Pythagorean theory . Thank you

Suppose $100 is deposited into an account and the amount doubles every 8 years. How much will be in the account in 40 years? (Us

Eva8 [605]

Thats 5 doublings

100^5
$10000000000

6 0

4 years ago

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41. Assuming that a man can complete the work alone in x days, his work in four days would be: a) b) X X C d) 4x x 42. If a man

Schach [20]

Percentage and ratio word problems require understanding of the relationship between variables from which the question is formed

The options that give the correct values of the duration of the work are;

$41. \ c) \ \dfrac{4}{x}$

$42. \ d) \ \dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

43. a) 35 days

44. c) 21·a + 28·b = 1

45. c) (42, 56)

Reasons:

41. Number of days it takes a man to complete the work alone = x days

Therefore;

$The \ work \ done \ by \ the \ man \ in \ one \ day = \dfrac{1}{x}$

$The \ work \ done \ in \ four \ days \ by\ the \ man = 4 \times \dfrac{1}{x} = \dfrac{4}{x}$

The correct option is $c) \ \dfrac{4}{x}$

42. Number of days it takes a man to complete the work alone = x days

$Work \ done \ by \ a\ man \ in \ one \ day = \dfrac{1}{x}$

$Work \ done \ by \ four \ men \ in \ one \ day = \dfrac{4}{x}$

Number of days it takes a boy to complete the work alone = y days

$Work \ done \ by \ a \ boy \ in \ one \ day = \dfrac{1}{x}$

$Work \ done \ by \ six \ boys \ in \ one \ day = \dfrac{6}{y}$

4 men and 6 boys work for 5 days to complete the work

Therefore, work done by 4 men and 6 boys in 1 day is therefore;

$\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

The correct option is therefore;

$d) \ \dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

43. As per the case study, we have;

Case 1

$\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

Which gives;

$\dfrac{6\cdot x + 4\cdot y}{y \cdot x} = \dfrac{1}{5}$

30·x + 20·y = y·x

Case 2

$\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$

Which gives;

$\dfrac{4\cdot x + 3\cdot y}{y \cdot x} = \dfrac{1}{7}$

28·x + 21·y = y·x

Therefore;

30·x + 20·y = 28·x + 21·y

∴ 2·x = y

Plugging in the value of y = 2·x, in Case 1 gives;

$\dfrac{4}{x} + \dfrac{6}{2 \cdot x} = \dfrac{1}{5}$

$\dfrac{2 \times 4 + 6}{2 \times x} = \dfrac{14}{2 \times x} =\dfrac{7}{x} = \dfrac{1}{5}$

7 × 5 = x

x = 7 × 5 = 35

The number of days, x, it takes a man to complete the work alone, is given by option; a) 35 days

44. For the equation $\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$ , if $a = \dfrac{1}{x}$ , and $b = \dfrac{1}{y}$ , we have;

$3 \cdot a+ 4\cdot y = \dfrac{1}{7}$

21·a + 28·y = 1

The correct option is option C. 21·a + 28·b = 1

45. A solution to the equation $\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$ , is given by the values of x, and y, that gives;

$\dfrac{1}{14} + \dfrac{1}{14} = \dfrac{1}{7}$

We have;

3 × 14 = 42

4 × 14 = 56

Therefore, a solution to the equation is (42, 56)

The correct option is $c) \ \underline{ (42, \ 56)}$

Learn more here:

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3 0

2 years ago

Which statement about the graph of y=14(35)x is true?

Semenov [28]

Answer:

you didn't put the different statements to choose from

4 0

3 years ago

2 3/4 written as fraction greater than one

sladkih [1.3K]

2 3/4 = 11/4 <=== written as an improper fraction

3 0

4 years ago

Read 2 more answers

Amanda ate 1/3 of her mom's pie. she gave the remaining 2/3 to 4 friends, What fraction did each friend get.

Semenov [28]

So she divided the 2/3 between 4 friends.

So each friend got 2/3 divided by 4, which gives:

(2/3)*(1/4) = 2/12 = 1/6

7 0

3 years ago