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3 years ago

500 people fill up 4/9 of the hall. What is the seating capacity of the hall?

2 answers:

7 0

If 4/9 of the hall hold 500 people, then 1/9 of the hall holds 125 people.
Times that by 9 and you have your answer which is 1125 people.

den301095 [7]3 years ago

7 0

The answer would be 1125 because you have to divide 500 by 4 then multiply it by 9

You might be interested in

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:

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

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

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

The weather forecast in a city is that for every week, 3 days are sunny 2 are cloudy, and 2 are rainy. On any chosen day, descri

Mnenie [13.5K]

It is more likely to be sunny than it is to be cloudy or rainy.
It is less likely to be cloudy or rainy than it is to be sunny.
it is equally likely to be cloudy or rainy.

7 0

3 years ago

Enter the value of n so the expression (-6y+1)+(4.7y-3.1) is equivalent to (ny-2.1)

Greeley [361]

If im correct, n= -1.3

7 0

3 years ago

Joan can mow a 10-acre field in 4 hours. How long would it take her to mow a 8-acre field?

Montano1993 [528]

Answer:

Step-by-step explanation:

10/4=2.5

8/2.5=3.2

3.2 hours

6 0

3 years ago

What is the slope-intercept form of 3x +2y=1?

klasskru [66]

Answer:

y = (-3/2)x + 1/2

Step-by-step explanation:

Note that slope intercept form = y = mx + b

Change the given equation so it matches the form:

3x + 2y = 1

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. First, subtract 3x from both sides:

3x (-3x) + 2y = 1 (-3x)

2y = -3x + 1

Next, Divide 2 from both sides:

(2y)/2 = (-3x + 1)/2

y = (-3/2)x + 1/2

y = (-3/2)x + 1/2 is your answer.

7 0

3 years ago