The student body of 205 wants to elect a president, vice president, and a secretary. Is an example of permutation or combination.

I think the answer might be 10

Answer:

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Step-by-step explanation:

We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.

(a) The probability that a male is selected, then two females is given by;

Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]

Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(b) The probability that a female is selected, then two males is given by;

Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]

Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{770}{2300}[/tex]  =  0.3348

(c) The probability that two females is selected, then one male is given by;

Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]

Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(d) The probability that three males are selected is given by;

Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{165}{2300}[/tex]  =  0.0717

(e) The probability that three females are selected is given by;

Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{364}{2300}[/tex]  =  0.1583

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Answer:x − 3 y = − 36

Step-by-step explanation:

Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37

Step-by-step explanation:

standard form = ax+by=c so you basically just have to take that and put it into the formula

Hope this helps

Answer:

6 units down

Step-by-step explanation:

Transformation is the movement of a point from its original position to a new position. If an object is transformed, all the point making the object is also transformed. There are four different transformations: Reflection, dilation, translation and rotation.

If y = f(x), y = f(x) + k is a translation k units up if k > 0 and is a translation k units down if k < 0

Given that the parent function is an absolute value represented by:

y = |x|

Therefore comparing y = |xl - 6 with y = f(x) + k, k < 0, therefore this is a translation of 6 units down

Answer: 9πcm²

Step-by-step explanation: area of the square= 36cm²

Therefore, the area of one side= √area = √36 = 6cms

Since the circle is touching the sides of the square, the side of the square = the diameter of the circle

Therefore the radius of the circle= side/2 = 3cm

The formula for the ares of the circle is πr²

π*3*3 = 9πcm²

Answer:

5/8

Step-by-step explanation:

The value of the expression is 8/15

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)

The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)

We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n

Here, n = 15.

So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30

= 8/15

Hence, The value of the expression is 8/15

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Answer:

(a) 26.43%

(b) 189 seconds

Step-by-step explanation:

(a) Data

Z-score is calculated as follows:

z = (x - mean)/sd

z = (240 - 228)/19

z = 0.63

We want to find the next probability P(Z>0.63), which is equivalent to 1 - P(Z≤0.63)

From table, 1 - P(Z≤0.63) = 1 - 0.7357 = 0.2643 or 0.2643*100 = 26.43%

(b) We want to find z1 at which P(Z≤z1) = 0.2. From the second table, z1 is between -2.05 and -2.06.

z = (x - mean)/sd

-2.055 = (x - 228)/19

(-2.055)*19 + 228 = x

x = 189 s

Answer:

Table 2

Step-by-step explanation:

The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.

We are interested in the number of blue pants and black shorts.

If we name them as p and b respectively, then we are looking for a table where s/p=2

Let's verify relevant data in all tables:

Table 1:

Table 2:

Table 3:

Table 4:

So only one of tables- the second one from top represents the required data.

Answer:

The second table

Step-by-step explanation:

I did the test.

Answer: B C D

Step-by-step explanation:

just answered it for AP3X

Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:

B. All of the radii of a circle are congruent

C .CPCTC

D. SSS triangle congruence postulate

" Angle bisector is defined as the ray which divides the angle into two equal parts."

According to the question,

A. Any Line segment can be extended indefinitely is not required to bisect any angle .

Therefore , it is not a correct option.

B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .

Therefore , Option B is a correct option.

C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.

Therefore, Option C is the correct option.

D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.

Therefore, Option D is the correct option.

Hence, Option B, Option C , Option D are the correct answer.

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Answer:

528

Step-by-step explanation:

So naturally at first sight for this question we would think -->

Oh 3 consecutive integers = 66 --> 66/3 = 22 (n-1), (n+1) so --> 21, 22, and 23.

But no. At second look it is the sum of 3 consecutive integers is greater than 66. So we find the next possible pair since it says smallest possible product.

We get the set (22, 23, 24). => Multiply the least and greatest integers together respectively 22 and 24 which amounts to => 528

And thus, we have out answer of 528

Hope this helps!

Answer:

Step-by-step explanation:

Let width = w units

Length = 4w - 3

Cost for lining corners of wall = $ 18.50

Perimeter of the wall = 18.50/0.25 =  74 ft

2*(length  +width ) = 74

2*(4w - 3 + w) =74

2*(5w - 3) =74

10w - 6 = 74   {Add 6 to both sides}

10w - 6 + 6 = 74 + 6

10w = 80

Divide both sides by 10

10w/10 = 80/10

w =  8 ft

Length = 4w - 3 = 4*8 - 3 = 32 - 3

Length = 29 ft

Area of the wall = length * width

                           = 29 * 8

                           =  232 square ft

Cost of painting the wall per square feet = 20 cents = 0.20

Cost of painting 232 square feet = 232 * 0.20

                                                             = $ 46.40

Answer:

-17.5℃

Step-by-step explanation:

Current temperature = 0 ℃

Rate of falling per hour = -3.5 ℃

Temperature in 5 hours = -3.5 * 5 = -17.5 ℃  

Answer:

answer is (0,1)

Step-by-step explanation:

check

by substituting x=0 and y=1 in the equation above

- 2(0)+1> -4

1> -4

Thereby (0,1) is the required solution to the inequality

Answer:

I'm confused what's the question ?

Answer:

Solution,

Finding the value of X,

[tex]11x + 2 = 68[/tex]

( being vertically opposite angles)

[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]

Value of X is 6

Now, finding the value of z

[tex]z + 68 = 180[/tex]

(sum of angle in linear pair)

[tex]z = 180 - 68 \\ z = 112[/tex]

Value of z is 112.

Hope this helps....

Good luck on your assignment...

Answer:

Step-by-step explanation:

1+2 cos α

[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]

Hey there! :)

Answer:

C. (0, 5)

Step-by-step explanation:

Where the equation crosses the y axis is known as the y-intercept.

In the equation y = mx + b, the b  value represents the y-intercept where x = 0. Therefore:

Rearrange the equation pictured:

y = 5 - 3x --> y = -3x + 5

The b value in this equation is 5, so

The y-intercept of this equation is (0, 5).

Answer:

Option C is the correct option.

Here,

When X=0

y= 5-3*0

= 5-0

=5

x=0

y=5

Hope this helps...

Good luck on your assignment..

Answer:

$3.55

Step-by-step explanation:

You need to add 29% of $2.75 to $2.75.

That means the price will be 129% of $2.75.

129% of $2.75 =

= 1.29 * $2.75

= $3.55

Answer:

A, C and D

Step-by-step explanation:

The missing inequality is:

y > 2x -4

To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.

Option A: (-2,-5)

2(-2) -4 = -8

y = -5 > -8

then, the point is solution

Option B: (0,-4)

2(0) -4 = -4

y = -4 = -4

then, the point is not solution

Option C: (1,1)

2(1) -4 = -2

y = 1 > -2

then, the point is solution

Option D: (3,5)

2(3) -4 = 2

y = 5 > 2

then, the point is solution

Option E: (5,5)​

2(5) -4 = 6

y = 5 < 6

then, the point is not solution

Answer:

[Distance to the Horizon]^2 =Height of the skydiver x Diameter of the Earth

D^2 = 1.4 x 7918

D^2 = 11,085.2

D = Sqrt(11,085.2)

D = ~ 105.28628......miles - Distance to Horizon.

Step-by-step explanation:

Answer:

284.4 I took the test ;)

Answer:

your answer would be 45 I hope this was helpful

Step-by-step explanation:

Answer:

The answer is A, 45.

Step-by-step explanation:

Answer: 2 1/10, 3.122, 3.19, 61/10

Step-by-step explanation:

Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)

2.1, 6.1, 3.122, 3.19.  Obviously, the smallest number is 2.1, because it has a 2 in the ones place.  Next, we see a tie in the ones place between 3.122 and 3.19.  Then we look at the tenths place and see another tie.  Then, at the hundredths place, we see that 3.19 is greater that 3.122.  Thus, the order of the numbers is 2.1,3.122,3.19,6.1.

Hope it helps <3

Answer:

Harry earns 26 and Hamish earns 20

Step-by-step explanation:

The computation of the amount earned by each one of them is shown below:

Let us assume the hairy be Y

And, the Hamish be M

It is given that Harry earns a dollar i.e more than 5/4

And, it is $2 less than  7/5

So, the equation would be

y = 1.25m + 1  ...........................(i)

And,

y= 1.4m -2  .............................(ii)

Now equal both the equations

1.25m + 1 = 1.4m - 2

3 = 0.15m

So, m = 20

Now put the values of m in any of the above equation to find out the value of Y

Y = 1.25m + 1

= 1.25 (20) + 1

= 26

The correct expression with the correct statement has matched below.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.

The price of a game that’s been discounted by 18% of its list price

It will be (x - 0.18x)  =  0.82x

The price of a toy that sells for 18% more than the amount needed to build the toy

It will be (x + 0.18x) = 1.18x

The volume of water remaining in a tank after 3/10 of its original volume is drained out.

It will be [ x - (3/10)x ] = 7/10x

The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.

It will be [ x + (3/10)x ] =  13/10x

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Answer:

90

Step-by-step explanation:

Total People = 250

Left the party at 11 pm = 70

Stayed = 250-70

=> 180

Couples that stayed = 180/2

=> 90

Answer:

90 Couples

Step-by-step explanation:

There were 250 total people at the beginning at the party. 70 people left at 11pm.

Subtract 70 from 250:

[tex]250-70=180[/tex]

There were 180 people that stayed.

A couple consists of two people. The question asks how many couples stayed at the party, not people.

Divide 180 by 2:

[tex]\frac{180}{2}= 90[/tex]

There would be 90 couples that stayed at the party.

Answer:

Step-by-step explanation:

Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.

We now only need to find a fraction that simplifies to 3/4.

8/12 = 2/3 [tex]\neq[/tex] 3/4

12/16 = 3/4 ✅

4/6 = 2/3 [tex]\neq[/tex] 3/4

6/9 = 2/3 [tex]\neq[/tex] 3/4

This means that the correct answer is B. 12 and 16.

Answer:

B. 12 and 16

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The measure of side a is 6.3 unit.

The ratios of the length of a side to the sine of the angle opposite the side must all be the same if A, B, and C are the measurements of the angles of an oblique triangle and a, b, and c are the lengths of the corresponding sides.

Given:

c= 16 and B= 67 degree

<C= 90 degree

Using sine law

b / sin B = c / sin C

b / sin 67 = 16 / sin 90

b/ sin 67 = 16 / 1

b = 16 sin 67

b = 16 x 0.9205

b = 14. 728

Using sine law

c / sin C = a / sin A

16 / sin 90 = a / sin 23

16 = a / sin 23

a = 6.25

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Answer:

see below

Step-by-step explanation:

1.the equations have different slopes?  They will intersect at one point so one solution

2.the equations have the same slope and different y-intercepts.  They are parallel lines with a different y intercept so they will never intersect - no solutions

3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions

Answer:

1. One solution

2. no solution

3. infinite number of solutions.

Step-by-step explanation:

How many solutions a system of linear equations have if: Questions.

(assuming a system of two equations)

1.the equations have different slopes?

One unique solution, which is at the intersection point.

2.the equations have the same slope and different y-intercepts.

The equations/lines are then parallel but NOT coincident.  They will never meet, therefore NO solution.

3.the equations have the same slope and same y-intercepts.

The two lines/equations are in effect coincident.  Therefore there is an infinite number of solutions.

Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution