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3 years ago

it takes kenny 25 minutes to inflate the tires of 55 bicycles how long will it take him to inflate the tires of 121 bicycles

Mathematics

2 answers:

alina1380 [7]3 years ago

5 0

it will take him 65.6 minutes to inflate all 121 bicycles

lubasha [3.4K]3 years ago

4 0

Answer: 121*25=3025 and 3205÷55= 55

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Emmanuel added 8 links per minute to his chain mail. Allesia started 20 minutes after Emmanuel and added 13 links per minute to

strojnjashka [21]

Answer: 52 minutes, 416 links

Step-by-step explanation:

8*20=160

13-8=5

160/5=32

32+20=52

52*8=416

8 0

3 years ago

Read 2 more answers

a sprinter running in the olympics starts at the 0 meter mark and ends at the 400 meter mark. it took him 65 seconds to run this

solniwko [45]

Answer:

I am not too sure but I think the answer would be 6

Step-by-step explanation:

3 0

3 years ago

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie

Dvinal [7]

For part (a), you have

$\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}$
$x=a(x-2)+b(x+3)$

If $x=2$ , then $2=b(2-3)\implies b=-2$ .

If $x=-3$ , then $-3=a(-3-2)\implies a=\dfrac35$ .

So,

$\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}$

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

$\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}$

In the remainder term, the denominator $x^2+x+2$ can't be factorized into linear components with real coefficients, since the discriminant is negative $(1-4\times1\times2=-7)$ . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

$x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i$
$\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)$
$\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)$

Then you have

$\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}$
$x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)$

When $x=-\dfrac12-\dfrac{\sqrt7}2i$ , you have

$-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)$
$\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib$
$b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)$

When $x=-\dfrac12+\dfrac{\sqrt7}2i$ , you have

$-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)$
$\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia$
$a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)$

So, you could write

$\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}$

but that may or may not be considered acceptable by that webpage.

5 0

3 years ago

Read 2 more answers

97/16 as mixed number

alexgriva [62]

If you would like to write 97/16 as a mixed number, you can do this using the following step:

97/16 = 6 1/16

Result: 97/16 equals to 6 1/16 as a mixed number.

8 0

3 years ago

A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement

balu736 [363]

Total marbles = 10+4 = 14
prob of green marble = 10/14 = .71
Then if you are getting 2 green marbles you have to first take out 1 green marble so now there are 9 green marbles and 13 total green marbles
prob of 2nd green marble = 9/13 = .69

So you would then multiply the probabilities of the individual events to get the total probability:
.71 * .69 = .4899 therefore(with rounding):

The probability of getting two green marbles is 49%

8 0

3 years ago

Read 2 more answers