What is an equivalent fraction to 9 divided by -12

A candle is 7in tall after burning for 1 h. The same candle is 5 1/2 in y’all after burning for 4 h. How tall will the candle be

viva [34]

Answer:

4.5 inch

Step-by-step explanation:

Given: A candle is 7 inch tall after burning for 1 hour.

Same candle is 5.5 inch tall after burning for 4 hours.

Lets assume time to burn candle be "x" and height of candle be "y".

Now, finding the rate of changes in height of candle per hour.

Let "m" represent the changes in height of candle per hour.

we know, $m= \frac{Changes\ in\ length}{Changes\ in\ time}$

∴ m= $\frac{5.5-7}{4-1} = \frac{-1.5}{3}$

m= $-0.5$

Next, forming an equation to know the original height of candle.

using equation; $y= mx+ original\ height$

We know, A candle is 7 inch tall after burning for 1 hour.

⇒ $7= -0.5\times 1+ original\ height$

⇒ $7= -0.5+ original\ height$

Adding both side by 0.5

⇒ $Original\ height= 7.5\ inches$

Hence, the original height of candle was 7.5 inches.

Again using the same equation to find the height of candle after burning for 6 hour.

$y= -0.5\times 6+ 7.5$

⇒ $y= -3+7.5$

∴ y= 4.5 inches.

Hence, The candle will be 4.5 inches tall after burning for 6 hour.

4 0

3 years ago

A special olympics event has 12 more boys than girls competing the total number of participants is 1000 how many boys conpeted a

kodGreya [7K]

Subtract 1000 by 12. Divide that answer by 2. Add 12 to that answer.

Equations:
1000 -12= 988 988÷2=494 494+12=506

506 boys and 494 girls competed at the special olympics event.

4 0

3 years ago

GUYS I REALLY NEED HELP!! THE STRUGGLE!!

Mazyrski [523]

Answer:

Last option is the correct answer.

Step-by-step explanation:

Total number of movies = 9+7+4=20

The total number of combinations of choosing 3 movies from total 20 is represented by 20C3. Then there are 9 action movies and we're choosing 3, the number of combinations will be 9C3,

Now, the probability of choosing all action movies will be:

$\frac{9C3}{20C3}$

As we know that probability of something which is not happening is given as : 1 - probability of something happening, so the probability of not choosing all action movies is given by: $1-\frac{9C3}{20C3}$

Hence, option D or last option is the right one.

6 0

4 years ago

Read 2 more answers

Help solving this math question

olga_2 [115]

22. B) $65,000,000 per year.

23. B) Education.

Step-by-step explanation:

Step 1; To find the average rate of change in annual budget between the two given years. We divide the difference in values for the two years by the period in between the two years. In 2008, the budget was $358,708,000 while in 2010 it was $488,106,000. The period in between was 2 years i.e 2009 and 2010.

The average rate of change = $\frac{488,106,000-358,708,000}{2}$ = $\frac{129,398,000}{2}$ = $64,699,000 per year.

So the average rate of change was $64,699,000 which approximately equals option B. $65,000,000.

Step 2; To find the human resources program's 2007 to 2010 ratio we divide the value in 2007 to the value in 2010. To find the other similar ratio, we divide the value in 2007 to the value in 2010 for all the other programs and determine which is closest to the human resources program.

Human resources program ratio = $\frac{4,051,050}{5,921,379}$ = 0.6841,

Agricultural / natural resources ratio = $\frac{373,904}{488,106}$ = 0.766,

Education's ratio = $\frac{2,164,607}{3,008,036}$ = 0.7196,

General government's ratio = $\frac{14,347,325}{14,716,155}$ = 0.9749,

Highways and transportation's ratio = $\frac{1,468,482}{1,773,893}$ = 0.827,

Public safety's ratio = $\frac{263,463}{464,233}$ = 0.5675.

The Human resources' program ratio is 0.6841 and the closest is Education's ratio which is 0.7196. So education is the answer.

4 0

3 years ago

A rectangular tract of land in Mathville has the dimensions 4x2 + 3x + 12 and 4x – 2. Another rectangular area of a land in Alge

Goryan [66]

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given the dimension

Length = 4x2 + 3x + 12

Width = 4x – 2

A) Area = (4x^2 + 3x + 12)(4x – 2)

Open the parenthesis

= 16x^3-8x^2+12x^2-6x+48x-24

Area of land in Mathville = 16x^3+4x^2+42x-24

For the land in Algebratown

Area = (5x^2 + x – 4)(2x + 1)

Area = 10x^3+5x^2+2x^2+x-8x-4

Area = 10x^3+7x^2-7x-4

B) difference between the area of Mathville and the area of Algebratown

= 16x^3+4x^2+42x-24 -(10x^3+7x^2-7x-4)

= 16x^3+4x^2+42x-24 -10x^3-7x^2+7x+4

collect like terms

= 16x^3-10x^3+4x^2-7x^2+42x+7x-24+4

= 6x^3-3x^2+49x-20

C) The difference if x = 9

Substitute x = 9 into the resulting function

A(x) = 6x^3-3x^2+49x-20

A(9) = 6(9)^3-3(9)^2+49(9)-20

A(9) = 2187-243+441-20

A(9) = 2,365

Hence the difference of the areas if x = 9 is 2,365

6 0

3 years ago