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Bess [88]
2 years ago
10

On section AB, whose length is 192 cm, take the point C so that AC: CB = 1: 3. The point D is taken on the AC section so that CD

= BC / 12. Find the distance between the midpoints of the AD and CB sections
50 points
Mathematics
1 answer:
jasenka [17]2 years ago
4 0

Answer:

  • 112 cm

Step-by-step explanation:

<u>Given:</u>

  • AB = 192 cm
  • AC : CB = 1 : 3
  • CD = BC/12
  • The distance between midpoints of AD and CB = x

<u>Find the length of AC and CB:</u>

  • AC + CB = AB
  • AC + 3AC = 192
  • 4AC = 192
  • AC = 192/4
  • AC = 48 cm

<u>Find CB:</u>

  • CB = 3AC = 3*48 = 144 cm

<u>Find the length of CD:</u>

  • CD = BC/12 = 144/12 = 12 cm

<u>Find the length of AD:</u>

  • AD = AC - CD = 48 - 12 = 36 cm

<u>Find the midpoint of AD:</u>

  • m(AD) = 36/2 = 18 cm

<u>Find the midpoint of CB:</u>

  • m(CB) = AC + 1/2CB = 48 + 144/2 = 48 + 82 = 130 cm

<u>Find the distance between the midpoints:</u>

  • x = 130 - 18 = 112 cm
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Tanya [424]

Problem 1

Answers:

Percentage of patients that were dogs = 46%

Standard Error = 0.07048404074682

Margin of error for 90% confidence interval = 0.11594624702851

Margin of error for 95% confidence interval = 0.13814871986377

Round the decimal values however you need them

------------

To get the first answer, you add up the numbers given (7,4,5,5,2) and divide that over 50. So 7+4+5+5+2 = 23 which leads to 23/50 = 0.46 = 46%; therefore phat = 0.46 is the sample proportion of dogs.

Use the SE (standard error) formula given to you with phat = 0.46 and n = 50 to get SE = 0.07048404074682

The critical z value at 90% confidence is 1.645; this value is found in your Z table (back of your stats textbook). Multiply the SE value by 1.645 to get 0.07048404074682*1.645 = 0.11594624702851

Also found in your textbook is 1.960 which is the z critical value at 95% confidence. Multiply this with the SE value to get 0.07048404074682*1.960 = 0.13814871986377

===============================================

Problem 2

Answer: Choice B) picking balls from a bin; the 60 randomly selected get chosen for the first bus, while the remaining 60 go to the second bus

-----------

Choice A is fairly vague on what the lower and upper boundaries are. What is the smallest number allowed? What about the largest? This isn't clear so it's possible that we could end up with more positive numbers than negative (eg: if we had an interval -10 < x < 110). So choice A is false. A similar issue shows up with choice D.

Choice B is true. Assuming the selection process is random and not biased, then each ball is equally likely for each selection. The fact that the balls are colored seems to be extra info which I'm not sure why your teacher threw that in there.

Choice C is false because choice B is true

Choice D is false for similar reasons as choice A. It's not clear where we start and where we end. If we had the interval 2 < x < 6 then x could take on the values {3, 4, 5} and we see that picking an odd number is twice as likely than picking an even. In this example, there is bias.

===============================================

Problem 3

Answer: Choice B) Roll a die; each number corresponds to a different class

------------

Choice A is false because choice B being the answer contradicts it

Choice B is true: there are 6 sides on the die, and each side is equally likely to be landed on, so each class is equally likely

Choice C is false because 2*2*2 = 8 represents the number of combos you can have when you flip three coins (one combo being HTH for heads tail heads) but there are 6 classes, not 8

Choice D is false because while we want 6 regions on the spinner. Each region must have the same area; otherwise, one class is weighted heavier than the others making it more likely you select that particular class.


7 0
3 years ago
Read 2 more answers
Whats 58788188 to the nearest million
In-s [12.5K]

Answer:

588,000,000.

Step-by-step explanation:

Inserting commas  every 3 digits from the right, we have:

587,881,188  so that is 587 million and 881,000.

As 8 is the next digit after the 587 we add 1 to 587 to make 588 million.

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3 years ago
A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)x , where x represents the number of days
Nitella [24]

Answer:

20 = initial population of the rabbits

1.014 = growth rate of the rabbits

the average rate of change from day 50 to day 100 is 0.8

Step-by-step explanation:

A population of rabbits in a lab, p(x), can be modeled by the function

p(x) = 20(1.014)^x

This model is exponential. Where 20 = initial population of the rabbits

1.014 = growth rate of the rabbits with 1.4% increase rate of the rabbits

To find the average rate of change from day 50 to day 100,

find the population p(50) and p(100). Subtract them and divide by 100 - 50 = 50. 

p(50) = 20(1.014)50 = 40.08... 

p(100) = 20(1.014)100 = 80.32... 

(80.32 - 40.08) / (100 - 50) = 40.24/50 = 0.8048. which is approximately 0.8 to the nearest tenth. 

The rate of change is 0.8. 

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