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3 years ago

How do I simplify these expressions? 5(x+8)+3 3.6x-7-5.1x 4+8x+2.2-10x

Mathematics

1 answer:

Aleks04 [339]3 years ago

8 0

Answer:

1. 5x +43

2. -1.5x - 7

3. 6.2 - 2x

Step-by-step explanation:

Equation 1:

5 (x+8) +3

First, we can distribute the 5 to the (x+8) and get 5x + 40. Distributing is when we multiply the 5 by the first number (x) and then by the second number (8) Because they aren't like terms (don't both have x's) we cannot combine then and must keep them separated by a subtraction sign

Now we have: 5x + 40 + 3

Next, we can combine the like terms. This means that any that have the same variable can be combined. So, the 5x has no other x's so he has to stay how he is. The 40 and the 3, however, can be added together to get 43.

Our finished equation is: 5x + 43

Equation 2:

3.6x - 7 - 5.1x

First, we can combine like terms as we learned in the last problem. This would be our x's since we have multiple.

We can add 3.6x and -5.1x and get -1.5x

Now we have: -1.5x - 7

Equation 3:

4 + 8x + 2.2 - 10x

We can start with either the numbers with x's or without but I'll just do the x's. So we have 8x and -10x. Adding these together would get us -2x.

Next, we can combine 4 and 2.2 and get 6.2.

Now, putting these back into our equation would look like this:

6.2 - 2x

I'm not sure how much my explanations helped, but I hope you understand!!

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

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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.

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