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3 years ago

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Find

x%20-%206%29" id="TexFormula1" title="( {4x}^{2} + 3x) + ( {7x}^{2} - 5x - 6)" alt="( {4x}^{2} + 3x) + ( {7x}^{2} - 5x - 6)" align="absmiddle" class="latex-formula">

1 answer:

marishachu [46]3 years ago

4 0

Answer:

$11x^2-2x-6$

Step-by-step explanation:

$(4x^2+3x)+(7x^2-5x-6)= \\\\(4x^2+7x^2)+(3x-5x)-6= \\\\11x^2-2x-6$

Hope this helps!

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Add (-3x^3+2x^2-4x+5)(x^3-x^2+1

a_sh-v [17]

Hope this helps
have a good day

5 0

3 years ago

Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adul

ddd [48]

Answer:

a) 0.194 = 19.4% probability that more than 7 preferred McDonald's

b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

50% of all young adults prefer McDonald's to Burger King when asked to state a preference.

This means that $p = 0.5$

12 young adults were randomly selected

This means that $n = 12$

(a) What is the probability that more than 7 preferred McDonald's?

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.121$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.054$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.016$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.003$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.000$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.121 + 0.054 + 0.016 + 0.003 + 0.000 = 0.194$

0.194 = 19.4% probability that more than 7 preferred McDonald's

(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.054$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.121$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.193$

$P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.226$

$P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.193$

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.054 + 0.121 + 0.193 + 0.226 + 0.193 = 0.787$

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?

Since $p = 1-p = 0.5$ , this is the same as b) above.

So

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

7 0

3 years ago

your brother 1/4 yor age.your sister is 8 years older than your brother.your sister is 12 years old.write and solve tan equation

nekit [7.7K]

Let <em>A</em> be your age, <em>B</em> be the age of your brother and <em>S</em> be the age of your sister.

Since your brother is 1/4 your age, then:

$B=\frac{1}{4}A$

Since your sister is 8 years older than your brother, then:

$S=B+8$

Since your sister is 12 years old, then:

$S=12$

Use the second equation to find your brother's age by plugging in <em>S=12</em>:

$\begin{gathered} S=B+8 \\ \Rightarrow12=B+8 \\ \Rightarrow B=12-8 \\ \therefore B=4 \end{gathered}$

Plug in <em>B=4</em> in the first equation to find your age:

$\begin{gathered} \frac{1}{4}A=B \\ \Rightarrow\frac{1}{4}A=4 \\ \Rightarrow A=4\times4\rbrack \\ \therefore A=16 \end{gathered}$

Therefore, you are 16 years old.

4 0

1 year ago

Please help me. I don't know how to find the slope of this graph.

choli [55]

Answer:

3/4

Step-by-step explanation:

We know this is a positive sloe because the line goes up from left to right.

We can pick to points (0,1) and (4,4)

We can find the slope from

m = (y2-y1)/(x2-x1)

= (4-1)/(4-0)

=3/4

6 0

4 years ago

Solve the system by elimination.<br> -8X – 10y = 20<br> -8x – 6y = -4

In-s [12.5K]

Answer:

(5, - 6 )

Step-by-step explanation:

Given the 2 equations

- 8x - 10y = 20 → (1)

- 8x - 6y = - 4 → (2)

Multiply (2) by - 1

8x + 6y = 4 → (3)

Add (1) and (3) term by term to eliminate the x- term, that is

- 4y = 24 ( divide both sides by - 4 )

y = - 6

Substitute y = - 6 into either of the 2 equations and solve for x

Substituting into (1)

- 8x - 10(- 6) = 20

- 8x + 60 = 20 ( subtract 60 from both sides )

- 8x = - 40 ( divide both sides by - 8 )

x = 5

solution is (5, - 6 )

6 0

3 years ago