-
Given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of
y = f(x - 4) + 3.

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:

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:

Step-by-step explanation:

Using Pythagoras theorem,

AC^2 = AB^2 + BC^2

AC^2 = 4^2 + 15^2

AC^2 = 16 + 225

AC^2 = 241

AC = √241

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:

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:

not sure,but I think the answer is 3 to 4

Answer:

n = 1/2

Step-by-step explanation:

So the equation is 4/5n - 1/5 = 2/5n.

So, the first thing that we need to do is get the variable on one side.

So, to do that we need to subtract 4/5n on both sides.

Now our equation is -1/5 = -2/5n

Now the last step is to simplify.

To do that, we need to multiply by the reciprocal of 2/5 on both sides.

That leaves us with 1/2 = n

Answer:

n = 2

Step-by-step explanation:

=> [tex]\frac{4}{5n} - \frac{1}{5} = \frac{2}{5n}[/tex]

Combining like terms

=> [tex]\frac{4}{5n } - \frac{2}{5n} = \frac{1}{5}[/tex]

=> [tex]\frac{4-2}{5n} = \frac{1}{5}[/tex]

=> [tex]\frac{2}{5n}= \frac{1}{5}[/tex]

Cross Multiplying

=> 5n = 2*5

=> 5n = 10

Dividing both sides by 5

=> n = 2

Answer:

For each additional pound, the price increases $1.50.

Step-by-step explanation:

Lets find the slope of the graph of othe given data.

Let x be the weight of pumpkin in pounds

Let y be the price of the pumpkin in dollars.

For 4 pound pumpkin the price is 6 dollars, so first point is (4,6)

For 8 pound pumpkin the price is 12 dollars, so first point is (8,12)

Find the slope between these points

m = y₂ - y₁ / x₂ - x₁

m = 12 - 6 / 8 -4

m = 6/4

m = 1.5

Which means that for every pound increase in weight, the price of pumpkin increases by 1.5 dollars

Answer:

B

Step-by-step explanation:

Answer:   [tex]6\dfrac{3}{8}\text{ inches}[/tex]

Step-by-step explanation:

Given: Original length = [tex]15\dfrac{1}{8}[/tex] inches

[tex]=\dfrac{8\times15+1}{8}=\dfrac{121}{8}[/tex] inches                      ( In improper fraction )

Length of piece cut from original = [tex]8\dfrac{3}{4}[/tex] inches

[tex]=\dfrac{4\times8+3}{4}[/tex][tex]= \dfrac{35}{4}[/tex] inches                 ( In improper fraction )

Length of piece leftover piece =  (Original length ) - (Length of piece cut )

[tex]=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}[/tex]

Hence, the leftover piece will be [tex]6\dfrac{3}{8}\text{ inches}[/tex]  long.

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:

m<y = 155

Step-by-step explanation:

If m<x = 155, then m<y = 155 (Because vertically opposite angles are congruent)

Answer:

155°

Step-by-step explanation:

The two angles are a pair of vertically opposite angles.

Verticall opposite angles are opposite to each other and are equal.

Angle x = Angle y

155 = 155

Answer:

12 different outfits

Step-by-step explanation:

2 x 2 x 3 = 12 outfits.

Answer:

12

Step-by-step explanation:

He has 2 possibilities for a shirt, 2 possibilities for a pant, and 3 possibilities for a cap. You just multiply them together:

2 * 2 * 3 = 12 outfits

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:

25 units.

Step-by-step explanation:

The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.

Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.

Now that we know the triangles are similar, we can construct a proportion...

[tex]\frac{16}{20} =\frac{20}{x}[/tex]

That means that 4/5 = 20/x

1/5 = 5/x

x = 25

Hope this helps!

Answer:

19900kk

Step-by-step explanation:

i need deez points fr doe

Step-by-step explanation:

convert the angle from radian to degree you will get 225°

To draw it draw first 180° then ad 45° to make it easy

Answer:

20

Step-by-step explanation:

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:

-(4x + 7)/2 - (3x - 2)/2 = (-4x - 7 - 3x + 2)/2 = (-7x - 5)/2

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:

13.896 kg

Step-by-step explanation:

You can find the mass of the bar by first finding the volume.

V = BH

where B = area of the base (the trapezium), and

H = height (distance trapezium between bases)

The area of a trapezium is

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and

h = the altitude of the trapezium (distance between the bases of the trapezium)

V = (b1 + b2)h/2 * H

V = (12 cm + 6 cm)(5 cm)/2 * 16 cm

V = 720 cm^3

The volume of the bar is 720 cm^3.

Now we use the density and the volume to find the mass.

density = mass/volume

mass = density * volume

mass = 19.3 g/cm^3 * 720 cm^3

mass = 13,896 g

Now we convert grams into kilograms.

1 kg = 1000 g

mass = 13,896 g * (1 kg)/(1000 g)

mass = 13.896 kg

Answer: 1.3896 kg

Answer:

30.24/16= $1.89 per gallon = c/g

Step-by-step explanation:

c = $30.24

g = 16

Divide c/g

Answer:

g gallon = $1.89 g

Step-by-step explanation:

Gallon = g

16 gallons = 16 g

Cost = $30.24

So,

16 gallons = $30.24

1 gallon = $30.24/16

1 gallon = $1.89

g gallon = $1.89 g

The answer is A) 5 cm³

Volume is represented by cubic units.

Hope it helps <3

Answer: [tex](x+10)^2+119=0[/tex]

Step-by-step explanation:

For a quadratic equation, the vertex form is given by : [tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.

The given quadratic equation: [tex]x^2 + 20x + 28 = 9[/tex]

Subtract 9 from both sides

[tex]=x^2+20x+19=0[/tex]

compare this to [tex]x^2+bx=c[/tex], and add [tex](\frac{b}{2})^2[/tex] both sides

b= 20

[tex]x^2+20+100+19=-100[/tex]   [(b/2)²=20/2=10]

[tex]\Rightarrow\ x^2+2(x)(10)+10^2+119=0[/tex]

[tex]\Rightarrow\ (x+10)^2+119=0\ \ \ [\because\ (a+b)^2=a^2+b^2+2ab][/tex]

So, the vertex form : [tex](x+10)^2+119=0[/tex]

Answer: 0.20

Step-by-step explanation:

As per given :

P(student enrolled in a math class ) = 65% = 0.65

P( student enrolled in a science class) = 43%= 0.43

P( student enrolled in both ) = 13% = 0.13

Formula of conditional probability :

[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]

Using the above formula,

The probability that the student is enrolled in a science class given that he is enrolled in maths class :

[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]

Hence, the probability that the student is also enrolled in a science class =  0.20 .

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:

A

Step-by-step explanation:

62 +65=127

C+127=180

C=180-127=53°

so x=53°

53-y=11

y=53-11=42

Answer: A

Step-by-step explanation:

Since ΔCDE and ΔGHI are congruent triangles, they are equal to each other. This means x-y=11. We want to find y, but we first need to find x. We can do that by finding x° on ΔGHI.

We know that the sum of the angles is 180° in a triangle. We are given 2 angles from ΔCDE. We can use those to find x°.

62+65+x=180             [combine like terms]

127+x=180                   [subtract 127 on both sides]

x=53

Now that we have x, we can find y by plugging in.

53-y=11                         [subtract both sides by 53]

-y=-42                           [divide both sides by -1]

y=42

The number of buttons in C is 17 buttons

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the three tins be A , B and C respectively

The number of buttons in tin A = x

The number of buttons in tin B = 4 times the number of buttons in tin A

                                                   = 4x

The number of buttons in tin C = 7 fewer buttons than tin A

                                                    = x - 7

The total number of buttons in tin A , tin B and tin C together = 137 buttons

So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C

So , the equation will be

Total number of buttons = x + 4x + ( x - 7 )

x + 4x + ( x - 7 ) = 137

6x - 7 = 137

Adding 7 on both sides , we get

6x = 144

Divide by 6 on both sides , we get

x = 24 buttons

So , the number of buttons in tin A is 24 buttons

So , number of buttons in tin B = 4 x 24

                                                   = 96 buttons

Therefore , the number of buttons in tin C = 17 buttons

Hence , the number of buttons in tin C is 17 buttons

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Answer: 62

Step-by-step explanation:

The surface area of a rectangular prism is 2(wl+hl+hw).

Simply plug in the values to get 62

Answer:

62cm ^2

Step-by-step explanation:

every cube has 6 sides,

2(3*5) + 2(2*3)+ 2(2*5)=

2(15)+2(6)+2(10)=

30+12+20=

62