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3 years ago

1. Solve the following equation: (1 Point) 3 - 4 = -3

Mathematics

1 answer:

Brut [27]3 years ago

6 0

Answer:

Step-by-step explanation:

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A researcher, interested in estimating a population mean wants to be 95% certain that the length of the confidence interval does

djyliett [7]

Answer:

$n=(\frac{1.96(20)}{5})^2 =61.47 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

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".

Solution to the problem

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

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =L/2 =5/2 =2.5, since the margin of error is the half of the length for the confidence interval, we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ from part a, replacing into formula (2) we got:

$n=(\frac{1.96(20)}{5})^2 =61.47 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

3 0

3 years ago

If f (x) = StartRoot x minus 3 EndRoot, which inequality can be used to find the domain of f(x)? Options Below

Aleksandr [31]

The inequality $x-3 \geq 0$ can be used to find the domain of $f(x)=\sqrt{x-3}$

Answer: Option B

<u>Step-by-step explanation:</u>

We have $f(x)=\sqrt{x-3}$ , domain is the set of all possible x-values which will make the function "work", and will output real y-values. Basically to find domain of any function means to find range of values of x that will give real values of y.

For the equation $f(x)=\sqrt{x-3}$ , we know that there's no value ( iota or complex numbers are there but here we will deal with real numbers ) of negative numbers under square root

∴ ${(} x-3 {)}$ must be greater than or equal to 0.

⇒ $x-3 \geq 0$

8 0

4 years ago

Read 2 more answers

Solve 112(14−6)−(−4)=−59

lesya [120]

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Answer:

112 ( 14 − 6 ) − ( −4 ) ?= −59

900 ≠ −59

False

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5 0

3 years ago

HELP!! PLEASE!! NEED DONE ASAP I WILL GIVE 100 POINTS AND MORE IF YOU CAN GET ALL 3 QUESTIONS DONE!! THANK YOU!! I WILL ALSO MAR

VARVARA [1.3K]

Answer:

I answered the questions but that formatting is very confusing and discourages anyone for trying to answer.

The last question is confusing. If I got it wrong, tell me. I will try to answer in the comment section then.

Step-by-step explanation:

Kayson is looking at two buildings, building A and building B, at an angle of elevation of 73°. Building A is 30 feet away, and building B is 35 feet away. Which building is taller and by approximately how many feet?

$\text{tan}\theta=\frac{h_{A}}{30} \Rightarrow h_{A}=\text{tan}73\º \cdot 30 \Rightarrow h_{A}\approx 98.12 \text{ feet}$

$\text{tan}\theta=\frac{h_{B}}{35} \Rightarrow h_{B}=\text{tan}73\º \cdot 35 \Rightarrow h_{B}\approx 114.47 \text{ feet}$

$\text{Difference} \approx 16.35$

Building B is around 16.35 feet taller than building A.

A Look at the figure below: an image of a right triangle is shown with an angle labeled y If sin y° = a divided by 6 and tan y° = a divided by b, what is the value of cos y°?

$\text{sin}(y)=\frac{a}{6}$

$\text{tan}(y)=\frac{a}{b}$

a is the opposite side; 6 is the hypotenuse; b is the adjacent side.

Therefore,

$\text{cos}(y)=\frac{b}{6}$

If sin f° = eight ninths and the measure of segment YW is 24 units, what is the measure of segment YX? triangle XYW in which angle W is a right angle, angle X measure f degrees, and angle Y measures d degrees.

This seems a bit confusing. The angles don't match. We have $90\º+62\º +21\º \approx 173\º$