There are 10 boys and 13 girls in Mr. Benson's fourth-grade class and 12
boys and 11 girls in Mr. Johnson fourth-grade class. A picnic committee
of six people is selected at random from the total group of students in both
clasties.
(a) What is the probability that all the committee members are girls?
(b) What is the probability that the committee has three girls and three
boys?

Answers

Answer 1
The number of ways 6 girls can be chosen from 24 girls is C(24, 6)
= 24! / (18! x 6!) = 134596
The number of ways 6 students can be chosen from 46 students is C(46, 6)
= 46! / (40! x 6!) = 9366819

a) P(6 girls are chosen) = 134596 / 9366819 = 0.01437 (4sf)

The number of ways 3 boys and 3 girls can be chosen is C(22, 3) x C(24, 3)
= [22! / (19! x 3!)] x [24! / (21! x 3!)] = 3116960

b) P(3 boys and 3 girls are chosen) = 3116960 / 9366819 = 0.3328 (4 sf)

Related Questions

Five times the sum of twice a number and 12 is -55. Find the number

Answers

5(2x+3) = 15
10x + 15 = 15
10x= 0

4 x^2+ 4x-14 x=0
Solve this please, you will get brainLiest. Thank you :)

Answers

Answer:

x could be 0 or it could be 5/2

Step-by-step explanation:

Answer:

x= 5/2

Step-by-step explanation:

4x^2 + 4x - 14x = 0

subtract 4x from 14x because they are like terms

4x^2 - 10x=0

4x^2 = 0 + 10x

4x^2 = 10x

x^2/x = 10/4

x=10/4

x=5/2

Will mark brainlest!
formula of (x+1)cube

Answers

Answer:

(x+1)^3=x^3+3x^2+3x+1

Answer:

[tex](x+1)^{3} = x^{3} + 3x^{2} +3x+1[/tex]

Step-by-step explanation:

[tex](x+1)^{3} = x^{3} + 3x^{2} +3x+1[/tex]

[tex](A+B)^{3} = A^{3} + 3A^{2}B+3AB^{2} + B^{3}[/tex]

What is the range of this function?

Answers

Answer:

[0, ∞)

0≤y<∞

Step-by-step explanation:

The range is the possible values that y can take

y  goes from 0 to positive infinity

[0, ∞)

0≤y<∞

Answer:

[tex]y\geq 0\\[/tex]

y ∈ [0, ∞)

Step-by-step explanation:

The range of a function is the set of all possible output values. In this case, one can see that the graph never goes below the value (0), therefore the range is y will always be greater than or equal to (0).

can someone please help me solve?

Answers

Answer:

0.75

Step-by-step explanation:

d = FE = 4

e = DF = 3

f = ED = 5

f/sin(F) = e/sin(E)

5/sin(90) = 3/sin(E)

5 = 3/sin(E)

sin(E) = 3/5 =0.6

E = asin(0.6) = 36.869898... degrees

tan(E) = tan(36.869898...) = 0.75

Answer for brainlest plssss

Answers

The answer is in the photo

Answer:

[tex] \displaystyle d) 36 \: {in}^{2} [/tex]

Step-by-step explanation:

the polygon can be separated in two parts

rectangletriangle

let's figure out the area of the rectangle

recall that,

[tex] \displaystyle A_{ \rm rect} =l \times w[/tex]

given that,

l=9w=3

thus substitute:

[tex] \displaystyle A_{ \rm rect} =9\times 3[/tex]

simplify multiplication:

[tex] \displaystyle A_{ \rm rect} =27[/tex]

let's figure out the area of the triangle

remember that,

[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times b\times h[/tex]

substitute the value of b and h:

[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times 9\times 2[/tex]

reduce fraction:

[tex] \displaystyle A_{ \rm triangle} = 9[/tex]

now the area of the polygon would be the total area of the rectangle and triangle thus

[tex] \displaystyle A_{ \rm polygon} = 27 + 9[/tex]

simplify addition:

[tex] \displaystyle A_{ \rm polygon} = 36[/tex]

hence our answer is D)

which function represents the inverse of the function f(x)=4x

Answers

Answer:

the answer is number 4 h(x) = 1/4 x

Answer:

the  answer is 4 h(x) = 1/4 x.

Step-by-step explanation:

Multiply 12x2y4z(-4x3y6z2)

Answers

Answer:

[tex]-48x^5 y^{10} z^3[/tex] should be the answer

Step-by-step explanation:

URGENT!!!

Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio

Cleopatra : Dalila : Ebony =
5 : 7 : 8

A) How many dollars do they have in total?

B) Dalila spends 12$ on a hat, how many dollars does she have left?

Answers

A)they have 20 dollar's in total

b)she is left with -12 dollar's

Explanation

total money = 5 + 7 + 8

                    = 20

Money Dalila had = 7 dollars

Money she spent = 12 dollars

money she is left with = 7 - 12 dollars

                                     = -5 dollars

Write the missing power of 10 in each equation.

0.80 × [ ] = 8
[ ] × 0.002 = 20
0.04 × [ ]= 4
[ ]× 0.5 = 500

Answers

1. 10 or 10 to the first power
2. 10000 or 10 to the fourth power
3. 100 or 10 to the second power
4. 1000 or 10 to the third power

help me please geometry!!

Find the missing side length.

Answers

Set up a ratio:

16/12 = 28/?

Cross multiply:

16? = 12 x 28

16? = 336

Divide both sides by 16:

? = 336/16

? = 21

23 points help plzzz

Which number is an integer?

O -3/4
O 1/5
O 2
O 4 2/3

Answers

The answer is 2 ez.

Answer:

2

Step-by-step explanation:

hope i helped :))

Which of the following represents the factorization of the polynomial below? 2x^2+5x+3

Answers

Answer:

(2x + 3)(x + 1)

Step-by-step explanation:

you didn't show them, the factors are

(2x + 3)(x + 1)

Answer:

[tex](x+1)(2x+3)[/tex]

Step-by-step explanation:

[tex]2x^{2} +5x+3[/tex]

[tex]2x^{2} +3x+2x+3[/tex]

[tex]x(2x+3)+2x+3[/tex]

[tex](x+1)(2x+3)[/tex]

explain why triangles in the figure are similar. then find the missing length x

Answers

Answer:

∨∨∨∨see below∨∨∨∨∨∨

Step-by-step explanation:   6  26  18  13

The two outside angles are congruent.  The two inside angles are supplemental thus they are equal.  The last two angles the high one and the lower one must sum to 180° in their respective triangles so they are equal since their similar angles are equal.

find x

4 is to x as 5 is to 7.5

   4/x = 5/7.5      solve for x

   4 × 7.5 / 5  = x

    30 / 5  =  x

       6 = x

If Volume of a Prism=36 m3

, then what is the volume of a pyramid?​

Answers

Answer!12 m³Solution!

V(volume of pyramid) = ⅓ x V(volume of prism)

V(pyramid) = 1 x 36 m³/3V(pyramid) = 12 m³

___________________________

And, to get the volume of prism, simply multiply the volume of pyramid by 3.

if volume of pyramid=12m³, then volume of prism is 36 .

Solution;:

V(volime of prism) = V(volume of pyramid) x 3

V(prism) = 12m³ x 3V(prism) = 36 m³

___________________________

Hence, there are 3 pyramids, and each pyramid has a volume of 12m³, these can exactly fit inside a prism with a volume of 36m³.

Find the area of the kite with diagonals a= 12 and b=9

A) 30
B) 72
C) 54
D) 108

Answers

maybe 108 is the answer.

Mark Brainliest please

Answer :

A=pq/2=12*9/2=54

Aysha has 40 cubes in a bag.
18 red cubes.
13 blue cubes.
9 yellow cubes.
Aysha adds some more red cubes into the bag.
Aysha is now going to take at random a cube from the bag
The probability now that she will take a red cube is 0.5.
Work out the probability that she will take a yellow cube.

Answers

Given:

Total number of cubes = 40

Red cubes = 18

Blue cubes = 13

Yellow cubes = 9

Aysha adds some more red cubes into the bag.

The probability now that she will take a red cube is 0.5.

To find:

The probability that she will take a yellow cube.

Solution:

Let Aysha adds x red cubes into the bag. Then,

Number of total cubes = 40+x

Number of red cubes = 18+x

Probability of getting a red cube is:

[tex]P(Red)=\dfrac{18+x}{40+x}[/tex]

The probability now that she will take a red cube is 0.5. So,

[tex]\dfrac{18+x}{40+x}=0.5[/tex]

[tex]18+x=0.5(40+x)[/tex]

[tex]18+x=20+0.5x[/tex]

[tex]x-0.5x=20-18[/tex]

[tex]0.5x=2[/tex]

Divide both sides by 0.5.

[tex]x=\dfrac{2}{0.5}[/tex]

[tex]x=4[/tex]

It means Aysha adds 4 more red cubes into the bag.

Now, the total number of cubes int he bag is:

[tex]40+4=44[/tex]

Probability of getting a yellow cube is:

[tex]P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}[/tex]

[tex]P(Yellow)=\dfrac{9}{44}[/tex]

Therefore, the required probability is [tex]P(Yellow)=\dfrac{9}{44}[/tex].

if △ABC = △DEF, which side is congruent to EF?
A. AB
B. BC
C. AC

Answers

Answer:

BC

Step-by-step explanation:

BECAUSE BC IT'S EQUAL TO EF

Answer:

B. BC

Step-by-step explanation:

By SSS rule in ∆ ABC and DEF,

AB = DEBC = EFCA = FD

What is the surface area of the rectangular prism below? 8 19 8​

Answers

The answer is c because S=Ph+2b

Answer:

736 units squared (c)

Step-by-step explanation:

Took the quiz

FACTOR b2 – 18b + 81

Answers

Answer:

(b-9)^2

Step-by-step explanation:

b^2-18b+81

=b^2-(9+9)b+81

=b^2-9b-9b+81

=b(b-9)-9(b-9)

=(b-9)(b-9)

=(b-9)^2

Hope this helps u!!


Soda is sold in aluminum cans that measure 7 inches in height and 2.8 inches in diameter.
How many cubic inches of soda are contained in a full can?

Answers

Answer:

Volume of soda in soda can = 43.1 inches³ (Approx.)

Step-by-step explanation:

Given:

Height of soda can = 7 inches

Diameter of soda can = 2.8 inches

Find:

Volume of soda in soda can

Computation:

Radius of soda can = Diameter of soda can / 2

Radius of soda can = 2.8 / 2

Radius of soda can = 1.4 inches

Volume of soda in soda can = Volume of cylinder

Volume of soda in soda can = πr²h

Volume of soda in soda can = (3.14)(1.4)²(7)

Volume of soda in soda can = (3.14)(1.96)(7)

Volume of soda in soda can = 43.1 inches³ (Approx.)

What are the coordinates for b?

Answers

Answer:

Step-by-step explanation:

(0,-3.5)

Answer:

(0, -3.5)

Step-by-step explanation:

The x coordinate is first

We stay on the y axis so the x coordinate is 0

The y coordinate is second

We go down 3 1/2 units so the y coordinate is -3 1/2

(0, -3.5)

Small circular disks are being cut from thin sheets of steel. The steel weighs 1.6 grams per square centimeter. The disks need to have a diameter of 5 centimeters.

(A) find the area of the disk to the nearest hundredth of a square centimeter. Show the steps in your calculation.

Answers

Answer:

[tex]A = 19.63cm^2[/tex]

Step-by-step explanation:

Given

[tex]d =5cm[/tex]

[tex]Weight = 1.6g/cm^2[/tex]

Required

The area (A) of the disk

This is calculated as:

[tex]A = \frac{\pi * d^2}{4}[/tex]

So, we have:

[tex]A = \frac{3.14 * 5^2}{4}[/tex]

[tex]A = \frac{3.14 * 25}{4}[/tex]

[tex]A = \frac{78.5}{4}[/tex]

[tex]A = 19.625[/tex]

[tex]A = 19.63cm^2[/tex] --- approximated

Hank can see the top of a tree in a mirror that is placed 475 cm from the tree when he stands 190 cm from the mirror. What is the height of the tree?

Answers

Answer:

The height of the tree is 430cm

Step-by-step explanation:

Given

The attached illustration

Required

The height of the tree

Let:

[tex]h \to[/tex]  Hank's height

[tex]H \to[/tex] Tree height

[tex]d \to[/tex] distance between Hank and Mirror

[tex]D \to[/tex] distance between tree and Mirror

From the question, we have:

[tex]\angle 1 = \angle 2[/tex]

This means that:

[tex]\frac{H}{D} = \frac{h}{d}[/tex]

Make H the subject

[tex]H = \frac{h}{d} * D[/tex]

So, we have:

[tex]H = \frac{172cm}{190cm} * 475cm[/tex]

[tex]H = \frac{172* 475cm}{190}[/tex]

[tex]H = \frac{81700cm}{190}[/tex]

[tex]H = 430 cm[/tex]

How many prime numbers less than 20

Answers

Answer:

Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17 and 19

Step-by-step explanation:

How to solve this problem

Answers

Step-by-step explanation:

x = 180-106 = 74°

y = x/2 = 74/2 = 37°

4z+6 =106

4z = 100

z = 25°

The vertices of a triangle are located on a coordinate grid as follows: A (2,2) ,B (2,-6) , and C (-5,-6) . What is the area of ABC ? A. 6 square units B. 12 square units C. 28 square units D. 56 square units

Answers

The answer for this question will be c. 28 square units.

Can someone please help ASAP!!

Answers

Step-by-step explanation:

you need to find:

uw:

uv:

vw= 8(already known)

Measure of W= 35

Measure of u= 90

measure of v= 180-90+35= 55

finding uv:

sin(35)= uv/8

0.57=uv/8

4.56=uv

finding uw:

sin(55)= uw/8

0.82= uw/8

6.56= uw

what does X = to? will mark brainliest if it is an ACTUAL ANSWER

Answers

Answer:

x = 53

Step-by-step explanation:

The sum of the angles of a triangle are 180

x + ( x+2) + 72 = 180

Combine like terms

2x+74  =180

2x+74-74 = 180-74

2x =106

Divide by 2

2x/2 = 106/2

x =53

What is £8.19 minus 10%

Answers

Answer:

7.391

Step-by-step explanation:

Find 10% of 8.19

8.19*10%

8.19 *.10

.819

Subtract this from 8.19

8.19-.819

7.391

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