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3 years ago

Whats the median of (20, 15, 14, 16, 17, 12, 20, 22)

Mathematics

1 answer:

Tatiana [17]3 years ago

5 0

Answer:

16.5

Step-by-step explanation:

Given data to us is ,

20, 15, 14, 16, 17, 12, 20, 22 .

Arrange it in ascending order .

= 12 , 14 , 15 , 16 , 17 , 20 , 20 , 22

The middle most observation will be median in case n is odd and average of middlemost observations if n is even , that is n = 8 .

=> Middlemost observations = 16 , 17

=> Mean = 16 + 17 /2 = 33/2 = 16.5

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A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2t from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

Use set builder notation to represent the following set. {... -3, -2, -1, 0} {x | x Z, x ≤ 0} {x | x N, x ≤ 0} {x | x R, x ≤ 0}

IceJOKER [234]

Answer:

$\boxed{\boxed{\left\{x\ |\ x\ \epsilon\ Z,\ x \le 0}\right\}}}$

Step-by-step explanation:

Set builder notation-

It is a notation for representing a set by enumerating its elements and stating the properties that its members must satisfy.

The given set is,

$\left \{.... -3, -2, -1, 0 \right \}$

This set is comprised of all negative integers. So symbol Z should be used in this case.

The set builder notation for this set is,

$\left\{x\ |\ x\ \epsilon\ Z,\ x \le 0}\right\}$

7 0

4 years ago

Which inequality is true? Use the number line to help.

goblinko [34]

The only true inequality is -3 1/2 > -4.5

3 0

3 years ago

Theo’sMom bought an eight-pack of juice boxes at the store for $4.Find The unit rate for the juice boxes

Elina [12.6K]

$4/8 = $0.5 per box
take the total cost and divide by total # of juice boxes

4 0

3 years ago

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(5x + 45 to the 6th power.)4

dsp73

Answer:

is it nail polish..............

4 0

3 years ago