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bonufazy [111]
3 years ago
7

these are the number of baskets joe scored in his basketball game. what is the mean of the data set? 3,3,4,4,8,8,8,10,12,20

Mathematics
2 answers:
Viktor [21]3 years ago
8 0

Answer:

8

Step-by-step explanation:

To find the mean, add all the numbers together and divide by the amount of numbers there are.

(3 + 3 + 4 + 4 + 8 + 8 + 8 + 10 + 12 + 20)/10 = answer

Simplify. First, solve the parenthesis, then divide.

(80)/10 = answer

8 = answer

8 is the mean of the data set.

~

jeka57 [31]3 years ago
7 0

Answer:

10.2 I do believe

Step-by-step explanation:

Add all the Numbers together and divide your answer by the amount of Numbers there are.

Example: 3,3,4,4,8,8,8,10,12,20 there are 10 numbers there. Add all of those numbers together are 102.

102÷10 = 10.2

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require
Aleksandr-060686 [28]

Answer:

r\approx 1.084\ feet

h\approx 1.084\ feet

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

  •  Produce a function which depends on only one variable
  •  Compute the first derivative and set it equal to 0
  •  Find the values for the variable, called critical points
  •  Compute the second derivative
  •  Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 ft^3. The volume of a cylinder is given by

\displaystyle V=\pi r^2h

Equating it to 4

\displaystyle \pi r^2h=4

Let's solve for h

\displaystyle h=\frac{4}{\pi r^2}

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

\displaystyle A=\pi r^2+2\pi rh

Replacing the formula of h

\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )

Simplifying

\displaystyle A=\pi r^2+\frac{8}{r}

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

\displaystyle A'=2\pi r-\frac{8}{r^2}=0

Rearranging

\displaystyle 2\pi r=\frac{8}{r^2}

Solving for r

\displaystyle r^3=\frac{4}{\pi }

\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet

Computing h

\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

\displaystyle A''=2\pi+\frac{16}{r^3}

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}

\boxed{ A=11.07\ ft^2}

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Jon has to pay $7.50 admission for the skating rink and $1.50 per hour to rent rollerblades. Write an equation for the cost (y)
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Answer:

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Step-by-step explanation:

The admission costs $7.50 and after x hours Jon has to pay $1.50*x. Then the cost y in dollars is

y = 7.50 + 1.50x where x is the number of hours.

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