500 yd

300 yd

400 yd

What is the area of the triangular field in square feet?

A 60,000 ft

B 120,000 ft2

C 540,000 12

D 1,080,000 ft2

The correct answer is option (A) 60,000 ft.

Step-by-step Explanation: In a triangle with all three sides given and no vertical height, we shall not apply the conventional (commonly used) formulae which is

Area = 1/2 B x H

Rather we shall apply the Heron’s Formulae which states as follows;

Area = [square root] s(s - a)(s - b)(s - b)

Where a, b and c are the three sides and a is the semi-perimeter.

We shall start with the semi-perimeter which is

s = (300 + 400 + 500)/2

s = 1200/2

s = 600

Therefore applying the Heron’s formula, the area is calculated as

A = [square root] 600(600 - 500)(600 - 400)(600 - 300)

A = [square root] 600 (100)(200)(300)

A = [square root] 3600000000

A = 60000

The area of the given triangle is 60,000 ft.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;