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3 years ago

Simplify Three over five Or three fifths

Mathematics

2 answers:

serg [7]3 years ago

7 0

3/5 cannot be simplified into a smaller fraction.

Ray Of Light [21]3 years ago

3 0

.6 or 3/5 is already simplified.

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The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales

mihalych1998 [28]

Answer:

We conclude that the mean number of calls per salesperson per week is more than 37.

Step-by-step explanation:

We are given that the Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors.

To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls.

Let $\mu$ = true mean number of calls per salesperson per week.

SO, Null Hypothesis, $H_0$ : $\mu \leq$ 37 {means that the mean number of calls per salesperson per week is less than or equal to 37}

Alternate Hypothesis, $H_A$ : $\mu$ > 37 {means that the mean number of calls per salesperson per week is more than 37}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of calls made last week = 40

s = sample standard deviation = 5.6 calls

n = sample of sale representatives = 41

So, test statistics = $\frac{40-37}{\frac{5.6}{\sqrt{41} } }$ ~ $t_4_0$

= 3.43

Hence, the value of test statistics is 3.43.

Now at 0.025 significance level, the t table gives critical value of 2.021 at 40 degree of freedom for right-tailed test. Since our test statistics is more than the critical value of t as 3.43 > 2.021, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the mean number of calls per salesperson per week is more than 37.

4 0

2 years ago

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

2 years ago

Simplify the expression. Write answer using only positive exponents. (1/3a^3)^-4

Artemon [7]

Answer:

81/a^12

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

PROBLEM: Juan hires an electrician. Juan pays a one-time fee of $30. Juan also pays $45 for each hour the electrician works. A.

PolarNik [594]

Answer:

A: C=45h+30

B: C=$322.50

Step-by-step explanation:

A: We'll start with the equation for the total charge. Juan is saying he will pay a one time fee of $30, meaning there is 30 dollars added to what ever the hourly wage is. This can be represented by the +30. Now if "h" represents the variable for which the hourly wage will be calculated, and he pays $45 dollars per hour this will be represented as 45h. As an example if I pay you 2 dollars per hour using the same variable "h", this would be represented as 2h. So if you worked for two hours you would get 4 dollars, this is proven by the fact the 2(2) (remeber im replacing the "h" with the hours you worked) obviously 2 times 2 is 4 proving my point. This information will give you the equation you see above.

B: Onto solving for how much Juan will pay. Now you say youre supposed to have 9 answer but this can't be true. All you need to do is plug the hours given into "h" and solve the equation. It should look something like:

C=45h+30

C=45(6.5)+30

Im using a decimal because it should be clear 1/2=0.5

C= 292.5+30

45x6.5 always go with PEMDAS, we are multiplying first. Then add 292.5 plus 30

This results in the answer of:

C=$322.50

3 0

2 years ago

A rocket is launched from the top of a 99-foot cliff with an initial velocity of 122 ft/s.

Harman [31]

Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
$0=-16 t^{2} +122t+99$
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
$-99=-16 t^{2} +122t+99$
$-16 t^{2} +122+198=0$

Now we can apply the quadratic formula $t= \frac{-b+or- \sqrt{ b^{2} -4ac} }{2a}$ where a=-16, b=122, and c=198
$t= \frac{-122+or- \sqrt{ 122^{2}-(4)(-16)(198) } }{(2)(-16)}$
$t= \frac{-122+ \sqrt{27556} }{-32}$ or $t= \frac{-122- \sqrt{27556} }{-32}$
$t= \frac{-122+166}{-32}$ or $t= \frac{-122-166}{-32}$
$t= \frac{-11}{8}$ or $t=9$

Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.

5 0

3 years ago

Read 2 more answers