Please help me Question 3 of 5

Find the value of x in the triangle shown below.<br> X°<br> 125°<br> 21°

coldgirl [10]

Answer: x= 34

Step-by-step explanation:

7 0

3 years ago

The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A

Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) 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".

$\bar X =65$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size

2) 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:

$df=n-1=11-1=10$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that $t_{\alpha/2}=1.81$

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

$65-1.81\frac{9}{\sqrt{11}}=60.09$

$65+1.81\frac{9}{\sqrt{11}}=69.91$

So on this case the 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

3 0

3 years ago

Angles C and E are complementary angles. Angle C measures (4× + 50). Angle E measures 28 degrees. Solve for x.

julsineya [31]

Answer:

x = 3

Step-by-step explanation:

4x + 50 + 28 = 90

4x + 78 = 90

4x = 12

x = 3

7 0

3 years ago

Read 2 more answers

Expand and simplfy (2x+1)(x+3)

Nina [5.8K]

Answer:

(2x+1)(x+3)

2x(x+3)+1(x+3)

2x2+6x+x+3

2x2+7x+3 (2x2 means two x square)

if you want you can also multiply 2x+3 by x+3

like this:

(2x+1)(x+3)

x(2x+1)+3(2x+1)

2x2+x+6x+3

2x2+7x+3 (2x2 means two x square)

They will both give you the same answer.

5 0

3 years ago

What are the missing sides and angles of this triangle? What is the area?

Butoxors [25]

This does not appear to be a right triangle. However, we know 2 sides and the included angle, so can find the unknown side length. Let x represent this length. Then:

x^2 = (9 m)^2 + (12 m)^2 - 2(9m)(12 m)*cos 30 degrees, or

x^2 = 81 + 144 - 216(sqrt(3) / 2). Please solve for x^2 and then solve the result for x, making sure to choose the positive value. The result will be the length of the side opposite the 30 degree angle.

With 1 of 3 angles known, and 3 of 3 sides known, you can use the Law of Sines to find the other two angles. As a reminder, the Law of Sines looks like this:

a b c
-------- = --------- = ----------
sin A sin B sin C.

You can give the 30-deg angle any name you want; then a, the length of the side opposite the 30-deg angle, which you have just found. And so on.

4 0

3 years ago