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2 years ago

A rectangle has an area of 8 square centimmetres and a perimeter of 12 cm. What are the width and breath?

1 answer:

8 0

Let the Length be L and the Width be W

The area is 8 cm²
LW = 8

The perimeter is 12
2(L + W) = 12
L + W = 6

Solve L and W:
LW = 8 --------------- (1)
L + W = 6------------ (2)

Equation (2):
L + W = 6
L = 6 - W -------------- Sub into (1)
(6 - W) W = 8
6W - W² = 8
W² - 6W + 8 =0
(W -2 )(W - 4) = 0
W = 2 or 4

When W =2, L = 6 - 2 = 4
When W = 4, L = 6 - 4 = 2

Answer: The Width is 2 cm and the Length is 4 cm

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3 years ago

Find f(-11/5) if f(n) = 5n + 6

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3 years ago

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C. 5 weeks.

Step-by-step explanation:

In this question we have a random variable that is equal to the sum of two normal-distributed random variables.

If we have two random variables X and Y, both normally distributed, the sum will have this properties:

$S=X+Y\\\\\ \mu_S=\mu_X+\mu_Y=30+60=90\\\\\sigma_S=\sqrt{\sigma_X^2+\sigma_Y^2}=\sqrt{10^2+20^2}=\sqrt{100+400}=\sqrt{500}=22.36$

To calculate the expected weeks that the donation exceeds $120, first we can calculate the probability of S>120:

$z=\frac{S-\mu_S}{\sigma_S} =\frac{120-90}{22.36}=\frac{30}{22.36}=1.34\\\\P(S>120)=P(z>1.34)=0.09012$

The expected weeks can be calculated as the product of the number of weeks in the year (52) and this probability:

$E=\#weeks*P(S>120)=52*0.09012=4.68$

The nearest answer is C. 5 weeks.

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