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saw5 [17]
3 years ago
8

Emily runs a hotel. She wants to hold a party in the banquet hall of her hotel. The hall has a size of 120,000 square feet. By f

ire code the maximum population density of the hall is 0.004 people per square foot. This includes all the people in the banquet hall. What is the maximum number of people that can attend the party if she has it in the banquet hall?
Mathematics
1 answer:
alexira [117]3 years ago
5 0

Answer:

480 People.

Step-by-step explanation:

120,000(0.004) = 480

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Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. The constant o
maria [59]

Answer:

Part 1) The equation is h=42y

Part 2) The number of hats Paula can knit is 42 per yard of yarn

Part 3) see the procedure

Part 4) For 378 yards of yarn Paula can knit 9 hats

Step-by-step explanation:

Let

h -----> the number of hats

y ----> the amount of yarn in yards  

k ---> constant of proportionality

Part 1) Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit

we know that

A relationship between two variables, h, and y, represent a proportional variation if it can be expressed in the form h/y=k or h=ky

we have

k=42

substitute

h=42y

Part 2) What does the constant if proportionality 42, represent in this problem?

The constant of proportionality represent the slope of the linear equation

The value of the slope is 42\ \frac{hats}{yd}

That means that the number of hats Paula can knit is 42 per yard of yarn

Part 3) Complete the table showing the yards of yarn and the number of hats Paula can knit

we have

h=42y

Part a) For y=0 yd Find the value of h

substitute in the linear equation the value of y and solve for h

h=42(0)=0\ hats

Part b) For h=3 hats Find the value of y

substitute in the linear equation the value of h and solve for y

3=42y

y=3/42\ yd  ----> y=1/14\ yd

Part c) For y=210 yd Find the value of h

substitute in the linear equation the value of y and solve for h

h=42(210)=8,820\ hats

Part d) For y=378 yd Find the value of h

substitute in the linear equation the value of y and solve for h

h=42(378)=15,876\ hats

Part 3) For h=11 hats Find the value of y

substitute in the linear equation the value of h and solve for y

11=42y

y=11/42\ yd  

Part 4) Interpret the meaning of the point (378,9)

we have that

y=378 yd

h=9 hats

That means -----> For 378 yards of yarn Paula can knit 9 hats

7 0
3 years ago
Let A and B be subsets of a universal set U and suppose n(U)=400, n(A)=135, n(B)=80, and n(A n B)=60. Find the number of element
Alexxandr [17]
Use A' for A complement, etc. and n = intersection ∩.
n(A' n B')
=n(A u B)'   by the de Morgan's law
=nU-n(nA+nB-n(AnB))     n(A u B) = nA + nB - n(AnB)  and nX'=nU-nX
=400-(135+80-60)
=400-155
=245
5 0
3 years ago
West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 12% grade, wh
Masteriza [31]

Answer:

120 ft

Step-by-step explanation:

A slope of 12/100 means for every 12 units of distance you move horizontally you descend by 100 of the same units vertically. Assuming now that the slope does not change, i.e it remains constant throughout your trip; descending by 1000 ft should mean you have moved horizontally by 120 ft so that the slope is maintained.

x/1000 = 12/100

x = 120 ft

3 0
3 years ago
Molly played an online game three times. Her scores were 5.5, -3.6, and 12.8. What was her average score for three games?
Ivahew [28]

In order to find the solution you must calculate the mean, or the average by adding the numbers together and dividing by how many numbers there are.

5.5 + -3.6 + 12.8 = 14.7

14.7 ÷ 3 = 4.9

4.9 is Molly's average score.

Hope this helps! <3


4 0
4 years ago
47. Consider the equation x^2/3 =19
rosijanka [135]
7.54 or 57 square rooted
3 0
3 years ago
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