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yulyashka [42]
3 years ago
14

1 of 5Find two numbers with a sum of 5 and a difference of 1.Big number:Small number:​

Mathematics
1 answer:
VLD [36.1K]3 years ago
5 0

Answer:

bid number = 3 and small number = 2. 3+2=5 3-2=1

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Simplify to create an equivalent expression. <br><br>1+4(6p-9)<br><br>please help. ​
irinina [24]

Answer: 24p - 35

4 * 6p = 24p

4 * 9 = 36

1 + 29p - 36

-36 + 1 = -35

29p - 35

5 0
3 years ago
monica sells lemonade over the summer and uses conical paper cups to serve the lemonade. Each cup is 8 centimeters tall.She star
GaryK [48]

Answer:

(a)205

(b)5 Packages

Step-by-step explanation:

\text{One gallon is equivalent to 3785 } cm^3

Therefore: \text{10 gallon= 3785X 10 =37850 } cm^3

Therefore, Volume of the lemonade Monica Started with is \text{37850 } cm^3

The diameter of the cup =8cm

Therefore, Radius =8/2 =4cm

Height of the Cup =11cm

Volume of a Cone=\frac{1}{3}\pi r^2 h

\text{Volume of the Cup}=\frac{1}{3}\pi *4^2*11 \\=184.31cm^3

The number of cups needed to empty the 10 gallon cooler =37850÷184.31

=205.36

\approx 205 Cups

(b)If the Cups are sold in packages of 50

Number of Package to be bought =205 ÷ 50 =4.1

She would need to buy 5 packages.

5 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
2 years ago
What is the cost of 12.6 gallons of gasoline if the price per gallon is $1.40?
12345 [234]
If

1 gallon = $1.40
12.6 gallons = $1.40 × 12.6

Plug those into your calculator and you'll get $17.64!
3 0
2 years ago
Read 2 more answers
if the x- and y- values in each pair of a set of ordered pairs are interchanged, the resulting set of ordered pairs is known as
Sliva [168]
<span>inverse of a function</span>
6 0
2 years ago
Read 2 more answers
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