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Softa [21]
3 years ago
8

The American Community Survey is completed by the US Census Bureau to obtain information about households in the US. One variabl

e of interest is how many people reside in each household (vacant households were recorded as having zero people). Based on data from 2014, here is the partially completed probability distribution of H, the number of people residing in a randomly selected US household:
H 0 1 2 3 4 5+
P(H) ? 0.24 0.30 0.14 0.11 0.09
Find the missing probability in the table
Mathematics
1 answer:
Marina CMI [18]3 years ago
3 0

Answer:

The missing probability is 0.12        

Step-by-step explanation:

We are given the following in the question:

  H:  0      1         2         3       4       5

P(H): x   0.24   0.30   0.14   0.11   0.09

Let x be the missing probability.

Property of discrete probability distribution:

\displaystyle\sum P(x_i) = 1\\\Rightarrow  x+ 0.24+ 0.30+ 0.14 +0.11 +0.09 = 1\\\Rightarrow x + 0.88 = 1\\\Rightarrow x  = 1 - 0.88\\\Rightarrow x = 0.12

Thus, the missing probability is 0.12

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DiKsa [7]

1: 3n^{2}+9n+6

notice that each part is divisible by 3

3n^{2} ÷ 3 = n^{2}

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes 3(n^{2} +3n+2)

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

3(n^{2} +2n+n+2)

Now that it's rewritten, you can factor out n + 2 from the equation.

<u><em>the answer is </em></u>

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is n^{2} +2n+n+2 and then each of those by 3, which is 3n^{2} +6n+3n+6 or 3n^{2}+9n+6, our origional equation

2: 28+x^{2} -11x

So I rewrote this as x^{2} -11x+28 (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

x^{2} -4x-7x+28

now we can factor out x from the first expression and -7 from the second

x(x-4)-7(x-4)

and lastly you factor out x-4,

<u><em>which would give you</em></u>

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to x^{2} -11x+28

3: 9x^{2} -12x+4

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as 3^{2} and 4 as 2^{2}, the equation becomes

3^{2} x^{2} -12x+2^{2}

now that 3^{2} x^{2} is ugly so it can be turned into (3x)^{2}

and -12x can be rewritten as -2*3x*2

so our equation now looks like (3x)^2-2*3x*2+2^{2}

There's a rule that says a^{2} -2ab+b^{2} = (a-b)^{2}

In our case, a=3x and b=2

<u><em>so the final answer is</em></u>

(3x-2)^2

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Solve the following inequality.
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Solving the inequality given algebraically, the solution of the inequality for the value of m is:

<u>m < -4 OR m > 3</u>

<em><u>Given the following </u></em><em><u>inequality</u></em><em><u>,</u></em>

<em><u /></em>\frac{m - 2}{3} < -2 \\

or

4m + 3 > 15

Let's solve algebraically for the value of m in both inequality statements given.

\frac{m - 2}{3} < -2 \\

  • Multiply both sides by 3

\frac{m - 2}{3} \times 3 < -2 \times 3\\\\m - 2 < -6

  • Add 2 to both sides

m - 2 + 2 < -6 + 2\\\\m < -4

Or

4m + 3 > 15

  • Subtract 3 from each side

4m + 3 - 3 > 15 - 3

4m > 12

  • Divide both sides by 4

\frac{4m}{4}  > \frac{12}{4} \\\\

m > 3

Therefore, solving the inequality given algebraically, the solution of the inequality for the value of m is:

<u>m < -4 OR m > 3</u>

<u></u>

<u></u>

Learn more here:

brainly.com/question/24434501

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A town uses positive numbers to track increases in population and negative numbers to track decreases in population. The populat
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