Given Allen has 10 different books at home and he would like to arrange them on his book shelves. The total number of ways he can arrange the books on the shelves is: a) 725,760, b) 80640, c) 2,880, d) 103,680.
a) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that two of the books: "Robinson Cruso" and "C Programming" cannot be next to each other.
Using permutation formula, we can get the total number of ways that he can arrange the books where two books, Robinson Cruso and C Programming, can't be next to each other:
Total number of ways = 10! - (9! x 2!)
= 725,760
b) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that the book: "Robinson Cruso" cannot be the first nor the last book in the row.
Using permutation formula, we can get the total number of ways that he can arrange the books, where the book Robinson Cruso cannot be the first nor the last book in the row:
Total number of ways = 8! x 2!
= 80640
c) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on two shelves putting 6 books on the top shelf and 4 books on the bottom shelf (in rows) so that the book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one.
The book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one. We can arrange these 2 books on the shelves in 1 way. There are 5 books remaining that he can arrange in 5! ways on the top shelf and 4 books remaining that he can arrange in 4! ways on the bottom shelf.
Therefore, the total number of ways he can arrange the books on the shelves is:
Total number of ways = 1 x 5! x 4!
= 2,880
d) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on three shelves putting 3 books on the top shelf, 3 books on the middle shelf, and 4 books on the bottom shelf (in rows) so that "C programming" and "SPSS" are both on the top shelf and "Harry Potter" cannot be on the bottom shelf.
Two of the books, "C programming" and "SPSS", are on the top shelf. We can arrange these 2 books in 2! ways.
There are 2 other books that can be arranged on the top shelf in 2! ways.
One of the books, "Harry Potter", cannot be on the bottom shelf. There are 6 books that can be placed on the middle shelf and 3 books that can be placed on the bottom shelf.
Therefore, the total number of ways he can arrange the books on the shelves is:
Total number of ways = 2! x 2! x 6! x 3!
= 103,680
Answer: a) 725,760b) 80640c) 2,880d) 103,680
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Need someones help on this!
Find the general solution for the differential equation
x sinθ dθ + (x3− 2x2cosθ) dx = 0
Therefore, x^2 - x^2cosθ + C = 0 is the general solution of the given differential equation.
General solution of the given differential equation is x^2 - x^2cosθ + C = 0, where C is the constant of integration.
To solve the differential equation, we have to integrate the given equation. Here, x sinθ dθ + (x^3 - 2x^2cosθ) dx = 0.
Let's integrate it using separation of variables.
x sinθ dθ = - (x^3 - 2x^2cosθ) dx
Dividing both sides by x^2, we get
sinθ dθ/x - (x - 2cosθ) dx/x^2 = 0
Now, integrate the above equation.
∫sinθ dθ/x - ∫(x - 2cosθ) dx/x^2 = ln|C|
Simplifying the above equation, we get
- cosθ/x + 1/x - x^(-1) sinθ = ln|C|
Multiplying both sides by -x, we get
cosθ - x + x^2 sinθ = -x ln|C|
Rearranging the terms, we get
x^2 - x^2cosθ + ln|C| = 0
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Snowy's Snowboard Co. manufactures snowboards. The company used the function P(x) = -5x2 -30% + 675 to model its profits, where P(x) is the profit in thousands of dollars and x is the number of snowboards sold in thousands. How many snowboards must be sold for the company to break even?
The number of snowboards that must be sold for the company to break even is: 9000
How to solve Profit Functions?The function that models the profit is given as:
P(x) = -5x² - 30x + 675
where:
P(x) is the profit in thousands of dollars
x is the number of snowboards sold in thousands
For the company to break even, it means that P(x) = 0. Thus:
-5x² - 30x + 675 = 0
Using quadratic formula to solve this gives us":
x = [-(-30) ± √((-30)² - 4(-5 * 675)]/(2 * -5)
x = 9
This is in thousands and means the break even will be when the sold amount is 9000 snowboards
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Si se tiene una tabla de 2.0 m de largo y de ancho 0.3 m, el área de toda la tabla es?
Answer:
solo multiplica los dos numeros 2x3= 6.
Answer:
aeaa axxd
Step-by-step explanation:
PLS PLE HELP IM BETYINY AND DONT GIVE ME THOSE LINKS THAT GIVE U A VIRUS
A small town is trying to establish a transportation system of large and small vans.
It can spend no more than $100,000 for purchasing both sizes of vehicles and no
more than $500 per month for maintenance. The town can purchase a small van for
$10,000 and maintain it for $100 per month. The large vans cost $20,000 each and
can be maintained for $75 per month. Each large van carries a maximum of 15
passengers
and each small van carries a maximum of 7 passengers. Find the
maximum number of passengers the transportation system can handle given the
constraints. How many large and small vans will they need to maximize the
number of passengers it can service?
32 is 10% of what number?
Find an equation of the plane tangent to the following surface at the given point. z=8-2x²-2y²; (5,3, – 60) Z=
z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
Given the function is z=8-2x²-2y² and point is (5, 3, – 60).
We need to find the equation of the plane tangent to the given surface at the given point. The gradient vector of the function f(x, y, z) is given by(∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k∂f/∂x= -4x and ∂f/∂y= -4y
Therefore, the gradient vector is given by-4xi -4yj + k
Therefore, the equation of the tangent plane is given byz - z1=∇f(x1, y1) . (x - x1)i + ∇f(x1, y1) . (y - y1)j + (-1) [f(x1, y1, z1)]
where (x1, y1, z1) is the given pointWe have f(5, 3, – 60) = 8 – 2(5²) – 2(3²) = – 60
Therefore, the equation of the plane is given byz + 60= (-20i - 12j + k) . (x - 5) - (16i + 24j + k) . (y - 3)
Thus, z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
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calculate the power of the pump which can lift 400kg of water to be stored in a water tank at a height of 19m and 40s (take g=10/s2)
What is the solution to this system
Answer:
the solution to the system is (1,3)
Step-by-step explanation:
x = 1 , y = 3
What is the vertex of the graph of the function f(x) = x2 + 8x - 2?
O (4.18)
O (0,-2)
O (-8,-2)
0 (4-18)
Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) = [tex]ax^{2} +bx +c[/tex]
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = [tex]x^{2} +8x - 2[/tex] a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = ([tex]-4^{2}[/tex]) + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
Answer:
Option D, (-4,-18)
Step-by-step explanation:
got it right on edge
1. What values of a, b, and c would you use in the quadratic formula for the following equation?
5x^2 +9x=4
A.a= -4, b = 9, c = 5
B.a=5, b= 9, c = -4
C.a=5, b= 4, c = 9
D.a= 5, b = 9, c=4
Answer:
D
Step-by-step explanation:
because it is the answer that I think of
how do i find a unit rate
Answer:
numerator divided by denominator
Step-by-step explanation:
The perimeter of a triangle is 44 inches. The length of one side is twice the length of the shortest side, and the length of the other side is eight inches longer than the length of the shortest side.
Choose a variable and tell what that variable represents.
Answer:
side a = Smallest = 9 inches
side b = 18 inches
side c = 17 inches
Step-by-step explanation:
The formula for the perimeter of a triangle = side a + side b + side c
side a = Smallest
The perimeter of a triangle is 44 inches.
The length of one side is twice the length of the shortest side
Hence:
b = 2a
The length of the other side is eight inches longer than the length of the shortest side.
Hence,
c = 8 + a
Hence, we substitute into the Intial formula
a + 2a + 8 + a = 44 inches
4a + 8 = 44
4a = 44 - 8
4a = 36
a = 36/4
a = 9 inches
Solving for b
b = 2a
b = 2 × 9 inches = 18 inches
Solving for c
c = a + 8
c = 9 inches + 8 = 17 inches
Rectangular prism surface area
Answer:
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
What single or double digit numbers make a SUM of 40?
Please help, I will award brainliest, rate, and thank. Please include all possible answers!!!
No links, no fake answers, you will be reported.
The sum numbers are 1, 2, 4, 5, 8, 10, 20, 40
how do you put this writing expression into a equation;
A number added to 13 all divided by 2
Answer:
Step-by-step explanation:
Let x be the number.
(x + 13)/2
How many solutions does the function x^2+2x+2x=0
a. 0
b. 1
c. 2
d. 3
Answer:
Equation is a quadratic equation (polynomial ax+by+c with highest degree 2), so it has two solutions.
Answer:
B. is correct because it only can go 1 way.
Step-by-step explanation:
4 Luke's math scores for this grading period are listed below. 84, 86, 83, 78, 92, 87, 92, 90, 88, 86 What is the mean of the data set graphed on the dot plot? (10 Points) X X Х ХХ ХХХ xx 日中 85 90 95 70 75 80 F H
Answer:
86.6
Step-by-step explanation:
Add them all up and divide by how many scores
state the equation of a line with slope m=2 and y intercept =3 then graph the line
Answer:
y=2x+3
The coefficient attached to x is the slope and the number being added to it is the y intercept.
Please see the attached image
Please help me! Only have about 10 minutes until I have to submit this assignment!
Answer:
626
Step-by-step explanation
HELPPPPPPP
What is the value of x?
Answer:
the angles are supplementary
so, 5x + 140 = 180
5x = 180 - 140
5x = 40
X = 40
5
X = 8
Write the equation of the
line that is parallel to
y = 1.5x – 6 and passes
through the point (4,2).
The equation of the line is (y - 2) = 1.5(x - 4)
What is line ?
Euclid described a line as an "unextended length" that "stands equally with respect to its points"; he introduced the postulates as the main unprovable properties from which he constructed all of geometry, now called Euclidean geometry to avoid confusion with other geometries introduced from the late 19th century (such as non-Euclidean, projective and affine geometry).
In modern mathematics, given the multiplicity of geometries, the concept of line is closely related to the way geometry is described. For example, in analytic geometry, a plane line is often defined as a set of points whose coordinates correspond to a given linear equation, but in a more abstract setting, such as drop geometry, the line may be an object other than the set. of the points located on it.
When geometry is described by a set of axioms, the concept of line is usually left undefined (so-called primitive object). The properties of the lines are then determined by the axioms that refer to them. One of the advantages of this approach is the flexibility it gives users of the geometry. Thus, in differential geometry a line can be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and allows physicists, for example, to think of the path of a light ray as a line.
Given, [tex]y = 1.5x - 6....(1)[/tex]
We are comparing equation (1) with y = mx+c and get m = 1.5
It is also given required equation passes through the point (4,2)
We know, if slope of a equation m and the equation passes through (a,b) then equation of the line (y-b) = m (x-a)
Here,
[tex]m = 1.5 \\ a = 4 \\ b = 2[/tex]
So, required equation of the line [tex](y - 2) = 1.5(x - 4)[/tex]
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f(x) = = -X1 + X1X2 X2 – I1X2 Determine if this function is Lipschitz continuous (specify local or global). Note that this function is defined on R2.
Previous question
To determine if the function[tex]F(x) = -x1 + x1x2x2 - i1x2[/tex]is Lipschitz continuous, we need to examine its partial derivatives and check if they are bounded.
The function F(x) is defined on [tex]R^2,[/tex] so let's calculate its partial derivatives with respect to x1 and x2
∂F/∂x1 = [tex]-1 + x2^2[/tex]
∂F/∂x2 = [tex]x1x2 - i1[/tex]
Now, to determine Lipschitz continuity, we need to check if the partial derivatives are bounded on the given domain.
For ∂F/∂x1, we can see that it is not bounded because as x2 approaches positive or negative infinity, the value of ∂F/∂x1 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x1 is not bounded.
For ∂F/∂x2, we can also see that it is not bounded because as x1 approaches positive or negative infinity, the value of ∂F/∂x2 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x2 is not bounded.
Since both partial derivatives are not bounded, we can conclude that the function F(x) = -x1 + x1x2x2 - i1x2 is not Lipschitz continuous, neither locally nor globally, on the domain [tex]R^2.[/tex]
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Mrs. Baxter deposits $2,000 in an account that earns 5% sample
interest, How much interest does Mrs Batter's investment en ter
8 years
The answer is $480!
Answer:
$800 in interest
Step-by-step explanation:
T = A(1 + rt)
T = 2,000(1 + .05(8))
T = 2,000(1.4)
T = 2800
2800 - 2000 = 800
ederal Government Employee E-mail Use It has been reported that 88% of federal government employees use e-mail. If a sample of 210 federal government employees is selected, find the mean, variance, and standard deviation of the number who use e-mail. Round your answers to three decimal places.
The mean, variance, and standard deviation of the number of federal government employees who use e-mail can be calculated using the binomial distribution formula.
Given that 88% of federal government employees use e-mail, we can define the probability of success (p) as 0.88 and the number of trials (n) as 210.
The mean of a binomial distribution is given by μ = np, where μ is the mean and n is the number of trials. Therefore, the mean of the number of federal government employees who use e-mail is μ = 210 * 0.88 = 184.8.
The variance of a binomial distribution is given by [tex]\sigma^2 = np(1-p)[/tex], where [tex]\sigma^2[/tex] is the variance and n is the number of trials. Therefore, the variance of the number of federal government employees who use e-mail is σ^2 = 210 * 0.88 * (1-0.88) = 21.504.
The standard deviation of a binomial distribution is the square root of the variance. Therefore, the standard deviation of the number of federal government employees who use e-mail is σ = sqrt(21.504) ≈ 4.637.
In summary, the mean of the number of federal government employees who use e-mail is 184.8, the variance is 21.504, and the standard deviation is approximately 4.637. These values represent the average, spread, and deviation from the mean, respectively, for the number of federal government employees who use e-mail in a sample of 210 individuals.
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Help There are 7 red marbles and 5 blue marbles in a bag.
(a) What is the ratio of red marbles to blue marbles?
(b) What is the ratio of blue marbles to all marbles in the bag?
How many solutions does the equation 5x + 3x – 4 = 10 have?
O Zero
O One
O TWO
O Infinitely many
be
????
Answer:
Step-by-step explanation:
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This Must Only Have One Solution, Because The Right Side Of The Equation Is Just Plainly Ten. Lets Solve This:
5x + 3x - 4 = 10
Add Four To Both Sides To Begin Simplifying.
5x + 3x = 14
Now, Combine Like Terms.
8x = 14
Divide:
8x/8 = 1X = X
14/8
X = 14/8
14/8 = 1.75
X = 1.75
Check:
(5 * 1.75) + (3*1.75) - 4 = 10
8.75 + 5.25 - 4 = 10
14 - 4 = 10
10 = 10.
This Is True, So X Does Equal 1.75
Helppp me please if u can thx .
What is the lateral surface of the prism shown here
If you know the answer pls help I’ll give brainliest
Answer:
The lateral surface area of the prism shown is 1021 unit^2.
Step-by-step explanation:
2((21*9)/2) + (17*16) + (21*16) + (14*16) = 1021 unit^2
Answer: The lateral surface area of a prism is the sum of the areas of its lateral faces. The total surface area of a prism is the sum of the areas of its lateral faces and its two bases
=ph where p represents the perimeter of the base and h represents the height of the prism.
Part C
Calculate the ratio of the lengths of the two line segments formed on each transversal. You will have two sets of calculations. Round your answers to the hundredths place. What do you notice about the ratios of the lengths for each transversal? How do they compare?
Answer:
Line segment PM = 4.2 length
ML = 6.2
ON = 3
NK = 2
Step-by-step explanation:
Just got it on plato your welcome:)
The segments formed by each transversals and the three parallel lines are
proportional according to the three parallel lines theorem.
The observations are;
The parallel lines divide the transversals in equal proportions, such that the ratio of the lengths of each transversal are equal.[tex]\displaystyle \mathrm{ Ratio \ of \ the \ segments ;\ }\frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}}[/tex]Reasons:
The question is a four part question
Let the equations of the parallel lines be as follows;
Line, x; y = x
Line, y; y = x + 1
Line z; y = x + 2
The points at which transversal 1 intersect the lines x, y, and z, are;
A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)
The length of segment [tex]\overline{AB}[/tex] = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)
The length of segment [tex]\mathbf{\overline{CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)
The ratio of the lengths of the segment formed by transversal 1 is therefore;
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{CB}}{\overline{AB}}} =\frac{2 \cdot \sqrt{37} }{2 \cdot \sqrt{37} } = 1[/tex]
The points at which transversal 2 intersect the lines x, y, and z, are;
D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)
The length of segment [tex]\overline{DE}[/tex] = √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)
The length of segment [tex]\overline{EF}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)
[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{EF}}{\overline{DE}}} =\frac{0.2 \cdot \sqrt{17} }{0.2 \cdot \sqrt{17} } = 1[/tex]
Therefore;
[tex]\displaystyle \frac{\overline{CB}}{\overline{AB}} = \frac{\overline{EF}}{\overline{DE}} = 1[/tex]Which gives;
The proportion with which the parallel lines divide the transversals are equal.The ratio of the lengths for each transversal are equal.The the comparison can also be made with the triangle proportionality theorem.
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