smaller number is 9
Answer the two numbers, smaller is 9 and larger is 12.
To check the correctness of answer, substituting the derived values of two numbers in the Eq…2
3x = 2y + 3
3 × 9 = 2 × 12 + 3
27 = 24 + 3
27 =27
Answer:
a. 0.45 b. 1
Step-by-step explanation:
We will be using Poisson Approximation of Binomial because n = 80,000 is large and probability (<em>p) </em>is very small.
We calculate for (a) as follows:
The probability that both partners were born on April 30 is
<em>p </em>= 1/365 X 1/365
<em>p </em>= 1/133,225
<em>p </em>= 0.00000751
Using Poisson Approximation, we have:
λ = n<em>p</em>
λ = 80,000 X 0.00000751
λ = 0.6
We use λ to calculate thus:
P (X 
1) = 1 - P ( X = 0)
= 1 - e^-λ
= 1 - e^-0.6
= 0.451
There is a 45.1% probability that, for at least one of these couples, both partners were born on April 30.
(b) To calculate the probability that both partners celebrated their birthday on the same day:
<em>p </em>(same birthday) = 365 X 1/365 X 1/365
= 1/365
λ = n<em>p</em>
λ = 80,000 X 1/365
λ = 219.17
P (X 1) = 1 - P ( X = 0)
= 1 - e^-λ
= 1 - e^-219.17
≈ 1
There is almost 100% probability that, for at least one of these couples, both partners celebrate their birthday on the same day of the year.
Answer:
41/120, 7/20, 43/120, 11/30, 3/8
Step-by-step explanation:
Write the numbers.
1/3 & 2/5
We need a common denominator, but not the least common denominator. Both 3 and 5 are factors of 60, so let's use 60 as the common denominator.
Multiply 1/3 by 20/20:
1/3 = 20/60
Multiply 2/5 by 12/12:
2/5 = 24/60
Let's multiply each fraction again, but this time by 2/2.
1/3 = 40/120
2/5 = 48/120
Now it's easy to find 5 numbers between 40 and 48, so we get:
41/120, 42/120, 43/120, 44/120, 45/120
Some of these fractions can be reduced, so our answer is:
41/120, 7/20, 43/120, 11/30, 3/8
Answer:
I believe the answer is 12x 5
The area of the countertop is (16-ft x 3-ft) = 48 feet² .
1 foot = 0.3048 meter (rounded)
(1 foot)² = (0.3048 meter)² = 0.0929 meter²
48 feet² = (48 x 0.0929) = 4.459 meter² (rounded)
