There are 10,080 different ways in which the friends can seat on the circular table.
In how many ways the friends can seat?
There are 9 friends, such that two of them need to be separated by exactly two people.
Because the table is circular, we can consider the first position as the position where Bob is.
Now let's count the number of options for each of the other 8 positions. (counting to the left).
The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)
For the next seat, we could seat Anna or one of the remaining 5 friends.
Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.
The total number of combinations is given by the product between the numbers of options, so we have:
C = 7*6*5*4*3*2*1
But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.
C = 2*(7*6*5*4*3*2*1) = 10,080
There are 10,080 different ways in which the friends can seat on the circular table.
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Item 6
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Juan buys one of the thickest books on the shelf. Min buys the third thinnest book on the shelf.
How much thicker is Juan’s book than Min’s book?
Answer:
There is no line plot
Step-by-step explanation:
A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.
(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)
Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Researching the problem on the internet, the coordinates are as follows:
Rock (3,2).Treasure (x,y).Tree (16,21).The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:
[tex]Ts - R = \frac{5}{14}(Tr - R)[/tex]
Hence, for the x-coordinate:
[tex]x - 3 = \frac{5}{14}(16 - 3)[/tex]
x - 3 = 5 x 13/14
x = 7.6.
For the y-coordinate:
[tex]y - 2 = \frac{5}{14}(21 - 2)[/tex]
y - 2 = 5 x 19/14
y = 8.8.
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Answer: the answer is b
Step-by-step explanation:
Write this number in standard form: 5,000,000 + 200,000+ 8,000 + 400+60+9
Answer:
5,208,469
Step-by-step explanation:
5,000,000 + 200,000+ 8,000 + 400+60+9
5,000,000
200,000
00,000
8,000
400
60
9
5,208,469
Sampling is used in the situations
A. Cooking rice in an utensil
B. Purchase of food commodity from
C. shopkeeper
D. All the above
E. Blood test of the patients
Answer:
all of the above
Step-by-step explanation:
please mark me as brainliest
Graph the equation by plotting three points. If all three are correct, the line will appear. -3y=2x-7 ....... 20 POINTS
First lets simplify to slope intercept (y=mx+b)
y=[tex](2x-7)/-3[/tex]
y=-2/3x+7/3
Point 1: (0,7/3) as when x is 0, y=7/3.
Point 2: lets plug x in as 3 to cross cancel.
[tex]\frac{-2}{3} *\frac{3}{1} = \frac{-2}{1}[/tex]
So (3,-2).
Lets do point 3: plug in -3.
[tex]\frac{-2}{3} *\frac{-3}{1} = \frac{2}{1} = 2[/tex]
So (-3,2).
Your three points are (0,2.33 repeat) or (0,7/3), (3,-2) and (-3,2)
Hopefully this helps you out, heart if it was helpful and please do not hesitate to ask any questions. I have also attached an image of the line
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The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.
I put 1/2x (y+z), I just want to make sure! thank you.
Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
Which point on the number line represents the product (Negative 4) (negative 2) (negative 1)?
A number line going from negative 10 to positive 10. Point A is negative 8, point B is negative 7, point C is 7, point D is 8.
The point on the number line represents the product (- 4), (- 2), and (- 1) will be the negative 8. Then the correct option is A.
What is multiplication?It is also known as the product. If the object n is given to m times, then we just simply multiply them.
The point on the number line represents the product (- 4), (- 2), and (- 1) will be
Then the product will be
-4 x -2 x -1 = -8
Then the correct option is A.
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Question 4: 11 pts
Elena wants to earn at least $180 a week to help her parents with bills. She determines that
she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can
only work 13 hours per week. Write and graph a system of linear inequalities that shows the
number of hours she can work so she can help her parents. Use x for the number of hours
babysitting and y for the number of hours bagging groceries.
our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph can be seen at the end.
How to get the system of inequalities?Here we have the variables:
x = number of hours babysitting.y = number of hours bagging groceries.We know that she can only work 13 hours per week, then we have:
x + y ≤ 13.
And she wants to earn at least $180 per week, then:
x*$15 + y*$10 ≥ $180.
So our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).
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$10,000 is invested for 4 years at an annual simple interest rate of 16%.
Answer:
$16,400
Step-by-step Explanation:
Step 1: We multiply $10,000 by 16%, getting $1,600.
Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.
Step 3: Add that to $10,000. We get $16,400 as the answer!
Please mark me as brainliest! I really need it!!! Thanks!Answer:
Simple interest = P x r x t
= 10,000 x 16/100 x 4
= $6400
Final amount = P (1 +rt)
= 10,000 (1 + 16/100 x 4)
= $16400
(or you can just add the simple interest to the principle amount to get the final amount)
Please help me answer this question
Step-by-step explanation:
look at the attachment above
Answer:
[tex]\textsf{1)} \quad -\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}[/tex]
[tex]\textsf{2)} \quad - \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]
Step-by-step explanation:
Question 1
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration of $e^{ax}$} \\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{a}e^{ax}+\text{C}$\\\\for $a\neq 0$\\\end{minipage}}[/tex]
Given integral:
[tex]\displaystyle \int xe^{-4x}\:\text{d}x[/tex]
Using Integration by parts:
[tex]\textsf{Let }\:u=x \implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=e^{-4x} \implies v=-\dfrac{1}{4}e^{-4x}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x & =uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x\\\\\implies \displaystyle \int xe^{-4x}\:\text{d}x & =-\dfrac{1}{4}xe^{-4x}-\int -\dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}+\int \dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}-\dfrac{1}{16}e^{-4x}+\text{C}\\\\& =-\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}\end{aligned}[/tex]
Question 2
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\\ \end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
Rewrite the given integral:
[tex]\begin{aligned}\displaystyle \int \sin^5 x \: \text{d}x & =\int (\sin x)^4 \cdot \sin x \: \text{d}x\\& =\int (\sin^2 x)^2 \cdot \sin x \: \text{d}x\end{aligned}[/tex]
Use the trig identity [tex]\sin^2x+\cos^2x \equiv 1[/tex] to rewrite [tex]\sin^2x[/tex] :
[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x = \int (1-\cos^2 x)^2 \cdot \sin x \: \text{d}x[/tex]
Integration by substitution
[tex]\textsf{Let }\:u=\cos x \implies \dfrac{\text{d}u}{\text{d}x}=-\sin x \implies \text{d}x=-\dfrac{1}{\sin x}\: \text{d}u[/tex]
Therefore:
[tex]\begin{aligned}\implies \displaystyle \int \sin^5 x \: \text{d}x & = \int (1-u^2)^2 \cdot \sin x \cdot -\dfrac{1}{\sin x}\: \text{d}u\\& = \int -(1-u^2)^2 \: \text{d}u\\ & =\int -1+2u^2-u^4 \: \text{d}u\\& =-u+\dfrac{2}{3}u^3-\dfrac{1}{5}u^5+\text{C}\end{aligned}[/tex]
Finally, substitute [tex]u = \cos x[/tex] back in:
[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x=- \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]
Which are the foci of the hyperbola represented by 5y2 – 4x2 – 80 = 0?
(–6, 0) and (6, 0)
(0, –6) and (0, 6)
(0, –5) and (0, 5)
(–5, 0) and (5, 0)
The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
The equation of the parabola is given below.
5y² – 4x² – 80 = 0
Then the equation can be written as
y² / 4 – x² / 5 – 4 = 0
y² / 16 – x² / 20 = 1
Then the value of eccentricity will be
a² = 16 and b² = 20
Then we have
e = √[1 + (b² / a²)]
e = √[1 + (20 / 16)]
e = 1.5
Then the focus of the parabola will be
⇒ (0, ±ae)
⇒ (0, ± 4 x 1.5)
⇒ (0, ±6)
⇒ (0, –6) and (0, 6)
Then the correct option is B.
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Theresa uses a unique box in the shape of a trapezoidal prism for her specialty candles. The area of the bas
of the box for the smaller candle is 125 cm² and the box is 12 cm tall. The box used for the larger candle has
a base whose area is 160% that of the smaller box, and it is 6 centimeters taller.
What percent of the volume of the smaller box is the volume of the larger box?
Pls explain ur Answer<3
Answer:
eyyyyyyyyyy wassupppppppp
Answer:
240%
Step-by-step explanation:
Volume of a prism is Bh (area of the base * height)
Let's start with the small prism.
B=125
h=12
Volume = 125*12 = 1500 cubic cm
Bigger prism base are is 160% of 125. 1.6 * 125 = 200
Height is 6 cm more = 12+6 = 18
V = 200 * 18 = 3600
To find the percentage, divide 3600 by 1500. You get 2.4, which is 240%
For the graph y=41 find the slope
Answer:
m=0 , b=41
Step-by-step explanation:
y=41y=0x+41, y=mx +by=0x+41, m=0, b=41therefore m=0, b=41Megan bought 3 tickets to the ballet for $57.50. How much would it cost for her to buy 15 tickets?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
.Let S =(5, 10, 15, 20, 25, 30} be the sample space of an experiment and let T = {5,10}, V = {5, 20, 30} and W = {10, 15, 25} be the events of the experimen.
I meed the true answer. tnx!
A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.
What is a set?A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
The complete question is given below.
Q13.
T ∪ V = Data points that are in T or V or both.
T ∪ V = {5, 10, 20, 30}
Q14.
T ∩ W = Data points that are in T and W both.
T ∩ W = {10}
Q15.
W' = Data points that are not in W.
W' = {5, 20, 30}
Hence, the set of W' is {5, 20, 30}.
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Using the distance formula calculate the distance show me example
Answer:
[tex]4\sqrt{26}[/tex]
Step-by-step explanation:
The distance formula is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Thus we can plug the numbers in:
[tex]\sqrt{(-2-(-6))^2+(10-(-10))^2}[/tex]
[tex]\sqrt{(4)^2+(20)^2}[/tex]
[tex]\sqrt{16+400}[/tex]
[tex]\sqrt{416}[/tex]
[tex]4\sqrt{26}[/tex]
Which of the following expressions are equal to -8/11 - 3/4 - 1/4
In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.
With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.
Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.
The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.
Hopefully this helps you out, brainliest would help me out.
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I need help, I need to find the volume of this
Answer:
396 Km³to the nearest hundred400 Km³Step-by-step explanation:
volume of a cuboid = Length × Width × Height Cubic units
6 × 11 × 6 =
66 * 6 =
396 Km³
to the nearest hundred
400 Km³
How would you know the answer (important)
Answer:
okay so I can't see the last option on ur sheet but when u graph this equation the point that lies on the curve is (2,-3) so that is the vertex but if I move up this curved line it passes through the Y axis at (0,-1), the Last answer that I can't see it wouldn't happen to be (-1,6) would it
Use the drawing tool(s) to form the correct answer on the provided graph.
Consider the function given below.
Plot this piecewise function on the provided graph.
Drawing Tools
Select
Point
Open Point
Line Segment
Ray
●
O
y = -2;
-10
--5;
Click on a tool to begin drawing.
-8
7;
-6
-8 <
-2 < <5
≤ 9
5 < 1
10
8-
6-
4-
2
< -2
Delete
Undo
8
Reset
10
The attached graph represents the piecewise function.
How to plot the graph?The complete question is in the image
The function is given as:
[tex]f(x) = \left[\begin{array}{cc}3&x \le -3\\2x + 1&-3 < x < 4 \\-2&x \ge 4\end{array}\right[/tex]
Next, we plot the functions by their domain
See attachment for the piecewise function.
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if f(x)=x+10 find f(7)
Answer:
17
Step-by-step explanation:
→ Substitute 7 f(x) into the function
7 + 10
→ Solve
17
Answer:
f(7) = 17
Step-by-step explanation:
To find f(7), substitute x = 7 in the function. Thus, you will receive:
[tex]\displaystyle{f(7)=7+10}\\\\\displaystyle{f(7)=17}[/tex]
Henceforth, the value of f(7) is 17.
Learn More:
https://brainly.com/question/27923727Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
How to solve separable differential equation
In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.
[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]
[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]
[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]
[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]
If u = ㏑ y and du = dy/y, then:
[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]
[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]
[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]
[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]
[tex]C = (\ln e)^{3}[/tex]
[tex]C = 1[/tex]
And finally we get the explicit expression:
[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]
[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
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Please answer all three questions Pleaseeeeee tysmm <3
Answer: 2 3/4 > 2.68 is correct (only)
Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68
The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.
Sqrt(63) = 7.93, and 7.93 > 8.11 is false.
Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2
Use the graph to Write an equation of the line(3,165)(1,55)
Answer:
y=55x
Step-by-step explanation:
(y1-y2)/(x1-x2)=(165-55)/(3-1)=55
55 is the slope
To find y-intercept:
y=55x+b
substitute 1 for x and 55 for y
55=55(1)+b
b=0
So y= 55x
the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
where (x₁, y₁) is one of the points on the line, m is the slope of the line.
First, calculate the slope (m) using the given points (3, 165) and (1, 55):
m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55
Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:
y - 165 = 55(x - 3)
Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):
y - 165 = 55x - 165
To isolate y, add 165 to both sides:
y = 55x
So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.
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sub to oiVJDF NvlC Nvlkjxdv Nlkj;zsdn
Mr.Baker is making a box using all of a 48-inch strip of oak. the box will be 14 inches wide. how long will the box be?
The length of the box made by Mr. Baker is 10-inch
Mr. Baker has strip of 48- inch long oak, by this strip he is making the rectangle box of width 14-inch.
The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.
As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.
The width of the box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches
Thus the Mr. Baker made the box which is 10 inches long.
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Tim has 9 pencils in his book bag. Jaime has 3 more pencils than Tim. Which of the following equations would describe n, the number of pencils that Jaime has in her book bag?
Which of the numbers below are whole numbers?
A. 6282
B. 650
C. 87
D. 99.8
E. 442.49
F. 1/10
Answer: A B C
Step-by-step explanation:
A whole number is like 1,500 and a nonwhole number is like 33.2 or like 55/100.
And have a good day.
An elephant went 119 km moving 42 km/h how many hours did the journey take?
2 1/6
2 1/2
2 5/6
Answer:
1 HR ---> 42 km
? .----> 119 km
119 * 1/42
2.833
Answer:
[tex]\boxed {2 \frac{5}{6}}[/tex]
Step-by-step explanation:
Formula used :
[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]
Solving :
Time = 119/42
Time = 17/6
Time = 2 5/6 hours
The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)
(t − 7)2 = (t + 7)2 − 112
t =
Answer:
No solution
Step-by-step explanation: