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2 years ago

All students in a year group were asked how they travelled to school.

Mathematics

1 answer:

Tems11 [23]2 years ago

5 0

Step-by-step explanation:

there are

150 + 83 + 57 + 10 = 300 students in total.

so,

100% = 300

1% = 100%/100 = 300/100 = 3

150 / 3 = 50%

83 / 3 = 27 2/3 % or 27.66666...%

57 / 3 = 19%

10 / 3 = 3 1/3 % or 3.333333...%

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You have been asked to analyze the popcorn recipes of three different local theatres in order to figure out which theatre has th

vovikov84 [41]

Given that the manager of Theatre A says that they usually go through about 15 cups of popcorn kernels and about 5 cups of oil each weeknight.

Then, the ratio value of oil to popcorn kernels for theatre A is 5 / 15 = 1 / 5.

Given that the manager of Theatre B says that they order 18 cups of oil and 72 cups of popcorn kernels each week.

Then, the ratio value of oil to popcorn kernels for theatre B is 18 / 72 = 1 / 4.

Given that the manager of Theatre C says that their concessions use 6 cups of oil and 32 cups of popcorn kernels on a busy Saturday.

Then, the ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.

7 0

3 years ago

Read 2 more answers

Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is

aniked [119]

Base case: For $n=1$ , the left side is 2 and the right is $2\cdot1^2=2$ , so the base case holds.

Induction hypothesis: Assume the statement is true for $n=k$ , that is

$2+6+10+\cdots+4k-2=2k^2$

We want to show that this implies truth for $n=k+1$ , that

$2+6+10+\cdots+4k-2+4(k+1)-2=2(k+1)^2$

The first $k$ terms on the left reduce according to the assumption above, and we can simplify the $k+1$ -th term a bit:

$\underbrace{2+6+10+\cdots+4k-2}_{2k^2}+4k+2$

$2k^2+4k+2=2(k^2+2k+1)=2(k+1)^2$

so the statement is true for all $n\in\mathbb N$ .

5 0

3 years ago

3^2-2^3 what is that

quester [9]

Answer:

Step-by-step explanation:

3^2-2^3

3^2 = 9

2^3 = 8

9-8 = 1

5 0

3 years ago

Read 2 more answers

Geometry question help!!!

pychu [463]

<ACB is congruent to <ADE.
They are the only angles that are marked with the same congruency marking.

7 0

3 years ago

The lengths of two sides of a right angled triangle are 20 cm and 30 cm.

Naddik [55]

Answers:

Part (a) 10*sqrt(13)
Part (b) 10*sqrt(5)

Those values are exact. They approximate to:

10*sqrt(13) = 36.0555

10*sqrt(5) = 22.3607

====================================================

Explanation:

Part (a)

If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.

Apply the pythagorean theorem

a^2 + b^2 = c^2

20^2 + 30^2 = c^2

400 + 900 = c^2

1300 = c^2

c^2 = 1300

c = sqrt(1300)

c = sqrt(100*13)

c = sqrt(100)*sqrt(13)

c = 10*sqrt(13) .... exact length

c = 36.0555 ...... approximate length

------------------------------------

Part (b)

If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.

Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.

a^2 + b^2 = c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 900-400

b^2 = 500

b = sqrt(500)

b = sqrt(100*5)

b = sqrt(100)*sqrt(5)

b = 10*sqrt(5) ..... exact length

b = 22.3607 ....... approximate length

3 0

3 years ago