[tex]|\Omega|=8\cdot7=56\\|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{56}=\dfrac{1}{28}[/tex]
Which of the following is a fifth root of the given complex number?
Answer:
D
Step-by-step explanation:
This result is true by De Moivre's theorem.
Construct a square matrix A of order 3
[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].
When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so
[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]
anybody can help me?
The graph that corresponds to the proportional relationship M = 3n is graph vs.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the relationship is:
M = 3n.
Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.
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C --------------------q ???
3. Match the polynomial to it's correct name.
1. Quadratic trinomial
2. Cubic monomial
3. Linear binomial
4. Quartic trinomial
a. h(x) = 15x+2
b. j(x)=x²-3x³ + 9x²
c. f(x)= 3x² - 5x+7
d. 8(x)=-5x³
Answer:
1. to c.
2. to d.
3. to a.
4. to b.
Step-by-step explanation:
These answers should be right.
Hope this helps!
The matching of the polynomials to their correct names are:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
How to Identify the Polynomials?A polynomial is an expression having more than one algebraic terms.
1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.
2) A cubic monomial is defined as a a monomial that has a degree of 3.
3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.
4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4
Thus:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
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Question 2 of 25
f(x) = 6x + 4. Find the inverse of f(x).
O A. f¹(x) = 4 − 6x
Ỏ B. f-1(2) = *
O c. f¹(x) = -6
OD. f¹(x) = 6x − 4
I NEED YA HELP BRO.!
The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6
How to determine the inverse function?The function is given as:
f(x) = 6x + 4
Rewrite as:
y = 6x + 4
Swap x and y
x = 6y + 4
Subtract 4 from both sides
6y = x - 4
Divide through by 6
y = (x - 4)/6
Rewrite as:
f^-1(x) = (x - 4)/6
Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6
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A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of the ring-shaped solid that remains.
The volume of the ring-shaped remaining solid is 1797 cm³.
The volume is the total space occupied by an object.
The volume of a sphere of radius r units is given as (4/3)πr³.
The volume of a cylinder with radius r units and height h units is given as πr²h.
In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.
The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.
Therefore, the volume of the ring-shaped remaining solid is given as,
= (4/3)π(9)³ - π(5)²(18) cm³,
= π{972 - 400} cm³,
= 572π cm³,
= 1796.99 cm³ ≈ 1797 cm³.
Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.
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Eden just bought a trough in the shape of a rectangular prism for her horses. She needs to know what volume of water to add to the trough. She knows that the height of the trough is 13 inches shorter than the width, and that the length is 33 inches longer than the width.
The volume of the trough, V(w), can be modeled by a polynomial function, where w is the width of the trough. Which of the following correctly models the situation and gives the rate of change of the volume over a width of 38 inches to 53 inches?
A. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 2167 cubic inches per inch
B. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 7658 cubic inches per inch
C. V(w)=w^2 + 429w
Rate of Change: 520 cubic inches per inch
D. v(w) = w^2 + 20w - 429
Rate of Change: 111 cubic inches per inch
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
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EG is a tangent to the circle below at point F.
Calculate the size of angle x.
Give reasons for your answer.
[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)
[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)
Please help and explain! :( I really need this
Select the correct answer.
Consider the absolute value functions c and d
An absolute value function where red line d intercepts d of x at (0, 4) and vertex at (minus 1, 2)
Which statement correctly describes these functions?
A.
The maximum value of d is 5 less than the minimum value of c.
B.
The maximum value of d is 3 less than the minimum value of c.
C.
The minimum value of d is 3 more than the maximum value of c.
D.
The minimum value of d is 5 more than the maximum value of c.
Answer:
d - the minimum value of d is 5 more than the maximum value of c
Step-by-step explanation:
we can see from the graph that d has a minimum value
that value is at (-1, 2) and the minimum is 2
for c the vertex is where the graph reflects itself
that point is (-4, -3) and the maximum is -3
that means that the minimum value of d is 5 more than the maximum value of c because 2 - (-3) = 5
A rectangular container with a square base, an open top, and a volume of 1,372 cm3 is to be made. What is the minimum surface area for the container
The minimum surface area for the rectangular container is [tex]588cm^{2}[/tex].
How to find the surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up. Compared to the definition of the arc length of a one-dimensional curve or the definition of the surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is much more complex.
Let s be the side of the square base and h be the height.
Surface Area=[tex]s^{2}+4sh[/tex]
Volume=[tex]s^{2}h[/tex]
According to the question,
[tex]s^{2}h=1372\\ h=\frac{1372}{s^{2} }[/tex]
So, surface area=[tex]s^{2} +4s(\frac{1372}{s^{2} })[/tex]
=[tex]s^{2}+\frac{5488}{s}[/tex]
Differentiate with respect to s,
Surface area=[tex]2s-\frac{5488}{s^{2} }[/tex]
Now, [tex]2s-\frac{5488}{s^{2} }=0[/tex]
[tex]2s=\frac{5488}{s^{2} } \\2s^{3}=5488\\ s^{3}=2744\\ s=14[/tex]
Find the value of h from the volume.
[tex]14*14*h=1372\\h=\frac{1372}{14*14}\\ h=7[/tex]
Thus, the minimum surface area=[tex]14^{2}+4*14*7[/tex]
=[tex]588cm^{2}[/tex]
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Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2?
The statement which best describes the translation from the graph y= 6x² to the graph of y = 6(x+1)² is; The translation represents a unit shift rightward.
Which phrase best describes the translation from the graph?The translation involved in the transformation of the graph as given in the task content represents a rightward shift of the graph y = 6x² by 1 unit.
On this note, it follows that the translation involved between the two graphs is; a unit shift to the right.
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Answer:
Step-by-step explanation:
one unit to the right
Suppose the length of each sude of a square is decreased by 4 ft if the perimeter of the square is now 32 feet what was the original length of each side
Answer:
12ft
Step-by-step explanation:
length of one side of the square now
32ft / 4 = 8ft
length of one side of the square before decreasing the length
(original lenght)
8ft +4ft = 12ft
Can someone help with these geometry fill in blank questions? Just 9, 10, 11, 12.. it’s urgent
A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 31 customers an average of 40 days to find a job. Assume the population standard deviation is 10 days. Calculate a 99% confidence interval of the population mean number of days it takes to find a job.
Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are:
[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]
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Use the table to find the products of the two polynomials. Write your answer in
descending order. B) (x2 + x – 2)(4x2 – 8x)
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is:
= 4x⁴ - 8x³ + 4x³ - 8x² - 8x² + 16x
= 4x⁴ - 4x³ - 16x² + 16x
The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x
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The expression (x+5)(x+8)+(x+5)(2x-3) can be written as the product of (x+5) and
Not mathematics, but can someone help me, and tell me what grade I deserve?
Answer:
I am not sure how that works but from the way it look and adding it up it comes to 66.6 but I was thinking around 75 - 85
Step-by-step explanation:
You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor?.
Answer:
4 legs from the bed and 4 from the chair im guessing since not all have 4
Hope This Help
Answer:
4 legs from the bed and 4 from the chair
Step-by-step explanation:
im a math wizard fr
1
Which is the equation of a line that has a slope 1/2 and passes through point (2, -3)?
Oy-x-4
0y=x-2
Oy-x+2
Oy=x+3
Answer:
[tex]y = \dfrac{1}{2}x-4[/tex]
Step-by-step explanation:
Equation of line in slope y-intercept form:[tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]
[tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]
[tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]
Please help! Which is the solution set of the following inequality?
Answer:
x<3
Step-by-step explanation:
3x - 4 < 17 - 4x
So, the -4 shall cross to the other side and replace the -4x which will now take the place of where the -4 used to be and the signs of both digits will change to a positive (+)
Remember the inequality sign (<) shall not change
so now the equation shall appear like this;
3x + 4x < 17 + 4
add both sides and it will appear like this;
7x < 21
simplify both sides by 7 and you'll get
x < 3
A globe company currently manufactures a globe that is 20 inches in diameter. if the dimensions of the globe were reduced by half, what would its volume be? use 3.14 for π and round your answer to the nearest tenth. 166.7 in3 1333.3 in3 523.3 in3 4186.7 in3
The volume of the modified globe would be 523.3 cubic inches (Option 3)
What is the volume of the globe with modified dimensions?
Information Given
The current diameter of the globe = 20 inches
We know that the radius of a sphere (globe) is half its diameter.
⇒ The radius of the globe = 10 inches
If the dimensions of the globe were reduced by half, the new diameter would be, [tex]\frac{20}{2} = 10[/tex] inches.
⇒ New radius of the globe, [tex]r = 10[/tex] inches
Calculating the Volume of the Modified Globe
The volume of a sphere (globe) is given by,
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
Here, [tex]r[/tex] is the new radius of the globe.
∴ The volume of the new globe would be,
[tex]V = \frac{4}{3} \pi (5)^{3}[/tex]
Use [tex]\pi =3.14[/tex]
⇒ [tex]V = \frac{4}{3} (3.14) (5)^{3}[/tex]
⇒ [tex]V = 523.333..[/tex] cubic inches
Rounding off the result to the nearest tenth, we get,
[tex]V = 523.3[/tex] cubic inches
Thus, if the dimensions of the globe were reduced by half, its volume would be 523.3 cubic inches.
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Terry runs a snowplowing business. income from snowplowing is given by the function f(x) = 35.5x 6, where f(x) is the income in dollars and x is the snowfall in inches received during a winter. if during the years 2006 to 2011, terry’s town received 53, 42, 55, 63, 58, and 47 inches of snowfall, what was his income (in dollars) during those years?
If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.
Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6
We have to find the income in dollars received if f(x) shows the income.
Function is a relationship between variables and it have each value of y for each value of x.
To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.
f(53)=35.5*53+6=1887.5
f(42)=35.5*42+6=1497
f(55)=35.5*55+6=1958.5
f(63)=35.5*63+6=2242.5
f(58)=35.5*58+6=2065
f(47)=35.5847+6=1674.5
Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.
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What is the completely factored form of 6 x squared minus 13 x minus 5? (2x - 5)(3x 1) (2x 5)(3x - 1) (2x - 1)(3x - 5) (2x 1)(3x 5)
Answer:
(2x - 5)(3x + 1)
Step-by-step explanation:
6x² - 13x - 5
ax² + bx + c
ac = 6 × (-5) = -30
-30 = -15 × 2
-13 = -15 + 2
6x² - 13x - 5 =
= 6x² - 15x + 2x - 5
= 3x(2x - 5) + 1(2x - 5)
= (2x - 5)(3x + 1)
Answer: its a.) (2x-5)(3x+1)
Step-by-step explanation:
6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)
and got it right on the test review.
Alice is playing a game in which she will roll 4 6-sided dice at the same time. She gets 5 points for each die that shows an even result. Let x represent the total number of points awarded on any given toss of the dice. What is the expected value of x
The expected value of x is 10.
It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).
The expected value of this random variable is n*p = 4*1/2 = 2.
The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.
Thus E(X) = 5*2 = 10.
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Use matrix method to find the point of intersection between the lines:
5x+3y-35=0 and 3x-4y=-8
Hello !
[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]
[tex]\Leftrightarrow AX = B [/tex]
With
[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]
[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
The solution is given by [tex]X=A^{-1}B[/tex].
[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]
[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]
The point of intersection between the lines is (4;5).
Have a nice day
Answer:
Point of intersection (4,5)
Step-by-step explanation:
5x + 3y - 35 = 0
3x - 4y = -8
⇒ 5x + 3y = 35
3x - 4y = -8
Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.
[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]
[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]
AX = B
[tex]\sf X =A^{-1}B[/tex]
[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],
Find the workout in the document attached.
What is the rectangular form of z = 6 (cosine (3 pi/4) +isin(3 pi/4) )?
Answer:
the answer is C, I got it too from the website, I got the answer from it
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.
Her work is shown below.
V = four-thirds (8) cubed. V = four-thirds (512). V = StartFraction 2,048 Over 3 EndFraction meters cubed.
What is Yolanda’s error?
Yolanda should have found the volume by multiplying 8 by Two-thirds.
Yolanda should have found the volume by multiplying 8 by Four-thirds.
Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.
Yolanda should have found the volume with the formula V = two-thirds (8) cubed.
Yolanda’s error during the calculation of the volume is that A. Yolanda should have found the volume by multiplying 8 by Two-thirds.
How to illustrate the volume?It should be noted that the volume of a sphere is simply 4/3πr³.
In this case, the sphere and a cylinder have the same radius and height and the volume of the cylinder is 8 meters cubed.
Based on the information given, Yolanda’s error during the calculation of the volume is that she should have found the volume by multiplying 8 by two-thirds.
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Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
1. Lines a and b are parallel by the converse of alternate interior angles theorem
2. l║m by the converse of consecutive interior angles theorem.
What is the Converse of Alternate Interior Angles Theorem?Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.
1. Lines a and b are parallel.
What is the Converse of Consecutive Interior Angles Theorem?Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.
2. Lines l and m are parallel.
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What is the domain of the function y= 2√x-6?
0-00
O 0
O 3
O 6≤x<∞
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
The domain of the function y= 2√x-6 is [6, ∞).
What is a function?A relation is a function if it has only One y-value for each x-value.
In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.
Therefore, we have x - 6 ≥ 0
Adding 6 to both sides, we get:
x ≥ 6
So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.
In interval notation, we can write the domain as:
Domain: [6, ∞)
Hence, the domain of the function y= 2√x-6 is [6, ∞).
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