The lateral surface area of a right square pyramid is given by s - 82.492. If the pyramid has height 10 feet and lateral surface
area 100 square feet, what is the length of a side b of its base?
a. $6.92586 ft
C. 1.36523 ft
b. 4.85868 ft
d. 9.36369 ft

a is the answer.

Step-by-step explanation:

S- 82.492 = Perimeter base x height /2 + base

Pyramid base

b x 10h = hb /2  + b =  100

6.92586 x 6.92586  x 10 = 479.675367396/2 =239.837683698+ base 47.9675367396 =287.805220438

479.675367396- 287.805220438 = 191.870146958

Proving each rectangle pyramid side is 1/4 of 287.805220438/4 = 72 +10 height =S- 82    (S = 82.492)

then 192/2 = 96 = 100 square feet

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;