10x + 25 = 50 a 25 b 2.5 c 250 d .25

From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa.

Semenov [28]

Answer:

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

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".

$\bar X =4.97$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.0461 represent the sample standard deviation

n=19 represent the sample size

Confidence interval

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:

$df=n-1=19-1=18$

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: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.10$

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

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

5 0

3 years ago

Lisa spends 1/5 of an hour doing her math homework and 1/3 of an hour doing her social studies homework. What fraction of an hou

Sveta_85 [38]

To solve this, all you have to do is add 1/5 and 1/3.
Well, you might be thinking, "But the denominators are not the same! Fractions have to have like denominators in order to be added together!" And you are right. So, all we have to do, is make them both have the same denominator. To do this, we have to multiply both the numerator and denominator by the same number to find an equivalent fraction.
For 1/5, we can multiply both the numerator and denominator by 3, to get 3/15.
Likewise, we can multiply both the numerator and denominator of 1/3 by 5, to get 5/15.
Now, you can easily add 3/15 and 5/15 because all you have to do is add the numerators, because the denominators are the same!
3/15+5/15=8/15, so she spends 8/15 hour on her math and social studies homework.
Hope I helped!

3 0

3 years ago

If line AD is a tangent to circle B at point C, and m∠ABC = 40º, what is the measure of ∠BAC? 90º 180º 50º 40º

zhenek [66]

We have a line tangent to the circle with center B at point C. We know that the angle formed between the tangent line at the point of intersection to the line extended from that point to the center of the circle is equal to 90°. In the problem, the 90° is for ∠BCA. We also know that the summation of all angles in a triangle is 180°. We have the solution below for the ∠BAC
180°=∠BAC + ∠BCA + ∠ABC
180°=∠BAC + 90° + 40°
∠BAC =50°
The answer is 50°.

4 0

3 years ago

Read 2 more answers

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length

zvonat [6]

The two ways to find the ratio of the length is to turn the inches into feet or the feet into inches

So the answer can be solved like this:

1/36ft to 1/4ft which is 9:1 (blueprint size to actual size)

or

1/3in to 3in which is also 9:1 (blueprint size to actual size)

3 0

3 years ago

5. From the choices below, choose an expression that is equivalent to the

blondinia [14]

Answer: -(22/4)

Step-by-step explanation:

8 0

3 years ago