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Alex
3 years ago
14

A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 points. How many 4 point problem

s are there?
Mathematics
1 answer:
Vinil7 [7]3 years ago
7 0
If you only have 3 point problems you have a total of 3*30=90 points, since the test has 100 points you need 10 extra points, so 10 of those 3 point questions have to be changed to 4 point questions.

So 20 3-point questions and 10 4-point questions.
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From a large number of actuarial exam scores, a random sample of scores is selected, and it is found that of these are passing s
Mnenie [13.5K]

<u>Supposing 60 out of 100 scores are passing scores</u>, the 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

  • The lower limit is 0.5.
  • The upper limit is 0.7.

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of \alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of \frac{1+\alpha}{2}.

60 out of 100 scores are passing scores, hence n = 100, \pi = \frac{60}{100} = 0.6

95% confidence level

So \alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.5

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.7

The 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

  • The lower limit is 0.5.
  • The upper limit is 0.7.

A similar problem is given at brainly.com/question/16807970

5 0
3 years ago
four apples and one banana cost £1.40 seven apples and one banana cost £2.00 work out the cost of an apple and the cost of a ban
beks73 [17]

Answer:

  • apple: £0.20
  • banana: £0.60

Step-by-step explanation:

Let "a" and "b" represent the costs of one apple and one banana, respectively. Then the purchases can be written ...

  4a +b = 1.40

  7a +b = 2.00

Subtracting the first equation from the second gives ...

  (7a +b) -(4a +b) = (2.00) -(1.40)

  3a = 0.60 . . . . simplify

  a = 0.20 . . . . . .divide by 3

Using this in the first equation, we have ...

  4(0.20) +b = 1.40

  b = 0.60 . . . . . subtract 0.80

The cost of an apple is £0.20; the cost of a banana is £0.60.

8 0
3 years ago
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What is 1/3 as a slope?

The answer is approximately 18.43º. A slope of 1 in 3 means the slope is 1/3. It also means a rise of 1 and a run of 3. On a graph, starting at the origin, go up 1 unit, then from there, go to the right 3 units.

(hope this helps) :)

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