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3 years ago

A random variable is a function that assigns numerical values to the outcomes of a random experiment. True or false?

Mathematics

1 answer:

Alex787 [66]3 years ago

4 0

Answer:

FALSE

Step-by-step explanation:

A random variable is a variable whose outcome depends on random criteria, such as a lottery game in which any number can be drawn randomly. That way, a randomized experiment will have random results that are not predetermined. For example, if the lottery has 80 numbers, the random variable function can achieve any result, which will depend on random criteria such as the luck of the player.

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What time is 17 hours after 1:00 p.m?

lana66690 [7]

Answer:

6am

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

∡C and ∡D are supplementary angles. If m∡D is nine less than twice m∡C, find m∡D.

Gala2k [10]

Answer:

D is 117

Step-by-step explanation:

Let the measure of angle C be x

The measure of D is 9 less than twice C

Mathematically that is 2x-9

If both are supplementary, they add up to be 180

Thus;

x + 2x - 9 = 180

3x = 180 + 9

x = 189/3

x = 63

Recall;

D = 2x-9= 2(63) -9 = 126 -9 = 117

6 0

3 years ago

The side lengths of a triangle are 11.3 centimeters, 14.7 centimeters, and x centimeters. The perimeter of the

guajiro [1.7K]

The perimeter of a triangle is the sum of all its side lengths

11.3 + 14.7 + x < 44

Combine like terms

26 + x < 44

Subtract 26 from both sides.

x < 18

6 0

3 years ago

Factor as the product of two binomials x^2-3x-10

cestrela7 [59]

Answer:

(x-5)(x+2)

Step-by-step explanation:

Hello there!

Your expression there has a highest power of $x^{2}$ , so there will be two constants that you need to find.

Your last term is -10, so the constants will have a product of -10. Also your middle term is -3x, so the terms will add up to -3

-5 and 2 fit the mold.

Have a great day!

If I am most helpful, mark me brainliest!

3 0

3 years ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8$

$r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

3 0

3 years ago