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3 years ago

You roll a 6-sided die two times.

Mathematics

1 answer:

IgorC [24]3 years ago

8 0

The probability is going to be 50 percent for the even as well as 50 percnent for the odd

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

How can i get the answer to 5 X 70 = 5 X ____ tens = ____ tens = _____

Maru [420]

Multiple 5x70 to get 350. Which makes the equation 350=5x and then you have to divide both sides by 5 to get x by itself. so 5x/5 and 350/5 makes x=70

3 0

3 years ago

Number 19: Please explain the answer. Thank you so much!

icang [17]

So we are looking for the GCF which is the largest factor that the two numbers have in common, so you would want to circle all of the number that the two have in common. So it would be 2 twos and 2 X's (2,2,x,x). Which is the most numbers that the two have in common.

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3 years ago

Perry pays $340 per month to lease her car. How much will she pay to lease her car for two years?

irinina [24]

$340 × 24 (12 months in one year)

= $8160

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3 years ago

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How can you use ratios to convert units of measurement

Yuliya22 [10]

You do
unit of measurement you are using (should be one for now): unit of measurement you want to convert it to.
next you put your measurement in the first one and make the second one your measurement multiplied by whatever your measurement is

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4 years ago