Events A and B are mutually exclusive. Suppose event A occurs with probability .33 and event B occurs with probability .38.

A small motor boat can go 182 nautical miles at a steady speed in 13 hours. How far can it go in 1, 2, 3, 4, 5, 6, 7, 8, 9 and

Rzqust [24]

Answer:

The answer is on google.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

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

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

7 0

2 years ago

Starks sculpture 30 cubed is a cube with sides 30 inches long. Whats its volume

Zolol [24]

Answer: $27000\text{ cubic inches}$

Step-by-step explanation:

Given : Starks sculpture 30 cubed is a cube with sides 30 inches long.

We know that the volume of a cube is given by :-

$\text{Volume}=(side)^3$

Then , the volume of Starks sculpture 30 cubed will be :

$\text{Volume}=(30)^3\text{ cubic inches}$

$\text{Volume}=30\times30\times30\text{ cubic inches}$

$\text{Volume}=27000\text{ cubic inches}$

Hence, the required volume = $27000\text{ cubic inches}$

7 0

3 years ago

A school has a virus going around, and 8/25 of the students are absent due to the virus. An additional 20 students are out due t

Stells [14]

Answer:

268 students are absent

Step-by-step explanation:

First, multiply 775 by (8/25) to get the number of students out from the virus (probably weren't wearing masks or 6 ft apart from each other). This gives you 248 students. You also know that an additional 20 students are out due to other reasons. Add 248 and 20 and you get a total of 268 absent students.

3 0

3 years ago

The boys and girls soccer clubs are fundraising for new uniforms. The boys soccer club is selling candy bars for $2 a piece. The

blondinia [14]

Answer:

2b + 4c = 800

c > 100

Step-by-step explanation:

6 0

2 years ago