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3 years ago

Write in vertex form (by completing the square)y=4x2+40x+96

1 answer:

6 0

$y=4x^2+40x+96\\ \\ The \ vertex \ form \ of \ the \ function \ is: \\ \\y = a(x - h)^2 + k \\ \\vertex =(h, k) \ is \ given \ by: \\ \\h = \frac{-b}{2a} , \ \ \ k = c -\frac{b^2}{4a} \\ \\a=4 , \ \ b=40 , \ \ c=96$

$h = \frac{-40}{2 \cdot 4}=\frac{-40}{8}=-5 \\ \\ k = 96 -\frac{40^2}{4 \cdot 4} =96-\frac{1600}{16} =96-100=-4 \\ \\ y = 4(x - (-5) )^2 + (-5)=4(x +5 )^2 -5$

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What's the formula to find the width

vlabodo [156]

2l + 2w = p

If you already have perimeter and length, you can use this formula to solve for width.

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3 years ago

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A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?

Vlada [557]

Answer:

I am not sure what the values needed to add in / etc, but here is the height of the box: 5

Step-by-step explanation:

A cube is a kind of rectangle where all the sides are the same. So to find volume, cube the length of any side. To find height, calculate the cube root of a cube's volume. For this example, the cube has a volume of 125. The cube root of 125 is 5. The height of the cube is 5.

(hopefully this is correct, have a nice day!)

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3 years ago

A box of candy hearts contains 52 hearts, of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orang

laiz [17]

<u>Answer-</u>

a. Probability that three of the candies are white = 0.29

b. Probability that three are white, 2 are tan, 1 is pink, 1 is yellow, and 2 are green = 0.006

<u>Solution-</u>

There are 19 white candies, out off which we have to choose 3.

The number of ways we can do the same process =

$\binom{19}{3} = \frac{19!}{3!16!} = 969$

As we have to draw total of 9 candies, after 3 white candies we left with 9-3 = 6, candies. And those 6 candies have to be selected from 52-19 = 33 candies, (as we are drawing candies other than white, so it is subtracted)

And this process can be done in,

$\binom{33}{6} = \frac{33!}{6!27!} =1107568$

So total number of selection = (969)×(1107568) = 1073233392

Drawing 9 candies out of 52 candies,

$\binom{52}{9} = \frac{52!}{9!43!} = 3679075400$

∴P(3 white candies) = $\frac{1073233392}{3679075400} =0.29$

Total number of ways of selecting 3 whites, 2 are tans, 1 is pink, 1 is yellow, and 2 are greens is,

$\binom{19}{3} \binom{10}{2} \binom{7}{1} \binom{5}{1} \binom{6}{2}$

$=(\frac{19!}{3!16!}) (\frac{10!}{2!8!}) (\frac{7!}{1!6}) (\frac{5!}{1!4!}) (\frac{6!}{2!4!})$

$=(969)(45)(7)(5)(15)=22892625$

Total number of selection = 3 whites + 2 are tans + 1 is pink + 1 is yellow + 2 greens = 9 candies out of 52 candies is,

$\binom{52}{9}=\frac{52!}{9!43!} =3679075400$

∴ P( 3 whites, 2 are tans, 1 is pink, 1 is yellow, 2 greens) =

$\frac{22892625}{3679075400} = 0.006$

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3 years ago

At a pizza resturant they have a choice of 20 toppings. If a customer choosea two topping pizza find the probability that they o

Naddika [18.5K]

Answer: The probability is 1/190 = 0.005

Step-by-step explanation:

The probability of ordering two specific toppings out of 20 is:

For the first selection he can order 2 of them, peperoni or sausage, so the probability for the first selection is 2/20 = 1/10 (the number of correct options divided by the total number of options)

For the second selection we have only one option, because we assume that the other one was selected previously, here we also had a total of 19 toppings because one already was selected, the probability in this selection is 1/19.

The joint probability is equal to the product of those two probabilities:

P = (1/19)*(1/10) = 1/190 = 0.005

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3 years ago

lauren is 4 years older than cole. their mom is 7 years older than triple coles age. the sum of the ages of cole, lauren, and th

babymother [125]

Answer:

Step-by-step explanation:

71-4

71/3-7

=16

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3 years ago

Read 2 more answers