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3 years ago

8

| 2. Create a word problem

1 answer:

Mariulka [41]3 years ago

3 0

13,748 x 214 = 2942,072

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An environment engineer measures the amount ( by weight) of particulate pollution in air samples ( of a certain volume ) collect

Serggg [28]

Answer:

$k = 1$

$P(x > 3y) = \frac{2}{3}$

Step-by-step explanation:

Given

$f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.$

Solving (a):

Find k

To solve for k, we use the definition of joint probability function:

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1$

Where

${ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }$

Substitute values for the interval of x and y respectively

So, we have:

$\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1$

Isolate k

$k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1$

Integrate y, leave x:

$k \int\limits^2_{0} y {dx} \, [0,x/2]= 1$

Substitute 0 and x/2 for y

$k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1$

$k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1$

Integrate x

$k * \frac{x^2}{2*2} [0,2]= 1$

$k * \frac{x^2}{4} [0,2]= 1$

Substitute 0 and 2 for x

$k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1$

$k *[ \frac{4}{4} - \frac{0}{4} ]= 1$

$k *[ 1-0 ]= 1$

$k *[ 1]= 1$

$k = 1$

Solving (b): $P(x > 3y)$

We have:

$f(x,y) = k$

Where $k = 1$

$f(x,y) = 1$

To find $P(x > 3y)$ , we use:

$\int\limits^a_b \int\limits^a_b {f(x,y)}$

So, we have:

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy$

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy$

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy$

Integrate x leave y

$P(x > 3y) = \int\limits^2_0 x [0,y/3]dy$

Substitute 0 and y/3 for x

$P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy$

$P(x > 3y) = \int\limits^2_0 y/3\ dy$

Integrate

$P(x > 3y) = \frac{y^2}{2*3} [0,2]$

$P(x > 3y) = \frac{y^2}{6} [0,2]\\$

Substitute 0 and 2 for y

$P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}$

$P(x > 3y) = \frac{4}{6} -\frac{0}{6}$

$P(x > 3y) = \frac{4}{6}$

$P(x > 3y) = \frac{2}{3}$

8 0

3 years ago

6.<br> The area of the book cover is 14 in.? and the length is 2} in. What is the width?

aleksley [76]

Answer:

the width is 7 inches

Step-by-step explanation:

A = l * w

14 = 2 * w

what does w equal?

14 / 2 = 7

2 * w / 2 = w

7 = w

4 0

3 years ago

Compare these amounts. use or =.<br><br>8oz ________ 8 cups

hichkok12 [17]

Answer:

8 cups is greater then 8 oz

Step-by-step explanation:

8 0

3 years ago

What is the product of 3.45 x<br> (1.93 x 10^4)

V125BC [204]

Answer:

66,585

Step-by-step explanation:

First, solve 10^4, which is 10,000. Then, do 1.93x10,000 and get 19300. Finally, multiply 19300 by 3.45 to get 66,585.

Always use pemdas and hope this helped!

6 0

2 years ago

Simplify (2z^5)(12z^3)/4z^4

Sphinxa [80]

Answer:

$6z^{4}$

Step-by-step explanation:

Given in the question an expression,

$\frac{ (2z^5)(12z^3)}{4z^4}$

Step 1

Apply exponential "product rule"

$x^{m}x^{n}=x^{m+n}$

$\frac{ 12(2)z^5)(z^3)}{4z^4}$

$\frac{ (24)z^5)(z^3)}{4z^4}$

$\frac{ 24(z^{(5+3)})}{4z^4}$

$\frac{ 24(z^{8})}{4z^4}$

Step 2

Apply exponential " divide rule"

$\frac{x^{m}}{x^{n}}=x^{m-n}$

$\frac{24/4(z^{8})}{z^4}$

$\frac{6(z^{8})}{z^4}$

$\frac{6(z^{8-4})}{1}$

$6z^{4}$

5 0

2 years ago