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Neporo4naja [7]

3 years ago

11

The sides of a rectangle are 15cm and 7cm long. How far is the point of the diagonal cross section from the sides of this rectan

gle?
please include explanation

1 answer:

irinina [24]3 years ago

6 0

Answer:

See below in bold.

Step-by-step explanation:

If we draw a line from the point of intersection to the longest side of the rectangle it will meet it at the midpoint.

The same thing will happen when the line is draw to the shortest side.

So the point of intersection is 1/2 * 7 = 3.5 cm from the longest side and 15/2 = 7.5 cm from the shortest side.

You might be interested in

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

a.

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

Solve for X and show work

Len [333]

I don’t know how to show how I got it but the answer is X=12.

7 0

3 years ago

Find h of the following cone

Reptile [31]

Sqrt55. Use the pythagorean theorem; 3^2 + x^2 = 8^2

6 0

3 years ago

Represent each of the following integers on the number line -4,3, -1,10,-8 and -15

MArishka [77]

Answer:

-15, -8, -4, -1, 3, 10

Step-by-step explanation:

On the number line, the integers would be set up as :-

-15, -8, -4, -1, 3, 10

Hope this helps, thank you :) !!

5 0

3 years ago

Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the d

larisa [96]

Answer:

a) $P(X$

$P(X>14) = 1-P(X$

b) $P(7< X$

c) We want to find a value c who satisfy this condition:

$P(x$

And using the cumulative distribution function we have this:

$P(x$

And solving for c we got:

$c = 20*0.9 = 18$

Step-by-step explanation:

For this case we define the random variable X as he amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train, and we know that the distribution for X is given by:

$X \sim Unif (a=0, b =20)$

Part a

We want this probability:

$P(X$

And for this case we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} = \frac{x-0}{20-0}= \frac{x}{20}$

And using the cumulative distribution function we got:

$P(X$

For the probability $P(X>14)$ if we use the cumulative distribution function and the complement rule we got:

$P(X>14) = 1-P(X$

Part b

We want this probability:

$P(7< X$

And using the cdf we got:

$P(7< X$

Part c

We want to find a value c who satisfy this condition:

$P(x$

And using the cumulative distribution function we have this:

$P(x$

And solving for c we got:

$c = 20*0.9 = 18$

3 0

3 years ago