₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!
Further explanation of combination and permutationThe term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1
In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6
ABCACBBACCABBCACBAAll the items above are different permutations however for combination they are same.
The difference mathematically is dividing by the number of arrangements
₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1
₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6
Therefore ₃C₃ = ₃P₃ / 3!
similarly
₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!
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{ ( - 4, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) } Write the set using set notation and in ascending order.
By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.
For this exercise, the elements of the given data set would be listed in ascending order as follows:
Set = {-4, -3, -3, -1, 0, 1, 2, 2}
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Factor: 64x³ + 125y³
64x³+125y³
= (4x+5y)( 16x²-20xy+25y²)
a³ + b³ = ( a + b )( a² - ab + b² )
64x³ + 125y³
= ( 4x )³ + ( 5y )³
= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]
= (4x+5y)( 16x²-20xy+25y² )
Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola bars and a box of tissues.
If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?
A. $3.92
B. $24.71
C. $40.50
D. $116.91
If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.
How is the total amount determined?Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.
We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.
Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.
The cost of gas per gallon = $2.91
The number of gallons of gas bought = 10
The total cost of gas = $29.10 ($2.91 x 10)
The total cost of granola bars and tissues = $11.40
The total amount spent = $40.50 ($29.10 + $11.40)
Thus, mathematically, Sebastian spent C. $40.50 at the gas station.
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A school is arranging a field trip to the zoo. The school spends 654.84 dollars on passes for 32 students and 2 teachers. The school also spends 281.92 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The money was spent on a pass and lunch for each student is $28.07
How to calculate the amount?It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.
Therefore the amount spent on pass will be:
= Total amount / Number of people
= 654.84 / 34
= 19.26
The amount spent on each student will be:
= 281.92 / 32
= 8.81
The amount spent in pass and lunch will be:
= 19.26 + 8.81
= $28.07
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Mara solved an exponential equation by using logarithms. This is her work.
Latex: 7 \cdot 3^x=189
7
⋅
3
x
=
189
7
⋅
3
x
=
189
Latex: 3^x=27
3
x
=
27
3
x
=
27
Latex: \log _3\!(3^x)= \log _3\!27
log
3
(
3
x
)
=
log
3
27
log
3
(
3
x
)
=
log
3
27
Latex: x \log _3\!3=9
x
log
3
3
=
9
x
log
3
3
=
9
Latex: x \cdot 1=9
x
⋅
1
=
9
x
⋅
1
=
9
Latex: x=9
x
=
9
x
=
9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3
b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3
c) The mistake she made throughout is not applying the basic rule of logarithm.
How to solve Exponential Equations using logarithm?
She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;
Step 1. 7 x 3^x = 189
Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.
Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3
Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;
x log 3 = 3log 3
Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3
Step 6. x = 9; This is wrong because x = 3
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Complete question is;
Mara solved an exponential equation by using logarithms. This is her work.
1. 7 x 3^x = 189
2. 3^x = 27
3. log^3 (^3) = log^27
4. xlog^33=9
5. x * 1 = 9
6. x = 9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.
C = $3,173 + $31u
If the company wants to keep the cost of operation under $14,000 per month, what is the maximum number of units they can produce?
A. 3,490
B. 350
C. 3,491
D. 349
If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.
How to find the number of units?Given function:
C = $3,173 + $31u
Hence,
Let u represent number of units
Let c represent the operation cost
Where c = $14,000 per month
$14,000 = $3,173 + $31u
Combine like terms
$14,000 - $3,173 = $31u
$10,827 = $31u
Divide both side by $31u
u = $10,827 / 31
u = 349 units
Therefore the correct option is D.
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△MNP≅△QST.
What is m∠S?
Enter your answer in the box.
Answer:
78°
Step-by-step explanation:
∠M=∠Q
∠N=∠S
∠P=∠T
Answer:
m∠S =78°---------------------
Given
Two congruent triangles △MNP≅△QSTWe know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):
∠M ≅ ∠Q, ∠N ≅ ∠S, ∠P ≅ ∠TAngle S corresponds to angle N, hence their values are equal:
m∠S = m∠N = 78°Given: 5(2x-4)=10
Prove: x=3
Drag the correct reason to the box.
After simplifying an equation the value of x is x = 3.
What is solving an equation?
Unifying Principle for Equation Solving
By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.
The variable term on one side of the equation can be separated using addition or subtraction.
To find the variable, use multiplication or division.
Consider, the given equation
5(2x - 4) = 10
10x - 20 = 10 Removing parenthesis
10x -20 + 20 = 10 + 20 Adding 20 on both sides
10x = 30 Simplifying
x = 3 Dividing both sides by 10
Hence, the value of x is, x = 3.
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1. A cone-shaped filter has a diameter of 10 inches and a height of 4 inches.
What is the volume of liquid the filter can hold? Round your answer to
the nearest hundredth.
The volume of liquid contained by cone is 105 inches cube.
What is volume?
It can be defined as the total content which can be held inside a container.
Main body:
the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] , where r = radius and h = height of cone
diameter = 10 , so radius = d/2 = 5 inches
V = [tex]\frac{1}{3}\pi 5*5*4[/tex]
V = 3.14 *5*5*4*1/3
v≈105 inches cube
Hence the volume is 105 inches cube.
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The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975. Judge whether a t-interval could be constructed using the data in the sample.
It could be said that the normal probability plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
If the data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975., on analysing
The normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
Therefore, It could be said that the normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
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Nolan went shopping for a new pair of sneakers because of a sale. The store was offering a 25% discount. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?
The number is 0.75.
From the question, we have
The store was offering a 25% discount.
number = 1-0.25
=0.75
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
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A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent
Step-by-step explanation:
there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.
so, the tax is $1.50 for every $100 of the assessed value of the house.
how many $100 units are in that value ?
180,000 / 100 = 1,800 units.
that means the tax for that house is
1800 × 1.5 = $2,700
in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be
2700 / 12 = $225.00
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and
a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Answer:
Strings packs cost $14 each
Step-by-step explanation:
Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Lenny: 2s
Lashae: 2s + b
when b = $16 then these equations are:
Lenny: 2s
Lashae: 2s + 16
together they spent $72 so:
lenny + Lashae = $72 or:
2s + 2s + 16 = 72
subtract 26 from both sides:
2s + 2s + 16 - 16 = 72 - 16
2s + 2s = 56
combine s terms:
4s = 56
divide both sides by 4:
4s/4 = 56/4
s = $14
For a 14-person team, how does the actual weekly labor cost compare to the target?
$15 over target $300 over target $600 over target
$1,800 over target
$6,000 over target
The actual weekly labor cost compared to the target is 240 hours
What are Time and Work?
According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.
The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.
Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.
Given
Regular Rate $15.00/hr
Overtime Rate $22.50/hr
Targeted Labour Cost $12,000/wk
Labour Hours Needed 800/wk
According to the question:
Overtime means each employee can work beyond the input of 40 hrs. Per week.
Labor requirement = 800 hrs.
14 men labor capacity = 14× 40 = 560 hrs.
So overtime hours required = 800-560=240 hrs
Hence,
The actual weekly labor cost compared to the target is 240
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A hexagon has exterior angle measures of (7n + 3), (10n-17)°,
(8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
Find the value of n.
Using the sum of exterior angle, the value of n is 11.
In the given question,
A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
We have to find the value of n.
As we know that the sum of exterior angle of any polygon is equal to 360°.
As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
So we can find the value of n by adding the all measures.
So the expression should be
(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°
Simplifying the bracket.
7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°
Solving the expression by solving the same term
(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°
33n-3 = 360°
Add 3 on both side
33n-3+3 = 360°+3
33n = 357°
Divide by 33 on both side
33/33 n= 363°/33
n = 11
Hence, the value of n is 11.
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Red- 5 skittles
Purple- 8 skittles
Yellow- 1 skittle
Orange- 2 skittles
Green- 4 skittles
Tomas reaches in a bowl and pulls out a green skittle. Without replacing the green skittle, what is the probability he picks a yellow skittle.
A. 1/100
B. 1/80
C. 1/95
D. 1/76
Answer:
I think its C. 1/95
Step-by-step explanation:
I am not sure this is the answer, i haven't done this math in ages so I'm a bit rusty so good luck on the test!
What is 10,483,190 in word form?
Answer:
Ten million, Four hundred eighty-three thousand, one hundred ninety
Step-by-step explanation:
Break it down! into the tens digit, hundreds digit, etc.
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
Answer:
none of them
Step-by-step explanation:
5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)
At the toaster company, the weekly cost to run the factory is $1400 and the cost of producing each toaster is an additional $4 per toaster. Find a function rule representing the weekly cost in dollars, f(x), of producing x toasters.
Answer:
I believe... f(x)=1400+4x
the side length of a square is √8 find the area.
is the number rational or irrational?
The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.
Is the number behind the area of the square a rational number?
Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:
A = l²
Where l is the side length of the square.
First, substitute the side length of the square in the area formula:
A = (√8)²
Second, use algebraic properties to simplify the expression and find the corresponding result:
A = ([tex]8^{\frac{1}{2} }[/tex])²
A = 8
This number represents a rational number as 8 is equivalent to the rational number 8 / 1.
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how to interpret data from a frequency distribution
Answer:
The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.
The number written on the right of each category is its frequency
Step-by-step explanation:
The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters
The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.
What is the length and width of the rectangle?The perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let x represent the width be represented by variable x.
Width w = xLength l = x + 6Perimeter = 64Plug the values into the equation above above.
P = 2( l + w )
64 = 2( (x + 6 ) + x )
64 = 2( 2x + 6 )
64 = 4x + 12
64 - 12 = 4x
52 = 4x
x = 52/4
x = 13
Hence, the dimensions of the rectangle are;
Width = x = 13m
Length = x + 6 = 13 + 6 = 19m
Therefore, the dimension of the rectangle are 13m by 19m.
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Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
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The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.
Answer: $4x4x
Step-by-step explanation:
Directions - Write an equation in slope-intercept (y = mx + b) form for each line.
The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2
How to determine the equation of the line?From the graph, we have the points to be given as
(-3,0) and (0,2)
Start by calculating the slope of the points using the following slope equation
m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3,0) and (0,2)
So, we have
m = (2 - 0)/(0 + 3)
Evaluate
m = 2/3
The equation is then calculated as
y = m(x - x₁) + y₁
Where
(x, y) = (0, 2) and m = 2/3
So, we have
y = 2/3(x - 0) + 2
Expand
y = 2/3x + 2
Hence, the equation in slope intercept form of the line is y = 2/3x + 2
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Name the points. I give you brainiac or whatever.
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
What are two other names for AB?
Will give Brainliest, answer quick please.
The other names of AB in the given figure are
collinear pointsline segmentWhat are collinear points?Collinear points refers to points that lies on the same plane and on the same straight line.
The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear
Points A, B and C are non colinear to points Q and R
Points AB are still part of line AC hence can be noted as part of line segment BC.
The line has arrow head and may also be called rays. In this case the are part of an arrow
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Solve the equation in the image below correct to 2 decimal places. in Logarithm Terms
The solution to the given equation is 5.630.
What is a logarithmic equation?
An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Here, we have
2^(x+1) = 3^(2x-5)
Taking logarithms on both sides, we get
(x+1)log2 = (2x - 5)log3
xlog2 + log2 = 2xlog3 - 5log3
log2 + log3⁵ = 2xlog3 - xlog2
log 2* 243 = x(log6 - log2)
log486 = x(log6/2)
log486 = xlog3
x = log486/log3
x = 5.630
Hence, the solution to the given logarithmic equation is 5.630.
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