Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes

To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour

Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.

Please ask me any questions you may have!

Answer:

a. 0.82%

b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) =  0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

z = -2.6, which yields 0.9953.

Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742

p (0.47 > x > 0.63) = 0.7211 = 72.11 %

c.

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

Thus, 1.28 = (x - 0.5) / (0.05)

From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

Answer:

Michael purchases 60 kg of dark chocolate alongside 40 kg of milk chocolate.

Step-by-step explanation:

Let d signify the kilograms of dark chocolate bought by Michael and m signify the kilograms of milk chocolate he acquires.

He must acquire a total of 100 kg of chocolate, thus

With dark chocolate priced at $12 per kg, the cost for d kg would be $12d. The price of milk chocolate is $10 per kg, indicating the cost for m kg is $10m. Michael intends to spend $1,120 on the chocolate, therefore

Taking the first equation

By inserting this into the second equation:

Michael ends up buying 60 kg of dark chocolate and 40 kg of milk chocolate.

Answer:

118.2°

Step-by-step explanation:

Dos líneas paralelas x e y son cortadas por la transversal w (ver el diagrama adjunto).

Se forman 8 ángulos (denominados 1, 2, 3, 4, 5, 6, 7 y 8).

Los ángulos 1 y 6 son ángulos del mismo lado cuando dos líneas paralelas x e y son cortadas por la transversal w.

Dos ángulos del mismo lado son suplementarios (suman 180°). Esto significa

Dado por lo que

Answer:

qt's length = 16

Step-by-step explanation:

The problem states that qrs is a right triangle,

where qr = 20

          sr =?

          qs = 25

          qt =?

1)

Calculate sr

hypotenuse² = base² + height²

sq² = sr² + rq²

25² - 20² = sr²

sr = √(25² - 20²)

sr = 15

2)

When altitude rt is dropped to hypotenuse qs, it creates

two right triangles: rtq and rts.

Δrtq

height = rt

base= tq = 25 - x

hypotenuse = qt = 20

Δrts

height = rt

base= ts = x

hypotenuse = sr = 15

Both triangles share the same height, which is rt

Using the Pythagorean theorem:

      Δ rtq                                           Δ rts

hypotenuse² - base² = height²

20² - (25 - x)² = 15² - x²

400 - (625 + x² - 50x) = 225 - x²

400 - 625 - x² + 50x = 225 - x²

-225 - x² + 50x - 225 + x² = 0

-450 + 50 x = 0

50x = 450

x = 450/50

x = 9

Base of Δ rtq = tq = 25 - x

                         tq = 25 - 9

                         tq = 16