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2 years ago

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Mr. Johnson is going to buy an 18 3 4 pound turkey for Thanksgiving. The turkey costs $ 2.80 per pound at the grocery store. If

the grocery store runs a 20 % discount on turkeys, how much will Mr. Johnson save (before taxes)?

1 answer:

bezimeni [28]2 years ago

4 0

Answer:

10.22 she save

Step-by-step explanation:

18 3/4 x 2.80=51.1

51.1 x 20%=10.22

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A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like alg

Yuki888 [10]

Answer:

Step-by-step explanation:

Let x be the number of students that like both algebra and geometry. Then:

1. 45-x is the number of students that like only algebra;

2. 53-x is the number of students that like only geometry.

You know that 6 students do not like any subject at all and there are 75 students in total.

If you add the number of students that like both subjects, the number of students that like only one subject and the number of students that do not like any subject, you get 75.

Therefore,

$x+45-x+53-x+6=75.$

Solve this equation:

$104-x=75,\\\\x=104-75,\\\\x=29.$

You get that:

29 students like both subjects;

45-29=16 students like only algebra;

53-29=24 students like only geometry;

24+6=30 students do not like algebra;

16+6=22 students do not like geometry.

a = 29, b = 16, c = 24, d = 30, e = 22

<h3>The correct choice is D.</h3>

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2 years ago

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Below are the data collected from two random samples of 500 American students on the number of hours they spend in school per da

lukranit [14]

To find the mean you must add up all the numbers you have together and then divide the buy the amount of numbers you added. When you add these numbers up you get 30, and we have 5 numbers here, when we divide 30 by 5 we get 6. So, Tara is correct in saying that the mean is 6.

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2 years ago

Use the Distributive Property to expand the expression z(−6.4−3.5x)

Pepsi [2]

Answer:

-6.4z- (3.5x)

Step-by-step explanation:

cant do z times x

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2 years ago

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Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

2 years ago

Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a s

Sliva [168]

Answer: 0.0129

Step-by-step explanation:

Given : Mean : $\mu=13.4\text{ years}$

Standard deviation : $\sigma=1.7\text{ years}$

Sample size : $n=40$

Let X be the random variable that represents the age of of the fleets.

Z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x = 14

$z=\dfrac{14-13.4}{\dfrac{1.7}{\sqrt{40}}}\approx2.23$

By using standard normal distribution table , the probability that the average age of these 40 airplanes is at least 14 years old will be

$P(x\geq14)=P(z\geq2.23)=1-P(z$

Hence, the the probability that the average age of these 40 airplanes is at least 14 years old =0.0129

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2 years ago