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Lady bird [3.3K]
3 years ago
13

Sara drove 96 miles on 3.2 gallons of gas. How many miles can Sara drive on 12.5 gallons of gas

Mathematics
2 answers:
jekas [21]3 years ago
7 0
375 miles 96 on 3.2 gallons of gas dived
Blababa [14]3 years ago
4 0

Answer:

375 miles

Step-by-step explanation:

Create a proportion where x is the number of miles she can drive on 12.5 gallons of gas:

\frac{96}{3.2} = \frac{x}{12.5}

Cross multiply and solve for x:

3.2x = 1200

x = 375

So, with 12.5 gallons of gas, Sara can drive 375 miles

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Write 0.000012001 in scientific notation. 0.000012001 =​
LUCKY_DIMON [66]

Answer:

<em>The answer is 1.2001 * 10^-5</em>

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The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,
strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

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=400 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=80 represent the population standard deviation

n=15 represent the sample size  

2) 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)

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

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

400-2.58\frac{80}{\sqrt{15}}=346.708    

400+2.58\frac{80}{\sqrt{15}}=453.292

So on this case the 99% confidence interval would be given by (346.708;453.292)    

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that t_{\alpha/2}=2.98

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

400-2.98\frac{80}{\sqrt{15}}=338.445    

400+2.98\frac{80}{\sqrt{15}}=461.555

So on this case the 99% confidence interval would be given by (338.445;461.555)    

4 0
3 years ago
If the current in a circuit is 2 +j2 amps and the resistance is 3-j2 ohms, what is the voltage
victus00 [196]

Answer:

The voltage is 10 + 2j volts.

Step-by-step explanation:

Ohm's first law:

By Ohm's first law, the voltage is the multiplication of the current by the resistance, that is:

V = R*i

The voltage is measured in Volts, the current in amps and the resistance in ohms.

In this question:

Both the current and the resistance have complex parts. We have to know that:

j^{2} = -1

We have that:

R = 3 - 2j, i = 2 + 2j

Then

V = R*i

V = (3 - 2j)*(2 + 2j)

V = 6 + 6j - 4j - 4j^{2}

V = 6 + 2j - 4(-1)

V = 10 + 2j

The voltage is 10 + 2j volts.

4 0
3 years ago
What is the value of x? Show me how you got your answer.
artcher [175]

Answer:

x = 30

since 3x = 90 degrees, then x = 90/3 = 30

Step-by-step explanation:

7 0
2 years ago
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