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3 years ago

7

In the figure below, what is the area of triangle ABC?

1 answer:

Serhud [2]3 years ago

5 0

The area of a triangle is base * height / 2

The length of the base is 16 - 12 = 4

The height is 31 - 0 =0

Then the area is 4*31/2 = 62

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Select the favorable Outcomes for rolling double sixes

ira [324]

We want double sixes. This means that we want both the first roll and the second roll to be 6.

The given point is given as (r1 , r2) where:
r1 is output from first roll
r2 is output from second roll

Since we want both outputs to be 6, therefore, the answer would be: (6,6)

4 0

4 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

The scores on a quiz are normally distributed. The mean of the quiz is 93 and the standard deviation is 4.2. By using the Empiri

xz_007 [3.2K]

Answer:

any score that lies between 88.8 and 97.2 is within one std. dev. of the mean

Step-by-step explanation:

One std. dev. above the mean would be 93 + 4.2, or 97.2. One std. dev. below the mean would be 93 - 4.2, or 88.8.

So: any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.

6 0

3 years ago

If two angles of a triangle have measures of 42° and 20°, what is the measure of the

iris [78.8K]

Answer:

118°

Step-by-step explanation:

the angle measures of a triangle will always add up to 180

so..

42+20=62

180-62=118

4 0

3 years ago

Read 2 more answers

Which coordinates represent a translation of B (1,2) 3 units to the left and 2 units up

alexandr402 [8]

Answer:

(-2,4)

Step-by-step explanation:

By going 3 back you go 0,-1,-2 then you are already up 2 so if you go up 2 more you are at (-2,4). Hope this helps!

6 0

2 years ago