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2 years ago

Ben orders a cost of us tovorite macaroni and cheese. The case contains 18 same-

Mathematics

2 answers:

Montano1993 [528]2 years ago

7 0

Answer:

highlighted answer is correct

Step-by-step explanation:

Greeley [361]2 years ago

5 0

The second answer is correct

You might be interested in

Find the value of n if (81)^5/n = 243

zavuch27 [327]

Answer:

N = 14348907

Step-by-step explanation:

81^5 = 3486784401

3486784401/243 = 14348907

Double Check

3486784401 / 14348907=243

So N = 14348907.

3 0

3 years ago

Dear Math Helper, You write a great column, and I hope you stay around for years to come. I run a small boarding school. We are

inessss [21]

The easiest way to determine the score is to use a calculator or spreadsheet and the appropriate probability function.

If you want the top 10%, the score corresponds to the 90th percentile. That score is 316.

If you want the top 15%, the score corresponds to the 85th percentile. That score is 313.

5 0

2 years ago

A poll asked 1057 American adults if they believe there was a conspiracy in the assassination of President Kennedy, and found th

AVprozaik [17]

Answer:

The 95% confidence interval of the proportion of Americans who believe in the conspiracy is $0.551< p < 0.610$

Step-by-step explanation:

From the question we are told that

The sample size is n =1057

The number that believe there was a conspiracy is k = 614

Generally the sample proportion is mathematically represented as

$\^ p = \frac{614}{1057 }$

=> $\^ p = 0.5809$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.96 * \sqrt{\frac{0.5809 (1- 0.5809)}{1057} }$

=> $E = 0.02975$

Generally 95% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.5809 - 0.02975< p < 0.5809 + 0.02975$

=> $0.551< p < 0.610$

4 0

2 years ago

Integrate e^x(sin(x) cos(x))

Karo-lina-s [1.5K]

$I=\int e^x(\sin(x)\cos(x))dx=\int e^x(\frac{1}{2}\sin(2x))dx=\frac{1}{2}\int e^x\sin(2x)dx$

$\text{If }u=\sin(2x)\to du=2\cos(2x)dx~\text{and}~dv=e^xdx\to v=e^x:\\\\
\text{Using }\int u\,dv=uv-\int v\,du:\\\\
I=\frac{1}{2}(e^x\sin(2x)-\int e^x(2\cos(2x))dx)\\\\
2I=e^x\sin(2x)-2\underbrace{\int e^x\cos(2x)dx}_{I_2}$

Looking for $I_2$ :

$\text{If}~u=\cos(2x)\to du=-2\sin(2x)dx~\text{and}~dv=e^xdx\to v=e^x:\\\\
I_2=e^x\cos(2x)-\int e^x(-2\sin(2x))dx\\\\ I_2=e^x\cos(2x)+2\int e^x(\sin(2x))dx\\\\ I_2=e^x\cos(2x)+2\int e^x(2\sin(x)\cos(x))dx\\\\ I_2=e^x\cos(2x)+4\int e^x(\sin(x)\cos(x))dx=e^x\cos(2x)+4I$

Replacing:

$2I=e^x\sin(2x)-2I_2\iff\\\\2I=e^x\sin(2x)-2(e^x\cos(2x)+4I)\iff\\\\
2I=e^x\sin(2x)-2e^x\cos(2x)-8I\iff\\\\
10I=e^x\sin(2x)-2e^x\cos(2x)\iff\\\\
I=\dfrac{e^x}{10}(\sin(2x)-2\cos(2x))\\\\
\boxed{\int e^x(\sin(x)\cos(x))dx=\dfrac{e^x}{10}(\sin(2x)-2\cos(2x))+C}$

6 0

3 years ago

Write the equation in slope -intercept form with slope of 4 that contains (-3, -6).

Elina [12.6K]

Formula for point-slope: $y-y1=m(x-x1)$
Plug in the values: $y + 6 = 4(x + 3)$

And there you have your answer in point-slope form

6 0

3 years ago