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Alekssandra [29.7K]
3 years ago
14

What is the difference between a histogram and a cumulative histogram?

Mathematics
1 answer:
diamong [38]3 years ago
3 0

Answer: The answer is provided below

Step-by-step explanation:

A histogram is a diagram which consist of rectangles whereby the area is proportional to frequency of a variable and the width is equal to class interval. A histogram is a commonly used graph that is used to show frequency distributions.

The cumulative histogram is a histogram whereby the vertical axis doesn't gives only the counts for a single bin, but gives the counts for that bin and all the bins for the maller values of a response variable.

Cumulative histograms are similar to normal histograms, but the main difference is that they graph cumulative frequencies unlike histograms that graph just frequencies.

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a small rocket is shot from the edge of a cliff suppose that after t seconds the rocket is y meters above the cliff where y=30t-
Natalka [10]

Answer:

Greatest height: 45 meters

Time for greatest height: 3 seconds

Height after 5 seconds: 25 meters above the cliff

Time for height of 40 meters: 7.123 seconds

Height after 7 seconds: -35 meters (35 meters below the cliff)

Step-by-step explanation:

to find the maximum height, we need to calculate the derivative of y in relation to t and then find when dy/dt = 0:

dy/dt = 30 - 10t = 0

10t = 30

t = 3 seconds

In this time, the height is:

y = 30*3 - 5*3^2 = 45 meters

After 5 seconds, the height is:

y = 30*5 - 5*5^2 = 25 meters

The time for the height of 40 meters is:

40 = 30t - 5t^2

t^2 - 6t - 8 = 0

Using Bhaskara's formula, we have:

Delta = 6^2 + 4*8 = 68

sqrt(Delta) = 8.246

t1 = (6 + 8.246) / 2 = 7.123 seconds

t2 = (6 - 8.246) / 2 = -1.123 seconds (negative value for time is not valid)

So the time when the rocket reaches 40 meters is 7.123 seconds

After 7 seconds, the height is:

y = 30*7 - 5*7^2 = -35 meters

The rocket will be 35 meters below the cliff.

5 0
3 years ago
Sylvia has a total of 16 trading cards: 8 superhero cards, 4 princess cards,2 villain cards, and 2 wildlife cards. what is the r
balu736 [363]
There as 16 cards, 2 of which are wildlife cards, so the ratio is 16 : 2. We can simplify it by dividing both sides by 2, so we'll get the ratio of 8 : 1.

I hope this helps! :)


5 0
3 years ago
Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compoun
aev [14]

Answer:

a) 29.4-1.96\frac{7}{\sqrt{10}}=25.06  

29.4+1.96\frac{7}{\sqrt{10}}=33.74  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

b) z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988  

p_v =P(z>1.988)=0.0234    

If we compare the p value and the significance level given \alpha=Step-by-step explanation:Previous conceptsA 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".  
Part a
Data given: 30 30 42 35 22 33 31 29 19 23
We can calculate the sample mean with the following formula:[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}= 29.4 the sample mean

\mu population mean (variable of interest)  

\sigma=7 represent the population standard deviation  

n=10 represent the sample size  

95% confidence interval  

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):  

29.4-1.96\frac{7}{\sqrt{10}}=25.06  

29.4+1.96\frac{7}{\sqrt{10}}=33.74  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

Part b

What are H0 and Ha for this study?  

Null hypothesis:  \mu \leq 25  

Alternative hypothesis :\mu>25  

Compute the test statistic

The statistic for this case is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988  

Give the appropriate conclusion for the test

Since is a one side right tailed test the p value would be:  

p_v =P(z>1.988)=0.0234  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis.    

8 0
3 years ago
Find the distance of the point (3,4) from the midpoint of the line joining (8,10) and (4,6)
Elis [28]

Answer:

Distance between point (3,4) and midpoint of line joining (8,10) and (4,6) = 5 units.

Step-by-step explanation:

Given:

Points:

A(3,4)\\B(8,10)\\C(4,6)

To find distance from point A to midpoint of  BC.

Midpoint M of BC:

M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\

M=(\frac{8+4}{2},\frac{10+6}{2})\\     [Plugging in points B(8,10)\ and\ C(4,6)]

M=(\frac{12}{2},\frac{16}{2})\\

M=(6,8)\\

Distance between A and M:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

D=\sqrt{(6-3)^2+(8-4)^2} \\   [Plugging in points A(3,4)\ and\ M(6,8)]

D=\sqrt{(3)^2+(4)^2} \\

D=\sqrt{9+16} \\

D=\sqrt{25} \\

D=\pm5

Since distance is always positive ∴ D= 5 units

4 0
3 years ago
Solve the Mode,Mean,Median,and Range
Semmy [17]
67, 66, 67, and 45, respectively.
4 0
3 years ago
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