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DerKrebs [107]
3 years ago
11

2x + 3y = 6 Solve for y

Mathematics
1 answer:
expeople1 [14]3 years ago
7 0

Answer:

y=allsolutions

Step-by-step explanation:

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Francine ran 3 1/2 laps around the circular track in the school gym. The track has a diameter of 1/2 miles. About how far does F
Juliette [100K]

Answer:

Francine run 5.495 miles

Step-by-step explanation:

Given :

Francine ran  3\frac{1}{2}  laps around the circular track in the school gym.

The track has a diameter of 1/2 miles.

To Find :  About how far does Francine run?

Solution :

First we need to calculate the perimeter of circular track :

Perimeter of circle :  2\pi r

Since we are given the diameter = 1/2 miles = 0.5 miles

So, Radius will be (Diameter/2) = 0.5/2 = 0.25 miles

So, The perimeter will be:

2\pi *0.25

0.5\pi

Since \pi =3.14

⇒0.5*3.14

⇒1.57

Thus the circular track is of 1.57 miles .

Since she ran   3\frac{1}{2}  = 7/2=3.5 laps

1 lap = 1.57 miles

So, 3.5 laps = 1.57*3.5 =5.495 miles .

Hence ,  Francine run 5.495 miles


6 0
3 years ago
Which of the following describes the quotient of 4 and -28? A) The quotient is undefined. B) The quotient is an integer. C) The
DanielleElmas [232]

Answer:

-1/7

Step-by-step explanation:

Divide the first expression by the second expression.

6 0
3 years ago
In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean
Nastasia [14]

Answer:

a) \bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

b) ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

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 represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n=80 represent the sample size  

Solution to the problem

Part a

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

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

For this case we can calculate the mean like this:

\bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

Part b

For this case is the sample size is doubled the margin of error would be:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

5 0
3 years ago
Manny walked a total of 3 miles. what is The reference point used to calculate the total distance that he walked was the same as
Firlakuza [10]
B. On a circular nature trail.
As Manny ended up at the same point from where he started after walking 3 miles, he walked in a circle.
8 0
3 years ago
Read 2 more answers
Can someone help with this true or false math
matrenka [14]

the answer is false

isididididododidid

3 0
2 years ago
Read 2 more answers
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