Using the arrangements formula, it is found that there are 1152 ways for the students to be arranged alternatively at the table.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
With the art students at the odd numbered places and the science students at the even numbered places, there are 4! x 4! ways.Same number of ways if they exchange, art even and science odd.Hence the number of ways is:
2 x 4! x 4! = 1152
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:26
Step-by-step explanation:
Answer:
102cm^3
Step-by-step explanation:
Chuck's birthday is 2 days before Linus's.
Lucy's birthday is 3 days after Marcy's.
Patty's birthday is 4 days before Lucy's. If
Marcy's birthday is March 10, when is
Patty's birthday?
Answer:
march 9
Step-by-step explanation:
10+3-4
=9
I think that's the answer
which table represents a linear function? y=3,7,11,15 y=3,8,15,21 y=3,9,3,9 y=3,9,27,81?
The table that represents a linear function is y=3,7,11,15
How to determine the table?For a table to represent a linear function, the table must have a constant rate of change i.e. a common difference
From the list of options, we have:
y=3,7,11,15
The difference between each y value is 4
i.e. 7 - 3 = 11 - 7 = 15 - 11 = 4
Hence, the table that represents a linear function is y=3,7,11,15
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Factor completely x^8- 16.
Answer:
Step-by-step explanation:
So in this example we'll be using the difference of squares which essentially states that: [tex](a-b)(a+b)=a^2-b^2[/tex] or another way to think of it would be: [tex]a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})[/tex]. So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:
[tex]x^8-16 = (x^4-4)(x^4+4)[/tex]
Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:
[tex]x^4-4 = (x^2-2)(x^2+2)[/tex]
So completely factored form is: [tex](x^2-2)(x^2+4)(x^4+4)[/tex]
I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because [tex]x^2+4 = x^2-(-4)[/tex]. and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: [tex]x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)[/tex] just something that might be useful in some cases.
We can factor this into [tex](x^{4}+4)(x^{4} -4)[/tex].
This is because we use difference of two squares where [tex]x^{2} -y^{2} = (x+y)(x-y)[/tex]
So we rewrite x^8-16 to x^8-4^2.
This can then be written to the equation I put at the start.
p.s. The reason its [tex]x^{4}[/tex] is because [tex]x^{4} * x^{4} = x^{8}[/tex]
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)
Which expression is equivalent to (3x² + 4x-7)(x-2)?
A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)
B. 2x(3x² + 4x-7)
OC. x(3x² + 4x-7) - 2
D. x(3x2 + 4x-7)+2(3x² + 4x-7)
Answer: A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)
Step-by-step explanation:
The expressions are equivalent by the distributive property.
Consider the function f(x) = 10(x2 – 7x). what are the additive and multiplicative inverses?
Answer:
Additive = -10x^2+70x
Multiplicative = 1/10x(x−7)
Step-by-step explanation:
The multiplicative inverse of a number is the reciprocal of that number. Since 10(x^2−7x)⋅ 1/10x(x−7)=1 , then 1/10x(x−7) is the multiplicative inverse of 10(x^2−7x) .
Since 10(x^2−7x)−10x^2+70x=0 , then −10x^2+70x
is the additive inverse of 10(x^2−7x).
Find the area of this,
Simplify your answer completely.
Answer:
[tex] \frac{2}{15} {cm}^{2} [/tex]
Step-by-step explanation:
Area of Rectangle = Length x Breadth
=
[tex] \frac{1}{5} \times \frac{2}{3} \\ = \frac{2}{15} {cm}^{2} [/tex]
Five times a number is greater than 25.
5x>25
x>5
Hope it helps!
Geometry
Surface area and volume
Answer:
[tex]volume=558.9[/tex]
Step-by-step explanation:
find the volume of the cone and the hemisphere and add them together
cone:
[tex]Vcone=\pi r^{2} \frac{h}{3} \\\\V=\pi (5.3)^2(\frac{8.4}{3} )\\V=\pi (28.09)(2.8)\\V=247.09\pi \\V=247.1[/tex]
hemisphere:
[tex]Vhemisphere=\frac{2\pi r^3}{3} \\V=\frac{2\pi (5.3)^3}{3} \\V=\frac{2\pi (148.877)}{3} \\V=\frac{297.754\pi }{3} \\V=\frac{935.421}{3}\\ V=311.8[/tex]
add the volumes together:
[tex]Vol=247.1+311.8\\Vol=558.9[/tex]
Jamie had seven posters, but only 3 could fit on his closet door. How many different ways can he arrange the three posters out of the seven on his door?
A. 52.5
B. 210
C. 1260
D. 5040
Answer:
210 ways
Step-by-step explanation:
7 P 3 = 210 ways
or 7 C 3 = 35 choices of 3 posters which can bearrranged in 6 different ways 6 * 35 = 210 ways
If the standard notation (original number) is 0.004430 cm, what would the sign of the exponent be?
Zero
Positive
Negative
Answer:
Negative
Step-by-step explanation:
When you move the decimal place to the right, the exponent in scientific notation is negative. In other words, when you are converting a number smaller than 1 into scientific notation, the exponent will be negative. In this case, because you are moving the decimal place to the right 3 places, the new number would be 4.430 x 10⁻³ cm.
When you move the decimal place to the left, the exponent in scientific notation is positive.
12) Becky bought a digital camera on the installment plan. The purchase price was $859.95. She paid $150 down
and made 12 monthly payments of $65.25. Find the finance charge she paid.
O a.) $71.45
Ob.) $75.35
Oc.) $74.50
Od.) $73.05
A teacher takes her AP calculus class of 8 students to lunch. They sit around a circular dining table.
a. How many seating arrangements are possible?
b. How many seating arrangements are there if the teacher has to sit on the chair closest to the soda fountain?
c. Among the students are one set of triplets. How many seating arrangements are there without all three of them sitting together?
Step-by-step explanation:
it is 8+1 people (8 students and 1 teacher).
a.
how many seating arrangements are possible ?
start with any of the 9 seats. there are 9 possibilities who will sit in that chair.
the next seat has then only 8 possibilities left. the next one 7. the next b one 6. and so on.
so, all possibilities are
9×8×7×6×...×1 = 9! = 362,880
b.
if the teacher is fixed to a specific seat, then this position is constant in all seating arrangements.
that means for the variable part we have only 8 people remaining.
and that gives us now only
8! = 40,320
possibilities
c.
how many combinations are there for the triplets, when they sit together, to arrange their internal sitting sequence ?
3! = 6
and we need to block these 6 combinations for each of the freely selectable seats as starting seat for such a block of 3.
to visualize this, let's give each seat an identifier.
we have the seats s1, s2, s3, ... s8, s9.
for all the combinations of these 9 seats, we need to eliminate the 6 combinations, where the triplets sit on s1, s2, s3.
and then the 6 combinations, where they sit at s2, s3, s4.
and then at s3, s4, s5. then at s4, s5, s6. ... s8, s9, s1. and s9, s1, s2.
it is not clear if b. still applies here (and the teacher has a fixed seat), or if we are back to the general a. scenario.
if we have again all 9 people picking their seats freely, and we only block the triplets from sitting together, then we need to block these 6 combinations for each of the 9 seats (as visualized above) giving us
9! / (9×3!) = 362,880 / 54 = 6,720 remaining possibilities.
if we have again the teacher blocking one fixed seat, then we need to block the 6 triplets combinations theoretically for each of the 8 remaining seats as above.
but : the teacher is now a separator disabling some of these blocks of 3.
e.g. let's say the teacher's seat is s9. then the teacher automatically separates the triplets in otherwise "illegal" blocks of 3.
s7, s8, s1 is now a valid seat combination for the triplets (because there is the fixed s9 in between).
the same for s8, s1, s2.
so, we need to eliminate the 6 combinations not for all 8 starting seats, but only for 6.
and that gives us
8! / (6×3!) = 40,320 / 36 = 1,120 remaining possibilities.
Which number line represents the solutions to 1-2x) = 4?
O+
O
O
O
-10 -8 -6 -4 -2 0 2 4 6
-10 -8 -6 -4 -2 0 2 4
+
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10 -8 -6 -4 -2 0
8
6
++
10
8 10
2 4 6 8 10
Answer: Option (3)
Step-by-step explanation:
[tex]|-2x|=4\\\\|2x|=4\\\\|x|=2\\\\x=\pm 2[/tex]
The number line represents the solutions to |-2x| = 4 is Number line C.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation: |-2x| = 4
We know the value inside the mod is always positive.
So, 2x = ±4
x= ±4/2
x= ±2
Thus, the required number line is C.
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In a video game, two objects move around the screen according to the equations r = 4cos(θ) and r = –1 2cos(θ). which coordinates represent a possible collision point of the objects?
The coordinates represents a possible collision point of the objects according to equations r = 4cos(θ) and r = –1/ 2cos(θ) cos(∅) are (-2,2π/3).
Given Equations r = 4cos(θ) and r = –1 2cos(θ).
We have to find the coordinates of collision.
The first object is moving around the screen r = 4cos(θ).
The second object is moving around the screen r = –1 /2cos(θ).
According to question
Coordinate can be found out by equating both the equations.
4cos(θ) =–1 /2cos(θ)
2cos(θ)=-1
cos(θ)=-1/2
θ=[tex]cos^{-1} (1/2)[/tex]
=120°
θ=-2π/3
Therefore the two equations are equal when
θ=2π/3
we have
r=4 cos(2π/3)=-2
and r=-1+2 cos(2π/3)
r=-2
Hence the coordinates that represent the collision point are (-2,2π/3).
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Answer: Option A on EDGE
Just took test
Step-by-step explanation:
Find cos(A). Show your work and reduce the ratio if necessary
Using relations in a right triangle, it is found that:
cos(A) = 3/5 = 0.6.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 30.The hypotenuse has length 50.Hence:
cos(A) = 30/50 = 3/5 = 0.6.
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Please help!!! Select the quadratic equation that has no real solution.
Answer:
[tex]25x^2-10x+4[/tex]
Step-by-step explanation:
You can use the quadratic formula to determine if a quadratic equation has real or imaginary solutions. The quadratic formula is: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]. What really matters in this case is the discriminant, which is the stuff under the radical which is: [tex]b^2-4ac[/tex]. This is because the solutions are only imaginary, if the discriminant is negative, because then you would be taking the square root of a negative number. So let's look through each example:
[tex]25x^2+20x-4[/tex]; a=25, b=20, c-4: [tex]20^2-4(25)(-4) = 800[/tex]. By examining this one example, it's important to note, if you have one negative number as a or c, then it cancels out the negative sign in the -4, and it becomes positive. So let's look at examples where a or c doesn't equal a negative number OR both a and c equal negative, that way they cancel out and over -4ac is still negative.
[tex]25x^2-10x+4[/tex]; a=25, b=-10, c=4. In this case both a and c are positive so -4ac will remain negative. This gives you: [tex](-10)^2-4(25)(4) = 100-400 = -300[/tex]. So this has a negative discriminant meaning it will have no real solution but rather imaginary solutions
For every 6 students who purchase a bag of M&M’s, there are 5 students who purchase a pack of gum. Use M for the number of students purchasing bags of M&M’s and G for the number students purchasing packs of gum, write an equation for this statement.
Answer:
M/6 = G/5
Step-by-step explanation:
We are given a relation between the numbers of students in two different groups. That relation can be used to write an equation.
Groups who bought M&Ms
If we consider M&M buyers to be 6 in a group, then the number of those groups is ...
M/6
Groups who bought gumSimilarly, the number of groups who bought gum will be ...
G/5
where there are 5 gum-buyers in each group.
EquationThe problem statement tells us that for each group of one kind, there is a matching group of the other kind. That is, the numbers of groups are equal:
M/6 = G/5
why do the graphs tan(x) and y=x^3 look alike?
The key features of the graph include the fact the graphs are periodic.
How to illustrate the graph?It should be noted that a graph is a diagram that represents ban interrelations between variables.
The tan graph is simply the visual representation of the tangent function for a range of angles.
In this case, the graphs have been attached and it can be seen that the tan graph repeats every 180° and is not a continuous curve.
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Answer: it is a ratio of vertical alignment w.r.t horizontal alignment
Step-by-step explanation:
The main difference is that graph of tan(x) is the ratio of sin(x)/cos(x) that is it is a ratio of vertical alignment w.r.t horizontal alignment whereas graph of x^3 is not trigonometric but algebraic in nature as ( x×x×x).
Question 12 of 40 Given right triangle ABC, which of the following statements must be true? Check all that apply. A C A. sin C = cos(90° - C) B. ZA and ZC are complementary C. sinC = cos(A-90°) D. sinC = cos(90° - A)
Angles are complementary
Option B and A are correctAnswer:
A and C are complementarty
sinC=cos90-C
Step-by-step explanation:
Just took the exam on a pex
good luck homedawg
You buy tomatoes in 25 pound cases. One portion of salad requires .75 ounces of tomatoes. How many portions can be made with one
case?
The amount of the portions can be made with one case will be 399.25 ounces.
What is conversion?Conversion means to convert the same thing into different units.
You buy tomatoes in 25 pounds (11.34 kg) cases.
We know that 1 pound (0.45 kg) is equal to 16 ounces (0.45 kg).
Then the number of the ounces in 25 pounds (11.34 kg) will be
⇒ 25 x 16
Multiply the numbers, then the expression will be
⇒ 400 ounces (11.33 kg)
In 25 pounds of tomatoes, there will be 400 ounces.
One portion of salad requires 0.75 ounces (0.02 kg) of tomatoes.
Then the amount of the portions can be made with one case will be
⇒ 400 – 0.75
⇒ 399.25 ounces
Thus, the amount of the portions can be made with one case will be 399.25 ounces.
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determine the slope of a line that is parrallel to the equation 3x + 6y =18
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of a line that is parallel to the equation [tex]\bf{3x+6y=18}[/tex].
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
First we should divide the whole equation by 6,
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}}[/tex] | simplify
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope-\dfrac{1}{2}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Educator should teach children how to properly use yard sticks to measure
a True b False
It is a. True that educators should teach children how to properly use yardsticks to measure.
What is a yardstick?A yardstick is a standard long tool used to measure lengths. It contains three feet, 36 inches, or 0.9144 meters.
Since it is three times the length of a standard ruler of 12 inches, it is recommended for teaching children.
Thus, truly, educators should teach children how to properly use yardsticks to measure.
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Given: Triangle ABC, AC=BC, AB=3, line segment CD is perpindicular to line segment AB, CD= sqrt 3 find AC
Based on the data given, the length of line segment AC is 2.29
What is the length of side AC?Based on the given data:
AC=BCAB=3line segment CD is perpendicular to line segment ABCD= sqrt 3The triangle ABC is an isosceles triangle.
The line segment AC is the hypotenuse of the the triangle ACD.
The length of AD = 3/2
[tex]AC = \sqrt{(\sqrt{3)^{2}} + (\frac{3}{2})^{2}}= 2.29[/tex]
In conclusion, the length of AC is 2.29
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please help ..
Use the function f(x) = 2x2 − x − 10 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
I have part a and b
The end behavior is that as the value of x increases the value of function increases.
How to get the graph of a function?A) We want to completely factor; f(x) = 2x² - x - 10
⇒ f(x) = 2x² - 5x + 4x - 10
⇒ 2x(x + 2) - 5(x + 2)
⇒ (2x - 5)(x + 2)
B) The x-intercept occurs at y = 0. Thus;
(2x - 5)(x + 2) = 0
x =5/2 and x = -2
C) f(x) = 2x² - x - 10
Thus, the end behavior is that as the value of x increases the value of function increases.
D) The graph steps has been attached
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he circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for Media and Engineering combined is 31,250,000, what is the total annual budget? Media 4% Support 19% Editorial 6% Engineering 21% Research 32% Sales 18%
Answer:
let's playthe games questiontag
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.
The two ways that can be used to find the area of a trapezoid include:
A = (a + b) × h/2A = a × hHow to illustrate the information?It should be noted that a trapezoid simply means a four sided shape that has parallel sides.
To find the area of the shape goes thus:
Find the length of each base.
Find the height of the trapezoid.
Substitute the values into the formula: A = (a + b) × h/2
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The surface area of a sphere is 6477 square inches. Which equation can be used to solve for the radius of the
sphere?
64m 4mr
647=2m³
6477= 2m²
64- 4m²
The expression πr² = 6477 can be used to solve for the radius of the sphere.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
Area of sphere A = 6477 square inches
A = 4πr²
A = 6477
4πr² = 6477
πr² = 6477
Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.
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If a, b and c are integers, which of the following statements is/are TRUE?
If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.
What is the proves?Note that:
If a|(bc), then a|b is true If ab|bc, then b|c is trueBecause:
Suppose one say a|b. Then one can see that an integer do exist which is n such that b = an.
Hence:
bc = (an)c = a(nc), so a|(bc) (the reverse is still the case or still applies)
Therefore, If a, b and c are integers then the correction option in the above case is that both equation 1 and 2 are correct.
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Place the steps for finding f(x) in the correct order.
H
11
K
f(1) = 41 + 7
0·0-0-0-0
For finding the inverse of a function you have to write it as an ecuation.
[tex]y = 4x + 7[/tex]
Invert the values of x and y.
[tex]x = 4y + 7[/tex]
Our objetive now in this new equation is to clear y. First, subtract 7 in both sides of the equation.
[tex]x - 7 = 4y[/tex]
Then, divide both sides by 4.
[tex] \frac{x - 7}{4} = y[/tex]
Finally, invert the values of x and y again and put the equation like a function.
[tex] {f}^{ - 1} (x) = \frac{x - 7}{4} [/tex]
This is correct because f(x) = x is the axis of symmetry for both functions (green one).