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3 years ago

11

Find the unit rate: 120 pencils in 3 boxes

2 answers:

Elena L [17]3 years ago

3 0

Answer: 120=3

/3 /3

40=1

Step-by-step explanation:unit rate 40:1

WARRIOR [948]3 years ago

3 0

The unit rate is 40 pencils per box

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54394 plus 13768<br><br><br> Thank you

kakasveta [241]

Answer:

$54394 + 13768 \\ \\ = 68162$

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2 years ago

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What is the range of the relation?<br> (-3,-2,0,2)<br> (-3,3)<br> (-4,-2,1,2)<br> (-4,-3,-2,1,0,2)

9966 [12]

Answer:

jn8huuojgui

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2 years ago

Geometry question for homework.

mars1129 [50]

So remember that the distance formula is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ .

1.

$\sqrt{(4-4)^2+(-2-(-5))^2}\\ \sqrt{0^2+3^2}\\ \sqrt{0+9}\\ \sqrt{9}\\ 3$

Distance between (4,-5) and (4,-2) is 3 units.

2.

$\sqrt{(1-(-1))^2+(1-4)^2}\\ \sqrt{2^2+(-3)^2}\\ \sqrt{4+9}\\ \sqrt{13}$

Distance between (1,1) and (-1,4) is √13 (or 3.61 rounded to the hundreths) units.

3 0

2 years ago

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

2 years ago

Which of the following values would complete the ordered pair if the point is on the graph of f (x) = -3x + 2 ?

Scrat [10]

Answer: the y-coordinate that completes the point is 5.

Explanation:

An ordered pair (x, y) indicates the x-and-y coordinates of a general point, where x is the input value of a function and y is the output value.

The output value is y = f(x) and must be found applying the rule (function) to the given input value.

In this case the rulte is f(x) = - 3x + 2, and the input value, x, is - 1 (the first value of the ordered pair).

This is the mathematical procedure:

x = - 1
f(x) = f (-1) = -3 (-1) + 2 = 3 + 2 = 5.

5 0

2 years ago

Read 2 more answers