38 2/5 divided by 100

A bakery needs to arrange 402

erma4kov [3.2K]

Hi there,

I hope you and your family are staying safe and healthy during this anomalous time.

To find the answer, we just need to:

$\frac{402}{15} = 26.8$

Thus,

We can estimate they will need 27 or 26 trays

Please leave 5 stars and a like if you find this answer helpful! Don't hesitate to reach out to me if you need more help.

~Garebear

6 0

2 years ago

A news item is spreading by word of mouth through a population of size 12,000 people. After t days, the number of people (in tho

Lilit [14]

Answer:

a) 2.303

b) $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) 1.3609

e) $\frac{dy}{dx}=0.04y(12-y)$

f) 4.5 thousand people(smaller)

7.5 thousand people (larger)

e) t=7.93 days (smaller)

t=10.06 days (larger)

g) 1.44

Step-by-step explanation:

The given function is $y=f(t)=\frac{12}{1+75e^{-0.48t}}$

To find how many thousand people have heard the news after 6 days, we substitute to get:

$f(6)=\frac{12}{1+75e^{-0.48*6}}=2.303$ thousands.

b) We rewrite to get: $f(t)=12(1+75e^{-0.48t})^{-1}$

We differentiate using the chain rule to obtain:

$f'(t)=-12(1+75e^{-0.48t})^{-2}\cdot 75e^{-0.48t}\cdot -0.48$

This simplifies to:

$f'(t)=432e^{-0.48t}(1+75e^{-0.48t})^{-2}$

We rewrite as positive index to get:

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) To find the rate at which the news is spreading after 8 days, we substitute t=8 into $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$ to get:

$f'(8)=\frac{432e^{-0.48\cdot 8}}{(1+75e^{-0.48\cdot 8})^{2}}=1.3609$

d) The solution to the logistic differential equation:

$\frac{dy}{dt}=ky(M-y)$

is

$y=\frac{M}{1+be^{-Mkt}}$

By comparison, M=12, and $Mk=0.48$

$12k=0.48\\k=0.04$

The differential equation is:

$\frac{dy}{dx}=0.04y(12-y)$

e) To how many people have heard the news when its rate of spread is 1.35 thousand per day, we equate the differential equation to 1.35 and so for t first.

$\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}=1.35$

This gives us: t=10.06 ot t=7.93

We substitute the times into the function to get:

$f(7.93)=\frac{12}{1+75e^{-0.48\cdot7.93}}$ =4.5 thousand: smaller value

$f(10.06)=\frac{12}{1+75e^{-0.48\cdot10.06}}=7.5$ thousand: Larger value

f) The two times that the news is spreading at rate 1.35 thousand people per day are:

$t=7.93$ days: Smaller value

$t=10.06$ : Larger value

g) To find the fastest rate at which the news spread we take the second derivative and equate it to zero.

$f''(t)=0$

This corresponds to where the horizontal line is tangent to

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

From the graph the point of tangency is:

(8.99,1.44)

Therefore the fastest rate at which the news spread is 1.44

7 0

3 years ago

A jar contains 20 green, 23 orange, 20 red, and 15 brown marbles. A marble is drawn at random. What is the probability that the

iogann1982 [59]

Answer: probability for the orange marble is 23/78 ; green= 20/78; red=20/78

Step-by-step explanation:there are 23 orangebmarbles out of all marbles which is 78 marbles and it doesn't help same for red and green marbles they both are 20 out of 78 marbles which is the total . So that is the probability of all the total marbles

5 0

3 years ago

Read 2 more answers

Use the graphs of f(x) and g(x) to describe the transformation from the graph of f to the graph of g. The graph of g is a vertic

Rudiy27

The answer to the equation at the end is 3

3 0

3 years ago

A company uses a process cost accounting system. its assembly department's beginning inventory consisted of 50,000 units, 3/4 co

wolverine [178]

Using the weighted average method, the equivalent units to be considered would only be that which is completed within the month and those completed in the ending inventory. Since the ending inventory is only ¼ or 25% completed, therefore the total equivalent units is:

total equivalent units = 127,500 units + (0.25)*40,000 units

total equivalent units = 137,500 units

Since the direct labor costs is given to be $24,000 therefore the direct labor cost per equivalent unit is:

direct labor cost per equivalent unit = $24,000 / 137,500 units

direct labor cost per equivalent unit = $0.1745

<span>direct labor cost per equivalent unit </span>= $0.17

Answer:

$0.17

8 0

3 years ago