Edward will choose 8 songs to listen to during his exercise workout. If there are 11 songs to choose from, how many different exercise song combinations are possible?
Answers
Given that Edward will choose 8 songs to listen to during the workout from 11 songs and we need to find the possible combinations.
Then, the required combinations will be
\(C_8^{11}\)Now,the general fornm is written as
\(C_r^n=\frac{n!}{r!(n-r)!}\)Here n = 11 and r = 8. On solving we have
\(C_8^{11}=\frac{11!}{8!(11-8)!}=\frac{11\times10\times9\times8!}{8!\times3!}=\frac{11\times10\times9}{3\times2}=11\times5\times3=165\)Hence, the required combinations are 165.
Related Questions
Jim has 44 nickels and dimes totaling $2.95. How many nickels does he have?
Answers
Jim has 29 nickels.
What is a Linear equation in two variables?If it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Given that, Jim has 44 nickels and dimes totalling $2.95
Let the number of nickels be x and that of dimes be y,
According to questions.
0.05x + 0.10y = 2.95 ..........(i)
x + y = 44 .......... (ii)
Solving the equations we get,
x = 29 and y = 15
Hence, the number of nickels is 29 and that of dimes is 15
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Emma and Lauren read a total of 47 books. Emma reads 17 more books than Lauren. Enter the number of books lauren read
Answers
Answer:30
Step-by-step explanation:47-17 = 30
30/2=15
Lauren read 15 books
4. Snyder’s Moving company has two segments of customer: Small Business (SB) and Residential. 10% of Snyder’s 2,200 clients fall into both categories, using Snyder’s as their mover of choice for both their business and personal needs. The remaining clients are split evenly between segments. A client who falls into one category will use Snyder’s once every 3 years. Clients who fall into both categories use Snyder’s twice every 3 years. SB moves cost 15% more to the clients than Residential moves due to additional insurance costs for Snyder’s. The average profit Snyder’s makes per move, regardless of which type, is $260. Snyder recently launched a marketing campaign to all SB-only clients to encourage them to use Snyder’s for residential moves. 10% of recipients decided to do so. Assuming the campaign cost $500 to execute, how profitable was it?
$12,480
$25,240
$50,480
$56,240
Answers
If the campaign of Snyder’s Moving company costs $500 to execute, it has been computed that the profit will be C. $50,480.
How to calculate the profit?Firstly, the customer base will be:
= 50% × [2200 - (10% × 2200)]
= 50% × (2200 - 220)
= 990
The increase in customers will be:
= 10% × 990
= 99
The additional profit will be:
= [(99 × $260) - $500] × 2
= ($25740 - $500) × 2
= $50480
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Answer:
10% SB clients will move due to the promotion. The Profit will be $25,240
Step-by-step explanation:
Find the number of clients in both SB and personal:
10% x 2200 = 220
Find the number of SB clients:
(2200 - 220)/2 = 990 ( the rest of clients will be evenly splitted)
Find the number of SB clients who will move:
10% x 990 = 99
Find the profit due to the move: (Number of ppl moved x Average Profit - Initial Investment)
99 x $260 - $500 = $25,240
A ski patroller pulls a rescue toboggan across a flat snow surface by exerting a constant force of 25 pounds on a handle that makes a constant angle of 22° with the horizontal (see figure). Find the work W done in pulling the toboggan 100 feet. (Round your answer to two decimal places.)
W = ft-lb
Answers
The work W done in pulling the toboggan 100 feet is given as follows:
2,318.96 ft - lb.
How to calculate the work?The equation for the work is given as follows:
W = Fdcos(a).
In which the parameters are given as follows:
F is the force.d is the distance that the object was pulled.a is the angle used to pull the angle.The parameters values for this problem are given as follows:
F = 25, d = 100, a = 22º.
Hence the work is obtained as follows:
W = 25 x 100 x cosine of 22 degrees
W = 2,318.96 ft - lb.
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Find the largest three-digit number that can be written in the form 3^m + 2^n, where m and n are positive integers.
Answers
Answer:
985
Step-by-step explanation:
\(let\ m=6\)
\(3^{6}=729\)\(999-729=270\)
\(2^{8}=256\) and \(2^{9}=512\) which would be to big of a number.
\(3^{6}+2^{8}=729+256=985\)
Therefore the largest three-digit integer in this system is 985
what is the midpoint of the segment shown below? (3,5) (2,2)
Answers
Answer:
(5/2, 7/2)
Step-by-step explanation:
Use the midpoint formula to solve for the midpoint:
\((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\\(\frac{3+2}{2},\frac{5+2}{2})\\\\(\frac{5}{2},\frac{7}{2})\)
If one student was chosen at random, determine the following probabilities
Answers
Answer:
he was male I don't really know
8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answers
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
I am thinking of two numbers the sum of the two is 10 and the difference is six
Answers
Hello! Let's write this numbers as x and y.
We know:
x + y = 10
x - y = 6
Solving using the method of elimination:
Now we just have to replace where's x by 8 in one of the equations, look:
So, the first number is 8 and the second number is 2.
The James used their sprinkler for 40 hours last month and the Jenkins used their sprinkler for 35 hours. The total output of the two houses was 1525 L. If their combined rate of usage was 40 L/hr, what is the rate of usage for each house?
Answers
Answer:
Step-by-step explanation:
.................8908989
The relationship between discrete math course grades x and business calculus course grades y is represented by the scatterplot
which statement is correct
Answers
Answer: their both wrong
Step-by-step explanation:
Question #7
Jerry is creating a comer shelf for his house. Examine his sketch below.
8.5 in.
8.5 in.
Enter the area of the corner shelf, in square inches. Round your answer to the
nearest tenth.
Answers
Answer:
The area is 56.7 square inches
Step-by-step explanation:
Given
See attachment for corner shelf
Required
The area
The corner shelf is a quadrant with radius;
\(r = 8.5in\)
The area of a quadrant is:
\(Area = \frac{\pi r^2}{4}\)
So, the area of the corner shelf is:
\(Area = \frac{\pi * 8.5^2}{4}\)
\(Area = \frac{\pi * 72.25}{4}\)
\(Area = \pi * 18.0625\)
Take \(\pi\) as 3.14
\(Area = 3.14 * 18.0625\)
\(Area = 56.7\) -- approximated
A rectangle has an area of 1008
square feet. Its width is six feet less
than twice the length. Find the
measures of the length and width of
the rectangle.
Answers
9514 1404 393
Answer:
length: 24 ftwidth: 42 ftStep-by-step explanation:
The area is the product of length and width. If L represents the length, then the width is (2L -6), and the area is ...
L(2L -6) = 1008
L² -3L -504 = 0 . . . . . divide by 2, put in standard form
(L -24)(L +21) = 0 . . . . factor
L = 24 . . . . makes the first factor zero
W = 2L -6 = 2(24) -6 = 42
The length of the rectangle is 24 feet; the width is 42 feet.
What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Answers
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars.
Answers
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
What is meant by expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
The dollar amount the club would contain if they reached half of their goal T + 50.
The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.
The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.
The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
The complete question is:
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?
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Meredith drives 5 miles to the northeast, then 15 miles to the southeast, then 25 miles to the
southwest, then 35 miles to the northwest, and finally 20 miles to the northeast. How many miles is
Meredith from where she started?
Answers
Solve the inequality - 6 x > 42
what happens to the inequality sign when you divide by a negative number
Answers
Answer:
the inequality sign changes when dividing by a negative number
Answer:
x < -7
Step-by-step explanation:
-6x > 42
First you want to divide off -6 to isolate x
\(\frac{-6x}{-6}\) = \(\frac{42}{-6}\)
keeping in mind what you do to one side of the equation you have to do to the other side.
Whenever you divide with a negative number the inequality sign flips from < to > and vice versa.
after you divide off the -6 your left with x < \(\frac{42}{-6}\) which equals -7.
Hope this helps.
Measurement of angle q
Answers
Answer:
34º
Step-by-step explanation:
The sum of the angles in a triangle is 180º
m∠Q = 180 - 90 - 56
m∠Q = 34º
a) Choose two vectors vw in R2 and a third vector b also in R2, and express b as a linear combination of v,w by finding scalars c₁,c2 such that c₁v + c₂w = b. Sketch the situation in R2 with an illustration that uses the parallelogram rule. (b) Repeat part (a) with vectors in R3 such that the augmented matrix [v w | b] gives a consistent system, again illustrating by graphing but this time in R3. (c) Why is it harder to find a consistent system for part (b) compared to part (a)? Explain your idea clearly using complete sentences.
Previous question
Next q
Answers
a) The linear combination of v, w by finding scalars c₁, c₂ such that c₁v + c₂w = b is [v w | b]
b) The graph of the equation is attached below.
c) The matrix representation is a useful tool for finding linear combinations of vectors, but it becomes more complex as the number of dimensions increase.
A linear combination of two vectors is when a third vector is expressed as a sum of the two vectors multiplied by scalars.
In R2, this can be represented using a parallelogram, where the vectors are drawn and the third vector is the diagonal of the parallelogram.
To find the scalars, we use the matrix representation [v w | b]. If the matrix gives a consistent system, it means that the third vector b can be expressed as a linear combination of the two vectors v and w.
In R3, the matrix representation is still used but it becomes more challenging to find a consistent system because there are more variables involved.
The vectors are graphed in 3D, and the third vector is found as the diagonal of a parallelogram that is now a parallelepiped.
However, it may not always be possible to find a consistent system in R3, as the third vector may not lie in the plane formed by the two vectors.
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Suppose LCM(a,b) = 20160, a=60. Find the smallest possible value of b.
Answers
Answer:
see below
Step-by-step explanation:
given:
LCM(a,b) = 20160, a=60
find:
smallest possible value of b
solution;
60, b = 20,160
b = 20,160 / 60
b = 336
60 x 336 = 20,160
= 2⁶ x 3² x 5 x 7
= (2² x 3 x 5) x (2⁴ x 3 x 7)
= (60) x (336)
LCM(60,336) = 1680
consider the 2² x 3 to get the prime number:
= 336 x 12
= 4032
therefore,
LCM(60,4032) = 20160
The smallest possible value of b is 336.
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
We have been given that
LCM(a,b) = 20160 and a = 60
We have to determine the smallest possible value of b
Since the product of two numbers equals the product of their HCF and LCM.
⇒ 60 × b = 20,160
⇒ b = 20,160 / 60
⇒ b = 336
⇒ 60 × 336 = 20,160
We need to write 20160 as the product of its prime factors, which is 20160.
⇒ 2⁶ × 3² × 5 × 7
⇒ (2² × 3 × 5) x (2⁴ × 3 × 7)
⇒ (60) × (336)
⇒ LCM(60,336) = 1680
Therefore, the smallest possible value of b is 336.
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15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.
Answers
Answer:
13.27 cm
Step-by-step explanation:
I am using (xy) to mean the length of the side xy
7^2 + (xy)^2 = 15^2
49 + (xy)^2 = 225
(xy)^2 = 225-49
(xy)^2 = 176
Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm
13.3cm
Step-by-step explanation:
The Pythagorean theorem is a^2+ b^2 = c^2
Plug the values into the equation.
7^2+ b^2 = 15^2
Simplify.
49 ÷ b^2 = 225
Subtract 49 from both sides.
b^2 = 176
Take the square root of both sides.
vb^2 = v176
b=13.266
b=13.3cm
A worker on an assembly line is required to take a short break every 90 to 120 minutes. The worker begins his job at 7:45 a.m. Which is not a time the worker could take his break?
Answers
Answer:
7:46 - 8:59
Step-by-step explanation:
This is their first 1-89 minutes of work, thus they are not able to go on break yet.
If you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years, you get the age of President Clinton when he was first inaugurated. How old was President G.H.W. Bush when he was inaugurated?
Answers
Answer:
64Step-by-step explanation:32+14=46
Step-by-step explanation:
lf you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years, you get the age of President Clinton when ...
1 answer
Age of President G.H.W. Bush is 37.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Age of President Bush = 54,
So, Age of President Clinton
=(54/2) + 14
=27+14
=41
Now, Age of President G.H.W. Bush
=46/2+14
=23+14
=37
Hence, the age of President G.H.W. Bush is 37.
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The function g is defined as follows for the domain given.
g(x) = 2x+1,
domain = (-5, -1, 2, 3)
Write the range of g using set notation. Then graph g
Answers
Answer:
g(x): 2(-5)+1= -10+1=-9
2(-1)+1= -2+1=-1
2(2)+1= 4+1=5
2(3)+1=6+1= 7
Hence, the range of \(g\) using the set notation is \((-9,-1,5,7)\).
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The function g is defined as follows for the domain given.
\(g(x) = 2x+1,\) and domain \(= (-5, -1, 2, 3)\)
So,
\(x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7\)
Hence, the range of \(g\) using the set notation is \((-9,-1,5,7)\).
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exactly how many planes contain points j,k, and n?
Answers
GEOMETRY 100 POINTS
Find the length of BC
Answers
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
What is lim x → 0 e^2x - 1/ e^x - 1
Answers
Hello, please consider the following.
\(\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }\)
Thank you
Which statements are true about the figure? Check all that apply,
The figure is a triangular prism,
The figure is a rectangular pyramid,
The figure has 6 vertices,
The figure has 6 faces,
The figure has 9 edges,
WILL MARK 5 STARS PLEASE SOS
Answers
has 6 vertices
Find the rate of ounces of water needed for each packet of flavoring
Answers
Answer:
24 ounces/ 2 packets = 12 ounces/ packet
Step-by-step explanation:
23 (12 ounces/packet) = 276 ounces of water
The the rate of ounces of water needed for each packet of flavoring would be 12.
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.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is the packets of flavoring added to an specific amount of water to make soup.
Now, for 24 ounces of water, 2 packets of flavoring are needed.
Then, for 1 packet of flavoring, (24/2) or 12 ounces of water is needed.
For 5 packets of flavoring, (12 x 5) or 60 ounces of water is needed.
So, the rate of ounces of water needed for each packet of flavoring would be -
r = (60 - 24)/(5 - 2)
r = 36/3
r = 12
r = 12
Therefore, the the rate of ounces of water needed for each packet of flavoring would be 12.
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x² -81 = 0 please help me
Answers
x² - 81 = 0 can be factored as (x-9)(x+9)=0. Therefore, the solutions are x=9 and x=-9.