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2 years ago

Write an equation for a circle with a radius of 5 and a center located at point (2,8)

1 answer:

5 0

A circles equation is
(x – h)^2 + (y – k)^2 = r^2
The center is at the point (h, k)
The radius is r.

Your circles equation is:
(x – 2)^2 + (y – 8)^2 = 5^2

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A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a jack .

EleoNora [17]

Answer:

2/52 so the chance is unlikely.

Step-by-step explanation:

well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.

6 0

1 year ago

In a large population, 76% of the households have cable tv. A simple random sample of 225 households is to be contacted and the

serious [3.7K]

Answer:

0.017559

Step-by-step explanation:

Data provided:

Probability of Households Having cable TV, p₀ = 76% = 0.76

Therefore,

The probability that the Households not having cable TV = 1 - 0.76 = 0.24

Sample size, n = 225 households

sample proportions is less than 82% i.e p = 0.82

Now,

The standard error, SE = $\sqrt{\frac{p_0(1-p_0)}{n}}$

SE = $\sqrt{\frac{0.76(1-0.76)}{225}}$

SE = 0.02847

and,

$Z=\frac{p-p_0}{SE}$

$Z=\frac{0.82-0.76}{0.02847}$

Z = 2.107

therefore,

P(sample porportions < 0.82) = P(Z < 2.107)

now from the p value from the Z table

we get

P(sample porportions < 0.82) = 0.017559

6 0

2 years ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

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Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":