Choose the best answer. The diagonals of a rectangle:
A.) are double the shortest side
B.) none of these
C.) are the same length
D.) are the not same length
​

Step-by-step answer:

This is a problem involving subtraction of fractions.

To solve the problem, we find out the increase of the fraction of container and equate it to the amount of water added.  Then we find the amount of water contained in the whole container (fraction = 1)

7 gallons = 4/5 - 3/10 = 8/10 - 3/10 =5/10 = 1/2 container

therefore, multiply by two on both sides,

14 gallons = 1 container

So container can hold 14 gallons.

The volume of a 3D object is the amount of space it contains. A fish tank, for example, is three feet long, one foot wide, and two feet tall. To get the volume, multiply the length by the breadth by the height, which is 3x1x2, or six. As a result, the fish tank has a volume of 6 cubic feet.

Volume of cuboidal container- LBH

Given after poring 7 gallons tank is 4/5 full

Hence 7 gallon=4/5x

x=7*5/4=35/4gallon

Hence container can hold 35/4 gallon i.e=8.75gallon

Learn more about volume

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Answer:

$ 1,965,334

Step-by-step explanation:

Annual sales of company in 1999 = $ 1,200,000

Geometric mean growth rate = 10.37 % = 0.1037

In order to forecast we have to use the concept of Geometric sequence. The annual sales of company in 1999 constitute the first term of the sequence, so:

[tex]a_{1}=1,200,000[/tex]

The growth rate is 10.37% more, this means compared to previous year the growth factor will be

r =1 + 0.1037 = 1.1037

We have to forecast the sales in 2004 which will be the 6th term of the sequence with 1999 being the first term. The general formula for n-th term of the sequence is given as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

So, for 6th term or the year 2004, the forecast will be:

[tex]a_{6}=1,200,000(1.1037)^{6-1}\\\\ a_{6}=1,965,334[/tex]

Thus, the forecasted sales for 2004 are $ 1,965,334

Answer:

Area of triangle = 73.1 m²

Step-by-step explanation:

Points to remember

Area of triangle = bh/2

Where b - base and h - height

To find the height of triangle

Let 'h' be the height of triangle

Sin 35 = h/17

h = 17 * Sin 35

 = 17 * 0.5736

 = 9.75 m

To find the area of triangle

Here b = 15 m and h = 9.75

Area = bh/2

 = (15 * 9.75)/2

 = 73.125 ≈73.1 m²

Answer:

[tex]A = 73.1\ m^2[/tex]

Step-by-step explanation:

We calculate the height of the triangle using the function [tex]sin(\theta)[/tex]

By definition:

[tex]sin(\theta) =\frac{h}{hypotenuse}[/tex]

Where h is the height of the triangle

In this case we have that:

[tex]\theta=35\°[/tex]

[tex]hypotenuse=17[/tex]

Then:

[tex]sin(35) =\frac{h}{17}[/tex]

[tex]h=sin(35)*17\\\\\\h =9.75[/tex]

Then the area of a triangle is calculated as:

[tex]A = 0.5 * b * h[/tex]

Where b is the length of the base of the triangle and h is its height

In this case

[tex]b=15[/tex]

So

[tex]A = 0.5 *15*9.75[/tex]

[tex]A = 73.1\ m^2[/tex]

Answer:

Q(-2,-7)

See attachment

Step-by-step explanation:

We need to form a simultaneous equation and solve.

The point P has coordinates (1,8). Let the other point Q also have coordinate (x,y).

Then the average rate of change is the slope of the secant line connecting P(1,8) and Q(x,y) and this has a value of 5.

[tex]\implies \frac{8-y}{1-x}=5[/tex]

[tex]\implies 8-y=5(1-x)[/tex]

[tex]\implies y=5x-3...(1)[/tex]

This point Q also lies on the given parabola whose equation is [tex]y=-(x-2)^2+9...(2)[/tex]

Put equation (1) into (2) to get:

[tex]5x+3=-(x-2)^2+9[/tex]

[tex]5x+3=-(x^2-4x+4)+9[/tex]

[tex]5x+3=-x^2+4x-4+9[/tex]

[tex]5x+3=-x^2+4x+5[/tex]

[tex]x^2+x-2=0[/tex]

[tex](x-1)(x+2)=0[/tex]

[tex]x=1,x=-2[/tex]

When x=-2, y=5(-2)-3=-7

Therefore the required point is Q(-2,-7)

Answer with explanation:

We know that the formula for binomial probability :-

[tex]P(x)=^nC_xp^x\ q^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is the total number of trials and p is the probability of getting success in each trial.

Given : The probability that consumers are comfortable having drones deliver their purchases = 0.28

The total number of consumers selected = 5

To find the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones , we substitute

n=5, x=3 , p=0.28 and q=1-0.28=0.72 in the above formula.

[tex]P(3)=^5C_3(0.28)^3\ (0.72)^{2}\\\\10(0.28)^3(0.72)^{2}\approx0.1138[/tex]

Thus, the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones = 0.1138

The student's question concerns finding the probability of getting exactly three successes in five binomial trials. The values are: n = 5, X = 3, p = 0.28, and q = 0.72. The random variables X represents the number of consumers comfortable with drone delivery, and p' the proportion of such consumers.

The student is asking about a probability problem involving a binomial distribution, which is a common topic in high school mathematics. In the scenario provided, we have the following information: the number of trials (n), which is 5 (being the number of consumers randomly selected); the number of successes (X), which is 3 (being the number of consumers comfortable with drone delivery); the probability of success (p), which is 0.28 (given that 28% of consumers are comfortable with drone delivery); and the probability of failure (q), which is 1 - p = 0.72.

To find the probability that exactly three out of five consumers are comfortable with drone delivery, we would use the binomial distribution formula:

P(X = x) = C(n, x) * px * qn-x

Where C(n, x) is the number of combinations of n items taken x at a time. This would give us the probability that when five consumers are randomly selected, exactly three are comfortable with drone delivery. As this problem involves a binomial distribution, defining the random variable X as 'the number of consumers comfortable with drone delivery' and p' as 'the sample proportion of consumers comfortable with drone delivery' makes it clearer.

Answer:

  3x² -4x +12

Step-by-step explanation:

This involves straightforward application of the distributive property

x(2x+3)+(x-3)(x-4)

= 2x² +3x +x(x -4) -3(x -4)

= 2x² +3x +x² -4x -3x +12

= 3x² -4x +12

Answer:

f(x) = 3x^2 - 4x + 12

Step-by-step explanation:

First, let's label the expression and do a little housekeeping:

X(2x+3)+(x-3)(x-4) should be f(x) = x(2x+3)+(x-3)(x-4).

If we perform the indicated multiplication, we get:

f(x) = 2x^2 + 3x + (x^2 - 7x + 12), or

f(x) = 2x^2 + 3x + x^2 - 7x + 12.  Combine like terms to obtain:

f(x) = 3x^2 - 4x + 12

Answer:

A = 676πcm²

Step-by-step explanation:

According to given data:

GY = 10 cm

XY = 16 cm

The formula for finding the area of the circle is:

A = πr²

Since we have two radius. By adding the two radius we get:

GY+XY=10+16

=26

Now put the value in the formula:

A=πr²

A = π(26cm)²

A = 676πcm²

Thus the correct option is 676....

Answer:

285  boxes are in the display

Step-by-step explanation:

Given data

top layer box = 1

last row box = 81

to find out

how many box

solution

we know that every row is a square so that if the bottom layer has 81 squares it mean this is 9² and every row has one lesser box

so that next row will have 8^2 and than 7² and so on till 1²

so we can say that cubes in the rows as that

Sum of all Squares = 9² + 8² +..........+ 1²

Sum of Squares positive Consecutive Integers formula are

Sum of Squares of Consecutive Integers = (1/6)(n)(n+1)(2n+1)  

here n = 9 so equation will be

Sum of Squares of Consecutive Integers = (1/6) × (9) × (9+1) × (2×9+1)

Sum of Squares of Consecutive Integers = 285

so 285  boxes are in the display

Answer:

  A. `x= 0`, `y= (3)/(2)`

Step-by-step explanation:

Dividing the first equation by 4 gives ...

  x = 0

Substituting that into the second equation gives ...

  3·0 +6y - 9

  y = 9/6 = 3/2 . . . . divide by 6, reduce the fraction

The solution of the set of equations is ...

  x = 0, y = 3/2

_____

The question here asks "what is the solution of y ?". That answer is y = 3/2.

Answer:

C =56.52 cm

C =56.52 cm

C =56.52 cm

A =254.34 cm^2

Step-by-step explanation:

To find the circumference of a circle, we use

C = 2 * pi *r

where pi is approximated by 3.14 and r is 9

C = 2 * 3.14 *9

C =56.52 cm

To find the area of a circle, we use

A = pi *r^2

where pi is approximated by 3.14 and r is 9

A = 3.14 *9^2

A =254.34 cm^2

Your answer would be 56.52 cm (18π) for the circumference, and 254.34 cm² (81π) for the area.

The formula for the circumference of a circle is 2πr. In this case, we know that the radius is 9, so substituting it in, you get 2 * 9 * π. Solving this, we get 18π as our circumference. Your question states to use 3.14 as π, so the final step is to multiply 18 by 3.14. 18 * 3.14 = 56.52. The unit in this case would just be cm, as we are looking at circumference, or length.

The formula for the area of a circle is πr². Again, we know r = 9, so just substitute it in the equation, to get π9², which can be solved to equal 81π. Then, using 3.14 as π, we get 81 * 3.14 = 254.34 as our final answer. The unit in this case would be cm², as this is concerning area.

Hope this helps!

Answer:

66

Step-by-step explanation:

11,22,33,44, and 55 are 5 consecutive multiples of 11.

11=11(1)

22=11(2)

33=11(3)

44=11(4)

55=11(5)

-----------------

You can see  consecutive multiples of 11 where we don't know the actual multiples will look like:

11n,11(n+1),11(n+2),11(n+3),11(n+4).

Now we are given the sum of the numbers I just mentioned is 220.

This means,

11n+11(n+1)+11(n+2)+11(n+3)+11(n+4)=220

Each term 11n,11(n+1),11(n+2),11(n+3),11(n+4), and 220 all have a common factor of 11 so divide both sides by 11:

1n+1(n+1)+1(n+2)+1(n+3)+1(n+4)=20

1 times anything is still just that anything:

n+n+1+n+2+n+3+n+4=20

Combine the like terms:

n+n+n+n+n+1+2+3+4=20

Simplify the combining:

5n+10=20

Subtract 10 on both sides:

5n     =10

Divide both sides by 5:

 n      =10/5

Simplify right hand side:

 n      =2

So if n=2, then the multiples of 11 in question look like this:

11n=11(2)=22

11(n+1)=11(3)=33

11(n+2)=11(4)=44

11(n+3)=11(5)=55

11(n+4)=11(6)=66

--------------------------Add up to see if sum is actually 220.

Putting into my calculator gives me a result of 220.

We are good.

Now you just have to determine what the greatest of the number 22,33,44,55, and 66 is...

The greatest listed here is 66.

The transformations resulted in image A’B’C’D’E' is:

           A(x,y) → (x-3,y-1)

The coordinates of the Point A is given by: A(-1,5)

and the coordinates of the Point A' is given by: A'(-4,4)

Let the translation be given by the rule:

              (x,y) → (x+h,y+k)

Here

(-1,5)  → (-4,4)

i.e.

-1+h= -4   and   5+k=4

i.e.

h= -4+1   and   k=4-5

i.e.

h= -3   and   k= -1

           The transformation is:

                A(x,y) → (x-3,y-1)

Answer:

$13.30

Step-by-step explanation:

divide your total by the hours

$79.80/6=$13.30

Answer:

  B.  9, 9x, 18x

Step-by-step explanation:

The value in each box is the product of the row heading and column heading. You can find the missing column heading by dividing the box value (162) by the row heading (18).

Answer:

The answer is B coz its completes the factorization

Each side of the square would be approximately 9.3 units long.

To predict the side length of the square when the area is 86.6 units, we need to use the model that Sam created. Sam likely developed a mathematical relationship between the area (x) and the length of one side of the square (f(x)). This relationship is typically expressed as a function, such as [tex]\( f(x) = \sqrt{x} \),\\[/tex] where [tex]\( x \)[/tex] represents the area and [tex]\( f(x) \)[/tex]represents the length of one side of the square.

In this model, the side length of the square is equal to the square root of the area. Therefore, to predict the side length when the area is 86.6 units, we substitute this value into the function:

[tex]\[ f(86.6) = \sqrt{86.6} \][/tex]

Now, we can calculate this:

[tex]\[ f(86.6) \approx \sqrt{86.6} \approx 9.3 \][/tex]

So, according to Sam's model, when the area is 86.6 units, the length of one side of the square is approximately 9.3 units. This means that if you were to draw a square with an area of 86.6 units, each side of the square would be approximately 9.3 units long.

With the function [tex](f(x) = \sqrt{x - 5} + 3\),[/tex] the predicted side length for an area of 86 is calculated by evaluating f(86).

This results in a side length of 12 units.

Therefore option b. 12 units is correct.

To find the predicted side length of a square when given the area, let's use the function provided by Sam:

[tex]\[f(x) = \sqrt{x - 5} + 3.\][/tex]

Here, x represents the area, and f(x) represents the predicted side length of the square.

Find f(x) for (x = 86):

1. Plug in[tex]\(x = 86\):[/tex]

[tex]\[f(86) = \sqrt{86 - 5} + 3 = \sqrt{81} + 3 = 9 + 3 = 12.\][/tex]

The predicted side length when the area is 86 is 12.

Given the function[tex]\(f(x) = \sqrt{x - 5} + 3\),[/tex]  the predicted side length when [tex]\(x = 86\)[/tex] is option b. 12 units.

Question : After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was f(x)= *square root sign* x-5+3 Use the model Sam created to predict the side length of the square when the area is 86.

a. 6

b. 12

c. 81

d. 144

Question 9:

Answer: False

Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 10=7+3. This will just be a line.

Question 10:

Answer: False

Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 7=2+5. This will just be a line.

Answer:

Second option: 2x^10y^12

Step-by-step explanation:

Divide

60/30 = 2

When exponents are divided, it subtracts.

20 - 10 = 10

2x^10

24-12 = 12

y^12

Simplify

2x^10y^12

Answer:

Option No. 2

[tex]2x^{10}y^{12}[/tex]

Step-by-step explanation:

Given equation is:

[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}\\=\frac{30*2 * x^{20-10}y^{24-12}}{30}\\\\=2*x^{10}*y^{12}\\=2x^{10}y^{12}[/tex]

The rules for exponents for numerator and denominators are used. The powers can be shifted from numerator to denominator and vice versa but their sign is changed.

So, the correct answer is option 2:

[tex]2x^{10}y^{12}[/tex]

The answer is:

If the green line has a slope of -4, the slope of the red line will also be -4.

So, the correct option is, C. -4

We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.

So, if two lines are parallel, and one of them (the green line) has a slope of -4, the slope of the other line (the red one)will also be -4.

Have a nice day!

Final answer:

Fido's share of the total dog food, when rounded to the nearest percent, is approximately 38% after considering the 4:3 ratio with Engle for the remaining food after Denver's part.

Explanation:

The question involves calculating Fido's share of the dog food in a ratio and expressing that share as a percentage. Denver eats 2/19 of the dog food, leaving 17/19 for Engle and Fido. Engle and Fido share this remaining dog food in a ratio of 4:3. To find out what fraction of the total dog food Fido gets, we first calculate the total parts that Engle and Fido's shares make, which is 4 + 3 = 7 parts. Fido's share is 3 parts out of these 7. We then multiply the fraction of the remaining food (17/19) by Fido's share (3/7) to get Fido's share of the total dog food.

Fido's share = (17/19) * (3/7) = (17*3) / (19*7) = 51/133

Now, we convert Fido's share to a percentage:

Percentage = (51/133) * 100% ≈ 38.35%

Rounded to the nearest percent, Fido's share is approximately 38% of the total dog food.

Answer:

1.x

2.z

3.v

Step-by-step explanation:

just took the test sorry if i'm wrong

Answer:

1.  The correct option is B.

2. The correct option is D.

3. The correct option is C.

Step-by-step explanation:

1.

Let left plane is plane (1), right plane is plane (2) and horizontal plane is plane (3).

From the given figure it is clear that plane (1) and (3) intersect each other and plane (2) and (3) intersect each other.

Point B lies on the intersection of plane (1) and (3), and line x passes through the point B.

Point A lies on the intersection of plane (2) and (3), and line w passes through the point A.

So, line x and w represent the intersection of two planes. Only line x is available in the options.

Therefore the correct option is B.

2.

Line z is the which intersect plane (1) at point C. So, z is the line that intersects one of the planes.

Therefore the correct option is D.

3.

Line y passes through A and B. Points A and B are point which are lie on the intersection of planes.

The line y has points on three of the planes.

Therefore the correct option is C.

Answer:

5

Step-by-step explanation:

The nth term of a geometric series is:

a_n = a₁ (r)^(n-1)

where a₁ is the first term and r is the common ratio.

Here, we have:

40 = a₁ (r)^(4-1)

160 = a₁ (r)^(6-1)

40 = a₁ (r)^3

160 = a₁ (r)^5

If we divide the two equations:

4 = r^2

r = 2

Now substitute into either equation to find a₁:

40 = a₁ (2)^3

40 = 8 a₁

a₁ = 5

Answer:

-2

Step-by-step explanation:

The equation is in the form

y = mx + b where m is the slope and b is the y intercept

The y intercept is where x = 0

In the table the value where x=0 is y=-2

So the equation becomes

y =-4x +-2

Answer:-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

That a and b are actually h and k, the coordinates of the vertex of the parabola.  There is a formula to find h:

[tex]h=\frac{-b}{2a}[/tex]

then when you find h, sub it back into the original equation to find k.  For us, a = 1, b = -5, and c = 8:

[tex]h=\frac{-(-5)}{2(1)}=\frac{5}{2}[/tex]

so h (or a) = 5/2

Now we sub that value in for x to find k (or b):

[tex]k=1(\frac{5}{2})^2-5(\frac{5}{2})+8[/tex]

and k (or b) = 7/4.

Rewriting in vertex form:

[tex](x-\frac{5}{2})^2+\frac{7}{4}[/tex]

The expression x^2 - 5x + 8 can be written as (x - 5/2)^2 + 1.75 by the process of completing the square, where a = 5/2, and b = 1.75.

To express

x^2-5x+8

in the form

(x-a)^2+b

, we need to complete the square.

First, let's divide the coefficient of x, -5, by 2 to get -5/2 and square that to get 6.25. So, we add and subtract this inside the expression.

Therefore, x^2 - 5x + 8 becomes x^2 - 5x + 6.25 - 6.25 + 8.

This can be rewritten as (x - 5/2)^2 - 6.25 + 8 or (x - 5/2)^2 + 1.75.

Hence, the expression x^2 - 5x + 8 can be written in the form (x - a) ^2 + b where a = 5/2 and b = 1.75.

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Answer:

1) 18+2y+4+10+2x+10

2) 42+2y+2x

3) 42+2x=-2y

4) -1(42-2x=2y)

5) (42-2x=2y)/2

y=21-x

Step-by-step explanation:

1) Original equation

2) Combine like terms

3) Since the problem is asking to find the value of Y, Isolate it

4) Multiply by a negative to make Y positive

5) Since what we have left isn't in simplest form, divide by 2

What is left is y=21-x or y=-x+21

The solution to the system of linear equations X + Y = 4 and 2X + 3Y = 0 is obtained using the elimination method, resulting in X = 12 and Y = -8.

To solve the system of linear equations X + Y = 4 and 2X + 3Y = 0, we can use the substitution or elimination method. Let's use the elimination method for this solution.

Therefore, the solution to the system is X = 12 and Y = -8, which corresponds to option D.

Answer:

D

Step-by-step explanation:

A: Difference means minus. A has no minuses anywhere. Not the answer.

B: Could be true if you allow irrational numbers. I'm guessing you are not allowed to give (2x - sqrt(11)y)(2x + sqrt(11)y). So B is not the answer

C: Take out the 7 as a common factor. 7(x^2 - 3y^2) If you allow C, you have to allow B so C is not the answer.

D: answer (5x - y)(5x + y)

Answer:

5:4

Step-by-step explanation:

If point B divides the segment AC in the ratio 2:1, then

AB=2x units and BC=x units.

If point D divides the segment AB in the ratio 3:2, then

AD=3y units and DB=2y units.

Since AD+DB=AB, then

[tex]3y+2y=2x\\ \\5y=2x\\ \\y=\dfrac{2}{5}x[/tex]

Now,

[tex]AD=3y\\ \\DC=DB+BC=2y+x=2y+\dfrac{2}{5}y=\dfrac{12}{5}y[/tex]

So,

[tex]AD:DC=3y:\dfrac{12}{5}y=15:12=5:4[/tex]

Answer:

AD:DC=6:9

Step-by-step explanation:

We know that:

AB:BC=2:1

AD:DB=3:2

We can conclude that:

AB+BC=AC

Then:

AB=2/3AC

BC=1/3AC

AD+DB=AB

Then

AD=3/5AB

DB=2/5AB

From the above we can replace:

AD=(3/5)(2/3AC)=6/15AC

On the other hand:

DC= DB+BC

DC=2/5AB+1/3AC

In terms of AC

DC=((2/5)(2/3AC))+1/3AC=4/15AC+1/3AC

DC=27/45AC=9/15AC

From:

AD=6/15AC

DC=9/15AC

we can say that:

AD:DC=6:9

Answer: Part a) [tex]P(a)=\frac{1}{\binom{r+w}{r}}[/tex]

part b)[tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}[/tex]

Step-by-step explanation:

The probability is calculated as follows:

We have proability of any event E = [tex]P(E)=\frac{Favourablecases}{TotalCases}[/tex]

For part a)

Probability that a red ball is drawn in first attempt = [tex]P(E_{1})=\frac{r}{r+w}[/tex]

Probability that a red ball is drawn in second attempt=[tex]P(E_{2})=\frac{r-1}{r+w-1}[/tex]

Probability that a red ball is drawn in third attempt = [tex]P(E_{3})=\frac{r-2}{r+w-1}[/tex]

Generalising this result

Probability that a red ball is drawn in [tex}i^{th}[/tex] attempt = [tex]P(E_{i})=\frac{r-i}{r+w-i}[/tex]

Thus the probability that events [tex]E_{1},E_{2}....E_{i}[/tex] occur in succession is

[tex]P(E)=P(E_{1})\times P(E_{2})\times P(E_{3})\times ...[/tex]

Thus [tex]P(E)[/tex]=[tex]\frac{r}{r+w}\times \frac{r-1}{r+w-1}\times \frac{r-2}{r+w-2}\times ...\times \frac{1}{w}\\\\P(E)=\frac{r!}{(r+w)!}\times (w-1)![/tex]

Thus our probability becomes

[tex]P(E)=\frac{1}{\binom{r+w}{r}}[/tex]

Part b)

The event " r red balls are drawn before 2 whites are drawn" can happen in 2 ways

1) 'r' red balls are drawn before 2 white balls are drawn with probability same as calculated for part a.

2) exactly 1 white ball is drawn in between 'r' draws then a red ball again at [tex](r+1)^{th}[/tex] draw

We have to calculate probability of part 2 as we have already calculated probability of part 1.

For part 2 we have to figure out how many ways are there to draw a white ball among (r) red balls which is obtained by permutations of 1 white ball among (r) red balls which equals [tex]\binom{r}{r-1}[/tex]

Thus the probability becomes [tex]P(E_i)=\frac{\binom{r}{r-1}}{\binom{r+w}{r}}=\frac{r}{\binom{r+w}{r}}[/tex]

Thus required probability of case b becomes [tex]P(E)+ P(E_{i})[/tex]

= [tex]P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}\\\\[/tex]

The probability that all r red balls will be obtained before any white balls are obtained is 1. Before two white balls are obtained, all red balls must be drawn, so the probability is 1/w. This is based on the assumption that the draws are random.

The subject of this question is probability theory, which falls under the broad subject of Mathematics. The first part of the question asks for the probability that all r red balls will be obtained before a white ball is obtained. The second part asks for the probability that all r red balls will be obtained before two white balls are obtained.

For part (a), the probability that all r red balls will be obtained before any white balls are obtained is 1 because the balls are drawn without replacement and we are considering r draws. Therefore, every draw will be a red ball before a white ball.

For part (b), as for drawing one white ball after obtaining all r red balls, the first white ball can be the (r+1)th draw. But before drawing the second white ball, all the red balls have to be obtained. Because the balls are drawn without replacement, the probability that all r red balls will be obtained before two white balls are obtained is 1/w, where w is the total white balls.

The main assumption here is that the draws are random. So the probability of drawing a red or white ball does not change after each draw. This question is at a High School level because it involves basic probability theory and combinatorial principles.

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Answer:

Part 1) 0.65 more than -4.35 ----------> -3.70

Part 2) 0.65 more than -4.35 ---------> 5.11

Part 3) 4.34 added to -8 ---------------> -3.66

Part 4) 9.14 added to -9.14 -------------> 0

Step-by-step explanation:

Part 1) we have

0.65 more than -4.35

The algebraic expression is equal to the sum of the number -4.35 plus 0.65

[tex]-4.35+0.65=-3.70[/tex]

Part 2) we have

1.98 added to 3.13

The algebraic expression is equal to the sum of the number 3.13 plus 1.98

[tex]3.13+1.98=5.11[/tex]

Part 3) we have

4.34 added to -8

The algebraic expression is equal to the sum of the number -8 plus 4.34

[tex]-8+4.34=-3.66[/tex]

Part 4) we have

9.14 added to -9.14

The algebraic expression is equal to the sum of the number -9.14 plus 9.14

[tex]-9.14+9.14=0[/tex]