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4 years ago

12

Find the percent change as an increase or decrease to 8 inches to 24 inches

2 answers:

Black_prince [1.1K]4 years ago

7 0

New value=24
Original value=8

Change in value= New value-original value
Change in value=24-8
Change in value=16
%increased=change in value/original value x100%
%increased= 16/8x100
%increased=200%

Doss [256]4 years ago

4 0

Think of the number 8 as 100%.

What multiplies 8 to 24?

3.

100% x 3 = 300% increase

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A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

Len [333]

Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

3 0

3 years ago

Which is the completely factored form of 3xsquared<br> -12x-15?

tekilochka [14]

Answer:

3(x - 5)(x + 1).

Step-by-step explanation:

3x^2 - 12x - 15

Dividing through by 3:

= 3(x^2 - 4x - 5)

We need 2 numbers whose sum is -4 and whose product = -5. That is -5 and +1 , so the factors are:

3(x - 5)(x + 1).

7 0

3 years ago

-(x-7)^2+5 standard form

Verizon [17]

Answer: −x^2+14x−44

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Jina worked 37 hours last month and earned 59 per hour. She spent $15 of her earnings since then. How much money does she have l

Drupady [299]

Answer:

$6.83

Step-by-step explanation:

37 x 59 = 2183

Because it is dollars you need to divide it by 100:

$21.83 - 15 = 6.83

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=4%2A%289%5E%7B2%7D%20%2F27%2A5%29" id="TexFormula1" title="4*(9^{2} /27*5)" alt="4*(9^{2} /27*

ratelena [41]

Answer:

60

Step-by-step explanation:

Simplify the following:

4×9^2/27×5

9^2/27×5 = (9^2×5)/27:

4×(9^2×5)/27

4×(9^2×5)/27 = (9^2×5×4)/27:

(9^2×5×4)/27

9^2 = 81:

(81×5×4)/27

81/27 = (27×3)/27 = 3:

3×5×4

3×5 = 15:

15×4

15×4 = 60:

Answer: 60

7 0

4 years ago