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3 years ago

An academic department with five faculty members narrowed its choice for department head to either candidate a or candidate

1 answer:

7 0

The probability that the first two votes drawn are both for candidate a is given by:
3C2/5C2 = 3/10
Having drawn two votes for candidate a on the first two draws, there are 2 votes for candidate b and one vote for candidate a remaining. The probability that a vote for candidate b will be drawn on the third draw is:
2/3.
After the first three draws, there reains one vote for candidate a and one vote for candidate b. The probability that a vote for candidate a will be drawn on the fourth draw is:
1/2.
The probability of the ordering aabab is therefore given by:
$\frac{3}{10}\times\frac{2}{3}\times\frac{1}{2}=\frac{6}{60}$
The answer is: 0.1.

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Please Help me I'm stuck

Tresset [83]

When reflecting across the Y axis, the Y values remain the same.

Now if you were reflecting across Y = 0, the x values would just be inverse ( opposite signs).

So this triangle if reflected across Y = 0 the new vertices would be (4,4) (2,3) and (5,2)

Now since the reflection line is y = -1, which is a one unit shift to the left of y = 0, subtract 1 unit from each X value.

The locations are now: A'(3,4), B'(1,3) and C'(4,2)

4 0

4 years ago

Is f(x)=3/4 a function?

Marat540 [252]

Answer:

Yes, f(x) = $\frac{3}{4}$ is a constant function.

Step-by-step explanation:

A function is defined to be a relation from 1 set of numbers to another set of numbers.

The main condition for a relation to be a function is that for every number in the domain there should be a unique image

Here the given function is f(x) = $\frac{3}{4}$

This function is a constant function and gives the value 0.75 for all values of x.

Hence the graph would be a straight line parallel to the x-axis passing through y = 0.75.

Hence the f(x) = 0.75 is a function.

4 0

3 years ago

Question 1,2, and 3 how do i factor those? Can you show the work and explain how?

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.

the answer is

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,

which would give you

(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

so the final answer is

$(3x-2)^2$

5 0

2 years ago

A calculator showed the answer to a multiplication problem as 2.8e–4.

jolli1 [7]

2.8 X 10-4. The last one

8 0

3 years ago

How to write (0,8] as an inequality

larisa86 [58]

Answer: $0 \ \textless \ x \le 8$

What is given to you is interval notation. We have the interval start at 0 and end at 8. The value 0 is not included in the interval as indicated by the parenthesis. So we go with a "less than" sign (instead of a "less than or equal to" sign)

The value 8 is included since a square bracket is used here. The use of "or equal to" is needed to make sure the endpoint 8 is included.

So x can be any number between 0 and 8. It can't be 0 but it can be 8.

3 0

3 years ago