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lisabon 2012 [21]

3 years ago

12

PLEASE SHOW YOUR WORK WITH YOUR ANSWER. Two bags had 50 kilograms of sugar each. After taking out 3 times as much sugar from bag

one than bag two, bag one had half as much sugar left as bag two. How much sugar is left in each bag?

1 answer:

Svetllana [295]3 years ago

4 0

Answer:

Bag 1: 20

Bag 2: 40

Step-by-step explanation:

Let x be the amount taken out of bag 2

Then the amount left in each bag can be written as:

Bag 1: 50-3x

Bag 2: 50-x

Since we know that half of bag 2 is bag 1, that gives us:

50-3x = 1/2(50-x)

-> 50-3x = 25-x/2

Now lets isolate x and solve:

25 = 5x/2

-> 50 = 5x

-> x = 10

So plug x bag in for the original equations:

Bag 1: 50-3x = 50-3(10) = 20

Bag 2: 50-x = 50-10 = 40

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Answer:

value of x = 5.8 mm

Step-by-step explanation:

We have given,

Two right triangles EDH and EDG.

In right triangle EDH, EH = 56mm , DH = 35 mm

Using Pythagoras theorem we can find ED.

i.e EH² = ED²+DH²

56²=ED²+35²

ED²=56²-35²

ED = √(56²-35²) = 7√39 = 43.71 mm

Now, Consider right triangle EDG

Here, EG=44.8mm , GD = x+4 and ED = 7√39

Again using Pythagoras theorem,

EG² = ED² + DG²

44.8²= (7√39)²+ (x+4)²

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3 years ago

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

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1 year ago

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Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

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Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

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

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What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{50}} = 5.94$

This is the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 591}{5.94}$

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What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

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8 0

3 years ago

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rusak2 [61]

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Step-by-step explanation:

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ZanzabumX [31]

Complete question :

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Step-by-step explanation:

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