Simplify each expression

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d

kozerog [31]

Answer: 49.85%

Step-by-step explanation:

Given : The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e. $\mu=61$ and $\sigma=9$

To find : The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and $34+3(9)$ .

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$ . (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$ = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%

4 0

2 years ago

What is the number whose 4/5 is 144?

anyanavicka [17]

Answer:

180

Step-by-step explanation:

Multiply 144 by the reciprocal of $\frac{4}{5}$ , that is

The reciprocal of $\frac{4}{5}$ is $\frac{1}{\frac{4}{5} }$ = $\frac{5}{4}$ , then

$\frac{5}{4}$ × 144 = $\frac{5(144)}{4}$ = 180

3 0

2 years ago

An air freshener starts with 30 grams of fluid, and the amount of fluid decreases by 12% per day. Express the amount of grams of

vampirchik [111]

Q = 30 (0.88)^t

Hope this helps :)

8 0

2 years ago

Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value

MArishka [77]

Answer:

y = 81-x
the domain of P(x) is [0, 81]
P is maximized at (x, y) = (54, 27)

Step-by-step explanation:

Given

x plus y equals 81
x and y are non-negative

Find

P equals x squared y is maximized

Solution

a. Solve x plus y equals 81 for y.

y equals 81 minus x

__

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

P equals x squared left parenthesis 81 minus x right parenthesis

__

c. Find the domain of the function P found in part b.

left bracket 0 comma 81 right bracket

__

d. Find dP/dx. Solve the equation dP/dx = 0.

P = 81x² -x³

dP/dx = 162x -3x² = 3x(54 -x) = 0

The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

P is maximized at (x, y) = (54, 27).

7 0

2 years ago

(-5,-1); 2y=2x-4 help me ASAP please

PIT_PIT [208]

Answer:

u trrahs at fritnote

Step-by-step explanation:

6 0

2 years ago