All categories

2 years ago

There are 40 monkeys and 60% of the monkeys are in the trees. How many monkeys are in the trees?

Mathematics

1 answer:

strojnjashka [21]2 years ago

7 0

Answer:

24 monkeys are in the tree

Step-by-step explanation:

We solve it by writing $\frac{60}{100}$ times $\frac{40}{1}$

Why is it over 100? Because every percent is out of 100!

$\frac{60}{100}$ X $\frac{40}{1}$ (your equation)

60 times 40 = 2400 and 100 times 1 = 100, We get, $\frac{2400}{100}$ ,

Lastly, we simplify the fraction by 100 on each side:

$\frac{2400}{100}$ / $\frac{100}{100}$

you get 24

You might be interested in

) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

CAN SOMEONE HELP ME WITH THIS?!

lutik1710 [3]

Answer:

a = 14

b = 24

c = 24.9

A = 33.2 degrees

B = 70 degrees

C = 76.8 degrees

Step-by-step explanation:

a/sin(A) = b/sin(B) = c/sin(C)

14/sin(A) = 24/sin(70)

sin(A)×24 = sin(70)×14

sin(A) = sin(70)× 14/24 = sin(70) × 7/12 = 0.548154029...

A = asin(0.548154029...) = 33.240464... degrees

the sum of all angles in a triangle is airways 180 degrees.

C = 180 - 70 - 33.240464... = 76.75954... degrees

24/sin(70) = c/sin(76.75954...)

c = 24×sin(76.75954...)/sin(70) = 24.86133969...

6 0

2 years ago

Solve for x and then find the measure of

masha68 [24]

Answer:
Of angle B...

5 0

3 years ago

Rewrite the slope-intercept form equation into standard form.<br> y = 5/2

Dahasolnce [82]

2y = 5 hope this helps :)

4 0

3 years ago

6 percent of what number is 2

ycow [4]

The answer is 33.3 repeating

5 0

2 years ago