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3 years ago

Who knows ?? Show all the steps

Mathematics

1 answer:

Olin [163]3 years ago

7 0

Move decimal of 12.75% to .1275
then multiply 85 and .1275 which is 10.8375
then round to the nearest cent then you get 10.84. Finally add 10.84 to 85 then the total cost is $95.84

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Surface integrals using a parametric description. evaluate the surface integral \int \int_{s} f(x,y,z)dS using a parametric desc

DiKsa [7]

You can parameterize $S$ using spherical coordinates by

$\vec s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ .

Take the normal vector to $S$ to be

$\dfrac{\partial\vec s}{\partial\vec v}\times\dfrac{\partial\vec s}{\partial\vec u}=36\langle\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v\rangle$

(I use $\vec s_v\times\vec s_u$ to avoid negative signs. The orientation of the normal vector doesn't matter for a scalar surface integral; you could just as easily use $\vec s_u\times\vec s_v=-(\vec s_v\times\vec s_u)$ .)

Then

$f(x,y,z)=f(6\cos u\sin v,6\sin u\sin v,6\cos v)=36\sin^2v$

and the integral of $f$ over $S$ is

$\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\int_0^{\pi/2}\int_0^{2\pi}36\sin^2v\left\|\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right\|\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}(36\sin^2v)(36\sin v)\,\mathrm du\,\mathrm dv$

$=\displaystyle2592\pi\int_0^{\pi/2}\sin^3v\,\mathrm dv=\boxed{1728\pi}$

7 0

3 years ago

The mean finish time for a yearly amateur auto race was 186.32 minutes with a standard deviation of 0.305 minute. The winning c

uranmaximum [27]

Complete Question

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

Find their respective z-scores.

Who had the more convincing victory?

A. Roger had a more convincing victory because of a higher z-score.

B. Karen a more convincing victory because of a higher z-score.

C. Roger had a more convincing victory, because of a lower z-score.

D. Karen a more convincing victory because of a lower z-score.

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

The mean of the current year is $\mu_c = 186.32 \ minutes$

The standard deviation is $\sigma_c = 0.305 \ minutes$

The time taken by the winning car for the current year is $x = 185.85 \ minutes$

The mean of the previous year is $\mu_p = 110.7 \ minutes$

The standard deviation the previous year is $\sigma_p = 0.115 \ minutes$

The time taken by the winning car for the previous year is $y = 110.48 \ minutes$

Generally the z-score for current year is mathematically evaluated as

$z_c = \frac{x- \mu_c}{\sigma_c }$

=> $z_c = \frac{ 185.85- 186.32}{0.305 }$

=> $z_c = -1.536$

Generally the z-score for previous year is mathematically evaluated as

$z_p = \frac{y- \mu_p}{\sigma_p }$

=> $z_p = \frac{ 110.48-110.7}{0.115 }$

=> $z_p = -1.913$

From the value obtained we see that $z_p < z_c$ , Hence Karen had a more convincing victory because of the lower z -score.

5 0

3 years ago

A large farm had 75 acres of wheat and 62.5 acres of corn the farm crew can harvest the wheat from 12 acres and the corn from 10

uranmaximum [27]

It takes 7 days to finish harvest wheat (75/12=6.25) and 7 to harvest corn (62.5/10=6.25). So the answer is 7

7 0

4 years ago

Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $5

vagabundo [1.1K]

If she gets 3% of what she sells you multiply the decimal form of the percent by the amount she has made:
50*.03=1.5
So she make $1.50 for every $50 of sales, so you multiply the amount she made by her commission each day by the number of days she worked:
1.5*30=45

She earned a total of $45<span />

4 0

3 years ago

Read 2 more answers

7x = 22 <br> What does x equal? Write your answer as a fraction

Veronika [31]

X= 22/7 periodttttttttt

8 0

3 years ago