The cheerleaders are practicing a dance routine in which all 36 of them need to be in a triangular formation. there will be two more cheerleaders in each row than the previous row. how many rows will be in the formation

Answers

Answer 1

Answer:

If you start with 1 cheerleader in row A, then you'll have 3 cheerleaders in row B (add on 2), and then 5 cheerleaders for row C (add on another 2), etc etc.

Note how: 1+3+5 = 4+5 = 9 which is a perfect square. Also note that 36 is a perfect square.

Rule: The sum of the first positive n odd numbers is going to be equal to n^2. In the example of adding the first three odd numbers (1,3,5), we have n^2 = 3^2 = 9 as the sum

So as you can see, we'll have n = 6 rows because n^2 = 6^2 = 36 and

1+3+5+7+9+11 = 36

which is the sum of the first six positive odd numbers. So we'll have 1 cheerleader in row A, 3 in row B, 5 in row C, 7 in row D, 9 in row E, 11 in row F to have 6 rows total.

Answer 2

Answer:

Final answer:

To determine the number of rows in the triangular formation, set up an equation and solve for x. The number of rows is 6.

Explanation:

To determine the number of rows in the triangular formation, we can set up a series of equations.

Let x be the number of rows.

The first row will have 1 cheerleader, the second row will have 3 cheerleaders, the third row will have 5 cheerleaders, and so on.

We can set up the equation: 1 + 3 + 5 + ... + (2x-1) = 36.

This is the sum of an arithmetic sequence with a common difference of 2. Solving for x, we get x = 6.

Therefore, there will be 6 rows in the formation.

Learn more about Number of rows in triangular formation here:

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The number of aluminum cans used each year varies directly as the number of people using the cans. If 500 people use 120000 cans in one year, how many cans are used each year in a city which has a population of 130000?

Answers

Answer

31,200,000

Explanation

Firstly, calculate the constant of proportionality.

Al ∝ N

Al = kN Where Al = number of aluminium cans, k = constant and N = number of people using the can.

Al = kN

k = Al/N

= 120000/500

= 240

Equation becomes;

Al = 240N

For 130000 cans;

Al = 240 × 130000

= 31,200,000

At Bayside High School, 55% of the student body are boys. Thirty-five percent of the boys are on honor roll, and 40% of girls are on honor roll. What percent of the student body is on honor roll? Round to the nearest percent

Answers

If 55% of the student body are boys, then 45% are girls.

35% of boys are on the honor roll, so 35% of 55% are on the honor roll.

40% of girls are on the honor roll, so 40% of 45% are on the honor roll.

So now we need to find each of those numbers...

35% of 55% =
.35 * .55 = .1925 multiply by 100 to convert to percent

19.25% of boys (in the student body) are on honor roll

40% of 45% =
.40 * .45 = .18 multiply by 100 to convert to percentage

18% of girls (in the student body) are on honor roll

Add the two together to get the total percentage of student body that is on the honor roll...

19.25% + 18% = 37.25%

Round to the nearest percent

37%

So,

35% of 55% is equal to the percent of boys on honor roll in the student body.

100 - 55 = 45%, which is the percent of girls in the student body.

40% of 45% is equal to the percent of girls on honor roll in the student body.

35% * 55% = 19.25%

40% * 45% = 18%

Adding them up, we get:
19.25 + 18 = 37.25%

Round it to the nearest percent.
37.25 --> 37%

Rounded to the nearest percent, 37% of the student body is on honor roll.

If x-2y=1, what is the value of 2 3x-6y?

Answers

I hope this helps you

a container was 1/2 filled with water. When 200 ml of water was poured out, it became 1/3 full. Find the capacity of the container in milliliters.

Answers

x=whole capacity
(x/2)=original amount
orginal amount-200=x/3
so
(x/2)-200=x/3
subtract x/2 from both sides
-200=(x/3)-(x/2)
make denomenators same
x/3 times 2/2=2x/6
x/2 tiimes 3/3=3x/6
now we have
-200=2x/6-3x/6
-200=-x/6
multiply both sides by 6
-1200=-x
multiply -1
1200=x

capacity is 1200 ml

Write an expression for the total cost, in pounds, of: X jumpers at £15 each and y shirts at £12 each

Answers

x jumpers at £15 each. Total = 15*x = £15x

y shirts at £12 each. Total = 12*y = £12y

Total cost = £15x + £12y

Total cost = £(15x + 12y)

Final answer:

The total cost, in pounds, for X jumpers at £15 each and Y shirts at £12 each can be written as the mathematical expression: 15X + 12Y, where X and Y are the quantities of jumpers and shirts respectively.

Explanation:

To write an expression for the total cost of X jumpers at £15 each and Y shirts at £12 each in pounds, you need to multiply the cost per item by the quantity of each items and then add these two products together.

So, the total cost can be given as: