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2 years ago

8

If 12 assemblers can compleate a certain job in 6 hours, how long will the same job take if the number of assemblers is cut back

to 9?

1 answer:

marshall27 [118]2 years ago

3 0

Answer:

8 hours

Step-by-step explanation:

total labor hours required

12 * 6 = 72

hours per worker with 9 workers

72/9 = 8

8 hours

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Karen, James, Frank, and Dan were left an inheritance by their late grandfather. If Karen receives one-eighth of the inheritance

pashok25 [27]

Count what fraction receive Karen, James and Frank in total:

since

Karen receives - $\frac{1}{8}$ ,

James receives - $\frac{1}{4}=\frac{2}{8}$ ,

Frank receives - $\frac{3}{8}$ ,

then $\frac{1}{8} +\frac{2}{8} +\frac{3}{8} =\frac{1+2+3}{8}=\frac{6}{8} =\frac{2\cdot 3}{2\cdot 4} =\frac{3}{4}$ .

All inheritance is the whole 1, then for Dan remains $1-\frac{3}{4} =\frac{4}{4} -\frac{3}{4} =\frac{4-3}{4} =\frac{1}{4}$ .

Answer: Dan receives one quarter of the inheritance.

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2 years ago

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3(k − 99) = –60 <br><br>k = ______

MArishka [77]

Answer:

k = 79

Step-by-step explanation:

3(k-99) = -60

(k-99) = -20

k= -20+99

k=79

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2 years ago

Elliot is 2 times as old as Tanya. 10 years ago, Elliot was 4 times as old as Tanya. How old is Elliot now?

Serggg [28]

Answer:

Step-by-step explanation:

To solve this, we are going to make an age table:

Age Now Age 10 years ago

Tanya

Elliot

Filling the in the Age Now column comes from the first sentence. If Elliot is 2 times Tanya's age and we don't know Tanya's age, then Tanya's age is x and Elliot's age is 2x:

Age Now Age 10 years ago

Tanya x

Elliot 2x

Filling in the Age 10 years ago column simply requires that we take their ages in the Age Now column and subtract 10 from each age:

Age Now Age 10 years ago

Tanya x x - 10

Elliot 2x 2x - 10

Since the question is How old is Elliot now based on the fact that 10 years ago....blah, blah, blah, we are using the ages in the 10 years ago column to write our equation. It says:

10 years ago, Elliot was 4 times as old as Tanya. Translated into mathspeak:

2x - 10 = 4(x - 10) and

2x - 10 = 4x - 40 and

-2x = -30 so

x = 15. That means that Elliot is 30 and Tanya is 15

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3 years ago

Whats 3 divided by 612

Novay_Z [31]

3 divided by 612=0.00490196

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2 years ago

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The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l

Licemer1 [7]

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

$c^2 = a^2 + b^2$

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

$c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x$

Now let's factorize to get solutions for x.

$0 = x(x-20)$

First solution:

$x = 0$

Second solution:

$x - 20 = 0\\x = 20$

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

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2 years ago