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2 years ago

A region c B region d C region a D region b

Mathematics

1 answer:

anyanavicka [17]2 years ago

3 0

Answer:

Region C

Step-by-step explanation:

y ≤ ¼ x + 3 maps the areas C and D including the common boundary line

y ≥ -x + 5 maps the areas B and C including the common boundary line

The common area mapped is C plus its boundaries

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What is an expression for 43 more than t

musickatia [10]

43 more than t

t + 43

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3 years ago

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A random sample of 42 college graduates who worked during their program revealed that a student spent an average 5.5 years on th

Neko [114]

Answer:

$5.5-2.701\frac{1.1}{\sqrt{42}}=5.04$

$5.5+2.701\frac{1.1}{\sqrt{42}}=5.96$

So on this case the 99% confidence interval would be given by (5.04;5.96)

And the best option would be:

a. 5.04 and 5.96

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=5.5$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=1.1 represent the sample standard deviation

n=42 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,41)".And we see that $t_{\alpha/2}=2.701$

Now we have everything in order to replace into formula (1):

$5.5-2.701\frac{1.1}{\sqrt{42}}=5.04$

$5.5+2.701\frac{1.1}{\sqrt{42}}=5.96$

So on this case the 99% confidence interval would be given by (5.04;5.96)

And the best option would be:

a. 5.04 and 5.96

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3 years ago

You can do one-half of a job in an hour. Your friend can do one-third of the same job in an hour. How long will it take to do th

Mariana [72]

You do: 1/2 job/hr

Your friend does: 1/3 job/hr

Together:   (1/2 + 1/3) job / hr

   = (3/6 + 2/6) job/hr

   = 5/6 job/hr .

Since you do 5/6 job/hr, the corresponding
inverse unit rate is
   6/5 hr/job

      = 1 and 1/5 hr/job

      = 1.2 hours/job

      = 1 hour 12 minutes per job.

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3 years ago

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

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3 years ago

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blondinia [14]

Answer:

X=62

Step-by-step explanation:

solve half of it like 90 degrees +22 degrees. then minus from 180 degrees

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