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3 years ago

If the median of five consecutive even integers is 20, what is the value of the smallest integer?

Mathematics

1 answer:

IceJOKER [234]3 years ago

5 0

Answer:

Step-by-step explanation:

Median means the middle number. So you can look at it like this:

Those are the variables for the numbers we do not know. We do know that they are all even numbers and they are consecutive, meaning in sequence. So if they are all even, then there should be a gap of 2 between each. They should also be in order. Knowing that, you can subtract 2 from 20 to get b, subtract 2 from b to get a, add 2 to 20 to get c, and add 2 to c to get d.

This should be your answer:

16, 18, 20, 22, 24

Consecutive, and even.

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Select the correct answer from each drop down menu

Illusion [34]

Answer:

1. 2 2. 1 3.(2,1)

Step-by-step explanation:

y=_x+3

plug y in by choosing a number in the y column.

1=_x+3

1=(2)(-1)+3

1=1

Part 2.

do the same

5=3(2)

5=6-1

5=5

4 0

3 years ago

How do you find the slope on a graph?

Katarina [22]

Answer:

I am unsure of the specifics, I always used slope-intercept form.

Step-by-step explanation:

If there is a specific question you are struggling with try entering the problem in m-a-t-h-w-a-y. This always helps me.

8 0

3 years ago

1. A tennis tournament starts with 120 players. During each round of the game, half of the players are eliminated from the tourn

lorasvet [3.4K]

Answer:

Exponential function; $y=120(\frac{1}{2})^x$ .

Step-by-step explanation:

We have been given that a tennis tournament starts with 120 players. During each round of the game, half of the players are eliminated from the tournament.

We can see that the change in number of eliminated players is not constant. The number of players in tournament is decreasing exponentially. Therefore, an exponential function best models the relationship between the number of players in the tournament, y, and the game round, x.

We know that exponential decay function is in form $y=a(b)^x$ , where,

y = Final amount,

a = Initial amount,

b = Decay factor,

t = Time

Since during each round of the game, half of the players are eliminated from the tournament, so decay factor would be $\frac{1}{2}$ .

Initially there were 120 players, so $a=120$ .

Therefore, our required equation would be $y=120(\frac{1}{2})^x$ .

6 0

4 years ago

A rocket is launched from a tower what time will the rocket reach its max

Lena [83]

Answer:

Step-by-step explanation:

A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the ball could be described by the function: h(t) = -16t2 + 144t + 160, where ‘t’ represents the time the ball is in the air in seconds and h(t) represents the height, in feet, of the ball above the ground at time t.

a) Graph the function h(t) = -16t2 + 144t + 160 (see below)

b) What is the height of the building?

The height of the building is also the height of the tennis ball before it is launched into the air. This occurs when t=0 so substitute 0 for t and you get:

H(0) = -16(0)2 + 144(0) + 160

The height of the building is 160 feet.

c) At what time did the ball hit the ground?

The ball hits the ground when the height is 0. Therefore, we are looking for a solution to: -16t2 + 144t + 160 = 0

Use the quadratic formula or put this into a calculator. The solution is t=10 and -1, but only 10 makes sense. Therefore, the ball hits the ground at 10 seconds.

d) At what time did the ball reach its maximum height?

You can put this into the calculator or you can realize that the maximum height is also

− the vertex. The x-value (‘t’ in this case) is 2

−144

which is (2)(−16) = 4.5.

Therefore, the ball reached its maximum height at 4.5 seconds.

e) What is the maximum height of the ball?

We calculated the time of the maximum height (4.5 seconds). Therefore, substitute 4.5 into the function to find the maximum height.

-16(4.5)2 + 144(4.5) + 160

The maximum height is 484 feet.

5 0

3 years ago

She needs to buy at least 100 chairs. Chairs with arms cost $80. Chairs without arms cost $70. Ms. Robinson can spend, at most,

stealth61 [152]

Answer:

50 chairs with arms and 50 without arms will cost $7500

Step-by-step explanation:

Create two equations using the given information. The unknowns are :

W = Number of chairs with arms

N = Number of chairs with No arms

First equation (associated with the total number of chairs to buy):

W + N = 100

Second equation (associated with the amount to spend):

80 W + 70 N = 7500

Solving: solve for W in the first equation: W = 100 - N

Use it to substitute for W in the second equation:

80 (100 - N) + 70 N = 7500

8000 - 80 N + 70 N = 7500

subtract 8000 from both sides and combine

- 10 N = - 500

Divide both sides by -10 in order to solve for N

N = -500 / (-10) = 50

Now use this value in the substitution equation to solve for W:

W = 100 - 50 = 50

So the person can buy 50 chairs with arms and 50 chairs without arms paying for them $7,500.

8 0

3 years ago