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kodGreya [7K]
2 years ago
14

The 300 people who were lined up outside the amusement park had all entered by 8:15 a.m. By 8:30, 550 more had entered. The numb

er who entered each 15 minutes increased steadily by 250 after that. All of the people were planning to stay for the parade at noon. a. How many people entered between 11:45 and noon, just in time for the parade ? b. Represent the problem as a series and write a formula for the nth term.
Mathematics
1 answer:
Tasya [4]2 years ago
7 0

Answer:

250; p= 300 + \frac{50}{3}t

Step-by-step explanation:

a. 15 minutes passed, so there would be 250 people who came in

b. You would create a formula, where t = time after 8:15 (in minutes), while p = people who are at the parade

300 + \frac{250}{15}t = p, which equals p= 300 + \frac{50}{3}t

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv
Rina8888 [55]

Answer:

14.42-1.96\frac{6.95}{\sqrt{36}}=12.150    

14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690    

So on this case the 95% confidence interval would be given by (12.150;16.690)    

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=14.42 represent the sample mean

\mu population mean (variable of interest)

\sigma=6.95 represent the population standard deviation

n=36 represent the sample size  

Solution to the problem

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 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

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

14.42-1.96\frac{6.95}{\sqrt{36}}=12.150    

14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690    

So on this case the 95% confidence interval would be given by (12.150;16.690)    

5 0
2 years ago
Alice has a 4-inch by 5-inch photo of your school’s championship girls’ ice hockey team. To celebrate their recent
Pachacha [2.7K]

Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.

Step-by-step explanation:

Step 1:

In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.

We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.

Step 2:

The original photo was a 4-inch by 5-inch photo.

Option 1 is 7-inch by 9-inch, so the ratios are

\frac{7}{4} = 1.75, \frac{9}{5} = 1.8. The ratios are different so this cannot be the enlarged photo's dimensions.

Option 2 is 8-inch by 10-inch, so the ratios are

\frac{8}{4} = 2, \frac{10}{5} = 2. The ratios are the same so this can be the enlarged photo's dimensions.

Option 3 is 12-inch by 16-inch, so the ratios are

\frac{12}{4} = 3, \frac{16}{5} = 3.2. The ratios are different so this cannot be the enlarged photo's dimensions.

So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.

7 0
2 years ago
Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds
svetlana [45]

Answer:

Yes, but it is not linear. It is exponential :  f(x) = 5\cdot 2^{x-1}

Step-by-step explanation:

On the first day we have 5 bacteria.

On the second day we will have 5*2 = 10 bacteria.

On the third day we will have 10*2 = 5*2*2 = 5*2^2 = 20 bacteria.

On the fourth day we will have 20*2 = 5*2*2*2 = 5*2^3 = 40 bacteria.

We can see that

                                                f(x) = 5\cdot 2^{x-1},

where x is a number of days and f(x) gives us the number of bacteria.

4 0
1 year ago
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to
wolverine [178]
The function for conversions from Fahrenheit to Celsius is:

Celsius = (Fahrenheit - 32) x 5/9 

C(76.1) = (76.1 - 32) x 5/9
             = (44.1) x 5/9
             =  24.5

Therefore, 76.1 degrees Fahrenheit = 24.5 degrees Celsius. 
5 0
2 years ago
Read 2 more answers
A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00. If the collection contains 25 quarte
Elenna [48]

Answer:

17

35

Step-by-step explanation:

9 0
2 years ago
Read 2 more answers
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