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3 years ago

Which is equivalent?

Mathematics

1 answer:

Arlecino [84]3 years ago

6 0

Steps to simplify:

(2x + 3)(x - 7)

~Use FOIL to multiply

(2x * x) + (2 * -7) + (3 * x) + (3 * -7)

~Simplify

=2x² - 14x + 3x - 21

~Combine Like Terms

2x² + (-14x + 3x) - 21

~Simplify

2x² - 11x - 21 (Option 2)

Best of Luck!

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A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr

Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. 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.

Random voting:

So 50% of voting yes, 50% no, so $p = 0.5$

15 members:

This means that $n = 15$

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

$p = P(X = 0) + P(X = 15)$

In which

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

$P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003$

$P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003$

$p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006$

0.006% probability that the final vote count is unanimous.

7 0

3 years ago

Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Sedbober [7]

Answer:

24/25

Step-by-step explanation:

Please see the attached image.

The cosine of an angle is the adjacent side relative to that angle over the hypotenuse.

Answer: 24/25

8 0

2 years ago

If F(x) = 5x-7 and G(x) = -2x+9 , what is F(G(x))?

dybincka [34]

Answer:

Step-by-step explanation:

7 0

3 years ago

The graph of a line passes through the points (0, -2) and (6.0). What is

9966 [12]

Answer:

$y=\frac{1}{3}x-2$

Step-by-step explanation:

The equation of a line is given in the form $y=mx+b$

Where

m is the slope with formula $m=\frac{y_2-y_1}{x_2-x_1}$

and

b is the y-intercept [y axis cutting point of line]

Given the two points (0, -2) and (6,0),

x_1 = 0

y_1 = -2

x_2 = 6

y_2 = 0

Now, we find m using formula:

$m=\frac{0+2}{6-0}=\frac{1}{3}$

Now we have

$y=\frac{1}{3}x+b$

Finding b, we plug in any (x,y) point. Lets put (6,0) and find b:

$y=\frac{1}{3}x+b\\0=\frac{1}{3}(6)+b\\0=2+b\\b=-2$

Thus,

equation of line = $y=\frac{1}{3}x-2$

5 0

3 years ago

Find the distance between the points (0,-9) and(4,-6)

Len [333]

Answer:

d=5

Step-by-step explanation:

1. use the distance formula: d= $\sqrt{(x_{2} - x_{2} )^{2} +(y_{2} -y_{1} )^{2}$

2. plug in the points: d= $\sqrt{(0-4)^{2} +(-9+6)^{2}$

3. solve problem inside parentheses: d= $\sqrt{(-4)^{2} +(-3)^{2}$

4. square -4 and -3: d= $\sqrt{16+9$

5. add:d= $\sqrt{25$

6. find square root: d=5

8 0

3 years ago