Jane and Mary are Comic book fans, and each one has collected all n of the limited-edition Comic book figurines, with no repeats. Jane and Mary would each like to display some subset of their collection at the upcoming Comic book convention. However, Mary does not want to be outdone. He must include every figurine that Jane brings, and at least one additional figurine. How many ways can Mary and Jane choose figurines in such a way for the convention?
Mary and Jane have multiple ways to choose their subset of figurines for the comic book convention.
How to illustrate the number of ways?We know that Mary must include every figurine that Jane brings, so Mary must choose a subset of her collection that is at least x+1 figurines.
Since Mary must also choose at least one additional figurine, the total number of figurines that Mary can choose from is n-(x+1) + 1 = n-x
The total number of ways that Mary and Jane can choose their subsets is the product of the number of ways each can choose their subsets.
So, the number of ways is
(choose x out of n) * (choose x+1 out of n)
This is also known as binomial coefficient, which can be represented as nCx or (n x)
Hence the number of ways is
nCx * (n-(x))C(x+1)
Mary and Jane have multiple ways to choose.
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****************EXTRA CREDIT!!**********************
Anya makes 14 baskets throughout a basketball game. Some of the baskets were worth 2 points. while the others were worth 3 points. in total, anya scored 30 point. how many 2-point baskets did she make?
Part A: Define your variables
Part B: Write two equations for this scenario.
Part C: Determine how many 2-point baskets Anya made.
let x = the number of 2-point baskets Anya made
y = the number of 3-point baskets Anya made
Equations:
x + y = 14
2x + 3y =
Multiply the 1st equation by 3 to get:
3x + 3y = 42
Subtract above equation by 2nd equation to get:
(3x-2x) + (3y - 3y) = 42 -30
x = 12
Anya made 12 2-point baskets.
The difference of 5 and the product of 5 and a number
Answer: 5-5x
Step-by-step explanation:
the supplement of an angle is 113 degrees what is the measure of the angle ?
A protractor is used to measure angles in degrees (°). With the aid of a protractor, one may measure and calculate angles in terms of degrees.
What is the measure of angle?Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilised. Using a protractor, for instance, we can observe that the black arrow in the image below crosses the 90° line at 100°. Thus, the angle has a 100° measurement.
Generally speaking, supplementary angles are those where the total of two angles is greater than 180 degrees. A supplement to another angle is stated to exist for each of the angles. By deducting an angle's complement from 180 degrees, we can calculate its value.
A 113 degree angle's complement is a 67 degree angle.
Therefore, the answer is 67 degree.
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. Can a square also be classified as a rectangle? * Yes! Or No! you will get brainless helpppppp
Answer: yes
Step-by-step explanation: a square is always a rectangle but a rectangle is only a square when all sides are equal
Answer:
Absolutely!
Step-by-step explanation:
Since a square has 4 right angles, it can also be classified as a rectangle.
-2(4x+5.5)=[tex]\frac{3}{4}x[/tex]+27.6+[tex]\frac{5}{4}x[/tex]
I need it now
also show work please
The value of x for the given expression -2(4x+5.5) = 3/4x +27.6+5/4x is, 3.86
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given expression,
-2(4x+5.5) = 3/4x +27.6+5/4x
-8x -11 = 3/4x + 27.6 + 5/4x
-8x-2x = 27.6 + 11
-10x = 38.6
x = -3.86
Hence, the value of x is -3.86
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A coin is flipped 200 times. The table shows the frequency of each event.
Outcome | Frequency
Heads | 96
Tails | 104
Determine the experimental probability of landing on heads.
A. 48%
B. 50%
C. 96%
D. 104%
Answer:
Below
Step-by-step explanation:
96 heads out of 200 flips
96/200 = 48 %
Answer: 48%
Step-by-step explanation: 96 is 48% of 200, therefore the probability of landing on heads is 48%.
There are `18` ounces of milk left in the container.
How many teaspoons of strawberry syrup would you need if you used all the milk?
The teaspoons of strawberry syrup you would need if you used up all the milk is 6. 75 teaspoons
How to find the teaspoons of strawberry syrup ?The question shows that the strawberry syrup recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk.
Given that there are 18 ounces of milk left in the container, the number of teaspoons needed would be:
= ( Number of ounces left x teaspoons used ) / 8 ounces
= ( 18 x 3 ) / 8
= 6. 75 teaspoons
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The first part of question is:
A strawberry syrup recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk.
Simplify completely quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2
The solution is x minus 2 divided by 6 open parentheses x + 12 close parentheses.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
=quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2
=((x²-100)/(x²+2x-120))/((6x+60)/(x-2))
Let's simplify some of the factors:
x² - 100 = x² - 10²
= (x - 10)(x + 10)
6x + 60 = 6 * x + 6 * 10
= 6 * (x+10)
x² + 2x - 120 = x² + 12x - 10x - 12 * 10
= (x * x - 10 * x) + (12 * x - 12 * 10)
= x(x - 10) + 12(x - 10)
= (x - 10)(x + 12)
The solution is amount x minus 2 over 6 open parentheses x + 12 close parentheses.
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What’s the answer please
Answer:
m is equal to [tex]34\sqrt{2}[/tex]
Step-by-step explanation:
We can use the cosine function to evaluate m.
Note that [tex]m[/tex] is the hypotenuse in this triangle.
[tex]cos(x)=\frac{A}{H}[/tex]
[tex]A[/tex] is the adjacent side
[tex]H[/tex] is the hypotenuse
Lets look at the 60 degree angle.
The side adjacent to it is [tex]17\sqrt{2}[/tex].
Therefore we can say that
[tex]cos(60)=\frac{17\sqrt{2} }{H}[/tex]
Lets solve for [tex]H[/tex].
[tex]cos(60)[/tex] is equal to [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2} =\frac{17\sqrt{2} }{H}[/tex]
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
[tex]1*H=17\sqrt{2}*2\\H=17\sqrt{2}*2\\H=34\sqrt{2}[/tex]
Find the additive inverse of 3−9x
Answer:
3(1-3x)
Step-by-step explanation:
factor out 3 from the expression
Multiply. V6. V22 . v55
Using exponents law, the required product is [tex]v^{83}[/tex]
What are Exponents?
A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable. Exponent times power is how you raise a number with an exponent to a power.
[tex]v^6 \times v^{22} \times v^{55}[/tex]
Use the exponents law:
[tex]a^m \times a^n = a^{m+n}[/tex]
So, we get [tex]v^{6+22+55} = v^{83}[/tex]
Thus, the required product is [tex]v^{83}[/tex]
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given the angle ABC equals 114. What is the angle BAD
Answer:
A. 63°
Step-by-step explanation:
You want to know the base angle in the isosceles triangle in the given figure.
Angle sumAngle ABC is the sum of its parts:
∠ABC = ∠ABD +∠DBC
The figure shows ∆DBC is equilateral, so ∠DBC = 60°. This lets us solve for the measure of angle ABD:
114° = ∠ABD +60°
54° = ∠ABD
Base angle∆ABD is isosceles, so the two base angles are congruent. The sum of angles in the triangle is 180°, so we have ...
∠ABD +∠BAD +∠BDA = 180°
54° +2(∠BAD) = 180° . . . . . . . ∠BAD =∠BDA
∠BAD = 90° -27° . . . . . . divide by 2, subtract 27°
∠BAD = 63°
Find the exact length of the curve. x = 1/3√y(y - 3), 4 ≤ y ≤ 16.
The exact length of the given curve is 62/3
We can calculate the above answer by following the steps given below,
We have been given the following values,
x = 1/3 √y (y - 3), 4 ≤ y ≤ 16
The curve is of the length, x = f(y) from y =a to y = b is given by:
x = 1/3 √y (y - 3)
x = 1/3 (- 3)
dx/dy = 1/3 [(3/2)- (3/2)]
= 1/3 [(3/2) - (3/2)]
= 1/2 [ - 1/]
= (y-1)/2√y = f'(y)
Now we will calculate the length of the curve
= [tex]\int\limits^a_b {\sqrt{1+f'(y)^{2} } } \, dy[/tex]
= [tex]\int\limits^a_b{\sqrt{1+ (\frac{y-1}{2\sqrt{y} } )^2} } \, dy[/tex] (here a= 4, b=16)
= [tex]\int\limits^{16} _4 {\sqrt{1+ (\frac{y^2+2y-1}{4y} } )^} } \, dy[/tex]
= [tex]\int\limits^{16} _4 {\sqrt{\frac{4y+ y^2+ 2y-1}{4y} } } \, dy[/tex]
= [tex]\int\limits^{16}_4 {\frac{y+1}{2\sqrt{y} } } \, dy[/tex]
= [tex]\int\limits^{16}_4 {\frac{1}{2}\sqrt{y} } \, dy+ \int\limits^{16}_4 {\frac{1}{2\sqrt{y} } } \, dy[/tex]
= [1/3 (64-8)] +[4-2]
= (56/3)+2
= 62/3
Therefore the exact length of the curve that we get after solving the equation for curve is x = 1/3, 4 ≤ y ≤ 16, is 62/3.
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Given:
What’s the statement and reasons
The statement and reasons are
1. AB ≅ BC, AE ≅ FC 1. Given2. AC ≅ AC 2. Reflexive property of congruence3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC4. ∆AEC ≅ ∆AFC. 4. SAS5. <AEC ≅ <AFC. 5. CPCTCHow to determine the proof of the trianglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two triangles are congruent by SAS,
Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
Part of the proof is as follows:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given
2. AC ≅ AC 2. Reflexive property of congruence
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shelby is attending a school orchestra concert. She sees her math teacher seated 45 feet ahead of her and her sciene teacher seated 28 feet to her right. How far apart are the two teachers?
If shelby is attending a school orchestra concert. The two teacher are far apart by 35ft.
How to find the length?Using Pythagoreans theorem formula to find the length
c² = √ a² -b²
Where:
c = Length of the hypotenuse
a = 45
b= 28
Let plug in the formula
c² = √45² - 28²
c² = √2025 -784
c² = √1241
c = 35ft
Therefore we can conclude that the two teacher are far apart by 35ft.
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Help needed! ( question attached )
Answer:
The circumference of the wheel is 2 * pi * r = 2 * 3.14 * 225 mm = 1413.8 mm.
The number of arcs between each spoke is 25 - 1 = 24.
So, the arc length between each spoke is the circumference of the wheel divided by the number of arcs, which is 1413.8 mm / 24 = 58.91 mm.
4.) You noticed that the store brand of your favorite drink is on sale at your local grocery
store for a 12 pack of cans for $2. You try it and like it. So, you go back and buy another 3
12-packs. How much money will you save over the course of a month if you drink one can a
day at work instead of spending $1.25 at the vending machine assuming there is 20 working
days in a month? How much would you save in a year?
So on solving the provided question, we can say that by unitary method saving = 25 - 7.3333333336 = $17.6666666664
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
by unitary method,
12 pack of can, costs = $2
cost of 3 12 pack can - $2 *3 = $6
12 pack can = 12 days
1 can = $2/12 = $0.1666666667
8 can = $0.1666666667*8 = $1.3333333336
original cost of 1 can = $1.25
ordinal cost of 20 cans = $1.25*20 = 25
sale cost of 20 cans = $1.3333333336 + $6 = 7.3333333336
saving = 25 - 7.3333333336 = $17.6666666664
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Sophia is going to invest in an account paying an interest rate of 3.4% compounded monthly. How much would Sophia need to invest, to the nearest dollar, for the value of the account to reach $1,450 in 14 years?
Answer:
To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal or investment amount
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the investment is held
Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:
r/12 = 0.034/12 = 0.002833
Now we can plug in the values into the formula:
A = P(1 + 0.002833)^(12*14)
A = P(1.002833)^(168)
We know that A = $1,450 and we want to find P (the initial principal or investment amount).
So we can rearrange the equation to find P:
P = A/(1.002833)^(168)
Solving for P, we get:
P ≈ $973.99
So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.
Step-by-step explanation:
Is 24/36 equal to 4/5?
Karen has 20 one-dollar bills. She wants to give each of her 6 children the same number of bill
give each child How many bills will Karen have remaining?
Answer:
2
Step-by-step explanation:
because 6 can't Divide 20 so,
18/6
rem:2
now,
Total money-Giving money
20-18
2$
August is selling tickets for his school play.
-Adults pay $7 a ticket while students pay $5 a ticket.
-August sells 35 tickets and collects $160.
How many of each type of tickets did he sell?
A. 40 students and 32 adults
B. 20 students and 15 adults
C. 4 students and 5 adults
D. 15 students and 20 adults
The number of each type of tickets which August sold is equal to: B. 20 students and 15 adults.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of student tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable a represent the number of adult tickets sold.Let the variable s represent the number of students tickets sold.Since Adults pay $7 a ticket while students pay $5 a ticket for a total cost of $205, an algebraic equation to model is given by;
7a + 5s = 205
For the sales of 35 tickets, we have:
a + s = 35
Solving for a, we have the following:
7a + 5(35 - a) = 205
7a + 175 - 5a = 205
2a = 205 - 175
2a = 30
a = 30/2
a = 15 adult tickets.
For the number of student tickets, we have:
s = 35 - a
s = 35 - 15
s = 20 student tickets.
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Complete Question:
August is selling tickets for his school play.
-Adults pay $7 a ticket while students pay $5 a ticket.
-August sells 35 tickets and collects $205.
How many of each type of tickets did he sell?
A. 40 students and 32 adults
B. 20 students and 15 adults
C. 4 students and 5 adults
D. 15 students and 20 adults
What is the equation of the function shown in the graph? A y=−2x B y=12x C y=2x D y=−12x
Answer:I don’t onos
Step-by-step explanation:I don’t know
The stadium capacity allows for players, radio and newspaper reporters, and stadium workers in addition to spectators. How many of these people could be at a game?
No. of players and reporters in stadium = 275
No. of spectators and stadium workers in stadium = 42225
What is seating arrangement?Seating Arrangement is a process of making a group of people sit as per a prefixed manner.
Given,
Stadium capacity = 42500
General capacity seating = 31750
Reserved Seating = 10475
Total spectator seating = 31750 + 10475
= 42225
No. of players, radio and newspaper reporters = 42500 - 42225
= 275
There could be 275 players, news and radio reporters and 42225 spectators in addition to stadium workers, at the game.
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Find the value of X please answer 4, and 5! 25 points!!!!!!!!!!!!!
Answer:
4) 100
5) 120
Step-by-step explanation:
Finding unknown angle in polygon:4) Number of sides in the polygon = n = 6
Sum of all the angles of n-sided polygon = (n -2)* 180
= (6 - 2) *180
= 4 * 180
= 720
x + x + 9 + 90 + 120 +156 + 145 = 720
Combine like terms,
2x + 520 = 720
Subtract 520 from both sides,
2x = 720 - 520
2x = 200
Divide both sides by 2,
x = 200÷2
[tex]\sf \boxed{x = 100^\circ}[/tex]
5) Sum of all the angles of 5 sided polygon = ( 5 - 2)*180
= 3 * 180
= 540
x + x + x + x + 60 = 540
4x + 60 = 540
4x = 540 - 60
4x = 480
x = 480 ÷ 4
[tex]\sf \boxed{x = 120^\circ}[/tex]
Answer:
4.) You need 720 degrees sum for 6 sided polygon.
5.) You need 540 degrees for a 5 sided polygon.
Step-by-step explanation:
4.) -
120 + 156 + 145 + 90= 511
720 - 511 = 209.
209 - 9 = 200
200 / 2 = 100
X is equivalent to 100 Degrees
-
5.) -
Since X is the same for all sides we'll take 60 from 540 = 480
480 / 4 = 120
X = 120
Let’s pretend the economy is in a horrible recession, inflation is rising, and interest rates are sky-high. As the chair of the Fed, what monetary role are you going to take? Why?
Answer:
Step-by-step explanation:
Well as the chair of the fed i would need to mandate things to help have maximum employment fair stable prices and to help moderate long term interest rates. The monetary role im going to take is commodity based money.
For questions 10-12, answer the questions about logic.
10. Write the inverse of
the statement below.
If you are over 18,
then you can vote.
11. Write the converse of
the statement below.
If this month is
February, then the
next month is March.
12. Write the
contrapositive of the
statement below.
If you have $400, then
you can afford a new
laptop computer.
If you cannot vote, then you are under 18. If the next month is not March, then this month is not February. If you cannot afford a new laptop computer, then you do not have $400.
What is Inverse, Converse and Contrapositive Statement?
Inverse Statement: The inverse statement, denoted pq, assumes the inverse of each of the original statements (if not p, then not q).
Converse Statement: The converse statement is notated as q→p (if q, then p).In the original "if-then" statement, the original statements trade places.
Contrapositive Statement: The conditional statement's inverse is "If not Q, then not P."
1) The inverse statement would be,
If you cannot vote, then you are under 18.
2) The converse statement would be,
If the next month is not March, then this month is not February.
3)The Contrapositive statement would be,
If you cannot afford a new laptop computer, then you do not have $400.
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The formula for the volume, V, of a sphere with radius r is V=4/3 pi(r^3). If the radius of a baseball is 1 3/10 inches, what is the volume to the nearest cubic inch
The volume of the baseball to the nearest cubic inch is 9 cubic inches.
What is Sphere?A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.
Volume is the space occupied by a three dimensional object.
Given that,
Radius of a baseball = 1 3/10 inches = (1 × 10 + 3) / 10 = 13/10 inches.
Also we know that,
Volume of a sphere = 4/3 π r³, where r is the radius.
Volume of the baseball = 4/3 π (13/10)³
= 4/3 π (1.3)³
= 4/3 π × 2.197
= 2.9293 π
= 2.9293 × 3.14
= 9.198 cubic inches.
≈ 9 inches³
Hence the volume of the baseball is 9 cubic inches.
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10. Write the statements to correctly complete the algebraic proof.
If 2x-13-5, then x = 4.
Given: 2x 13 = -5
Prove: x 4
Proof:
1.
2.
3. 2x=8
4₁
Statements
X=4
2x 13+13= -5+13
W
(6 pts)
2x-13 = -5
Substitution Property
Reasons
1.
2. Addition Property
3.
4.
Division Property
Given
For solving the equation we are using
subtraction property and ,the division property.What is an Equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The equation is 2x = 13 - 5
here by subtracting 5 from 13 we get 8
so 2x = 8
or x = 4 (proved)
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Which equation has the same solution as: 7-8(x-3) = x -14
Answer: x = 5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
7 − 8(x − 3) = x − 14
7 + (−8)(x) + (−8)(−3) = x + − 14 (Distribute)
7+ (−8x) + 24 = x + (−14)
(−8x) + (7+24) = x − 14 (Combine Like Terms)
−8x + 31 = x − 14
−8x + 31 = x − 14
Step 2: Subtract x from both sides.
−8x + 31 − x = x − 14 − x
−9x + 31 = −14
Step 3: Subtract 31 from both sides.
−9x + 31 − 31 = −14 − 31
−9x = −45
Step 4: Divide both sides by -9.
−9x/−9 = −45/−9
x = 5