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DanielleElmas [232]

3 years ago

11

54,000 families have incomes less than $20,000 per year. This number of families is 60% of the families that had this income lev

el 12 years ago. What was the number of families who had incomes less than 20,000 per year 12 years ago?

1 answer:

tangare [24]3 years ago

4 0

54000/.6= 90000, so answer should be 90,000

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A box of Georgia peaches has 3 bad and 12 good peaches. (a) If you make a peach cobbler of 12 peaches randomly selected from the

Eddi Din [679]

Answer:

a) 0.21% probability that there are no bad peaches in the peach cobbler.

b) 99.79% probability of having at least 1 bad peach in the peach cobbler

c) 7.91% probability of having exactly 2 bad peaches in the peach cobbler.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the peaches are chosen is not important. So the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

(a) If you make a peach cobbler of 12 peaches randomly selected from the box, what is the probability that there are no bad peaches in the peach cobbler?

Desired outcomes:

12 good peaches, from a set of 12. So

$D = C_{12,12} = \frac{12!}{12!(12 - 12)!} = 1$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{1}{455} = 0.0021$

0.21% probability that there are no bad peaches in the peach cobbler.

(b) What is the probability of having at least 1 bad peach in the peach cobbler?

Either there are no bad peaches, or these is at least 1. The sum of the probabilities of these events is 100%. So

p + 0.21 = 100

p = 99.79

99.79% probability of having at least 1 bad peach in the peach cobbler

(c) What is the probability of having exactly 2 bad peaches in the peach cob- bler?

Desired outcomes:

2 bad peaches, from a set of 3.

One good peach, from a set of 12.

$D = C_{3,2}*C_{12,1} = \frac{3!}{2!(3-2)!}*\frac{12!}{1!(12 - 1)!} = 36$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{36}{455} = 0.0791$

7.91% probability of having exactly 2 bad peaches in the peach cobbler.

3 0

3 years ago

4x-4=4x + ___ <br> What is the answer

irakobra [83]

Answer:

-4

Step-by-step explanation:

4x - 4 = 4x + ?

-4

4x - 4 = 4x + (-4) ---> 4x - 4 = 4x - 4

done

7 0

3 years ago

Read 2 more answers

The summer monsoon brings 80% of India's rainfall and is essential for the country's agriculture.

Natasha_Volkova [10]

Answer:

Step 1. Between 688 and 1016mm. Step 2. Less than 688mm.

Step-by-step explanation:

The <em>68-95-99.7 rule </em>roughly states that in a <em>normal distribution</em> 68%, 95% and 99.7% of the values lie within one, two and three standard deviation(s) around the mean. The z-scores <em>represent values from the mean</em> in a <em>standard normal distribution</em>, and they are transformed values from which we can obtain any probability for any normal distribution. This transformation is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ (1)

$\\ \mu\;is\;the\;population\;mean$

$\\ \sigma\;is\;the\;population\;standard\;deviation$

And <em>x</em> is any value which can be transformed to a z-value.

Then, z = 1 and z = -1 represent values for <em>one standard deviation</em> above and below the mean, respectively; values of z = 2 and z =-2, represent values for two standard deviations above and below the mean, respectively and so on.

Because of the 68-95-99.7 rule, we know that approximately 95% of the values for a normal distribution lie between z = -2 and z = 2, that is, two standard deviations below and above the mean as remarked before.

<h3>Step 1: Between what values do the monsoon rains fall in 95% of all years?</h3>

Having all this information above and using equation (1):

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

For z = -2:

$\\ -2 = \frac{x - 852}{82}$

$\\ -2*82 + 852 = x$

$\\ x_{below} = 688mm$

For z = 2:

$\\ 2 = \frac{x - 852}{82}$

$\\ 2*82 = x - 852$

$\\ 2*82 + 852 = x$

$\\ x_{above} = 1016mm$

Thus, the values for the monsoon rains fall between 688mm and 1016mm for approximately 95% of all years.

<h3>Step 2: How small are the monsoon rains in the driest 2.5% of all years?</h3>

The <em>driest of all years</em> means those with small monsoon rains compare to those with high values for precipitations. The smallest values are below the mean and at the left part of the normal distribution.

As you can see, in the previous question we found that about 95% of the values are between 688mm and 1016mm. The rest of the values represent 5% of the total area of the normal distribution. But, since the normal distribution is <em>symmetrical</em>, one half of the 5% (2.5%) of the remaining values are below the mean, and the other half of the 5% (2.5%) of the remaining values are above the mean. Those represent the smallest 2.5% and the greatest 2.5% values for the normally distributed data corresponding to the monsoon rains.

As a consequence, the value <em>x </em>for the smallest 2.5% of the data is precisely the same at z = -2 (a distance of two standard deviations from the mean), since the symmetry of the normal distribution permits that from the remaining 5%, half of them lie below the mean and the other half above the mean (as we explained in the previous paragraph). We already know that this value is <em>x</em> = 688mm and the smallest monsoons rains of all year are <em>less than this value of x = </em><em>688mm</em>, representing the smallest 2.5% of values of the normally distributed data.

The graph below shows these values. The shaded area are 95% of the values, and below 688mm lie the 2.5% of the smallest values.

3 0

3 years ago

An employee at a homemade wooden toy store earned $860 over the past week. The employee needs to pay 14% for Federal Income Tax

Sindrei [870]

Answer:
$713.8

Explanation:
14%of 860 = 120.4

3% of 860 = 25.8

so, subtract the sum of the above 2 values from 860.

860 - (120.4+25.8) = 860-146.2 = 713.8

Hope this helps

4 0

3 years ago

Read 2 more answers

An obtuse angle measures between:

velikii [3]

Anything over 90 and bellow 180 degrees is a obtuse.

5 0

3 years ago

Read 2 more answers