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Veronika [31]
3 years ago
5

0.9 of Karen's Science score is equal to 0.75 of her Math score and 0.8 of her Chemistry score. Given that Karen scored 96 marks

for her Math, what was her total score of the 3 subjects?
Mathematics
1 answer:
DochEvi [55]3 years ago
5 0

You have to formulate equations for this problem.

Let S = Science score

      M = Math score

       C = Chemistry score

To illustrate the given:

0.9S = 0.75M

0.9S = 0.8C

You are given that Karen’s Math score is 96 marks. You have to substitute the Math score to the first equation.

0.9S = 0.75(96)

0.9S = 72

S = 80

Therefore, Karen’s Science score is 80. Now, you have to substitute the Science score to the second equation.

0.9(80) = 0.8C

0.8C = 72

C = 90

So, Karen’s Chemistry score is 90.

Therefore, the total score of the 3 subjects is 266 (96 + 80 + 90).

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∠A and ∠B are vertical angles. If m∠A=(3x-30)° and m∠B=(2x-9)°,then find the value of x.
olganol [36]

Answer:

x = 21°

Step-by-step explanation:

Vertical angles have the same measures, therefore:

3x - 30 = 2x - 9

x - 30 = -9

x = 21°

8 0
3 years ago
There are 48 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time
Stella [2.4K]

Answer:

a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n trials, the mean is \mu*n and the standard deviation is s = \sigma\sqrt{n}

In this question:

n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71

These values are in minutes.

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{250 - 240}{27.71}

Z = 0.36

Z = 0.36 has a pvalue of 0.6406

64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?

The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.

5 0
3 years ago
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. Find the speed of
Leokris [45]

Answer: the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

The boat travelled 252 miles downstream and the same distance upstream.

The trip downstream took 12 hours. Assuming the boat travelled with the wind when going downstream, the total speed would be (x + y) mph.

Distance = speed × time

The expression for distance travelled downstream is

252 = 12(x + y)

Dividing through by 12, it becomes

21 = x + y- - - - - - - - - - 1

The trip back took 84 hours. Assuming the boat travelled against the wind when going back(upstream), the total speed would be (x - y) mph.

The expression for distance travelled upstream is

252 = 84(x - y)

Dividing through by 84, it becomes

3 = x - y- - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

24 = 2x

x = 24/2

x = 12 mph

Substituting x = 12 into equation 1, it becomes

21 = 12 + y

y = 21 - 12

y = 9 mph

7 0
3 years ago
A snail travels 5 meters in 20 minutes. He travels the same amount of time per meter. How long will it take him to travel 11 met
Llana [10]

Answer:

<h2>4</h2><h2>11</h2>

Step-by-step explanation:

20:5=4 (minutes for 1 meter)

4*11=44 minutes for 11 meters

or

20 : 5 = x : 11

x = 20*11:5

x = 44

or

20:5* 11=44

7 0
3 years ago
Find the angle measure of one internal angle for regular hexagon ABCDEF.
babunello [35]

Answer:

Each interior angle of a polygon equals:

180 degrees - (360 / number of sides)

180 - (360 / 6)

= 180 -60

= 120 degrees

http://www.1728.org/polygon.htm

Step-by-step explanation:

5 0
3 years ago
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