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3 years ago

7. Find two consecutive even integers such that twice the smaller is

Mathematics

1 answer:

Arturiano [62]3 years ago

7 0

Answer:

Step-by-step explanation:

The difference between two consecutive even integers is 2

and even integer is always twice some integer

So:

2x ← smaller of numbers

2x+2 ← larger of numbers

2×2x ← twice the smaller of numbers

3(2x+2) ← three times the larger

3(2x+2)-26 ← 26 less than 3 times the larger

twice the smaller is 26 less than 3 times the larger:

3(2x+2) - 26 = 2×2x

6x + 6 - 26 = 4x

+20 +20

6x - 4x = 20

2x = 20

2x+2 = 20 + 2 = 22

Check: 2×20=40; 40+26 = 66; 66÷3=22

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If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000

zavuch27 [327]

Answer:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the retirement savings of a population, and for this case we know the distribution for X is given by:

$X \sim N(100000,20000)$

Where $\mu=100000$ and $\sigma=20000$

We are interested on this probability

$P(X>117000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

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2 years ago

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2 years ago

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Answer:

17 for 1 point shots and 35 for two point shots.

Step-by-step explanation:

let the number of 1 point shots be x

let the number of 2 point shots be y

x + y = 52 (1)

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subtracting (1) from (2)

y = 35

from (1) x = 52 - y = 52 - 35 = 17

Hence number of 1 pointers = 17

number of 2 point shots = 35

checking; 17 + 35 =52 ; and 17+ 2*35 = 87

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2 years ago

Below are the range and standard deviation for a set of data. Use the range rule of thumb and compare it to the standard deviati

Liula [17]

Solution: We are given:

$Range =2.76$

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Therefore the estimated standard deviation is 0.690

is this an acceptable approximation?

Answer: c. Yes, because the error of the range rule of thumb's approximation is less than 15%.

Explanation:

The difference between estimated standard deviation and actual standard deviation is:

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Now let's find the percentage of error

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