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denpristay [2]
2 years ago
11

In a basketball arena, all four sides are filled with people. If each side of the arena is 20 ft. X 30 ft., and each person take

s up 2.5 square feet, approximately how many people are in the arena?
Mathematics
1 answer:
nasty-shy [4]2 years ago
8 0

Answer:

<h2><em><u>960 people </u></em></h2>

Step-by-step explanation:

If each side of the basketball arena is 20 ft. X 30 ft, the area of each side of the basketball arena = 20ft * 30ft = 600ft².

Since all the four sides are filled with people, the total area of the 4 sides will be expressed as 4*600 = 2400ft²

If each person takes up 2.5ft², total number of people in the arena will  be gotten by simply dividing the area of all the four sides by the area took up by each person.

Total number of people in the arena = area of all the four sides by the area/ area took up by each person.

Total number of people in the arena = 2400/2.5

Total number of people in the arena  = 960 people.

<em><u></u></em>

<em><u>Hence there are approximately 960 people in the arena.</u></em>

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For questions 2-5, the number of pieces in a regular bag of Skittles is approximately normally distributed with a mean of 38.4 a
aleksley [76]

Answer:

a. -1.60377

b. 0.25451

c. 0.344

d. Option b) 78th

Step-by-step explanation:

The number of pieces in a regular bag of Skittles is approximately normally distributed with a mean of 38.4 and a standard deviation of 2.12.

a)What is the z-score value of a randomly selected bag of Skittles that has 35 Skittles? a) 1.62 b) -1.62 c) 3.40 d) -3.40 e)1.303.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

z = 35 - 38.4/2.12

= -1.60377

Option b) -1.62 is correct

b) What is the probability that a randomly selected bag of Skittles has at least 37 Skittles? a) .152 b) .247 c) .253 d).747e).7534. .

z = (x-μ)/σ

Mean of 38.4 and a standard deviation of 2.12.

z = (37 - 38.4)/2.12

= -0.66038

P-value from Z-Table:

P(x<37) = 0.25451

The probability that a randomly selected bag of Skittles has at least 37 Skittles is 0.25451

Option c) .253 is.correct

c) What is the probability that a randomly selected bag of Skittles has between 39 and 42 Skittles? a) .112 b) .232 c) .344 d).457 e).6125.

z = (x-μ)/σ

Mean of 38.4 and a standard deviation of 2.12.

For 39 Skittles

z = (39 - 38.4)/2.12

= 0.28302

Probability value from Z-Table:

P(x = 39) = 0.61142

For 42 Skittles

z = (42 - 38.4)/2.12

= 1.69811

Probability value from Z-Table:

P(x = 42) = 0.95526

The probability that a randomly selected bag of Skittles has between 39 and 42 Skittles is:

P(x = 42) - P(x = 39

0.95526 - 0.61142

0.34384

= 0.344

Option c is.correct

d) What is the percentile rank of a randomly selected bag of Skittles that has 40 Skittles in it? a)82nd b) 78th c) 75th d)25th e)22nd

z = (x-μ)/σ

Mean of 38.4 and a standard deviation of 2.12.

z = (40 - 38.4)/2.12

= 0.75472

P-value from Z-Table:

P(x = 40) = 0.77479

Converting to percentage = 0.77479× 100

= 77. 479%

≈ 77.5

Percentile rank = 78th

7 0
2 years ago
For each system of equations, drag the true statement about its solution set to the box under the system?
natta225 [31]

Answer:

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- The system of equation has zero number of solution if the coefficients

 of x and y are the same and the numerical terms are different

- The system of equation has infinity many solutions if the

   coefficients of x and y are the same and the numerical terms

   are the same

- The system of equation has one solution if at least one of the

  coefficient of x and y are different

* Lets solve the problem

∵ y = 4x + 2 ⇒ (1)

∵ y = 2(2x - 1) ⇒ (2)

- Lets simplify equation (2) by multiplying the bracket by 2

∴ y = 4x - 2

- The two equations have same coefficient of y and x and different

  numerical terms

∴ They have zero equation

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

∵ y = 3x - 4 ⇒ (1)

∵ y = 2x + 2 ⇒ (2)

- The coefficients of x and y are different, then there is one solution

- Equate equations (1) and (2)

∴ 3x - 4 = 2x + 2

- Subtract 2x from both sides

∴ x - 4 = 2

- Add 4 to both sides

∴ x = 6

- Substitute the value of x in equation (1) or (2) to find y

∴ y = 2(6) + 2

∴ y = 12 + 2 = 14

∴ y = 14

∴ The solution is (6 , 14)

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

3 0
2 years ago
What is the maximum vertical distance between the line y = x + 56 and the parabola y = x2 for −7 ≤ x ≤ 8?
atroni [7]
-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units
5 0
1 year ago
Your school organizes a clothing drive as a fundraiser for your class trip. The school earns $100 for every 400 pounds of donati
noname [10]

Answer:

$550

Step-by-step explanation:

400x=2200, x is the number of groups needed to get 2200 pounds.

If you divide both sides by 400, you'll get x=5.5

Next, multiply 5.5 by $100 because each group gives $100

hope this helps!

4 0
1 year ago
Read 2 more answers
A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s
kondaur [170]
Hello,

g=9.81m/s²= 9.81/0.3048 =32.18.. ft/s² rounded to 32

h=-g/2*t²+vt+h0
if t=0,h=0 ==>h0=0

==>h=-16*t²+vt
50 ft in 2.5s ==> 25 ft in 1.25s

25=-16*1.25²+v*1.25
==>v=50/1.25=40

Equation h=-16t²+40*t
6 0
1 year ago
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