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enyata [817]
3 years ago
13

Jacob kept track of the number of hours that he spent playing soccer each week for several weeks he spent 3, 6, 7, 8, and 11 hou

rs. What is the range of the data set?
Mathematics
1 answer:
Sloan [31]3 years ago
4 0

Answer:

8

Step-by-step explanation:

The range of the data set is determined by the maximum - minimum.

The max value is 11

The min value is 3

11-3=8

The range of the data set is 8.

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A school director must randomly select 6 teachers to participate in a training session. There are 30 teachers at the school. In
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An object is launched from a platform. its height in meters X seconds after the launch is modeled by h(x)=-5x^2+20x+60 how m
Alex

Answer:

6 seconds after launch.

Step-by-step explanation:

You should make sure  there aren't odd symbols in your question when you post it.

Assuming it is just the equation -5x^2 + 20x + 60, if you graph it you can see the path of the ball.  at x=0 this is the starting point It then hits the ground when it touches the x axis.  So this is finding zeroes of a quadratic.

You could do this several ways; find a way to factor it, guess and check, the quadratic formula or completing the square.  I will complete the square as that is what I am most used to.  If you would like to see another let me know.

The first step in completing the square is making sure the x^2 has a coefficient of 1, so now it has -5 so we have to factor out -5 from the equation.

-5x^2+20x+60 = -5(x^2 - 4x - 12)

Now you only really need to focus on the factored expression, but I will continue writing everything.  The next step is to find (b/2)^2 where b is the coefficient of the x term.  In this case -4.  so (b/2)^2 = (-4/2)^2 = 4.

Again, focusing on x^2 - 4x - 12 you want to add and subtract (b/2)^2 from that expression.  since you are adding and subtracting you are not changing the value, but we can use this.

-5(x^2 - 4x - 12) = -5(x^2 - 4x - 12 + 4 - 4)

Here you want to rearrange it a bit.  Originally c was the constant term, -12, now you want it to be the positive (b/2)^2, which is positive 4. also you can combine the two other constant terms.  the original c and -(b/2)^2, but I will hold off for now so I don't do too much at once.

-5(x^2 - 4x - 12 + 4 - 4) = -5(x^2 - 4x + 4 - 12 - 4)

Now you focus on x^2 - 4x + 4.  Hope fully you recognize this is the same as (x-2)^2.  This always happens at this step of the process.  also notice -2 = b/2.  Using only variables here are the first steps.

ax^2 + bx + c

a(x^2 + (b/a)x + (c/a))

a(x^2 + (b/a)x + (c/a) + (b/(2a))^2 - (b/(2a)^2)

a(x^2 + (b/a)x + (b/(2a))^2 + (c/a) - (b/(2a))^2)

a((x + b/(2a))^2 + (c/a) - (b/(2a))^2)

Again, being able to make x^2 - 4x + 4 into (x-2)^2 or x^2 + (b/a)x + (b/(2a))^2 into (x + b/(2a))^2 willa lways happen.  this is because if you expand (x + b/(2a))^2 you always get x^2 + (b/a)x + (b/(2a))^2.

Now I would combine the -12-4

-5(x^2 - 4x + 4 - 12 - 4) = -5((x - 2)^2 - 12 - 4) = -5((x - 2)^2 - 16)

If you redistribute the -5 you get vertex form, but I am going to stop here  because I will just undo that in the next step.  So this is the form you want.  Finally we can find when it equals 0.  So, you set this equal to 0 and use algebra to solve.

-5((x - 2)^2 - 16) = 0

Divide both sides by -5

(x-2)^2 - 16 = 0

add 16 to both sides

(x-2)^2 = 16

Take the square root of both sides, but also count botht he positive and negative version of the answer.  the reason is both 2 and -2 squared get you 4.

x - 2 = +/-4

I am using +/- to indicate I am using both positive and negative 4.  Now though add 2 to both sides.  since you have +/- 4 you are going to get two different results.  -4+2 and 4+2

x = -2 and 6.

now, the question wants times after x=0 (the start) so you only get 6.  so x=6, or in other words 6 seconds after launch.

Let me know if you have any questions.

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1 mile = 5280 ft.....so 1/3 of a mile is : 1/3 * 5280 = 5280/3 = 1760 ft

and the store sells yarn in sets of 340 ft...
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