Write a decimal and a percent for 73 over 100

Mathematics

2 answers:

sergey [27]3 years ago

5 0

0.73 or 73%
divide 100 into 73. you get .73 move the decimal to the right twice and you get 73%

Brut [27]3 years ago

3 0

It's 0.73 as a DECIMAL.
and it's 73% as a PERCENT.

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An article reported that what airline passengers like to do most on long flights is rest or sleep; in a survey of 3697 passenger

maw [93]

F(x,n,p)=C(n,x)p^x*(1-p)^(n-x)
n=9, p=0.8 =>
f(x,9,0.8)=C(9,x)0.8^x*(0.2)^(9-x)

The function f(x,9,0.8) is then calculated using the above formula
x f(x)
0 0.0000001 0.0000182 0.0002953 0.0027534 0.0165155 0.0660606 0.1761617 0.3019908 0.3019909 0.134218

Check Sum f(x), [x=0,9] = 1.0 ok

4 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$