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tankabanditka [31]

3 years ago

7

Last month Alicia’s agency booked $14500 in airline fees on orbit airlines. If orbit pays agencies a commission of 4.1%, how muc

h commission should the company receive?

1 answer:

avanturin [10]3 years ago

3 0

Answer:

$594.50

Step-by-step explanation:

Multiply the initial fee by the commission in decimal form

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The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.

Anton [14]

Answer:

a) The evidence suggest the true mean life of a biomedical device > 5500

b) (5487.94, +∞)

c) There is evidence to support that the mean is equal to 5500

Step-by-step explanation:

Here we have

(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500

Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is

H₀: μ = 5500

Therefore, the alternative hypothesis will be

Hₐ: μ > 5500

The test statistic is then found by;

$t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}} =\frac{5617.8-5500 }{\frac{234.5 }{\sqrt{15}}} \approx 1.95$

The P value from the T table at df = n - 1 = 15 - 1 = 14 is

0.025 < P < 0.05

The P value is given as 0.036 from the T distribution at 14 derees of freedom df

Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ: μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500

(b) The 95% confidence interval is given as

$CI=\bar{x}\pm t_\alpha \frac{s}{\sqrt{n}}$

Which gives t $_\alpha$ = $\pm$ 2.145

$CI=5617.8\pm 2.145 \times \frac{234.5}{\sqrt{15}}$

The confidence interval of the lower bound on the mean is then

(5487.94, +∞)

c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.

6 0

3 years ago

What is the value of n?

vitfil [10]

9(n+7) = 18(n+1)
9n + 63 = 18n + 18
9n = 45
n = 5

answer
n = 5

3 0

3 years ago

Find the exact value of sin 105 degrees

STALIN [3.7K]

Answer:

$\frac{\sqrt{6}+\sqrt{2}}{4}$

Step-by-step explanation:

I'm going to write 105 as a sum of numbers on the unit circle.

If I do that, I must use the sum identity for sine.

$\sin(105)=\sin(60+45)$

$\sin(60)\cos(45)+\sin(45)\cos(60)$

Plug in the values for sin(60),cos(45), sin(45),cos(60)

$\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}$

$\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}$

$\frac{\sqrt{6}+\sqrt{2}}{4}$

4 0

3 years ago

Read 2 more answers

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

a.

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

b.

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

A canvan crosses 1,738 miles of desert in 85 days l. It traveled 22 miles on the first day and 28 miles on the second day. If th

joja [24]

Answer:

Okay. So first you add 22+28=50. Then subtract 1,738-50=1,688. Then divide 1,688 by 2 witch should give you an answer of 844 miles each day. Hope it helped!

Step-by-step explanation:

3 0

3 years ago