Can you check my answer?
Which of the following is an example of why irrational numbers are 'not' closed under addition?

√4 + √4 = 2 + 2 = 4, and 4 is not irrantonal
1/2 + 1/2 = 1, and 1 is not irrational
√10 + (-√10) = 0, and 0 is not irrational
-3 + 3 = 0, and 0 is not irrational

I was thinking:
–3 + 3 = 0, and 0 is not irrational
because it came up with a different number besides 3.,

Answers

Answer 1

-3+3 = 0 is an example of adding two rational numbers to get another rational number.

-3 = -3/1
3 = 3/1
0 = 0/1
each can be written as a fraction of whole numbers, so that's why they are rational

The actual answer is choice C

We are adding the square root of 10, written sqrt(10) in shorthand, to the negative version of the same number. Doing so leads to 0. This is using the property x + (-x) = 0. The left hand side of choice C has two irrational numbers. They add to 0 on the right hand side which is rational. The fact that we added two irrational numbers to get an rational result indicates that irrational numbers are not closed under addition.

Related Questions

Describe the graph of a system of linear equations that has infinite solutions.

Answers

tbe graph of a system of linear equations that has infinite solutions is a point because it can have a line go though it in infinite ways

For a school group, a skating rink charges a flat fee of $50 for skates for the students to use the skating rink.
•For 40 Students the skating rink charges 180.
•For 75 students, the skating rink charges 293.75
Which question represents the amount the skating rink charges for x students?
A)y=3.25x+35
B)y=3.25x+ 50
C)y=4.50x+ 35
D) y=4.50x+ 50

Answers

The function has a variable part and a fixed part.
That fixed part is given by the fee for skates, which is $50.
The variable part depends on the quantity of students which is called 'x'. For this part, you are provided with a couple of points where the linear function passes by, they are: A(40,180) and B(75,293.75).

So, first thing to do is getting the slope:
[tex]m= \dfrac{293.75-180}{75-40} = \dfrac{113.75}{35} \\ \\ m=3.25[/tex]

Linear function structure is:
[tex]y=mx+b[/tex]
Where b is the y-intercept, which in this case is the fixed part, 50.
Finally, the function is:
[tex]y=3.25x+50[/tex]

Attached picture shows its graph.

Warren wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if warren has 500 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a.let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). write an function for the area a of the enclosure in terms of w . (hint first write two equations with w and l and
a. solve for l in one equation and substitute for l in the other). a ( w ) = 1/2w
b.what width w would maximize the area? w = ft
c.what is the maximum area? a = square feet

Answers

l +2w = 500
a = lw

a) l = 500 -2w
.. a = (500 -2w)*w

b) The zeros of the above equation are w=0, w=250. The vertex of this quadratic is on the line of symmetry, halftway between the zeros, at w=125 ft.

c) a = (500 -2*125)*125 = 31,250 . . . . square feet

Let's solve this step by step.
a. We begin by establishing the relationship between the width (w) and the length (l) using the total amount of fencing available (500 feet). Since one side of the pen is against the barn, we only need to fence the other three sides. Thus, the total amount of fencing used will be for two widths and one length, or $2w + l$.
Setting up the equation for total fencing, we get:
\[2w + l = 500\]
Now, to express $l$ in terms of $w$, we solve for $l$:
\[l = 500 - 2w\]
Next, we can write the function for the area $A$ of the enclosure in terms of $w$. Since area is $width \times length$, we substitute our expression for $l$:
\[A(w) = w \cdot l\]
\[A(w) = w \cdot (500 - 2w)\]
\[A(w) = 500w - 2w^2\]
This is the function that expresses $A$ in terms of $w$.
b. To find the width $w$ that maximizes the area, we take the derivative of $A(w)$ with respect to $w$ and set it equal to zero to find the critical points.
\[A'(w) = \frac{d}{dw}(500w - 2w^2)\]
\[A'(w) = 500 - 4w\]
Setting $A'(w)$ equal to zero and solving for $w$:
\[500 - 4w = 0\]
\[-4w = -500\]
\[w = \frac{500}{4}\]
\[w = 125\]
The width that maximizes the area of the enclosure is 125 feet.
c. Now let’s find the maximum area by substituting $w = 125$ back into the area function $A(w)$:
\[A(125) = 500 \cdot 125 - 2 \cdot 125^2\]
\[A(125) = 62500 - 2 \cdot 15625\]
\[A(125) = 62500 - 31250\]
\[A(125) = 31250\]
The maximum area that Warren can enclose is 31,250 square feet.

Ivan earns $8 each time he walks his neighbors dog.he already walked his neighbors dog 5 times.how many more times does he need to walk the dog to earn enough money to buy a game that costs $88

Answers

He needs to walk the dog 6 more times. This is because it takes 11 walks to get to $88 and he only has done 5 so far. Subtract 5 from 11 to get your answer.

Answer:

6 more times

Step-by-step explanation:

find the approximate surface area of a bowling ball with a raius of 5 inches

Answers

The surface area would be 100 pi, or rounded to 314.159.

Formula for the surface area of a sphere: SA = 4·π·r2

Formula for the volume of a sphere: V = (4/3)·π·r3

Surface area to volume ratio: ( 4·π·r2 ) / ( (4/3)·π·r3 ) = 3 / r

Radius = 5 ---> 3/5

what’s the inverse of y=4x^2-2

Answers

Interchange the x and y and solve for the resulting y.
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y

The graph of these two is below.

The original is in red
The inverse is in blue and green

How to find the equation of a circle

Answers

hmmm lemme do the first one only

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{5}{ h},\stackrel{3}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\ (x-5)^2+(y-3)^2=2^2\implies (x-5)^2+(y-3)^2=4[/tex]

Final answer:

To find the equation of a circle, use the formula (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is its radius. You apply this knowledge to other circular calculations, such as the angular velocity or the position and velocity of a moving point on the perimeter of the circle.

Explanation:

Finding the Equation of a Circle

To find the equation of a circle, you need to know the circle's radius (r) and the coordinates of its center (h,k). The general form of the equation is (x - h)² + (y - k)² = r². The values of h and k are the x and y coordinates of the center of the circle, respectively. If you recall the formula for the circumference of a circle, which is 2πr, and the area, which is πr², you can see that these both incorporate the radius of the circle in their calculations, similar to how the radius is used in the equation of the circle. When given certain dimensions or related motion problems, you can substitute known values into the equation to solve for the unknowns.

For example, if a circle has a radius of 5 units and its center is at the point (3,4), the equation would be (x - 3)² + (y - 4)² = 25. To find equations related to circular motion, like in the scenario of a student on a merry-go-round, knowing the radius also allows for determining the angular velocity and the velocity of a shadow or any point moving in circular motion.

A high school student working part-time as a pizza delivery man had a gross income of 6324 last year. If his federal tax rate was 10% and his state tax rate was 4.2% what was the amount withheld from his pay last year in fenderal tax, state tax, and FICA combined

Answers

$1381.79 is the answer

Answer:

$1381.79 withheld from his pay last year.

Step-by-step explanation:

A student working as a pizza delivery man and earned = $6324.00

first we calculate all the taxes at the given tax rates

Federal Tax Rate = 10% of 6324.00

= 0.10 × 6324 = $632.40

State Tax Rate = 4.2% of 6324.00

= 0.042 × 6324 = $265.608

FICA is comprised of taxes for social security and medicare. For social security tax rate is 6.2% and for medicare tax rate is 1.45% which add up to 7.65%.

FICA combined Tax Rate = 7.65% of 6324.00

= 0.0765 × 6324 = $483.786

Now we add all the taxes to get what amount withheld from his pay

= 632.40 + 265.608 + 483.786 = $1381.79

$1381.79 withheld from his pay last year.

HELP!!...................

Answers

solve for r and then c by replacing x with 5 then subtract:

r = x^2 +5x + 14 = 5^2 +5(5) +14 = 25 +25 +14 = 64

c = x^2-4x +5 = 5^2-4(5) + 5 = 25-20 +5 = 10

r- c = 64-10 = 54

so the store will have a profit of 54,000 after it's 5th month

Answer is C

(r-c)(5) is equivalent to r(5) - c(5). Since r(x) is the amount of money that a business earns and c(x) is the amount of money that the business uses, r(x) - c(x) is the business’s profit. We input 5 into r(x) = x^2 + 5x + 14 to get 64. We input 5 into c(x) = x^2 - 4x + 5 to get 10. We substitute 64 for r(5) and 10 for c(5) in r(5) - c(5) to get 64-10, or 54. Since the problem says that it is in hundreds of dollars, the amount of profit the business makes is $5400 after its fifth month

Convert -1.2 repeating as a mixed number

Answers

I believe that the answer is -1 and 2/10ths not 100% but I hope that this helps

I actually don't know this one sorry

△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ? Enter your answer, in simplest form, in the boxes. :

Answers

Let
h1---------------> height of △ABC
b1---------------> base of △ABC
h2--------------->height of △DEF
b2---------------> base of △DEF

we know that
h1=20 in
h2=24 in

Since they are similar, their bases must be in the same proportion:
h1/b1=h2/b2------> 20/b1=24/b2-----------> 24b1=20b2
b1=20b2/24-------------> equation 1

Area of △ABC=b1*h1/2
Area of △DEF=b2*h2/2

Let
r------>[the ratio of the area of △ABC to the area of △DEF]
r=[b1*h1/2]/[b2*h2/2]------> [b1*h1]/[b2*h2]
r=[20b1]/[24b2]---------------> equation 2

I substitute 1 in 2
r=[20(20b2/24)]/[24b2]--------> r=20²/24²-------> r=0.6944

the answer is
the ratio of the area of △ABC to the area of △DEF is 0.69

A bakery bakes 10 cakes per hour & had 3 from the day before. What equation represents this?

A.y = 10x + 3
B.y = 3x + 10
C.y = x + 13
D.y = 13x

Answers

y represents the total number of cakes the bakery make.
x represents the number of hours spent

y = 10x + 3

-----------------------------
Answer: 10x + 3
-----------------------------

Can someone help me please, how to add this? Thank you!

Answers

Answer:
Choice B) [tex]9.9 \angle \underline{76.10^{\circ}}[/tex]

============================================

Explanation:

The given vectors in polar form are
(17,60)
(8,220)
by polar form I mean (r,theta) where
r = magnitude
theta = angle

Convert the polar form (r,theta) = (17,60) to component form
x = r*cos(theta)
x = 17*cos(60)
x = 8.5
y = r*sin(theta)
y = 17*sin(60)
y = 14.72243186
The component form of the first vector is (x,y) = (8.5, 14.72243186)

Do the same for the second vector
x = r*cos(theta)
x = 8*cos(220)
x = -6.1283555
y = r*sin(theta)
y = 8*sin(220)
y = -5.1423009
The component form of the second vector is (x,y) = (-6.1283555, -5.1423009)

Now we add the vectors. Add up the corresponding components
(8.5, 14.72243186)+(-6.1283555, -5.1423009)
(8.5+(-6.1283555) , 14.72243186+(-5.1423009))
(2.3716445, 9.58013096)

So,
(x,y) = (2.3716445, 9.58013096)
is the component form of the resultant vector. Its the vector we get after adding the two original vectors

The last step is to convert this back to polar form
r = sqrt(x^2+y^2)
r = sqrt(2.3716445^2+9.58013096^2)
r = 9.869326564
which is roughly 9.9

theta = arctan(y/x)
theta = arctan(9.58013096/2.3716445)
theta = 76.09548164
which rounds to 76.10

So we end up with (r,theta) = (9.9, 76.10) pointing to choice B as the answer

-7(3x+5) use Distributive property to solve

Answers

the answer is -21x-35

- 7(3x + 5 )

= ( - 7 )(3x + 5)

= ( - 7 )(3x) + ( - 7)(5)

Answer: = - 21x - 35

What is the ratio of CDs & DVDs

Answers

A. 2:1
B. 1:4
C. 1:2
D. 1:5

Help please been stuck on this for a week.

Answers

They give the formula as:
Surface Area = (2 • π • r²) + (2 • π • r • height)
However the 2*PI*r^2 part of the formula is used to calculate the 2 "ends" of a cylinder. Since the problem states that you are NOT to count any of surface area of the "ends" then you only need the (2 • π • r • height) part of the formula.
So, r = 3 inches and height = 8 * 3 inches, the side area equals
2 * PI * r * height
2 * 3.14159 * 3 * 24 =

452.39 cubic inches which is the lateral area.

What is the measure of angle x, help

Answers

y = 180 - 51 -56 = 73

x = 180 - 73 - 72 = 35

x = 35 degrees

y=180-51-56
=73
x=180-72-73
=35°

Triangle ABC was dilated and translated to form similar triangle A'B'C'.

What is the scale factor of the dilation?

A. 1/5
B. 2/5
C. 5/2
D. 5/1

Answers

Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.

On this exercise is asked to find the scale factor by which the triangle ABC was
dilated to produce the triangle A'B'C'.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.

As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.

Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)

Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)

As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.

correct answer is 5/2

Jim runs a food cart and during a business outdoor Festival he sold $8470 worth of food he sells hot dogs for $2.50 and steak sandwiches for $10 if he sold a total of 985 items that they how many of each item did he sell?

Answers

The first thing we do for this case is to define variables:
x: hot dogs
y: steak sandwiches
We write the following system of equations:
2.50x + 10y = 8470
x + y = 985
Resolving graphically we have:
x = 184
y = 801
Note: see attached image for the solution.
Answer:
He sold:
hot dogs = 184
steak sandwiches = 801

PLEASE HELP PLEASE HURRY!!!!!!!!!
BRAINLIEST AVAILABLE

Answers

Rule for 1 is the rule for 1 is 14 times 3.5^x and it is exponential

The second one is is also exponential and the rule is 32 times .25^x and the last one is is linear and the rule is 5x+-4

I'm just going to give you the answers. You can figure out how they were obtained. Actually the hints are at the bottom of your exercise. You need only juggle them a bit to get the answers.

1]
y = 14 * (7/2)^x This is never going to linear.

2]
y = 32/(4)^x This also is not linear.

3]
y = 5x - 4 This one is linear

If you have a graphing calculator, you might think about graphing these three. The questions are a bit of by guess and by golly. You just have to keep on trying things until you get it. Look at 0 as an x value first.

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm

Answers

You can solve this problem by applying the Angle Bisector Theorem. Let's call the lenghts we want to calculate: "x":

7.4/x=6/4

When we clear "x", we obtain:

6x=(7.4)(4)
x=(7.4)(4)/6
x=4.9 cm (This is the shortest possible length of the third side of the triangle)

Let's find the longest possible length:

4/6=7.4/x

When we clear the "x", we have:

4x=(7.4)(6)
x=(7.4)(6)/4
x=11.1 cm (This is the longest possible length of the third side of the triangle)

Answer:

11.1 cm, 4.9 cm

Solve 2x^3-5x^2-11x-4=0

Answers

A graphical calculator shows solutions to be
x = {-1, -0.5, 4}

The factorization will be
.. (2x+1)(x +1)(x -4) = 0

Censorship was established in the Bill of Rights. True or false! First answer will be marked brainliest!

Answers

false is the answerrrrrr

Answer:

make the other brainliest but its false

Step-by-step explanation:

I WILL GIVE BRAINLIEST FOR Correct Answer

A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.

EXPLAIN YOUR ANSWER

a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.

Answers

Answer:

a. 15052.1ft b. 6122ft

Step-by-step explanation:

Trey wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 31
feet and its width is 24
feet. Suppose each pack of seed covers 12
square feet. How many packs of seed will he need to cover the backyard?

Answers

The first step to solve this problem is to compute for the area of the rectangular backyard. The formula in computing the area of a rectangle is:

A = LW

Substituting the given measurement to the formula:

A = 31 (24)

A = 744 square feet

The area of the backyard is 744 square feet.

Since each pack of seed covers 12 square feet, you need to divide this to the total area of the backyard.

Therefore, you need 62 (744 / 12) packs of seed to cover the backyard.

Final answer:

Trey will need 62 packs of seed to cover his backyard.

Explanation:

To find the number of packs of seed Trey will need to cover his backyard, we need to calculate the total area of the backyard and then divide it by the area covered by each pack of seed.

The formula to find the area of a rectangle is length x width. For Trey's backyard, the length is 31 feet and the width is 24 feet, so the area is 31 x 24 = 744 square feet.

Each pack of seed covers 12 square feet, so we divide the total area of the backyard by the area covered by each pack of seed: 744 / 12 = 62 packs of seed.

Learn more about Calculating area of a rectangle here:

https://brainly.com/question/18101587

#SPJ2

Guys please help me

this is a system of equation word problem

Answers

The starting weight was 185, and the rate of change was -3 (per day).
.. w = 185 -3d . . . . . . d is the number of days, w is the weight in pounds

Evaluating this for d=7, we have
.. w = 185 -3*7 = 164
The point is represented by the ordered pair (7, 164).

The value on day 7 corresponds to the weight loss due to rejection. We might conclude the reaction to rejection was the cause of death.

Which function has a domain of all real numbers except x=π/2 ±nπ?

A. y=secx
B. y=cosx
C. y=1/sinx
D. y=cotx,

Answers

A. y=secx This problem deals with the various trig functions and is looking for those points where they are undefined. Since the only math operations involved is division, that will happen with the associated trig function attempts to divide by zero. So let's look at the functions that are a composite of sin and cos. sin and cos are defined for all real numbers and range in value from -1 to 1. sin is zero for all integral multiples of pi, and cos is zero for all integral multiples of pi plus pi over 2. So the functions that are undefined will be those that divide by cos. tan = sin/cos, which will be undefined for x = π/2 ±nπ cot = cos/sin, which will be undefined for x = ±nπ sec = 1/cos, which will be undefined for x = π/2 ±nπ csc = 1/sin, which will be undefined for x = ±nπ Now let's look at the options and pick the correct one. A. y=secx * There's a division by cos, so this is the correct choice. B. y=cosx * cos is defined over the entire domain, so this is a bad choice. C. y=1/sinx * The division is by sin, not cos. So this is a bad choice. D. y=cotx, * The division is by sin, not cos. So this is a bad choice.

Answer:

y=cos x

Step-by-step explanation:

A P E X

using these complex zeros (1,1,-1/2,2+i,2-i) factor f(x)=-2x^5 +11x^4 -22x^3 +14x^2 +4x -5

Answers

[tex]\bf \begin{cases} x=1\implies &x-1=0\\ x=1\implies &x-1=0\\ x=-\frac{1}{2}\implies 2x=-1\implies &2x+1=0\\ x=2+i\implies &x-2-i=0\\ x=2-i\implies &x-2+i=0 \end{cases} \\\\\\ (x-1)(x-1)(2x+1)(x-2-i)(x-2+i)=\stackrel{original~polynomial}{0} \\\\\\ (x-1)^2(2x+1)~\stackrel{\textit{difference of squares}}{[(x-2)-(i)][(x-2)+(i)]}[/tex]

[tex]\bf (x^2-2x+1)(2x+1)~[(x-2)^2-(i)^2] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)-(-1)] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)+1] \\\\\\ (x^2-2x+1)(2x+1)~[x^2-4x+5] \\\\\\ (x^2-2x+1)(2x+1)(x^2-4x+5)[/tex]

of course, you can always use (x-1)(x-1)(2x+1)(x²-4x+5) as well.

The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.

V(t)=24,500(0.95^t)

Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.

Answers

Initial value means t equals 0. Therefore
24,500*(0.95^0) =
24,500*1 = 24,500
Hence, the initial value is £24,500

The value after 13 years means t equals 13. Therefore
24,500*(0.95^13) =
12,576.88
Hence, the value after 13 years is about £12,577

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg and the hypotenuse 2 cm more than the shorter leg. how long should the sides of the triangle be?

Answers

The only Pythagorean triple with legs in arithmetic sequence is the 3-4-5 triangle.

The sides should be 3 cm, 4 cm, 5 cm.

Other Questions

Which three sources of energy were productive for canada? A: solar B: tidal C:hydroelectric D: geothermal They sang a song of joy. verb: Which type of context clue can be used to determine the meaning of the bolded word in the following sentence?We were told by our teacher not to include any superfluous details in our papers that would add length but not substance.A. comparisonB. description C. example D. restatement The ability to distinguish between two nearby objects is called What is the first step of the buyer decision process?a. purchase decisionb. need recognitionc. alternative evaluationd. information searche. postpurchase behavior? When you present a decorating plan to a client, what is one element youshould emphasize?A. Your credentialsB. How each choice fits their needs and budgetC. The color scheme youve chosenD. The importance of a large deposit on the job What is 5% in a decimal and a fraction? Which word has a negative connotation? A. Horde B. Mass C.Crowd D. Multitude Read the following excerpt. The politician tried to refute all the allegations against him. Unfortunately for him, though, the evidence was far too compelling. As much as he tried, he couldn't sway voter opinion, and he lost the election.Using the context, the word sway means influence reject defer question Who is generally accepted as Tutankhamun's father?Select one:a. Akhenaten b. Ramesses II c. Thutmose II d. Mentuhotep VIepted as Tutankhamun's father? When does Mephistophilis first visit Faustus?A.When Faustus is reading the Bible.B.When Faustus resolves to study necromancy.C.After the good and evil angels first appear, but before Valdes and Cornelius arrive.D.When Faustus is in the grove performing an incantation. In lines 97110, Douglass presents a long list of things that black people are doing. Then in lines 123130, he presents a list of the wrongs that are done to slaves. How do these two different lists serve Douglass's purpose in giving the speech? natural selection is best described as 1. Which of the following statements by Mme. Loisel represents a fact? (1 point)"Only I dont have an evening dress and therefore I cant go to that affair.""Its embarrassing not to have a jewel or a single gemnothing to wear on my dress.""Theres nothing more humiliating than to look poor among a lot of rich women."2. What is the connotation of the word common as it is used in this excerpt from "The Necklace"?The other, not recognizing her, showed astonishment at being spoken to so familiarly by this common person. (1 point)typical five criterion team bikes cost $ 11,300. How much would the club have to pay for a dozen criterion team bikes? Karen ditched her little sister so we could go to the year - end party. ditched means __________. Justin lives in saint paul and goes to school in minneapolis. in the morning, he has 333 transportation options (bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home. if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train? A bicycle manufacturer is reducing the number of spokes on each bicycle wheel by 4. A wheel on one of the company's new cross-country bikes has 32 spokes. Which equations could be used to determine the number of spokes s that a wheel on a cross-country bike used to have? A. S + 32 = 4 B. S + 4 = 32 C. S - 32 = 4 D. S - 4 = 32 Lists words and page numbers where the words can be found. A.table of contents B.glossary C.index D.title page E.appendix Why must lobbyists register with the government and report their activities annually?