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Question
How many ways can 2 identical red chairs and 4 identical blue chairs be arranged in one row ?
Answer · 21 votes
There is a formula that applies to this situation. The number of distinct permutations of n things, a of which are indistinguishable, b of which are indistinguishable, atc., is `(n!)/(a!b!...)` Here there are 6 chairs, 2 of which are indistinguishable and 4 of which are indistinguishable, so the number of permutations is `(6!)/(2!4!)=(6.5.4.3.2.1)/(2.1.4.3.2.1)=(6.5)/(2)=15`
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18 blue chairs and 27 red chairs have to be arranged in rows in such a way that there are an equal no. of chairs of the same colour in each row, what is the maximum no. of chairs that can be arranged in each row and how many rows can the chairs be arranged in?
Answer · 27 votes
Answer: highest number of chairs in each row is 9Total rows is 5Step-by-step explanation:Find the Highest Common Factor of 18 and 27The HCF of 18, 27 is 9Thus the maximum no of chairs that can be arrranged in each row is 9Total rows is (18+27)/9 = 5Please brainlist my answer, if helpful!
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There are 15 different ways to arrange the 2 identical red chairs and 4 identical blue chairs in one row.
To find the number of ways the 2 identical red chairs and 4 identical blue chairs can be arranged in one row, we need to calculate the total number of arrangements considering that the chairs of the same color are identical.
The total number of chairs is 2 red + 4 blue = 6 chairs.
Since the chairs of the same color are identical, the arrangements will be different only if the arrangement of colors is different. Therefore, we need to find the number of arrangements of 2 red and 4 blue chairs.
To calculate this, we can use the formula for permutations with repetition. The formula is given by:
P(n; n1, n2, ..., nk) = n! / (n1! * n2! * ... * nk!)
Where:
n is the total number of objects (chairs in this case).
n1, n2, ..., nk are the number of objects of each type (number of red and blue chairs in this case).
In our case, we have 6 chairs in total, and we want to arrange 2 red and 4 blue chairs. So, the number of arrangements is:
P(6; 2, 4) = 6! / (2! * 4!)
= (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 4 * 3 * 2 * 1)
= 15
Therefore, there are 15 different ways to arrange the 2 identical red chairs and 4 identical blue chairs in one row.
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Janice is starting classes at Hellenson University in the fall. The cost of tuition for one year is $14,700. Janice earned an engineering scholarship that covers one-third of her tuition. She has also saved $1,000 to use for this year's tuition. Janice and her parents have agreed to each pay half of the remaining tuition. How much money will they each pay for Janice's tuition this year?
Answer: 4400
Step-by-step explanation:
The scholarship covers $14,700 / 3 =
14700/3=4900
4900 of Janice's tuition.
After the scholarship, Janice still needs to pay $14,700 - $4900 = 9800 for tuition.
Janice has saved $1000, so she needs to come up with an additional $9800 - $1000 = 8800 for tuition.
Janice and her parents will each pay $8800 / 2 = 4400
Please give the answer 5 stars if you find it helpful!
Happy to help!
if traingle PAG is comgruent to riangle DEN, use words numbers and or symbols to state two conclsuions that can be made based upon cpctc
dr. wade wilson is interested in whether or not people who watch adventure movies actually have quicker reaction times than people who read literary novels. he gathered a sample of 120 adventure movie lovers and a sample of 123 literature students who do not go to movies at all. all take a test of reaction times. what kind of statistical test should he run?
The statistical test which should be run by Dr wade Wilson is independent sample t test.
To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups. An example of a parametric test is the Independent Samples t Test. Additionally called the Independent t Test.
When you wish to compare the means of just two groups—no more, no less—use an independent samples t test! This test is typically used to detect whether two population means differ.
Hence if dr. wade wilson is interested in whether or not people who watch adventure movies actually have quicker reaction times than people who read literary novels then he must use independent sample t test.
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Number 49. Please help Graphing inequalities? Why is the answer A? Please do a step by step explanation for each answer choice.
I don't see the picture. Can you send it in the message.
If a fair die is rolled 4 times, what is the probability, rounded to the nearest thousandth, of getting at least 3 twos?
7.08 is the probability, rounded to the nearest thousandth.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur.
We can discuss the probabilities of various outcomes to determine how likely they are whenever we are uncertain about the result of an event. Statistics describes the examination of events subject to probability.
Probability of getting a six on rolling a dice = 1/3
Here ,
n = 4 , p = 1/3
So, For P(X <= 1) = P(X = 0) + P(x = 1)
4C0 * (1/6)^0 * (1 - 1/3)^(4-0) + 4C1 * (1/3)^1 * (1-1/3)^(4-1)
= 1 * 1 * (5/3)^4 + 4 * (1/3) *
= 5.75 + 1.33
= 7.08
= 7.08 (nearest thousandth)
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what is the value of 18 to the third power
Answer:
5832
Step-by-step explanation:
the confidence interval approach is the correct method by which to determine sample size. true false
The confidence interval approach is the correct method by which to determine sample size. True
Confidence Interval:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
Your desired confidence level is usually one minus the alpha (α) value you used in your statistical test:
Confidence level = 1 − α
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Find the volume of a cube if one face of which has an area of 64 sq.metre
The volume of a cube is 512 m3.
Given,
The one-face area is nothing but the area of a square since it is a cube.
So, (a2) = 64 m2.
Then, a = 8m
Hence, the side of the cube is 8 m.
Formula to calculate the volume of the cube :
The volume of the cube = a3
Volume = (8)3
Volume = 512m3
Therefore, the volume of the cube is 512m3.
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Just answer it, dont have to show work
The equations that are false for all real numbers of x are given as follows:
x² + 4 = 0.square root of x - 1 = -2.2(x - 4) = 2x - 4.How to obtain the equations which are false?To obtain the equations which are false, we have to consider the domain and the range of the functions in this problem.
We start at the first equation, given as follows:
x² + 4 = 0.
Isolating x², we have that:
x² = -4.
However, the range of the function y = x² is composed only by non-negative numbers, meaning that y = x² will never assume a value of -4, meaning that this statement is false for all real numbers.
The same holds true for the third item, which is the square root of x - 1 = -2. The range of the square root function is also composed by non-negative numbers, thus the statement is also false for all real numbers.
The final statement that is false is given as follows:
2(x - 4) = 2x - 4.
Applying the distributive property, we have that:
2x - 8 = 2x - 4
0x = 4
x = 4/0 (division by zero does not exist on the real set).
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Which is the equation for a line that passes through
the points (-6, -13) and (-12, 5)?
Answer:
y = -3x - 31
Step-by-step explanation:
y = mx + b
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex] m=\frac{5-(-13)}{-12-(-6)} [/tex]
[tex] m=\frac{18}{-6} [/tex]
m = -3
y = -3x + b
-13 = -3(-6) + b
-13 = 18 + b
b = -13 - 18
b = -31
I have this question can anyone solve
The double bar graph collected from the survey is given by the image presented at the end of the answer.
How to build the double bar graph?A bar graph shows the number of times that each observation appears in the data-set.
The double bar graph means that for each input on the bar graph, there are going to be two bars.
The meaning of each bar is given as follows:
Number of people who like watching the sport.Number of people who like participating in the sport.The colors for each bar are given as follows:
blue bar: people who like watching the sport.red bar: people who like participating in the sport.Then the data of the table is used to give the height of each bin in the double bar graph.
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Problem 5 Claire is planning to buy a phone plan for two cell phones that costs $350 for the phones themselves and $65 per month for service. Claire's daughter offers to chip in $125 for her phone and $12 per month for her phone. Write as many expressions as you can to represent the cost to Claire of the two phones and their service for m months.
The cost to Claire for the phones and their service for m months is $350 + $65*m.
The cost to Claire for the two phones is $350, and the cost for the service for m months is $65m, for a total cost of $350 + $65m.
What are expressions to represent the cost to Claire?Generally, Claire will pay a total of $350 + $65*m for the two phones and their service for m months.
The total cost for Claire for the two phones and their service for m months is $350 + $65*m.
The cost of the phones and service for m months to Claire is $350 + $65*m.
Claire will pay $350 for the phones and $65m for the service for a total of $350 + $65m for m months.
The cost to Claire for the two phones and their service for m months is $350 + m*$65.
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We need help please.
Answer:
The slope is 3 or 3/1.
Step-by-step explanation:
I figure this out by finding out the two beginning points with this: (x1, y1) , (x2, y2). The two beginning points (-3, -5) , ( -2,-2). Then from there you are counting by 3 to get to the next point. I hope this helps.
what is infinity times infinity (it was a bonus question)
Answer: infinity
Step-by-step explanation:
Elena's distance and times for a training run are given by the equation y=8.5x, where x represents distance in miles and y represents time in minutes
Elena is covering a distance of 8 miles in one minute.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.
Given is that Elena's distance and times for a training run are given by the equation → y = 8.5x
Now, if we consider the equation, it can be seen that the number {8.5} gives the unit rate or slope of the graph of the straight line. So, she is running at a speed of 8.5 miles per minute.
Therefore, Elena is running at a speed of 8.5 miles per minute.
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A beetle is moving along a straight line at a constant rate. It moves 23 of a foot in 15 of a minute.
What is the average speed of the beetle?
The average speed of the beetle is 1.53 feet per minute.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, it moves 23 of a foot in 15 of a minute.
Here, the average speed
= 23/15
= 1.53 feet per minute
Therefore, the average speed of the beetle is 1.53 feet per minute.
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There are two investment options:
Option 1: An initial investment of $5 that increases by 50%
every year.
Option 2: An initial investment of $0.01 that doubles
every year.
Part A
Write an equation for each option to model the value A of the account after œ years.
Part B
Explain which investment will eventually have the greatest value.
The exponential functions obtained from the details of the question indicates the investment that will eventually have the greatest value is option 2.
What is an exponential function?An exponential function is a function that has the argument as an index of a constant value.
The details of the two investments are presented as follows;
Option 1; Initial investment = $5
Percentage by which the investment increases every year = 50%
Option 2; Initial investment = $0.01
Amount by which the investment increases every year = The investment doubles every year
Part A;
The investment model in option 1 follows a compound interest pattern, which is an exponential function, therefore;
Amount, A = P·(1 + r)⁽ⁿ⁻¹⁾
Where, P = The principal invested = $5
r = The interest rate = 50% = 0.5
n = The number of years of investment
Therefore, A = 5 × (1 + 0.5)⁽ⁿ⁻¹⁾
The investment pattern of option 2 also follows an exponential function pattern of the form;
aₙ = a·r⁽ⁿ⁻¹⁾
Where;
aₙ = The amount or value of the investment after n years = A
a = The first term = $0.01
r = The common ratio = 2
n = The number of years
Therefore, A = 0.01×2⁽ⁿ⁻¹⁾⁾
Part B
The growth factor of option 1 is 1.5 while the growth factor of option 2 is 2, however the initial value of option 1 makes the amount of option 1 initially larger than the amount from option 2
At the point the value of both investment are the same, we get;
0.01×2⁽ⁿ⁻¹⁾⁾ = 5 × (1 + 0.5)⁽ⁿ⁻¹⁾
Solving indicates, n ≈ 22
Therefore, the value of investment 2 eventually grows to that of investment 1 after 22 years, and based on the equations, surpasses the value of investment 1
The investment that will eventually have the greatest value is investment 2
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5. Which of the following is an arithmetic
sequence?
A
B
C
D
-2, -5, -8, -11, -14, -17, ...
0,5, 0, 10, 0, 15, ...
2, 4, 8, 16, 32, ...
5, 11, 17, 23, 29, 36, ...
Answer:
A. -2, -5, -8, -11, -14, -17, ...
Step-by-step explanation:
The difference between consecutive terms is constant.
What is 213 divided? Also how do you break 23 into tens and ones?
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
5/7 of.... is 1/7. What is the missing number?
The missing number is [tex]\frac{1}{5}[/tex]
Let the missing number be x.
now, [tex]\frac{5x}{7}[/tex] = [tex]\frac{1}{7}[/tex]
on cross multiplying we get,
x= [tex]\frac{7}{35}[/tex]
on simplifying,
x= [tex]\frac{1}{5}[/tex]
Hence, the missing number is [tex]\frac{1}{5}[/tex]
What is cross multiplying?
An equation involving a variable as a component of two fractions set equal to one another can be solved by cross multiplying. Cross-multiplying lowers the proportion to one straightforward equation, enabling you to solve for the variable in issue. The variable serves as a placeholder for an unknowable number or quantity.
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A kangaroo hopped directly toward a lake at a constant velocity for 30seconds. In one-third of that time, the kangaroo hopped 60meters. What was the kangaroo's velocity?
Answer: The animal hopped 60 meters in 10 seconds
6 m/s (lol)
Step-by-step explanation:
First off ok and second off bye <3
which statement must be true?
Answer:
DF=FE
Step-by-step explanation:
first to make it easier we can find the angles to each side
the sum of all angles of a triangle equal 180 degrees so to find x we set all the angles equal to 180
(3x+5)+(4x-15)+(2x+10)=180
9x+0=180
/9. /9
x=20
now we can find each angle
3(20)+5
60+5
D=65 degrees
4(20)-15
80-15
E= 65 degrees
2(20)+10
40+10
F=50 degrees
Angle D and E are the only angles equal to each other so answer C and d ARE INCORRECT
Since there are 2 of the same angles this is an isosceles triangle
the 2 of the same angles are the base so the side going up are connecting to the top angle F so the sides will be DF and FE and these are equal
hopes this helps
Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50
The number of boxes of sugar that Alonso can buy are 4.5 boxes.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.
The money remaining after buying 12 eggs : {r} = $(55 -2.75).
Cost of one box of sugar = $11.5
The number of boxes that he can buy are -
n = (55 - 2.75)/11.5
n = 4.5 boxes {approx.}
Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.
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The number of fish in a pond decreased by this year compared to last year.
Last year, there were fish in the pond.
How many fish are in the pond this year?
Answer:
number from last year - number of decrease
Step-by-step explanation:
The numbers are missing from the problem, but this is what you need to do.
Start with the number of fish in the pond last year.
Subtract the number of decrease.
s: One skis fast.
Express the statement One does not ski fast symbolically.
The given statement can be expressed as ~S.
What is a negation of a statement?
A negation of a statement is a statement that is the opposite of the original statement. In other words, a negation of a statement is a statement that is true if and only if the original statement is false, and vice versa.
To express the statement "One does not ski fast" symbolically, we can use the negation symbol
Using the symbol "S to represent the statement "One skis fast", we can express the statement "One does not ski fast" symbolically as:
~S
This can be read as "Not S" or "It is not the case that S."
Hence, the given statement can be expressed as ~S.
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What values of b and c make AGHI AZYX?
G
b
||
CE
48
I
b
H
X
17
Y
8c
Z
The value of b = 17 and c = 6 makes ΔGHI ≅ ΔZYX.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Here, we have
Given the sides of both the triangle and
we have to find the value of b and c that makes ΔGHI ≅ ΔZYX
b = 17 and,
48 = 8c
c = 6
Hence, the value of b = 17 and c = 6 that makes ΔGHI ≅ ΔZYX.
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A circle has a diameter of 14 inches. A central angle of 85° intercepts an arc of the circle.
What is the intercepted arc length to the nearest tenth of an inch?
The intercepted arc measures 11.78 to the closest tenth of an inch.
What is intercepted arc?Remember that an arc is a portion of a circle's circumference.
Therefore, an intercepted arc is an arc that is created when one or more chords or line segments intersect a circle and come together at a vertex.
It's vital to keep in mind that the lines or chords can come together inside, outside, or in the center of a circle.
An interrupted arc and the inscribed and central angles of a circle have some intriguing correlations.
An inscribed angle is created in geometry between chords or lines that cut through a circle.
The center angle is a joint created by the intersection of two radii.
According to our question-
angel/360=arc/circumference
85/360=
d= 14 inches
Hence, The intercepted arc measures 11.78 to the closest tenth of an inch.
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x − 3y = −12 2x − y = 1 (1 point) a line includes points 0 comma 1 and negative 3 comma negative 4. A line includes points 0 comma negative 4 and negative 6 comma negative 2 a line includes points 0 comma 4 and 1 comma 3. A line includes points negative 2 comma 2 and negative 4 comma 0 a line includes points 0 comma negative 1 and 1 comma negative 3. A line includes points 6 comma negative 10 and 3 comma negative 11 a line includes points 0 comma 4 and 3 comma 5. A line includes points 1 comma 1 and 2 comma 3
By graphing the system of equations, we can see that the solution is (3, 5).
How to solve the system of equations?
I assume we want to solve the following system of equations graphically:
x - 3y = -12
2x - y = 1
To do so we only need to graph both the lines on the same coordinate axis and find the point where the lines do intersect. The graph can be seen below.
There we can see that the intersection is at (3, 5), so that is the solution of the system of equations.
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True or false. When y is positive, the value of y^2 is always greater than the value of y. Why?
however if you have 0.5^2 which is 0.25 is that not smaller than 0.5
Answer: False
Step-by-step explanation:
If [tex]y=0.5[/tex], then [tex]y^2=0.25[/tex], whereas [tex]y=0.5[/tex].
Therefore, this is a counterexample. Hence, the statement is false.
Explain how the number line is used to determine the sum of -3 + 7 !!
Answer: Look at the explanation:
Step-by-step explanation: First, you start at -3 on the number line. Then, since we are adding 7, we would add 7 spaces to the right. That should lead us to our answer; 4. Another way how to model this is 7 + -3 or 7-3. They all equal 4. I hope this helped!
