Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length? A. x4 ≥ 1 B. x3 ≤ 27 C. x2 ≥ 16 D. 2≤ |x| ≤ 5 E. 2 ≤ 3x+4 ≤ 6

Answers

Answer 1

Answer:

Step-by-step explanation:

E

Answer 2

Answer:

B

Step-by-step explanation:

Edge


Related Questions

Denver, Engle and Fido are all dogs who eat differing amounts of dog food. Denver gets 2 19 of the dog food. Engle and Fido share the rest of the food in the ratio 4 : 3 What is Fido's share of the dog food? Show your answer as a percentage, rounded to the nearest percent if necessary

Answers

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.

Suppose that a company's annual sales were $1,200,000 in 1999. The annual growth rate of sales from 1999 to 2000 was 16 percent, from 2000 to 2001 it was ?5 percent, and from 2001 to 2002 it was 22 percent. The geometric mean growth rate of sales over this three-year period is calculated as 10.37 percent. Use the geometric mean growth rate and determine the forecasted sales for 2004.

Answers

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

these three lengths create a triangle, true or false, will mark brainliest

Answers

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.

What is the solution of y ? 4x = 0 and 3x + 6y = 9? A. `x= 0`, `y= (3)/(2)` B. `x= (1)/(3)`, `y= (4)/(3)` C. `x = 1`, `y = -1` D. `x= (1)/(4)`, `y= (2)/(3)`

Answers

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.

WANT FREE 20 POINTS + BRAINLIEST? ANSWER THIS GEOMETRY QUESTION CORRECTLY AND I GOT YOU :)

Use the given diagram to answer the question.

1. Which line is the intersection of two planes shown?
A. v
B. x
C. y
D. z

2. Which line intersects one of the planes shown?
A. w
B. x
C. y
D. z

3. Which line has points on three of the planes shown?
A. v
B. x
C. y
D. z

Answers

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.

Given image A’B’C’D’E’.

If the pre-image contained Point A (-1, 5), which of the transformations resulted in image A’B’C’D’E’?

A(x, y) → (x - 3, y + 1)
A(x, y) → (x - 3, y - 1)
A(x, y) → (x + 3, y - 1)
A(x, y) → (x + 3, y + 1)

Answers

The second option (x-3, y-1) is your answer. You can just compare the original coordinates of a which is (-1,5) with the new A (-4,4). To get from -1 to -4 you have to subtract 3 from it and to get from 5 to 4 you have to subtract one from it.
Answer:

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

           A(x,y) → (x-3,y-1)

Step-by-step explanation:

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)

For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 81 boxes and the taop layer has only 1 box, how many boxes are in the display?

Answers

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

Could somebody please help me with some graphing in math?

"Consider the graphed quadratic function with one point located at point P. Plot a point on the graph that has integer coordinates and represents an average rate of change of 5 with point P."

Thank you for helping me out!

Answers

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)

What is the value of a1 for a geometric sequence with a4=40 and a6=160?

Answers

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

Peter paid $79.80 for renting a tricycle for 6 hours. What was the rate per hour for renting the tricycle? (Input only numeric values and decimal point, and report prices to two decimal places, such as 12.30.)

Answers

Answer:

$13.30

Step-by-step explanation:

divide your total by the hours

$79.80/6=$13.30

CAN SOMEONE HELP ME FIND THE AREA OF THIS TRIANGLE

Answers

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]

Which binomial could be rewritten as a difference of two squares? A) x^2 + y^2 B) 4x^2 − 11y^2 C) 7x^2 − 21y^2 D) 25x^2 − y^2

Answers

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)

Based on a​ survey, assume that 28​% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

Answers

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

Final answer:

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.

Explanation:

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.

Find the circumference and area of a circle with a radius 9 cm.

Answers

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!

What is the value of y? 18+2y+4+10+2x+10

Answers

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

express x^2-5x+8 in the form (x-a)^2+b where a and b are top-heavy fractions.

Answers

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]

Final answer:

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.

Explanation:

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.

Learn more about Completing the Square here:

https://brainly.com/question/36246034

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The container that holds the water for the football team is 3/10 full. After pouring in 7 gallons of water, it is 4/5 full. How many gallons can the container hold?

Answers

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.

What is Volume ?

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.

How to solve?

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

https://brainly.com/question/27710307

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five consecutive multiples of 11 have a sum of 220. what is the greatest of these numbers

A. 33
B. 44
C. 55
D. 66

Answers

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.

Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.

Answers

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]

HELP PLEASE 30 POINTS

Answers

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:

I need answer for this

Answers

Parallel lines have the same slope. Answer -4
Hello!

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

Why?

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!

Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. (a)What is the probability that all r red balls will be obtained before any white balls are obtained? (b) What is the probability that all r red balls will be obtained before two white balls are obtained?

Answers

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]

Final answer:

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.

Explanation:

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.

Learn more about Probability Theory here:

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Point B ∈ |AC| so that AB:BC=2:1. Point D ∈ |AB| so that AD:DB=3:2. Find AD:DC
Thanks plz answer I don’t get it

Answers

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

Solve the system of linear equations below. X + y = 4 2x + 3y = 0 A. X = -6, y = 2 B. X = -1, y = 5 C. X = 11 5 , y = 9 5 D. X = 12, y = -8

Answers

Final answer:

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.

Explanation:

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.

Rewrite the first equation as Y = 4 - X.Substitute the expression for Y into the second equation: 2X + 3(4 - X) = 0.Simplify and solve for X: 2X + 12 - 3X = 0 which simplifies to -X + 12 = 0, yielding X = 12.Substitute X back into the first equation: Y = 4 - 12, giving Y = -8.

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

Solve the equation of exponential decay.
A company's value decreased by 11.2% from 2009 to 2010. Assume this continues. If the company had a value of
$9,220,000 in 2009, write an equation for the value of the company years after 2009

Answers

Answer:

$9,220,000(0.888)^t

Step-by-step explanation:

Model this using the following formula:

Value = (Present Value)*(1 - rate of decay)^(number of years)

Here, Value after t years = $9,220,000(1 -0.112)^t

          Value after t years =  $9,220,000(0.888)^t

Simplify the expression. Use the varbiables, numbers, and symbols that are shown. Drag them to the appropriate box in the polynomial. Use standard polynomial format. X(2x+3)+(x-3)(x-4)

Answers

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

How to calculate the surface area of a cylinder

Answers

A = 2 (pie) r h + 2 (pie) r^2
r= radius
h= height

A construction crew is lengthening a road. The road started with a length of 51 miles, and the crew is adding 2 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 33 days.

Answers

Answer:

Total length after 33 days will be 117 miles

Step-by-step explanation:

A construction crew is lengthening a road. The road started with a length of 51 miles.

Average addition of the road is = 2 miles per day

Let the number of days crew has worked are D and length of the road is L, then length of the road can represented by the equation

L = 2D + 51

If the number of days worked by the crew is = 33 days

Then total length of the road will be L = 2×33 + 51

L = 66 + 51

L = 117 miles

Total length of the road after 33 days of the construction will be 117 miles.

Which expression is equivalent to

Answers

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]

Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX.



Marco wants to create a new circle using GX as a radius. What will be the area of Marco’s new circle?

10
16
356
676
R for GY=10
R for XY=16

Answers

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....

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