. There are 11 boys and 5 girls that tried out to
sing a duet in a chorus concert. If the
director must choose two, what is the
probability that both students chosen are
boys?

Answers

Answer 1

We want to find the probability that the two students chosen for the duet are boys. We will find that the probability that both students chosen for the duet are boys is 0.458

If we assume that the selection is totally random, then all the students have the same probability of being chosen.

This means that, for the first place in the duet, the probability of randomly selecting a boy is equal to the quotient between the number of boys and the total number of students, this is:

P = 11/16

For the second member of the duet we compute the probability in the same way, but this time there is one student less and one boy less (because one was already selected).

Q = 10/15

The joint probability (so both of these events happen together) is just the product of the individual probabilities, this will give:

Probability = P*Q = (11/16)*(10/15) = 0.458

So the probability that both students chosen for the duet are boys is 0.458

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Related Questions

6/7 divided by 12/14 please show the work

Answers

Answer:

1

Step-by-step explanation:

When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.

Hope this helps!

hope this help u and good luck


You buy 3.9 pounds of trail mix. The mix
costs $2.78 per pound. What is the total
price for the trail mix?

Answers

Answer:

Answer:

28+66+86=180

180=180

Step-by-step explanation:

Since there is a triangle and the 3 measures from the angles we can find the value of x using the hint given that the sum of the interior angles must be 180°

Write the equation

\begin{gathered}x+(2x+10)+(3x+2)=180\\\end{gathered}

x+(2x+10)+(3x+2)=180

Simplify left side of the equation

\begin{gathered}6x+12=180\\\end{gathered}

6x+12=180

Solve equation for x

\begin{gathered}6x=180-12\\6x=168\\x=28\end{gathered}

6x=180−12

6x=168

x=28

Replace x into the 3 angles and find their respectives values

\begin{gathered}A=x\\A=28\\\\B=2x+10\\B=2*28+10\\B=56+10\\B=66\\\\C=3x+2\\C=84+2\\C=86\end{gathered}

A=x

A=28

B=2x+10

B=2∗28+10

B=56+10

B=66

C=3x+2

C=84+2

C=86

Check if the answers are correct

\begin{gathered}28+66+86=180\\180=180\end{gathered}

28+66+86=180

180=180

PLEASE MARK ME AS BRAINLIEST

what percent of 75cm is 5cm​

Answers

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

Which of the following have a sum of 0? (Pick 2) *

1:The football team gained 10 yards on the first play, gained 10 yards on the second play, and lost 10 yards on the third play. What was the overall change in yardage?
2: While playing the integer game, Sam pulled the following cards: 8, 4, 5, -6, -8, -3. What is the sum of Sam's hand?
3: -15 - 8 + 12 + 11
4: 6 + (-5) - 7 + (-4) + (-4)

Answers

Answer:

The answer is number 3.

Step-by-step explanation:

-15 - 8 = -23

12 + 11 = 23

When you subtract -23 from 23 you have a sum of 0

Therefore the answer is 0

someoneplease help me
GIVING BRAINLIST TO FIRST RIGHT ANSWER
A. (4,-2)
B. (0,1)
C. (1,0)
D. (-1,0)

Answers

Answer:

C (1,0)

Step-by-step explanation:

Answer:

C. (1,0)

Step-by-step explanation:

When you go 3 to the left, you end up at (0, -2). When you go up 2, you get (1,0).

Mary had 60$ and spent 3/4 on a coat. plus she brought a skirt with 1/2 she had left . how much do she have left?

Answers

3/4 of $60 = $45 for the coat
60 - 45 = $15 left
1/2 of $15 = $7.50 for the skirt
15 - 7.50 = $7.50 left

A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swimming?

Answers

If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.

Given the following data:

Width of rectangle = 6 metersLength of rectangle = 8 meters

To determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.

Note: The diagonal side of the rectangular pool represents the hypotenuse.

Mathematically, Pythagorean's theorem is given by the formula:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

Substituting the given parameters into the formula, we have;

[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]

Hypotenuse = 10 meters.

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what's a real number?

Answers

Answer:

Real Numbers are numerical values that can represent distance on a line. An example of it being one is 15 and an example of it NOT being one is ∞.

Answer all of them plzz​

Answers

Answer:

a) (2x+3) (x+4)

b) (5x-3) (x-1)

c) (-2x-3) (x-3)

d) 3(x-1) (3x-8)

e) -2(3x+5) (x-2)

f)  h(4x-3) (3x-4)

g) -(x-3) (x+7)

h) (3x-2) (x+3)

i)  2(2x+1) (x-2)

j) (3h+2) (h-7)

Step-by-step explanation:

your welcome :)

Answer:

a)

(x+4)(2x+3)

b)

(x-2)(5x-3)

c)

(-x+3)(2x-3)

d)

3(x-1)(3x-8)

e)

2(-x+2)(3x+5)

f)

h(3x-4)(4x-3)

g)

(x+7)(-x+3)

h)

(x+3)(3x-2)

i)

2(x-2)(2x+1)

j)

(h-7)(3h+2)

Hope this helps!

solve each system of linear equations 3x+y=9, 7x+y=32 ​

Answers

Answer:

x=23/4, y=-33/4

Step-by-step explanation:

3x+y=9

7x+y=32

3x+y=9

y=9-3x

7x+y=32

7x+(9-3x)=32

7x+9-3x=32

4x+9=32

4x=23

x=23/4

3x+y=9

3(23/4)+y=9

69/4+y=9

y=-33/4

The solution set to the given system of linear equations is -

{x} = 5.75 and {y} = - 8.25.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a system of linear equations as -

3x + y = 9

7x + y = 32 ​

We can write -

3x + y = 9

y = 9 - 3x

Now, we can write the equation as -

7x + y = 32

7x + 9 - 3x = 32

4x + 9 = 32

4x = 23

x = 5.75                         .... (1)

The, we can write {x} as -

y = 9 - 3 x 5.75

y = 9 - 17.25

y = - 8.25                         ... (2)

Therefore, the solution set to the given system of linear equations is -

{x} = 5.75 and {y} = - 8.25.

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One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?

Answers

Answer:

Step-by-step explanation:

J

B = 3J

T = J + 5

J + 3J + J + 5 = 60

5J = 55

J = $11

B = $33

T = $16

The amount earned by Jim, Bill and Tom is equal to [tex]\boldsymbol{\$ 11},\boldsymbol{\$ 33},\boldsymbol{\$ 16}[/tex].

"Important information"

Let .

The amount earned by Jim be [tex]\boldsymbol{x}[/tex].

Amount earned by Bill [tex]=\boldsymbol{3x}[/tex]

Amount earned by Tom [tex]=\boldsymbol{x+5}[/tex]

Total amount earned by all [tex]=\boldsymbol{\$ 60}[/tex][tex]x+3x+x+5=60\\5x=55\\x=11[/tex]

So,

Amount earned by Jim [tex]=\boldsymbol{\$ 11}[/tex]

Amount earned by Bill [tex]=3(11)[/tex] [tex]=\boldsymbol{\$ 33}[/tex]

Amount earned by Tom [tex]=11+5[/tex] [tex]=\boldsymbol{\$ 16}[/tex]

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Solve x2 + 5x – 3 = 0 using the quadratic formula.
Solve (2x – 1)2 = 8 using the quadratic formula.

A) x = –1∕2 + , x = –1∕2 –
B) x = 1∕2 + , x = 1∕2 –
C) x = 1∕2
D) x = –1∕2

Answers

Answer:

d

Step-by-step explanation:

distribute two through the parentheses

=4x-2

move the constant to the right side and change its sign

=4x=8+2

=4x=10

divide both sides by 4

x=5/2

ASAP ASAP!! HELP!! A supermarket needs to display 64 boxes of detergent.
The boxes need to be stacked with the same number of boxes in each row.
There should be at least 3 rows with at least 4 boxes in each row.
Choose the correct answers from the drop-down boxes to complete all the ways the boxes of detergent can be stacked.


Choose...
rows with 16 boxes in each row;

8 rows with
Choose...
boxes in each row;

16 rows with
Choose...
boxes in each row.

Answers

Answer:

Its the first one

Step-by-step explanation:

4x4=16 8x2=16 so its the first

These three lines should say:

4 rows with 16 boxes in each row

8 rows with 8 boxes in each row

16 rows with 4 boxes in each row

16. Use the vertical line test to determine whether the relation is a function.

Answers

Answer:

neither of them are

Step-by-step explanation:

1. How can you tell by looking at each graph that a proportional relationship exists between the quantities? 2. Find the constant of proportionality for each graph. Write your answer as y = kx.

Answers

Answer:1. How can you tell by looking at each graph that a proportional relationship exists between the quantities?

relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

2. Find the constant of proportionality for each graph. Write your answer as y = kx.

y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.

Step-by-step explanation:

log, a Consider the graph of the function f 2- X O -2 2 4 6 8 10 -2 - What are the features of function gif g(t) = -|(r) - 1; oyintercept at (0,-1) X-intercept at (1,0) range of (-1,00) domain of (0, 0) vertical asymptote of g = 0​

Answers

Answer:

X-intercept at (1/2 ,0)

domain of (0, infinity)

Vertical asymptote of x = 0

Step-by-step explanation:

Plato I got it right on the test

Evaluate the difference quotient for the given function.

f(t) = g(t) h(t) , where g(t) = cos(t) and h(t) =sin(t)

Answers

Assuming you mean f(t) = g(t) × h(t), notice that

f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

[tex]\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}[/tex]

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

[tex]\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}[/tex]

or

[tex]\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}[/tex]

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)

please someone help me this is the third time i have had to post this question bc of bots

Answers

Answer: It,ll increase

Step-by-step explanation:

Answer:

Add all of the numbers together then multipy them by 25

Step-by-step explanation:

35X25=875

HELp PLeaSE ‼️‼️URGENT

Find the equation of the line of best fit for the points (-4, 10).(-1, 5), (2, -1) (3, (5, --- 7). O
A. y = -2x + 2
B. y = 2x - 2
C. y = 2x - 0.98
D. y = -2x - 0.98

THANKS ^_^ ! ! !

Answers

I think it's B ( I might be wrong)

Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon
About

how many gallons will her car use on the trip?

O 12
O 70
067
034

Answers

The number of gallons of fuel required for 200 miles will be 6.7 gallons. The correct option is C.

What is an expression?

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that Becky is planning a two 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon.

The total miles covered in two trips will be,

100 + 100 = 200 miles

The amount of fuel will be calculated as:-

Fuel = 200 /  30

Fuel = 6.7 gallons

Therefore, the fuel quantity will be 6.7 gallons.

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HELP ME OUT PLEASE!!!

Determine which graph shows y as a function of x.​

Answers

bottom right graph. it’s the only one that passes the vertical line test, making it the only function

8. There are 18 trumpets in a music room. These trumpets will be placed in 3 equal rows. Which number sentence can be used to find the number of trumpets in each row?​

Answers

Answer:

18÷3=6

Step-by-step explanation:

18 trumpets have to be DIVIDED into 3 rows so you would divide 18 by three to get 6 trumpets in each row.

Two mechanics worked on a car. The first mechanic charged $75 per hour, and the second mechanic charged $45 per hour. The mechanics worked for a
combined total of 25 hours, and together they charged a total of $1425. How long did each mechanic work?

Answers

Answer:

First mechanic 10 hours, Second is 15 hours

Step-by-step explanation:

x + y = 25, so y = 25 - x

75x + 45y = 1425

Substitute in the first equation

75x + 45(25 - x) = 1425

75x + 1125 - 45x = 1425

30x = 300

x = 10

Therefore, y = 15

Answer:

they both worked

8 hours

how do you convert a whole number to a fraction?

Answers

Answer:

Step-by-step explanation:

Example 1: Changing the whole number 5 into a fraction.

Take the whole number (5), add a line below it (/), then add a 1 to the denominator.

5 = 5/1

Example 2: Changing the whole number 5 into a fraction.

Take the whole number (5), multiply it by 2 add a line below it (/), then add a 2 to the denominator.

5 = (5*2)/2 = 10/2

***This can be reduced to 5/1***

Example 3: Changing the whole number 5 into a fraction.

Take the whole number (5), multiply it by 3 add a line below it (/), then add a 3 to the denominator.

5 = (5*3)/3 = 15/3

***This can also be reduced to 5/1***

If you follow the pattern, you will realize all whole numbers are fractions already.

They are fractions with a denominator of 1. This fraction can be manipulated with all of the same standard rules you would traditionally use with fractions, even when the denominator isn’t shown.

A fraction is simply a way to describe portions of a whole. The denominator simply tells you how many pieces to break the whole into. When the denominator is 1, you are breaking the whole into one piece (or not breaking it apart at all.

I hope this helps.

A small boat leaves a port town and travels due north for 7.4 miles and then turns due east for 3.6 miles
and stops. If the boat's captain then turns back to town. a) how far does the boat travel and b) along
what bearing would the boat have to travel from its stopped position?

Answers

11 miles far does the boat travel

Step-by-step explanation:

hope it helps

The total distance travelled will be 22 miles and the bearing will be 60.89° .

It is given that a boat travels from port town to north for 7.4 miles and then east for 3.6 miles and stops at destination.

We have to find out the total distance travelled and bearing from stopped position.

What are bearings ?

A bearing is the angle in degrees measured clockwise from north i.e., 30° from north.

As per the question ;

Boat travels from port town to north for 7.4 miles and then east for 3.6 miles and it then stops at destination.

So ;

a)

Total distance travelled from port town to destination is ;

= 7.4 miles + 3.6 miles

= 11 miles

And

If boat's captain turns back to town , then total distance will be ;

= 11 + 11

= 22 miles

b)

We know that ;

cos θ = B/H

The bearing would be ;

cos θ = [tex]\frac{3.6}{7.4}[/tex]

cos θ = 0.486

θ = [tex]cos^{-1}[/tex] (0.486)

θ = 60.89°

Thus , the total distance travelled will be 22 miles and the bearing will be 60.89° .

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Jamal wrote that 9 – 8.4 = 6.

Answers

9−8.4=6

0.6≠6

False

I don't know...

Answer:

0.6 his answer is false.

Step-by-step explanation:

...

40 in^2 to cm^2

Have to find the cm

Answers

Answer:

101.6cm²

Step-by-step explanation:

1 inch = 2.54cm

that means:

40in² × 2.54 = 101.6cm²

What is -6(-3+5r)=-5-7r

Answers

Answer:

r = 1

Step-by-step explanation:

Use the distributive property to multiply −6 by −3+5r.

18−30r=−5−7r

Add 7r to both sides.

18−30r+7r=−5

Add −30r and 7r to get −23r.

18−23r=−5

Subtract 18 from both sides.

−23r=−5−18

Subtract 18 from −5 to get −23.

−23r=−23

Divide both sides by −23.

r=−23/−23​

Divide −23 by −23 to get 1.

r=1

Enter the number that belongs in the green box

Answers

Answer:

9 because there the same length

Answer:

the measure of the seg CD is 9

Step-by-step explanation:

It is 9 because the shape is a parallelogram. One of the properties of a parall is that opposite sides are congruent which makes side BA equals side CD

write me 2 equivalent fractions of 3/4=_=_

Answers

Answer:

6/8 and 12/16

Step-by-step explanation:

Important: 3/4 looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3/4. To find an equivalent fraction to 3/4 , or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By multiplying the original fraction by 2, we get:

3x2/3x2=6/8

List of Equivalent Fractions of 3/4:

3/4, 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36, 30/40, 33/44, 36/48, 39/52, 42/56, 45/60, 48/64, 51/68, 54/72, 57/76, 60/80 ...

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