Due to concerns about the underinflation of footballs, the National Football League (NFL) created a series of standards that must be met for the weight, length, and the long and short circumferences of each ball. It is stated that the balls are to be inflated to between 12.5 to 13.5 pounds. The pressure output by the ball pump is approximately Normal with a mean of 13 pounds and a standard deviation of 0.25 pounds. At each game, the home team must supply 12 balls to the referee 2 hours and 15 minutes prior to the start of the game for inspection.

(a) What is the probability that a randomly selected ball will not meet the inflation specifications?

Answer:

Part A

The vertex of the graph lies at (40,18). This is the maximum value on the graph. This means the balloon reached a maximum altitude of 1,800 meters about 40 minutes after its launch.

Part B

One of the x-intercepts of the function lies somewhere between x = 82 and x = 83. This is this point where the balloon is at zero altitude, or sea level. So, the balloon stays in the air for a little over 82 minutes. There is another x-intercept to the left of the origin. But a negative time value doesn’t make sense. So, we won’t considerate it for this scenario.

Part C

The -y-intercept of the function lies at (0,2). This is the starting point of the balloon’s journey. The point the balloon launched from was 200 meters above sea level.

Part D

We can’t interpret negative time values in this situation. So, the domain of the function is restricted to positive values of x. A negative y-value indicates an altitude below sea level. While some locations have negative altitudes, we can consider only positive values for this scenario. So, we should only consider positive values of y. So the domain of the function is restricted to only those values of x that produce positive values of y. Since we can’t see the x-intercept clearly from the graph, we’ll consider the domain of the function to be [0, 82].

Part E

Average rate of change on [0, 20] = f(20)-f(0) / 20-0

= 14-2 / 20

= 12 / 20

=0.6

Average rate of change on [60, 80] = f(80)-f(60) / 80-60

= 2-14 / 20

= -12 / 20

= -0.6

In this case, the rate of change represents the change in the balloon’s altitude within a time interval. The average rate of change on [0, 20] is positive. This indicates that the balloon is ascending, or climbing, during the first 20 minutes of its journey.

The average rate of change on [60, 80] is negative. This indicates that the balloon is descending between 60 and 80 minutes. Although negative, the rate of change in the second interval has the same absolute value as the rate of change for the first interval. So, during the last 20 minutes the balloon is descending at the same rate it was ascending during the first 20 minutes.

Answer:1.7

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

add up the total amount of ppl which was 300 people. 75300 people were females with blue cars. Simplfy and you'll get 1/4 or 25%.

Answer:

C, 21 students

Step-by-step explanation:

if you count out each dot plotted it equal 21 people

answer:

22.5

step-by-step explanation:

3 X 3 = 9

6 X 3 = 18

7.5 X 3 = 22.5

Answer:

c = 24.34

Step-by-step explanation:

Here, we can use the cosine rule

Generally, we have this as:

a^2 = b^2 + c^2 - 2bcCos A

12^2 = 14^2 + c^2 - 2(14)Cos 19

144 = 196 + c^2 - 26.5c

c^2 - 26.5c + 196-144 = 0

c^2 - 26.5c + 52 = 0

We can use the quadratic formula here

and that is;

{-(-26.5) ± √(-26.5)^2 -4(1)(52)}/2

(26.5 + 22.23)/2 or (26.5 - 22.23)/2

24.37 or 2.135

By approximation c = 24.34 will be correct

Answer: B

Step-by-step explanation:

Answer:

Solution given:

perpendicular distance =height [p]=40m

base or horizontal distance [b]=198m

Hypotenuse or zip line [h]=?

Now

By using Pythagoras law

h²=p²+b²

h²=40²+198²

h=√40804

h=202m

So the Zip line is 202m long.

Answer:

8 g/cm cube

Step-by-step explanation:

[tex]Density= \frac{mass}{volume}[/tex]

Density = [tex]\frac{40}{5}[/tex]

Density = 8 g / cm cube

Hope this helps :)

Answer:

$7.2 A.t a wholesale

Step-by-step explanation:

80%of $36

The mathematical order is :

80÷100×36

80÷100×36=$28.8

When we have found the 80% that is added

We subtract it from the retail price.

$36-$28=$7.2

At the end we are left with our wholesale prices.

Answer:

x= -1, y=1

Step-by-step explanation:

First label the 2 equations.

7x +6y= -1 -----(1)

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

Then choose which term you would like to eliminate. To eliminate the y term, multiply equation (2) by 3 such that the coefficient of y is 6.

(2) ×3:

-3x +6y= 9 -----(3)

Since the coefficient of y is positive 6 in both equations, subtract one equation from the other.

(3) -(1):

-3x +6y -(7x +6y)= 9 -(-1)

Expand:

-3x +6y -7x -6y= 9 +1

-10x= 10

x= 10 ÷(-10)

x= -1

Substitute x= -1 into (2):

-(-1) +2y= 3

1 +2y= 3

2y= 3 -1

2y= 2

y= 2 ÷2

y= 1

------------------------------------------------------------

2nd method: eliminating the x term

(2) ×7:

-7x +14y= 21 -----(3)

Since the coefficient of y in equation (1) is a positive 7, while that in equation (3) is a negative 7, add the 2 equations together to eliminate the x term.

(1) +(3):

7x +6y -7x +14y= -1 +21

20y= 20

y= 20 ÷20

y= 1

Substitute y= 1 into (2):

-x +2(1)= 3

-x +2= 3

-x= 3 -2

-x= 1

x= -1

Answer:

Step-by-step explanation:

[tex]5 {a}^{3} + 3a + 7 {a}^{3} - 2a - 4 {a}^{2} \\ \\ (5 {a}^{3} + 7 {a}^{3} ) + ( - 4 {a}^{2} ) + (3a - 2a \: ) \\ \\ 12 {a}^{3} - 4 {a}^{2} + a[/tex]

I hope that is useful for you :)

Answer:

32 pieces for each person but there will be 2 pieces left over

Step-by-step explanation:

Answer:

Each person will get 32 pieces. That's to be even.

Step-by-step explanation:. :D

Answer:1444.4

Step-by-step explanation:

part 1:To start do 10 times 10 then multiply that by 3.14 then multiply that again by 2.

Part 2:then multiply the radius by the height and then multiply that number by 3.14 then multiply it by 2.

Part 3: then add both together

Answer:

1,444.4

Explanation:

S=2πr2+ 2πrh

S=628+816.4

S=1,444.4

*☆Hope this helped!☆*

Answer:

21

Step-by-step explanation:

I have done this question before.

Answer:

58° = measure of arc AC

Step-by-step explanation:

The measure of an angle formed by 2 chords is equal to 1/2 the sum of the measures of the intercepted arcs.

65 = (measure of arc AC + measure of arc BD)/2

     =  (measure of arc AC + 72)/2

130 = measure of arc AC + 72

58° = measure of arc AC

Answer:

23m

Step-by-step explanation:

Answer:

Step-by-step explanation:

(f + g)(2) = 2(2) + 3 + (2)^2 - 1 = 10

(f - g)(4) = 2(4) + 3 - (4)^2 + 1 = -4

(f / g)(2) = (2(2) + 3) / ((2)^2 -1) = 7/3

(f * g)(1) = (2+3)(1-1) = 0

Answer:

$16.70

Step-by-step explanation:

9.5 miles / .25 = 38

The first mile is 1.25 so we do this

37 * .35 = 12.95

12.95 + 1.25 = 14.2

14.2 + 1.25 + 1.25(two additional passengers) = 16.70

Answer:

Step-by-step explanation:

Answer:

instead of the 4, you can put the 80 and do the 20x4?

Step-by-step explanation:

i dont know if you can do that for whatever ur doing, just a suggestion

I lost my train of thought, but i was thinking of something like that

Answer:

The fifth term is the middle term of nine, with coefficient given by all the ways of choosing  4  items out of  8 , namely the ways of choosing  4   a 's out of  8  binomial factors.

Step-by-step explanation:

The third term of the expansion is 56a⁵b³

The expression is given as:

(a + b)^8

The above expression is a binomial expression, and the nth term of the expression is:

(a + b)^n = nCr * a^(n - k) * (b)^k

Where k = 0, 1, 2.....

So,we have:

(a + b)⁸ = ⁸C₃ * a⁸⁻³ * b³

Evaluate the combination expression

(a + b)⁸ = 56a⁵b³

Hence, the third term of the expansion is 56a⁵b³

Read more about probability at:

https://brainly.com/question/251701

Answer:

Solution given:

5+x/2=4

x/2=4-5

x=-1×2

x=-2

Answer:

30

Step-by-step explanation:

1 * 6 = 6

5 * 6 = 30

6:30

When you reduce it will be back to 1:5

Answer:

23 Ft

Step-by-step explanation:

Answer:

Slope m = 3.95

Step-by-step explanation:

Mathematically :

The equation of a line is written as y = mx + b

where

m is the slope

b is the y- intercept.

From the above question, we are told:

A farmer charges for his coffee beans using the equation C = 3.95p,

where C is the cost of the coffee beans and p is the number of pounds of coffee beans.

Comparing both equations:

y = mx + b

C = 3.95p

C = y

mx = 3.95p

b = 0

Therefore, the slope is 3.95

Answer:

Step-by-step explanation

there is a square and it has 4 sides and if each are 300 you have to multiply  but remember to put the 2 zeros cause 300 has 2 zeros

Answer:

$32.09

Step-by-step explanation:

Um....yeah I just used an online calculator lol

Answer:

Number one is Linear, Number two is Exponential, and Number three is quadratic

Step-by-step explanation: