Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate. What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.

Answers

Answer 1
Answer: The answer is 0.24

To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur. In this method, the probabilities of each event are multiplied. Here we have two events:

1. The probability that the pianist will be a boy,

2. The probability that the alternate will be a girl.


So, let's calculate these probabilities:

There are in total 5 children:

2 boys + 3 girls = 5 children.

1. The probability that the pianist will be a boy is 2 boys out of 5 children, which is 2/5.

2. The probability that the alternate will be a girl is 3 girls out of 5 children, which is 3/5.


The probability that the pianist will be a boy and the alternate will be a girl is:

2/5 × 3/5 = 6/25

6/25 × 4/4 = 24/100 = 0.24

Answer 2
Answer:

the answer is 30 percent


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Determine whether the following pairs of lines are parallel,perpendicular,or neither. y=2x+1 2x+y=7

Answers


In order to answer this one, you have to remember:

--> Parallel lines have equal slopes.

--> Perpendicular lines have negative reciprocal slopes.

                       (One slope  =  - [ 1/the other slope ]

The question gives us two lines:

#1).  y = 2x + 1
#2).  2x + y = 7

The first equation is in nice slope-intercept form, and we can see
right away that the slope of its graph is  2 .

The second equation is not in slope-intercept form, so we need to
massage it slightly before we can spot the slope of its graph.

                                            2x + y =          7

Subtract  2x  from each side:      y = -2x + 7 .  <== slope-intercept form.
                                                                                Slope = -2 .
Now we know both slopes.

#1).  Slope =  2
#2).  Slope = -2

Are the slopes equal ?  I don't think so.  2  is not equal to  -2 .
The lines are not parallel. 

Are the slopes negative reciprocals ?  I don't think so. 
2 is not equal to  -[ 1/(-2) ].
The lines are not perpendicular.


Find the greatest common factor of 10y^3, 4y^6, and -18y

Answers

For 10 y^(3) ,  4y^(6) , -18y
The common factor;
2y

Graph with a line going through points zero comma two point five and four comma two point five.Select the equation of the line that passes through the point (3, -1) and is parallel to the line on the graph.

a) y = -1

b) y = 3

c) y = x -1

d) y = 3x - 1
*graph is attached for 1st question*


Graph with a line going through points negative 2 comma zero and 0 comma negative one.

Select the equation of a line that is perpendicular to the line on the graph and passes through the point (-1, 2).

y = 2x + 4

y = - 2x + 2

y = - 1 over 2 x + 2

y = 2x - 1

Answers

Answer:

1 - y=-1

2 - y=2x+4

Step-by-step explanation:

The general form of a straight line is y=mx+b, where m = slope and b = y-intercept.

Ques 1: We are given that the line passes through (0,2.5) and (4,2.5).

Then the slope of the line is given by,

m=(2.5-2.5)/(4-0)=0

Then, the y-intercept is given by,

y=0x+b\n\n2.5=b

That is, the equation of the line is y=2.5

Since, 'Two parallel lines have equal slope'.

Then, the line parallel to y=2.5 have slope 0 i.e. y=b.

As, the line passes through the point (3,-1) i.e. y= -1 for any value of x.

Then, the equation of line is y=-1

So, option A is correct.

Ques 2: We are given that the line passes through (-2,0) and (0,-1).

Then the slope of the line is given by,

m=(-1-0)/(0+2)=(-1)/(2)

Then, the y-intercept is given by,

-1=(-1)/(2)* 0+b\n\nb=-1

That is, the equation of the line is y=(-1)/(2)x-1

Since, 'The product of slopes of two perpendicular lines is -1'.

Then, we have,

m* (-1)/(2)=-1\n\nm=2

The line perpendicular to y=(-1)/(2)x-1 have slope 2.

As, the line passes through the point (-1,2) with slope 2.

The y-intercept is given by,

2=2* -1+b\n\n2=-2+b\n\nb=4

Thus, the equation of the line is y=2x+4

So, option A is correct.

y= - 1

The graph of the first line is 0. The graph of the second line will also be equal to 0. Replacing in the general equation of a line y=mx+c;
y=(0)x+c
y=c
Using the point (3,-1)
-1=c
y=-1

Work the following pricing problems for services rendered. (For all calculations use hundredths.)Labor time = 4 1/2 hours
Overhead rate = 95%
Retail price of parts = $134.75
Total cost of job = $241.98
Hourly rate?

Answers

Answer:

Hourly Rate = $12.22 per hour

Step-by-step explanation:

\text{Labor Time = }4\tfrac{1}{2}=4.5\thinspace{ hours}

Overhead Rate = 95%

Retail price of parts = $134.75

Total cost of job = $241.98

Cost of labor = Total cost - Retail price

                      = 241.98 - 134.75

                      = $107.23

Now, labor works for 4.5 hours and ears a total amount of $107.23

\implies\text{Amount earned in one hour or hourly rate = }(107.23)/(4.5)\n\n\implies \text{Hourly rate = }\$23.83\text{ per hour}

Now, Labor will get 95% overhead rate

⇒ The labor is getting 100% already but an overhead of 95% is also given

\text{So, Hourly Rate = }(23.83)/(1+0.95)\n\n\bf\implies\textbf{Hourly Rate = }\$12.22\textbf{ per hour}

Answer:

12.22

Step-by-step explanation:

Solve for x₁ and x₂
6x₁+3x₂=60
6x₁-2x₂=80

Answers

\left \{ {\big{6x_1+3x_2=60\ \ \ \ \ \ \ \ \ \ \ } \atop \big{6x_1-2x_2=80\ /\cdot(-1)}} \right. \n\n \left \{ {\big{6x_1+3x_2=60\ \ \ \ } \atop \big{-6x_1+2x_2=-80}} \right. \n-----------\n3x_2+2x_2=60-80\n5x_2=-20\ /:5\n\nx_2=-4\n\n6x_1+3x_2=60\ /:3\n2x_1+x_2=20\ \ \ \Rightarrow\ \ \ 2x_1+(-4)=20\ \ \ \Rightarrow\ \ \ 2x_1=24\ /:2\n\nx_1=12\n\n \left \{ {\big{x+1=12} \atop\big {x_2=-4}} \right.
first let's change the "x1" to "A" Nd the "x2" to "B" __ so now the problem reads "6A + 3B = 60" And "6A - 2B= 80" we want to isolate variable. and the easiest one is the "B" by getting rid of the "A". set up a subtraction problem where you take one equation away from the other. 6a-6a=0. 3b - (-2b) = 5b and 60-80=-20. so your new equation reads 5B= -20. you wanna get B on one side so yu divide 5 on both sides giving you b= -4 or "x2"=-4. from there you can plug -4 into any one of the original equations. ex: 6A -2(-4)=80 then 6A + 8=80 then you subtract 8 from both sides because you're trying to isolate the "A" variable. which leaves you with 6A = 72. and now you wanna get"A" on one side so yu divide 6 from both sides and get A=12 or "x1"=12. do a quick check and plug in these numbers into any one of the equation.

The table shows the height of the tree that Margo planted over an 11-month period. A 2-column table with 6 rows titled Growth of Margo's Tree. The first column is labeled Month with entries 1, 3, 5, 7, 9, 11. The second column is labeled Height of Tree (feet) with entries 1.4, 1.5, 2.1, 2.7, 3.0, 1.8. Which statement can be supported by the information in the table?

Answers

The statement that can be supported by the information in the table is that the tree increased in height each month until the time period between month 9 and month 11.

What is s table?

It should be noted that a table simply means a list of numbers to that depicts a particular information.

In this case, the statement that can be supported by the information in the table is that the tree increased in height each month until the time period between month 9 and month 11.

Learn more about table on:

brainly.com/question/25630111

#SPJ2

Answer:

3. The tree increased in height each month until the time period between month 9 and month 11.