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3 years ago

13

The amount of money,y, in cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y-inte

rcept is 8.

1 answer:

victus00 [196]3 years ago

5 0

Amount of money received when x tickets are sold=$Y

Number of tickets sold=X

Slope of line= $\frac{1}{4}$

And , y- intercept = 8

Equation of line having slope m and y-intercept c is given by,

y = m x + c,

Expressing the above statement in terms of linear equation in two variable i.e a line is

Y = $\frac{1}{4}$ X + 8

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Why are probability and statistics important?

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Studying probability and statistics will allow you to see the world from an entirely different perspective, since the subjects will give you the tools to model and analyze situations, which involve uncertainty.

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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

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

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

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

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

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3 years ago

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Marrrta [24]

Given:

A figure of a circle and two secants on the circle from the outside of the circle.

To find:

The measure of angle KLM.

Solution:

According to the intersecting secant theorem, if two secant of a circle intersect each other outside the circle, then the angle formed on the intersection is half of the difference between the intercepted arcs.

Using intersecting secant theorem, we get

$\angle KLM=\dfrac{1}{2}(Arc(JON)-Arc(KM))$

$(3x-4)=\dfrac{1}{2}(271-(x+6))$

$(3x-4)=\dfrac{1}{2}(271-x-6)$

Multiply both sides by 2.

$6x-8=265-x$

Isolate the variable x.

$6x+x=265+8$

$7x=273$

Divide both sides by 7.

$x=\dfrac{273}{7}$

$x=39$

Now,

$\angle KLM=(3x-4)^\circ$

$\angle KLM=(3(39)-4)^\circ$

$\angle KLM=(117-4)^\circ$

$\angle KLM=113^\circ$

Therefore, the measure of angle KLM is 113 degrees.

5 0

3 years ago

A bat is sitting in a tree. He leaves the tree and flies up to a speed of 4 meters per second in 8 seconds. How far does he trav

Mariulka [41]

Answer:

32 meters

Step-by-step explanation:

4*8=32 and you have to do this because he flies 4 meters per second and in 8 seconds

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3 years ago