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3 years ago

Last year, Jay was 96 inches tall. This year, he is 108 inches tall. What is the percent increase in Jay’s height

Mathematics

1 answer:

Lerok [7]3 years ago

3 0

Answer: 12.5%

Step-by-step explanation:

108-96=12, so he grew 12 inches.

12/96=0.125,

0.125*100=12.5, 12.5%

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A fair die is rolled 10 times. Find the expected value of:a) the sum of the numbers in the ten rolls;b) the number of multiples

velikii [3]

Answer:

a) 3.5

b) 3.33

c) $6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}$

Step-by-step explanation:

As given,

A fair die is rolled 10 times

Expected value of Sum of the number in 10 rolls = $\frac{1}{6}(1+2+3+4+5+6) = \frac{21}{6}$

= 3.5

∴ we get

Expected value of Sum of the number in 10 rolls = 3.5

Ley Y : number of multiples of 3

Y be Binomial

Y - B(n = 10, p = $\frac{2}{6}$ )

Now,

Expected value = E(Y) = np = 10× $\frac{2}{6}$ = 3.33

Let m = total number of faces in a die

⇒m = 6

As die is roll 10 times

⇒n = 10

Now,

Let Y = number of different faces appears

Now,

Expected value, E(Y) = m - m $\left(\begin{array}{ccc}m-1\\m\end{array}\right)^{n}$

= $6 - 6\left(\begin{array}{ccc}6-1\\6\end{array}\right)^{10} = 6 - 6\left(\begin{array}{ccc}5\\6\end{array}\right)^{10}$

5 0

3 years ago

Find the mass of the lamina that occupies the region D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye

Alona [7]

Answer:

The mass of the lamina is 1

Step-by-step explanation:

Let $\rho(x,y)$ be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

$m=\int\limits \int\limits_D \rho(x,y) \, dA$ .

From the question, the given density function is $\rho (x,y)=xye^{x+y}$ .

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

$I=\int\limits^1_0\int\limits^1_0xye^{x+y}dydx$ .

Since D is a rectangular region, we can apply Fubini's Theorem to get:

$I=\int\limits^1_0(\int\limits^1_0xye^{x+y}dy)dx$ .

Let the inner integral be: $I_0=\int\limits^1_0xye^{x+y}dy$ , then

$I=\int\limits^1_0(I_0)dx$ .

The inner integral is evaluated using integration by parts.

Let $u=xy$ , the partial derivative of u wrt y is

$\implies du=xdy$

and

$dv=\int\limits e^{x+y} dy$ , integrating wrt y, we obtain

$v=\int\limits e^{x+y}$

Recall the integration by parts formula: $\int\limits udv=uv- \int\limits vdu$

This implies that:

$\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy$

$\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}$

$I_0=\int\limits^1_0 xye^{x+y}dy$

We substitute the limits of integration and evaluate to get:

$I_0=xe^x$

This implies that:

$I=\int\limits^1_0(xe^x)dx$ .

$I=\int\limits^1_0xe^xdx$ .

We again apply integration by parts formula to get:

$\int\limits xe^xdx=e^x(x-1)$ .

$I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(-1)=1$ .

No unit is given, therefore the mass of the lamina is 1.

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3 years ago

State the slope and y-intercept<br> y=3x+4

WARRIOR [948]

slope intercept form: y=mx+b

y=3x+4

slope is also m

b is the y-intercept

answer:

slope is 3

y-intercept is 4

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Andrej [43]

Answer:

500.61

Step-by-step explanation:

5 multiplied by 100 = 500

1/10 = 0.1, So 6 multiplied by 0.1 = 0.6

1/100 = 0.01, So 1 multiplied by 1 = 0.01

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