Answer:
Step-by-step explanation:
#1 Number of ways picking 2 from 6 = 6C2 = 15
#2 Arranging them in a circle (consider 1 pair AB)
can be done
1,5 (ABBBBB) or (5,1)
2,4 ( AABBBB) or (4,2)
3,3
1,1 (ABABAB)
all up = 7 ways
#3 = product of #1 and #2 = 15x7 = 105
There are 60 different ways the students can place the beads on the necklace using exactly two colors.
To find the number of different ways the students can place the beads on the necklace using exactly two colors, we need to consider the different arrangements that can be made.
We can first choose the two colors to be used, which can be done in C(6, 2) = 15 ways (where C(n, r) represents the combination of n items taken r at a time).
Once the colors are chosen, we can arrange the beads on the necklace in two ways: either clockwise or counterclockwise.
We can also flip the necklace to get a different arrangement.
Therefore, for each combination of colors, there are 2 x 2 = 4 different arrangements possible.
Thus, the total number of different ways the students can place the beads on the necklace is 15 x 4 = 60.
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Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets for $20. The venue has the capacity to hold
400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise $5,000 for her school:
How many Pre-sale Tickets tickets must she sell to make her goal?
A)400
B)300
C)250
D)100
The number of presales tickets can be obtained as 300. The correct option is (B).
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
Since, total number of people are 400.
Suppose the number of pre-sales tickets be x.
Then, the number of at door tickets is given as 400 - x.
As per the question, the following equation can be written for total money raised as,
⇒ 10x + 20(400 - x) = 5000
⇒ 10x = 3000
⇒ x = 300
Hence, the number of pre-sales tickets is given as 300.
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Answer: The answer would be 100.
Step-by-step explanation:
What sentence represents the number of test questions in the problem
below?
A test is worth 50 points. Multiple-choice questions are worth point, and
short-answer questions are worth 3 points. If the test has 20 questions, how
many multiple-choice questions are there?
A. The number of multiple-choice questions plus the number of
short-answer questions is 50.
B. The number of multiple-choice questions minus the number of
short-answer questions is 50.
• C. The number of multiple-choice questions times the number of
short-answer questions iS 20.
D.
The number of multiple-choice questions plus the number of
short-answer questions is 20.
Answer:
D
Step-by-step explanation:
The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions
Four decimal fractions that are smaller than 0.5
Answer: 0.4<0.5
Step-by-step explanation:
Solve the following equations
2(3x - 1) + 2(4x+5) =8
Answer
x = 0
____________
Work[tex]2\left(3x-1\right)+2\left(4x+5\right)=8\\2\left(3x-1\right)+2\left(4x+5\right)\\2\cdot \:3x-2\cdot \:1\\2\cdot \:3=6\\2\cdot \:1=2\\=6x-2\\=6x-2+2\left(4x+5\right)\\2\left(4x+5\right)\\2\cdot \:4x+2\cdot \:5\\2\cdot \:4=8\\2\cdot \:5=10\\=8x+10\\=6x-2+8x+10\\6x+8x-2+10\\14x-2+10\\14x+8\\14x+8=8\\14x+8-8=8-8\\14x=0\\\frac{14x}{14}=\frac{0}{14}\\x = 0[/tex]
_____________
Answer:
x = 0
Step-by-step explanation:
Given equation,
→ 2(3x - 1) + 2(4x + 5) = 8
Now the value of x will be,
→ 2(3x - 1) + 2(4x + 5) = 8
→ 6x - 2 + 8x + 10 = 8
→ 14x + 8 = 8
→ 14x = 8 - 8
→ x = 0/14
→ [ x = 0 ]
Hence, the value of x is 0.
How long will it take
you to
drive 135 miles at a speed of
45 miles per hour?
Answer: It takes 3 hours to drive 135 miles at a speed of 45 miles per hour.
Step-by-step explanation:
Define Time and Distance and Speed:
The length of distance traveled is proportional to the time taken to cover the distance, and we can represent this relationship as
Distance ∝ Time (Eq. 1)
The speed of any object is directly proportional to the distance traveled and inversely proportional to the time taken.
Speed ∝ Distance (Eq.2)
Speed∝1/Time (Eq.3)
Then, we can represent each parameter through the following equations:
Speed =Distance/Time
Distance=Speed × Time
Time =Distance/Speed
We can write:
Distance covered by driving: d=135 miles
Driving speed: s=45 mph
Recall the formula for the relationship of time, distance, and speed.
Time =Distance/Speed
Substitute d=135 and s=45 into the above formula, and simplify.
t=d/s
t=135/45
t=3 hours
Thus, it takes 3 hours to drive 135 miles at a speed of 45 miles per hour.
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Find the distance between the points (1, 0) and (-3, 2)
Answer:
the distance is 4 unit squares
Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
The mass of the wire is found to be 40π√2 units.
How to find the mass?To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass = [tex]\int_a^b \delta\left|r^{\prime}(t)\right| d t[/tex]
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
[tex]\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}[/tex]
Further simplifying;
[tex]\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}[/tex]
Now, use integration to find the mass of the wire;
[tex]\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}[/tex]
Therefore, the mass of the wire is estimated as 40π√2 units.
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
what is the midpoing of (-5,4) and (7,-5)
Answer:
(1,-1/2)
Step-by-step explanation:
Add both x values and divide by 2
Add both y values and divide by 2
( -5+7 )/2 = 1
(4 - 5)/2 = -1/2
(1,-1/2)
the table gives info about number of people voting for each part at an election there are 52852 people who can vote target was 88% of people who can vote was the target met maths soulotion
The target of achieving 88% votes from people is not achieved
Given that the golden party got 12598 votes, the pink party got 9112 votes, the brown party got 20059 votes and the purple party got 4466 votes. and 52,852 people can vote
The total number of people participated in voting=12598 + 9112 + 20059 + 4466
The total number of people who participated in voting=46,235
Percentage of people who participated in voting= [tex]\frac{46235}{52852}[/tex]×100
The percentage of people who participated in voting=87.5%
The target is 88%, 88%>87.5% i.e. lesser than the actual voting percentage
Therefore, The target of achieving 88% votes from people is not achieved
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A) ((7.4), (6, 3). (5, 2)}
Function?
Explain:
Answer:
Yes
Step-by-step explanation:
This function is called a discrete function since the function isn't continuous like a line but consists of individual points.
Also, the points in the function don't share the same x-coordinate, so the function passes the vertical line test.
(a) Write an expression for a number that is
three more than r.
.
Answer:
r+3
Step-by-step explanation:
r is an expression. To get an expression that is 3 more, just add 3
r+3
x - 4b
this is about algebra I had a doubt please answer this as well as the question above
Do variables have values? Like would they have a value of 1?
Answer: YES
Step-by-step explanation:
Variable have values it can be constant or changing.
for example if it is assigned a constant value 5 then it is a constant
if it has a function that varies from one value to another then it too has value but it frequently changes.
Just treat variable as a container containing some water in it sometimes we know about its quantity and sometimes it is unknown.
They may or may not have a value of 1 depending on what values you are assigning to them
hope it was of help
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The following table gives a partial set of values of a polynomial function. x −2 −1 0 1 2 3 g(x) 14 2 0 4 6 −2 Between which two values would a relative minimum most likely occur? (2 points) −2 and 0 0 and 2 −1 and 1 1 and 3
From -1 to 0, the function goes decreases, and from 0 to 1 the function goes increases. Then we will have the minimum between -1 and 1.
Between which two values would a relative minimum most likely occur?Here we have the table:
x: -2, -1, 0, 1, 2, 3g(x): 14, 2, 0, 4, 6, -2You can see that:
g(-1) = 2
g(0) = 0
So the function goes downwards from x = -1 to x = 0.
g(1) = 4
So the function goes upwards between 0 and 4.
Then, from -1 to 0, the function goes decreases, and from 0 to 1 the function goes increases. Then we will have the minimum between -1 and 1.
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Guys pls help solve 8i. I have a huge test tomorrow
Also pls show full working out bc yeah
Answer:
7/8
Step-by-step explanation:
This is a counting exercise. Think of the 200 persons that you have to separate into two groups:
1) A group that satisfies the condition of the question
2) A group that does not satisfy the condition
Then, count how many persons are in group 1, and divide that by the total (200). That is your probability.
For (i), you will find 175 persons in group 1. Even though there are many persons with not blue AND not fair hair, they are only in the group once, so don't count them double.
Then 175/200 = 7/8
In fact, you could reverse the question by counting how many people do not satisfy the condition. That group are the persons that have both blue eyes and fair hair. That is the only way to not satisfy the condition. That amount is 25, you can read it from the table.
The chance of being in that group is 25/200 = 1/8.
P(group 1) + P(group 2) = 1
So you now have two ways of getting your answer.
P(group 1) = 1 - 1/8 = 7/8.
Find the distance between (10,6), (1,-4)
Pls help! shannon is designing a new rectangular flag for the school's color guard and is determining the angles at which to cut the fabric. she wants the measure of 22 to be three times as great as the measure of z1. she thinks the measures of 23 and 24 should be equal. finally, she wants the measure of 26 to be half that of 25. determine the measures of the angles. 3
The angles are: ∠1 = 22.5°, ∠2 = 67.5°, ∠3 and ∠4 = 45°, ∠5 = 135° and ∠6 = 67.5°.
The flag is rectangle; hence, each corner will be 90°. Now, sum of ∠1 and ∠2 and sum of ∠3 and ∠4 will be 90°. We are given ∠2 is three times the ∠3. So, forming the equation -
∠2 = 3 ∠3
∠2 = 3 ∠1
∠1 + ∠2 = 90
∠1 + 3 ∠1 = 90
4 ∠1 = 90
∠1 = 22.5°
∠2 = 90 - ∠1
∠2 = 90 - 22.5
∠2 = 67.5°
According to Shannon, ∠3 = ∠4
∠3 + ∠3 = 90
2 ∠3 = 90
∠3 = 45° = ∠4
∠2 and ∠6 are the opposite angles and hence are also equal. Also, according to Shannon, ∠6 = 1/2 ∠5.
67.5 = 1/2 × ∠5
∠5 = 67.5 × 2
∠5 = 135°
Hence, each angle is: ∠1 = 22.5°, ∠2 = 67.5°, ∠3 and ∠4 = 45°, ∠5 = 135° and ∠6 = 67.5°.
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The ratio of 6th grade basketball players to 6th grade volleyball players is 5:2 if THERE ARE 30 BASKETBALL PLAYERS HOW MANY VOLLEYBALL AYERS ARE THERE
Answer: There are 12 volleyball players
Step-by-step explanation:
If the ratio of basket to volleyball players is 5:2 and there are 30 known basket ball players that means the ratio can be written as 30:x.
If 30 is 5 parts (5x) and volleyball players is 2 parts (2x) we need to figure out the value of 1 part (x)
This can be done by
5x=30
x=6
Now we know what 1 part is, we can now use that two figure out 2 parts
2x or 2(6)
2(6) = 12
So the ratio is 30:12. This can be confirmed by dividing both sides of the radio by 6 to get 5:2
Evaluate the expression 30-14divided by 2
Answer:
23
Step-by-step explanation:
You have to do the division first unless it is a fraction.
14/2 = 7
30 - 7 = 23
If it was a fraction (with 30 - 14 on top and 2 on the bottom) Then the answer would be 8 > 30 - 14 = 16/2 = 8
Hope this helps.
Two shops each charge a rental fee plus an hourly fee to rent a canoe. How many
hours must a canoe be rented for the total costs at both shops to be the same?
Rental fee
Hourly fee
Shop A Shop B
$2
$8
$5
$4
The time when the two total costs would be equal is 6 hours.
When would the total cost be equal?The equation that can be used to represent the total cost of renting a canoe is a linear function. A linear equation is an equation that has a single variable raised to the power of 1. A linear equation increases by a predetermined constant. An example of a linear equation is 2x + 2.
The form that the equation would be is:
Total cost = rental fee + (cost per hour x number of hours)
Total cost at Shop A = $2 + $5h
Total cost Shop B = $8 + $4h
When the total costs are equal, the two above equations would be equal.
$2 + $5h = $8 + $4h
Combine similar terms: $$5h - $4h= $8 - $2
Add similar terms: h = 6 hours
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What is the value of x − 7 if x = −18?
Answer:
x - 7 = -25
Step-by-step explanation:
The value of x is,
→ x = -18
Then the value of x - 7 will be,
→ x - 7
→ -18 - 7
→ -25
Hence, the answer is -25.
guys im new and i need help withe some first one
1. -2 2/3 divided by 4/3
2. -2 1/4 divided by (-5/8)
3. 1/2 divided by 2/5
4.11/3 divided by 4/5
Answer:
#1 = -2
Step-by-step explanation:
First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.
you first multiply the whole number (ignoring the negative sign for now) by the denominator:
2*3=6
then you add the numerator:
6+2=8
finally you put that number over the denominator and then put the negative sign back:
-8/3
Next, you can use keep change flip to solve the division
You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:
-8/3 divided by 4/3 becomes -8/3 x 3/4
finally you multiply across as you would normally and simplify
-8/3 x 3/4= -24/12
-24/12 simplified is -2
:D
if you need help with the rest just comment on this response and I'll try to answer as soon as I can
The solution set of a linear system whose augmented matrix is [ 1 2 3 ] is the same as the solution set of =, if =[ 1 2 3 ].
x+2x+x=d is solution set of a linear system whose augmented matrix.
What does matrix mean?
A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.First statement
[ 1 2 3 | d][x]
[ 1 2 3]x=d
x+2x+3x=d
Second statement
Ax=d
Given that A = [ 1 2 3]
[ 1 2 3]x=d
x+2x+3x=d
x+2x+x=d
Then, they are going to have the same solution
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Solve the equation −108 = 6x for x.
Answer:
[tex] \sf \large \: x = −18[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
−108 = 6x
Step 1: Flip the equation.
6x = −108
Step 2: Divide both sides by 6.
6x/6 = −108/6
x = −18
The midpoint of \overline{\text{AB}}
AB
is M(1, -3)M(1,−3). If the coordinates of AA are (-6, -7)(−6,−7), what are the coordinates of BB?
Answer:
the coordinates of BB would be: B(8,1)
The stock market closed on Tuesday at
-284 points. On Wednesday, it closed at -8
points. Find the change in points from
Tuesday to Wednesday.
-2 9 2 is the change in points from Tuesday to Wednesday in stock market.
What does the term "stock market" mean?
Buyers and sellers can trade equity shares of public firms in stock exchanges. Due to their ability to democratize access to investor trading and capital exchange, stock markets are essential elements of a free-market economy. Prices are discovered and traded in stock markets in an efficient manner.What does the stock market represent?
ETFs, stock index and stock options, equity swaps, single-stock futures, and stock index futures are a few examples. These last two may be traded over-the-counter or on futures exchanges, which are separate from stock exchanges and have a history that may be traced back to commodities futures markets.The stock market closed on Tuesday = -284 points
On Wednesday it closed = -8
the change in points from Tuesday to Wednesday = -284 - 8 = -2 9 2
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If there is an increase in the money supply that causes prices to rise and
leads to inflation, what happens to money?
• A. It loses purchasing power.
• B. It changes from fiat money to commodity money.
•
C. It changes from commodity money to fiat money.
•
D. It gains purchasing power.
SUBMIT
Mathematics of personal finance
The increase in the money supply that causes prices to rise and leads to inflation, loses purchasing power.
What is inflation?
Inflation refers to the persistent rise in the general prices of commodities in the economy over a period of time. If the prices of goods and services increase in an economy without an increase in income of people, it reduces the purchasing power of individuals.
This follows the law of demand which states that; the higher the price, the lower the quantity demanded; the lower the price, the higher the quantity demanded.
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An online store sells old video games and DVDs as a bundle. A bundle of two video games and three DVDs can be purchased for $90.00. A bundle of one video game and two DVDs can be purchased for $51.50. Find the cost of one video game and the cost of one DVD in the bundle.
Using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
How to Apply System of Equations to Solve a Problem?Given the problem above, we would do the following:
Video games = vDVDs = dUsing the information given, we would form two equations for the system as shown below:
2v + 3d = 90 ---> equation 1
v + 2d = 51.5 ---> equation 2
Multiply equation 2 by 2 to get equation 3
2v + 4d = 103 ---> equation 3
Subtract equation 1 from equation 3
d = 13
The cost of one DVD = d = $13.00
Substitute d = 13 into equation 2
v + 2d = 51.5 ---> equation 2
v + 2(13) = 51.5
v + 26 = 51.5
v = 51.5 - 26
v = 25.5
The cost of one video game = v = $25.50.
Therefore, using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
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Graph the inequality 1
The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.
Graph of InequalitiesFrom the question, we are to graph the given inequality
The given inequality is
1 < y + 7x ≤ 12
First, we will separate the inequality
1 < y + 7x and y + 7x ≤ 12
1 < y + 7x
We will determine two points on the line
1 = y + 7x
When x = 0
1 = y + 7(0)
1 = y
y = 1
(0, 1)
When y = 8
1 = y + 7x
1 = 8 + 7x
1 -8 = 7x
-7 = 7x
x = -7/7
x = -1
(-1, 8)
We can use these two points to plot the line of 1 < y + 7x
Also,
We will determine two points on line y + 7x ≤ 12
y + 7x = 12
When x = 0
y + 7(0) = 12
y + 0 = 12
y = 12
(0, 12)
When y = 5
5 + 7x = 12
7x = 12 - 5
7x = 7
x = 7/7
x = 1
(1, 5)
We can use these two points to plot the line of y + 7x ≤ 12
The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.
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Y is inversely proportional to the square of x. if y=3 when x=3 then y =1/3 when x is _______. help me isuck at proportionals
Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary and to produce the graph
Answer step by step
A. Y = (x - 2)^2 - 3
B. Y = (x + 2)^2 - 3
C. Y = - ( x - 2 )^2 - 3
D. Y = 1/2 ( x + 2)^2 - 3
The quadratic equation is:
y = (x - 2)^2 - 3
So the correct option is A.
Which equation best represents the graph shown below?
The graph clearly is the graph of a quadratic equation, there we can see that:
The y-intercept is y = 1.
The vertex is (2, -3)
Remember that if we know that a quadratic equation has a vertex (h, k), then the equation can be written as:
y = a*(x - h)^2 + k
In this case, the vertex is (2, -3), replacing that we get:
y = a*(x - 2)^2 - 3
Now, we can find the value of a, the leading coefficient, by using the fact that the y-intercept is y = 1, evaluating in zero we should get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then we conclude that the quadratic equation is:
y = (x - 2)^2 - 3
So the correct option is A.
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