A group of individuals containingbboys andggirls is lined up in random order;that is, each of the (b+g)! permutations is assumed equally likely. What is theprobability that the person in theith position, 1≤i≤b+g, is a girl?

Explanation:

Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.

Statements  Reasons

1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given

2. AB ≅ AC and AY ≅ AX  2. definition of isosceles triangle

3. AB = AC and AY = AX  3. definition of congruency

4. AY • AC = AX • AC  4. multiplication property of equality

5. AY • AC = AX • AB  5. substitution property of equality

6. AY • AC/AX = AB  6. division property of equality

7. AC/AX = AB/AY  7. division property of equality

8. Corresponding sides are proportional  8. Definition of proportional

9. △ABC ~ △AYX  9. SAS similarity theorem

_____

The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.

Answer:

I think its A. ∠A ≅ ∠A; reflexive property

Step-by-step explanation:

Answer:

The diameter is 91.

Step-by-step explanation:

The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91

Answer:

91 yards

Step-by-step explanation:

The circumference of a circle can be found using the following formula:

c=π * d

We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.

285.74= 3.14 *d

We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14

285.74/3.14= 3.14*d/3.14

285.74/3.14=d

Divide

91=d

d= 91 yards

The diameter of the field is 91 yards.

Answer:

110

Step-by-step explanation:

example:

rounded 20+20+20+30 = 90

original 25+25+25+35 = 110

Answer:

See the step-by-step

Step-by-step explanation:

This answer is based on the idea that magnitude is absolute value.

Absolute value is a number's distance from zero.

1. Magnitude is never negative. (True)

2. The magnitude of -1.9 is  |–1.9| which is 1.9. (True)

3. The absolute value of a number is greater than its magnitude. (False, they are the same (?, maybe)

4. The numbers –4 and 4 have the same magnitude. (True)

5. The magnitude of Negative two-thirds is less than the magnitude of Two-thirds. (False)

Answer:

Which statements are true? Check all that apply.

Magnitude is never a negative value.

The magnitude of –1.9 is |–1.9| which is 1.9

The numbers –4 and 4 have the same magnitude.

Step-by-step explanation:

Answer:

Slope would equal 3.

slope= (y2-y1)/(x2-x1)

Plug in you get (8-2)/8-6)

Simplify (6)/(2)=3

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

As we know that all four sides and angles of a square are equal to each other plus the diagonal is right angled to each other as they intersect at 90 degree i.e perpendicular

It contains the identical length i.e congruent

Hence the given statement is true i.e diagonal of a square are congruent  to each other

Step-by-step explanation:

You could simply say the numbers in 0.7 one at a time like this:

=> zero point seven

OR

You can also see 0.7 as a fraction (7/10) and should therefore be said and written as follows:

=> seven tenths

Hope this helps.. Good Luck

0.7 means the same thing as 7 tenths.

Below, I have made a place value chart.

You will see that 0.7 means 0 units and 7 tenths.

Answer:

-11/9 is the slope

Step-by-step explanation:

Use the formula and u will find this is the answer, hope this helped!

Y2 - Y1 / X2 - X1

(-9 - 2) / (6 - (-3))

<!> Brainliest is appreciated!

Answer:

-11/9

Step-by-step explanation:

In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:

[tex]\frac{-9-2}{6-(-3)}[/tex]

The negatives cancel out and become postive, so the denominator will then read to be 6+3:

[tex]\frac{-9-2}{6+3}[/tex]

[tex]-\frac{11}{9}[/tex]

Answer:  4 + (−5)

An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.

Step-by-step explanation:  The arrow from 0 running to 4 is the graph of  how the point on the line is a positive 4: Four added to 0

The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5

4 + (-5) = -1  is the additive inverse of  4-5= -1  

The descriptions of the number lines are well done, but difficult to sort out.

Answer:

4 + (−5)

Step-by-step explanation:

it is got it correct

Answer:

Below.

Step-by-step explanation:

Step 1:  it is  5  x 10^-6 not 5 x 10^-5.

Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.

Answer: yes that is correct explanation:

Answer: 12 minutes

Step-by-step explanation:

7 km ........ 4 minutes

21 km ...... ?

21/7 x 4= 12 minutes

Answer: 12 minutes.

Step-by-step explanation:

It is easy to put the numbers into a ratio form to work it out. So-

4 minutes for 7 km = 4 : 7

Then ? minutes for 21 km = ? : 21

You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.

Therefore your answer is 12 minutes.

Answer:

The total number of students who attended the talk is 100.

Step-by-step explanation:

We are given that halfway through the talk, 10 women withdrew and it  was observed that the number of men was twice that  of women.

Then, almost at the end of the talk,  45 men withdrew and it was observed that the number of women was  twice that of men.

Let the number of women who attended the talk be 'w' and the number of men who attended the talk be 'm'.

Now, according to the question;

                          [tex]m = 2 \times (w-10)[/tex]

                          [tex]m = 2w-20[/tex]   ----------------- [Equation 1]

                             [tex](w-10) = 2(m-45)[/tex]

                              [tex]w-10= 2m-90[/tex]

                              [tex]w= 2m-80[/tex]

                              [tex]w= 2(2w-20)-80[/tex]        {using equation 1}

                              [tex]w= 4w-40-80[/tex]

                              [tex]4w-w= 120[/tex]

                              [tex]3w= 120[/tex]

                               [tex]w=\frac{120}{3}[/tex]  = 40

Now, putting the value of w in equation 1 we get;

                               [tex]m = 2w-20[/tex]

                               [tex]m = 2(40) -20[/tex]

                                    = 80 - 20 = 60

So, the number of men who attended the talk is 60 and the number of women is 40.

Hence, the total number of students who attended the talk is (60 + 40) = 100.

Answer:

21

Step-by-step explanation:

substitution

Answer:

21

Step-by-step explanation:

Plug in x as -2.

3(-2)² - 4(-2) + 1

3(4) - - 8 + 1

12 + 8 + 1

= 21

Answer:

521

Step-by-step explanation:

Composite figure.

Draw a straight down from C to line segment AB. This forms a triangle.

Now, the area of this figure=

Area of semicircle+area of rectangle+ area of triangle.

Rectangle area formula = l times w

Length - 20

Width =14

14 times 20 = 280

Area of rectangle = 280

Semicircle area = area of circle/2

Area of circle = π[tex]r^2[/tex]

Diameter =20= 2r

r=10

π[tex]r^2[/tex]= π 10^2 =100π

100 times 3.14 =314

314/2 = 157

Area of semicircle = 157

Area of triangle= bh/2

Triangle's base= 32-20=12

Triangles height = 14

14 times 12 = 168

168/2 = 84

Area of triangle: 84

Area of semicircle+area of rectangle+ area of triangle.

157+280+84 =521

Answer:

B

Step-by-step explanation:

I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.

Answer:

B

Step-by-step explanation:

It is too blurry BTW but B is correct

Answer:

A

Step-by-step explanation:

Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)

Answer:

y=3/4 x+2

Step-by-step explanation:

y=mx+b

take two points from graph

(0,2) and (4,5)

find b when x=0 then y=b=2

find m : y2-y1/x2-x1=5-2/4-0

m=3/4

y=3/4 x +2

Answer:

[tex]\boxed{x = \frac{21}{8} }[/tex]

Step-by-step explanation:

=> 8x-6 = 15

Adding 6 to both sides

=> 8x = 15+6

=> 8x = 21

Dividing both sides by 8

=> x = 21/8 (In its simplest form)

Answer:

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Step-by-step explanation:

tan(sin⁻¹x + cos⁻¹y)

Use angle sum formula:

[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]

To evaluate these expressions, I suggest drawing right triangles.

For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1.  Therefore:

sin θ = x/1

θ = sin⁻¹x

Using Pythagorean theorem, the adjacent side is √(1−x²).  Therefore:

tan θ = x / √(1−x²)

tan(sin⁻¹x) = x / √(1−x²)

Draw a new triangle.  This time we'll make y the adjacent side to angle θ.

cos θ = y/1

θ = cos⁻¹y

Using Pythagorean theorem, the opposite side is √(1−y²).  Therefore:

tan θ = √(1−y²) / y

tan(cos⁻¹y) = √(1−y²) / y

Substituting:

[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]

Multiply top and bottom by √(1−x²).

[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]

Multiply top and bottom by y.

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

There are only r red counters and g green counters in a bag.  A counter is taken at random from the bag.  The probability that the counter is green is 3/7  The counter is put back in the bag.  2 more red counters and 3 more green counters are put in the bag.  A counter is taken at random from the bag.  The probability that the counter is green is 6/13

Find the number of red counters and the number of green counters that were in the bag originally.

Answer:

Total number of green counters = 9

Total number of red counters = 12

Step-by-step explanation:

Recall that probability is given by

P = number of desired events/total number of events

The probability that the counter is green is 3/7

P(green) = 3/7 = 3x/7x

Where 3x is the number of green counters

7x is the total number of counters

So then red counters are

red counters = 7x - 3x = 4x

4x is the number of red counters

P(green) = 3/7 = 3x/3x + 4x

The counter is put back in the bag.  2 more red counters and 3 more green counters are put in the bag. The probability that the counter is green is 6/13

So after addition of 3 green and 2 red new counters,

P(green) = 6/13 = (3x + 3)/(3x + 4x + 3 + 2)

Now solve for x

6/13 = (3x + 3)/(3x + 4x + 3 + 2)

6/13 = (3x + 3)/(7x + 5)

6(7x + 5) = 13(3x + 3)

42x + 30 = 39x + 39

42x - 39x = 39 - 30

3x = 9

x = 9/3

x = 3

So total number of green counters are

green counters = 3x = 3*3 = 9

So total number of red counters are

red counters = 4x = 4*3 = 12

Answer:

248.96 which is approximately 249

Step-by-step explanation:

2.2^7

The coefficients are;

1,7,21,35,35,21,7,1

So the terms we want to use are 1,7,21 and 35

We can write 2.2 as 2+ 0.2

So the approximations are;

1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3

= 128 + 89.6 + 26.88 + 4.48 = 248.96

Answer:

B. not found in a toy store

Step-by-step explanation:

Given:

T = the set of things found in a toy store.

V = the set of things that cost more than $50.

T∪V = the set of things that found in a toy store or cost more than $50.

T∩V = the set of things that found in a toy store and cost more than $50.

The set T′ is the complement of the set T and it consists of the  set of things that are not found in a toy store.

The correct option is B

Answer:

10\7

Step-by-step explanation:

7x-4=6

7x=6+4

7x=10

7x\7=10\7

x=10\7

Answer:-13/3

Step-by-step explanation:

Answer:

D. the slope of f(x) is greater than the slope of g(x)

Step-by-step explanation:

slope of f(x) =rise/run

=y2 -y1 / x2 -x1

slope of f(x)= -1-2/1-0= -3

g(x)= -5x-6

slope of g(x)= -5

-3>-5

D. the slope og f(x) is greater than the slope of g(x)

Answer:

C. -10,000

Step-by-step explanation:

As x approaches zero, f(x) approaches infinity or negative infinity.

Answer: C. -10,000

Answer:

-10,000

Step-by-step explanation:

Answer:

For 75 g butter ≈ 27 fingers

Step-by-step explanation:

Using unitary method

For 20 fingers = 55 g butter

For 1 g butter = 20/55 fingers

=> For 1 g butter = 4/11 fingers (Simplified form)

Multiplying both sides by 75

=> for 75 g butter = [tex]\frac{4}{11} * 75 {fingers}[/tex]

=> For 75 g butter ≈ 27 fingers ( approximately )

Answer:

The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.

Answer:

The two inequalities are :

option B and option C.

Step-by-step explanation:

Explanation:

Daniel moves no more than 30 of his sheep and goats into another field. This means the summation of sheep and goats will be at maximum 30.

that is why it is s+g<30

And more than 7 of his animals are sheep means sheep are greater than 7. that is why =s>7

The right inequalities which corresponds to Daniel's animals are s+g<=30 and s>7 which are on option A and C.

It is a type of an equation in which we have to use greater than, less than, greater than or equal to , less than or equal to signs.

There are total 30 animals of Daniel and s represents the number of sheeps and g responds the number of goats so the first inequality will be

s+g<=30

There are more than 7 sheeps so the second inequality will be

s>7

Hence the right inequalities are s+g<=30, s>7.

Learn more about inequality at https://brainly.com/question/24372553

#SPJ2

Answer:

0.723 seconds

Step-by-step explanation:

Let h = 0

0 = -16t² + 6t + 4

Let’s solve by completing the square.

Subtract 4 from both sides.

-4 = -16t² + 6t

Since the coefficient of -16t² is -16, divide both sides by -16.

1/4 = t² - 3/8t

The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.

Then we need to add (b/2)² = 9/256 to both sides to complete the square.

Add 9/256 to both sides.

73/256 = t² - 3/8t + 9/256

Factor right side.

73/255 = (t-3/16)²

Take the square root on both sides.

±√(73/255) = t-3/16

Add 3/16 to both sides.

3/16 ± √(73/255) = t

The answer has to be positive, not negative.

0.72254626884 = t

0.723 ≈ t

Answer:

Rounding to the nearest hundredth, it is 0.72

Answer:

See explanation

Step-by-step explanation:

True Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]

False Mathematical Statement

[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]

To show using a counterexample that the statement isn't true.

[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]

Therefore, the mathematical statement is false.