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Taya2010 [7]
3 years ago
8

Read the true statement below and tell whether the converse, inverse, and contrapositive are also true.

Mathematics
1 answer:
IgorC [24]3 years ago
5 0

Converse: False because he can live somewhere else but still belong in Hawaii

Inverse: False because he can live somewhere else but still belong in Hawaii

Contrapositive: True because Honolulu belongs to Hawaii so if he doesn't live in Hawaii he absolutely can't live in Honolulu

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Suppose you take a 15 question True or False quiz and you guess on every problem. You only get 3 correct. (a) What is the probab
lana66690 [7]

Answer:

0.648

No, that is not an unusually low number of correct guesses.

Step-by-step explanation:

Suppose you take a 15 question True or False quiz and you guess on every problem. You only get 3 correct. Then

  • p=\dfrac{3}{15}=\dfrac{1}{5}=0.2 - correct;
  • q=1-p=1-0.2=0.8 - o\incorrect.

The probability of getting 3 or fewer correct guesses is

P(\text{3 or fewer})\\=P(0)+P(1)+P(2)+P(3)\\ \\=C^{15}_0p^0q^{15-0}+C^{15}_1p^1q^{15-1}+C^{15}_2p^2q^{15-2}+C^{15}_3p^0q^{15-3}\\ \\=1\cdot q^{15}+15pq^{14}+105p^2q^{13}+455p^3q^{12}\\ \\=(0.8)^{15}+15\cdot 0.2\cdot (0.8)^{14}+105\cdot (0.2)^2\cdot (0.8)^{13}+455\cdot (0.2)^3\cdot (0.8)^{13}\\ \\\approx 0.648

Using the criteria that a number 3 is unusually low if P(3 or fewer) ≤ 0.05, we can state that 3 is not an unusually low number of correct guesses.

5 0
3 years ago
What is the equation of the line in slope-intercept form that is perpendicular to the line y=3/4x-2 and passes through the point
tatyana61 [14]

Answer:

A

Step-by-step explanation:

You have to plug numbers into point slope formula (make sure to use a slope of -4/3 since its perpendicular) and then solve for y.

7 0
3 years ago
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the c
Arturiano [62]

Incomplete Question:

The content of the pie chart is as follows:

<em>Hamsters  = 9% ; Snakes  = 10% ; Cats  = 23% </em>

<em> Birds  = 21% ;  Dogs  = 26% ;  Fish  = 11%</em>

<em></em>

Answer:

The number of citizens who chose cat or fish is 47,600

Step-by-step explanation:

Given

Number of citizens = 140,000

Required

Determine the number of those that chose fish or cats

First, we need to calculate the percentage of those whose pets are either cats or fish

Percentage = Cat + Fish

Substitute 23% for cat and 11% for fish

Percentage = 23\% + 11\%

Percentage = 34\%

Next, is to multiply the calculated percentage by the number of citizens

Cat\ or\ Fish = Percentage * Number\ of\ Citizens

Cat\ or\ Fish = 34\% * 140000

Cat\ or\ fish = 47600

<em>Hence, the number of citizens who chose cat or fish is 47,600</em>

4 0
3 years ago
A person standing on level ground is 2000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diag
antoniya [11.8K]

Answer:

12

Step-by-step explanation:

The formula for the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. Therefore, the tangent of angle x is 420/2000=0.21. Taking the arctangent of that to get the angle, you get about 12 degrees. Hope this helps!

7 0
3 years ago
An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume
Lynna [10]

Answer:

a) 21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

b) ME=2.58\frac{52}{\sqrt{350}}=7.17

c) ME=2.58\frac{52}{\sqrt{100}}=13.42

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".  

Part a

\bar X=21 represent the sample mean  

\mu population mean (variable of interest)  

\sigma=52 represent the population standard deviation  

n=350 represent the sample size  

99% 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 0.99 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):  

21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

Part b

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{350}}=7.17

Part c

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{100}}=13.42

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0
3 years ago
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