Two friends, Andrew and Liz, are playing a game using this spinner. If thespinner lands on region 4, Andrew wins. If it lands on region 3, Liz wins. If itlands on any other region, neither wins. Is this a fair game?
Since we have the following probabilities:
\(\begin{gathered} P(1)=P(4)=\frac{1}{4} \\ P(2)=P(3)=P(5)=P(6)=\frac{1}{8} \end{gathered}\)then, this is not a fair game, since Andrew has a 1/4 probability of winning and Liz has a 1/8 probability of winning
Jayla, Keisha and Melanie are sisters. Keisha is 3 years older than Jayla. Melanie is 3 years older than Keisha. If you add their ages together, you get 42.
1. Write an equation or draw a picture to represent this scenario.
2. How old are the sisters? How do you know?
If you are extremely good at slopes, pls look at the screenshot below and help me!
Answer:
B.) y= 6x+10 y=6x+8 and no solution
Step-by-step explanation:
2. (a) [5pts.] Length and Dot Product in R¹. Suppose u and v' are unit vectors in R". Prove > || u’ – V || = √2√√1 – u - v (b) [5pts.] Orthonormal Bases. Suppose U = {₁,..., un} is an orthonormal basis for R" and x ER". Prove if x' u₁ = || u}'|| for all i, 1 ≤ i ≤n, then x = U₁ + ... + un -
(a) To prove the equation ||u' - v|| = √2√(1 - u · v) in R², where u and v are unit vectors, we can use the properties of the dot product and vector norms.
First, let's expand the norm on the left side of the equation:
||u' - v||² = (u' - v) · (u' - v)
Expanding the dot product, we have:
||u' - v||² = (u' · u') - 2(u' · v) + (v · v)
Since both u and v are unit vectors, their norms are equal to 1:
||u' - v||² = (1) - 2(u' · v) + (1)
Simplifying, we have:
||u' - v||² = 2 - 2(u' · v)
Now, let's focus on the right side of the equation:
√2√(1 - u · v) = √2√(1 - (u' · v))
Taking the square of both sides, we have:
2 - 2(u' · v) = 2 - 2(u' · v)
Therefore, the equation ||u' - v|| = √2√(1 - u · v) holds in R².
(b) To prove that if x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ and x ∈ Rⁿ, then x = u₁ + ... + un.
Since U is an orthonormal basis, each ui is a unit vector, and they are linearly independent, forming a basis for Rⁿ. We can write any vector x ∈ Rⁿ as a linear combination of the basis vectors:
x = c₁u₁ + c₂u₂ + ... + cnun
Now, let's calculate the dot product of x with each basis vector ui:
x · ui = (c₁u₁ + c₂u₂ + ... + cnun) · ui
= c₁(u₁ · ui) + c₂(u₂ · ui) + ... + cn(un · ui)
Since the basis vectors are orthonormal, the dot product of any two distinct basis vectors is zero:
(uj · ui) = 0 (for j ≠ i)
Therefore, the dot product simplifies to:
x · ui = ci(u · ui)
Given that x · ui = ||ui|| for all i, we have:
ci(u · ui) = ||ui||
Since ui is a unit vector, the dot product (u · ui) is equal to the norm of u:
ci ||ui|| = ||ui||
This equation holds for all i, 1 ≤ i ≤ n. Since ||ui|| is non-zero (as ui is a unit vector), we can divide both sides of the equation by ||ui||:
ci = 1
Hence, each coefficient ci is equal to 1. Therefore, we can rewrite x as:
x = u₁ + u₂ + ... + un
If x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ, then x can be written as the sum of the basis vectors: x = u₁ + u₂ + ... + un.
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Find the amount of interest.
P= $2,000
R=4%
T= 1 Year
A) $8,000
B) $80
C) $800
D) $50,000
Answer:$80
Step-by-step explanation:
Calculate 18% tip on a 6250 dinner bill
solve the system of equations
−4x+3y=−2
y=x−1
x =
y =
the third term of an arithmetic progression is 4x - 2y and the 9th term is 10 x - 8 y find the common difference
\(\bold{\huge{\purple{\underline{ Solution }}}}\)
Given :-The third term of an AP arithmetic progression is 4x - 2yThe 9th term of an AP is 10x - 8y To Find :-We have to find the common difference of the given AP? Let's Begin :-We know that,
For nth term of an AP
\(\bold{\red{ an = a1 + (n - 1)d }}\)
Here, a1 is the first term of an AP n is the number of terms d is the common differenceWe have ,
\(\sf{ a3 = 4x - 2y ...eq(1)}\)
\(\sf{ a9 = 10x - 8y ...eq(2)}\)
But, From above formula :-
\(\sf{ a3 = a1 + (3 - 1)d}\)
\(\sf{ a3 = a1 + 2d...eq(3)}\)
And
\(\sf{ a9 = a1 + (9 - 1)d}\)
\(\sf{ a9 = a1 + 8d...eq(4)}\)
From eq(1) and eq( 3) :-
\(\sf{ a1 + 2d = 4x - 2y }\)
\(\sf{ a1 = 4x - 2y - 2d ...eq(5)}\)
From eq(2) and eq( 4) :-
\(\sf{ a1 + 8d = 10x - 8y }\)
\(\sf{ a1 = 10x - 8y - 8d ...eq(6)}\)
From eq( 5) and eq(6) :-
\(\sf{ 4x - 2y - 2d = 10x - 8y - 8d }\)
\(\sf{ -2d + 8d = 10x - 4x - 8y + 2y }\)
\(\sf{ 6d = 6x - 6y }\)
\(\sf{ 6d = 6(x - y) }\)
\(\sf{ d = }{\sf{\dfrac{ 6(x - y) }{6}}}\)
\(\bold{\blue{ d = x - y }}\)
Hence, The common difference of the given AP is x - y.
The common difference of the given arithmetic progression is; d = x - y
What is the nth term of an arithmetic sequence?Formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term in the sequence
d is common difference
Thus;
a₃ = 4x - 2y
a₉ = 10x - 8y
Using the general formula, we know that;
a₃ = a + (3 - 1)d
a₃ = a + 2d ----(eq 1)
a₉ = a + 8d -----(eq 2)
Subtract eq 1 from eq 2 to get;
a₉ - a₃ = 6d
Put the given values of a₃ and a₉ to get;
10x - 8y - (4x - 2y) = 6d
6x - 6y = 6d
divide through by 6 to get;
d = x - y
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La trayectoria de un cuerpo en movimiento rectilíneo está determinada por: s = 115t + 12t^3 en metros y segundos. Determina la aceleración del cuerpo a los 12 segundos de origen.
Answer:
a = 864 m/s^2
Step-by-step explanation:
You have the following equation for the motion of a body:
\(s(t)=115t+12t^3\)
The acceleration of the body is given by the second derivative of s(t):
\(\frac{ds}{st}=115+12(3)t^2=115+36t^2\\\\\frac{d^2s}{dt^2}=\frac{d}{dt}\frac{ds}{dt}=36(2)t=72t\\\\a(t)=72t\)
After t = 12 s you obtain for the acceleration:
\(a(t=12)=72(12)=864\frac{m}{s^2}\)
hence, the acceleration is 864m/s^2 for t=12s
If x is a binomial random variable with n = 20 and p = 0.25, the expected value of x is:_________
The expected value with a sample size of 20 and a probability of 0.25 will be 5.
What is the expected value?The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.
E(x) = 20 x 0.25
E(x) = 5
The expected value with n = 20 and p = 0.25 will be 5.
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a triangle has a base of 10 inches and a height of 4.5 in what is the area of the triangle in square inches
Answer: 22.5
Step-by-step explanation:
1/2 base x height
2. Swee took 3 hours to drive from Nilai to Ipoh at an average speed of 84km/h. In the return journey, he took 30 minutes more than the travelling time from Nilai to Ipoh. Calculate the average speed, km/h, of Swee return journey.
Concept: Proportion, to find the km/h return journer
3 hours to 84 km/hr = 3.5 hours to x km/hr
(since its inverse proportion, multiply the 1st to 2nd and 3rd to 4th)
Inverse proportion: as the other quantities increase, the other one decreases
Solution:3 : 84 = 3.5 : x
3(84) = 3.5x
252 = 3.5x (divide 3.5 both sides)
x = 72
Therefore, Swee took 72 km/hr thats why he took 3 and 30 minutes travelling time.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Find the Laplace transform of the following functions. 3. f(t) = 3sinht + 5cosht 4. f(t) = 4e-6 + 3sin2t +9 = -6
The Laplace transform of the following functions are:
1. f(t) = 3sinht + 5cosht
To find the Laplace transform of f(t) = 3sinht + 5cosht,
use the following formula:
\($$\mathcal{L}\{f(t)\} = \frac{s}{s^{2} + a^{2}} $$\)
Where a is a constant. Let a = 1.
\($$ \begin{aligned} \mathcal{L}\{f(t)\} &= \mathcal{L}\{3sinht + 5cosht\} \\ &= 3\mathcal{L}\{sinht\} + 5\mathcal{L}\{cosht\} \\ &= 3\left(\frac{1}{s-1} \right) + 5\left(\frac{s}{s^{2} + 1^{2}} \right) \\ &= \frac{3}{s-1} + \frac{5s}{s^{2} + 1} \end{aligned} $$\)
Therefore, the Laplace transform of f(t) = 3sinht + 5cosht is
\($$\mathcal{L}\{f(t)\} = \frac{3}{s-1} + \frac{5s}{s^{2} + 1} $$\)
2. f(t) = 4e-6 + 3sin2t +9 = -6
To find the Laplace transform of f(t) = 4\(e^-6\)+ 3sin2t +9 = -6,
use the following formula:
\($$\mathcal{L}\{f(t)\} = \mathcal{L}\{4e^{-6} + 3sin2t -6 \} $$\)
Taking Laplace transform of each term, we get
\($$ \begin{aligned} \mathcal{L}\{4e^{-6} + 3sin2t -6 \} &= \mathcal{L}\{4e^{-6}\} + \mathcal{L}\{3sin2t\} - \mathcal{L}\{6\} \\ &= 4\mathcal{L}\{e^{-6}\} + 3\mathcal{L}\{sin2t\} - 6\mathcal{L}\{1\} \\ &= 4\left(\frac{1}{s+6}\right) + 3\left(\frac{2}{s^{2} + 2^{2}}\right) - 6\left(\frac{1}{s}\right) \\ &= \frac{4}{s+6} + \frac{6}{s^{2} + 4} - \frac{6}{s} \end{aligned} $$\)
Therefore, the Laplace transform of f(t) = 4\(e^-6\) + 3sin2t +9 = -6 is
\($$\mathcal{L}\{f(t)\} = \frac{4}{s+6} + \frac{6}{s^{2} + 4} - \frac{6}{s} $$\)
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The Laplace Transform of a function f(t) is defined as F(s) = L{f(t)}.
Find the Laplace transform of the following functions below.
3. f(t) = 3sinht + 5cosht
Using the following Laplace transforms:
L{sinh(at)} = a / \((s^2-a^2)\),
L{cosh(at)} = s / \((s^2-a^2)\), and
L{a cosh(at)} = s / \((s^2-a^2)\)
where a is a constant,
we can find the Laplace transform of the given function f(t) = 3sinht + 5cosht.
L{3sinht + 5cosht} = 3 L{sinh(t)} + 5 L{cosh(t)}
Substituting the Laplace transforms:
\(3 * [a / (s^2-a^2)] + 5 * [s / (s^2-a^2)] = [3a + 5s] / (s^2-a^2)\)
Therefore, the Laplace transform of the function f(t) = 3sinht + 5cosht is F(s) = [3a + 5s] /\((s^2-a^2)\).4.
f(t) = \(4e^{(-6t)\)+ 3sin(2t) + 9
Using the Laplace transform of the unit step function, \(L{e^{-at} u(t)} = 1 / (s+a)\), and
the Laplace transform of sin(at), L{sin(at)} = a / \((s^2 + a^2)\),
we can find the Laplace transform of the given function f(t) =\(4e^{(-6t)\) + 3sin(2t) + 9.
L{\(4e^{(-6t)\) + 3sin(2t) + 9}
= 4L{\(e^{(-6t)\) u(t)} + 3L{sin(2t)} + 9L{1}
Substituting the Laplace transforms:
4 * [1 / (s+6)] + 3 * [2 / (\(s^2\) + 4)] + 9 * [1 / s] = [36\(s^2\) + 78s + 76] / [(s+6)(\(s^2\) + 4)]
Therefore, the Laplace transform of the function f(t) = \(4e^{(-6t)\) + 3sin(2t) + 9 is F(s) = [36\(s^2\) + 78s + 76] / [(s+6)(\(s^2\) + 4)].
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Lindane (hexachlorocyclohexane) is an agricultural insecticide that can also be used in the treatment of head lice.
Draw the other chair conformation (B) of Lindane and inspect which of the following statements are correct.
a)B is more stable than A b)A is more stable than B c)A is not the correct representation of Lindane
d)The two chair conformation of Lindane are degenerate.
Here, Statement a) B is more stable than A is correct, while statements b), c), and d) are incorrect.
Lindane, also known as gamma-hexachlorocyclohexane, exists as a mixture of two stereoisomers. These stereoisomers have different chair conformations, often referred to as conformer A and conformer B. I will describe these conformations to help you analyze the statements provided.
Conformer A: In conformer A, one of the chlorine atoms is positioned in an axial (up) position, while the other five chlorine atoms are in equatorial (outward) positions. This arrangement is less stable due to steric hindrance caused by the axial chlorine atom, which experiences stronger interactions with neighboring groups.
Conformer B: In conformer B, the axial and equatorial positions of the chlorine atoms are interchanged compared to conformer A. The chlorine atom that was previously axial is now equatorial, and vice versa. This arrangement reduces the steric hindrance, leading to a more stable conformation.Now, let's analyze the provided statements:
a) B is more stable than A:
This statement is correct. Conformer B is indeed more stable than conformer A because it minimizes steric hindrance by placing the chlorine atoms in more favorable positions.b) A is more stable than B:
This statement is incorrect. As explained above, conformer B is more stable than conformer A.
c) A is not the correct representation of Lindane:
This statement is incorrect. Both conformers A and B are valid representations of Lindane, and the compound exists as a mixture of these conformations.
d) The two chair conformations of Lindane are degenerate:
This statement is incorrect. Degenerate conformations have the same energy level. In the case of Lindane, conformer B is more stable than conformer A, indicating that they have different energy levels and are not degenerate.
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5x+4y=-30
3x-9y=-18
how do I do an elimination
Consequently, x = -6 and y = 0 provide the system of equations answer. The response gathering yields "(-6,0)" as the outcome.
What is an elimination sentence?She came back to compete in the meeting's final event, winning the knockout race. Their quick removal is the letdown. Take pride in your quick removal.
To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:
To find: multiply the second solution by 4.
12x - 36y = -72
Eliminate x by combining the two equations:
5x + 4y + 12x - 36y = -30 - 72
Simplify and combine like terms:
17x - 32y = -102
Solve for x:
17x = 32y - 102
x = (32/17)y - 6
Substitute this expression for x into one of the original equations, and solve for y:
5x + 4y = -30
5[(32/17)y - 6] + 4y = -30
Simplify and solve for y:
(160/17)y - 30 = -30
(160/17)y = 0
y = 0
Substitute this value for y back into either of the original equations and solve for x:
3x - 9y = -18
3x - 9(0) = -18
3x = -18
x = -6
So the solution to the system of equations is x = -6 and y = 0. Therefore, the solution set is {(-6,0)}.
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Triangle TUV is shown. What is the measure of angle TVU?
259
18
V
what is the mass of x divided by 12
The value of expression is,
⇒ x ÷ 12
We have to given that;
The algebraic expression is,
⇒ x divided by 12
Hence, We can formulate;
The value of correct expression is,
⇒ x ÷ 12
⇒ x / 12
Thus, The value of expression is,
⇒ x ÷ 12
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Find the absolute maximum and minimum, if either exists, for the function on the indicated interval. = - f(x) = 2x3 – 12x2 + 18x + 20 (A) (-1,6] (B) (-1, 3] [ (C) [2, 6]
On the interval [2, 6], the absolute maximum is 128 at x = 6, and there is no absolute minimum since the interval is not closed.
to find the absolute maximum and minimum of the function f(x) = 2x³ - 12x² + 18x + 20 on the indicated intervals, we need to evaluate the function at the critical points and endpoints within each interval. let's analyze each interval separately:
(a) (-1,6]:1. find the critical points by setting the derivative equal to zero:f'(x) = 6x² - 24x + 18 = 0simplifying the quadratic equation, we get:
x² - 4x + 3 = 0factoring, we have:(x - 1)(x - 3) = 0so, the critical points are x = 1 and x = 3.
2. evaluate the function at the critical points and endpoints:f(-1) = 2(-1)³ - 12(-1)² + 18(-1) + 20 = 2 + 12 - 18 + 20 = 16f(1) = 2(1)³ - 12(1)² + 18(1) + 20 = 2 - 12 + 18 + 20 = 28
f(3) = 2(3)³ - 12(3)² + 18(3) + 20 = 54 - 108 + 54 + 20 = 20threfore, on the interval (-1,6], the absolute maximum is 28 at x = 1, and the absolute minimum is 16 at x = -1.
(b) (-1, 3]:using the same critical points from the previous interval, let's evaluate the function:f(-1) = 16 (as we found in part a)f(1) = 28 (as we found in part a)
therefre, on the interval (-1, 3], the absolute maximum is 28 at x = 1, and there is no absolute minimum since the interval is not closed.
(c) [2, 6]:1. evaluate the function at the endpoints:f(2) = 2(2)³ - 12(2)² + 18(2) + 20 = 16 - 48 + 36 + 20 = 24f(6) = 2(6)³ - 12(6)² + 18(6) + 20 = 432 - 432 + 108 + 20 = 128
, on the interval [2, 6], the absolute maximum is 128 at x = 6, and there is no absolute minimum since the interval is not closed.to summarize:
- on the interval (-1, 6], the absolute maximum is 28 at x = 1, and the absolute minimum is 16 at x = -1.- on the interval (-1, 3], the absolute maximum is 28 at x = 1, and there is no absolute minimum.- on the interval [2, 6], the absolute maximum is 128 at x = 6, and there is no absolute minimum.to find the absolute maximum and minimum of the function f(x) = 2x³ - 12x² + 18x + 20 on the indicated intervals, we need to evaluate the function at the critical points and endpoints within each interval.
let's analyze each interval separately:(a) (-1,6]:1. find the critical points by setting the derivative equal to zero:
f'(x) = 6x² - 24x + 18 = 0simplifying the quadratic equation, we get:x² - 4x + 3 = 0factoring, we have:
(x - 1)(x - 3) = 0so, the critical points are x = 1 and x = 3.2. evaluate the function at the critical points and endpoints:
f(-1) = 2(-1)³ - 12(-1)² + 18(-1) + 20 = 2 + 12 - 18 + 20 = 16f(1) = 2(1)³ - 12(1)² + 18(1) + 20 = 2 - 12 + 18 + 20 = 28f(3) = 2(3)³ - 12(3)² + 18(3) + 20 = 54 - 108 + 54 + 20 = 20
, on the interval (-1,6], the absolute maximum is 28 at x = 1, and the absolute minimum is 16 at x = -1.(b) (-1, 3]:using the same critical points from the previous interval, let's evaluate the function:
f(-1) = 16 (as we found in part a)f(1) = 28 (as we found in part a)
, on the interval (-1, 3], the absolute maximum is 28 at x = 1, and there is no absolute minimum since the interval is not closed.(c) [2, 6]:1. evaluate the function at the endpoints:
f(2) = 2(2)³ - 12(2)² + 18(2) + 20 = 16 - 48 + 36 + 20 = 24f(6) = 2(6)³ - 12(6)² + 18(6) + 20 = 432 - 432 + 108 + 20 = 128 to summarize:- on the interval (-1, 6], the absolute maximum is 28 at x = 1, and the absolute minimum is 16 at x = -1.- on the interval (-1, 3], the absolute maximum is 28 at x = 1, and there is no absolute minimum.
- on the interval [2, 6], the absolute maximum is 128 at x = 6, and there is no absolute minimum.
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In an experiment with a bag of marbles, P(green) = three fourths. Interpret the likelihood of choosing a green marble.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The probability of picking a green marble is 3/4 or 0.75. This means it is likely the event would occur. Therefore, option A is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, an experiment with a bag of marbles, P(green)=3/4.
Probability is used to determine how likely it is that a random event would happen. The probability that a random event occurs lie between 0 and 1. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of picking a green marble is 3/4 or 0.75. 0.75 is more than 0.5. This means it is likely the event would occur.
Therefore, option A is the correct answer.
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The mass of a test sample is 10 g, and it has a volume of 2.5 cm³. What is its density?
A. 10 g/cm³
B. 2.5 cm³/g
C. 4 g/cm³
D. 4 cm³/g
E. 0.25 g/cm³
The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³ thus option (C) will be correct.
What is density?Density or mass density is the mass of any object per volume.
For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.
Density can be uniform or non-uniform.
Density is the division of mass and volume and the mass must be for the quantity of the volume only.
Given that,
Mass = 10 g
Volume = 2.5 cm³
Density = 10/2.5 = 4 g/cm³
Hence "The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³".
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let n be a three digit positive integer with all different signs. what can we say about the difference between n and its reverse
By using the expanded form of a number, it can be concluded that
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number
Let the three digit positive integer be n = abc where a, b and c are distinct positive integers
n can be written as 100a + 10b + c
Its reverse is n' = cba
n' can be written as 100c + 10b + a
Difference between the number and its reverse
= 100a + 10b + c - 100c - 10b -a
= 99a - 99c
= 99(a - c)
= Since a and c are distinct, a - c \(\neq\) 0
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
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Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x = –2
Answer:
\((a)\ x = 3y - 2\)
\((b)\ y = -3x - 2\)
\((e)\ 3y - x = -2\)
Step-by-step explanation:
Given
\(y =3x -2\)
Required
Equations that can create consistent and independent systems
For a pair of equation to have consistent and independent systems, the equations must have different slopes.
An equation of the form \(y = mx + c\) has m has its slope.
In \(y =3x -2\)
\(m = 3\) --- slope
Considering the options
\((a)\ x = 3y - 2\)
Make y the subject
\(x = 3y - 2\)
\(3y = x+2\)
Divide by 3
\(y = \frac{1}{3}x+\frac{2}{3}\)
The slope is:
\(m_1 = \frac{1}{3}\)
Hence, (a) can make a consistent and independent system with \(y =3x -2\)
\((b)\ y = -3x - 2\)
The slope is:
\(m= -3\)
Hence, (b) can make a consistent and independent system with \(y =3x -2\)
\((c)\ y = 3x + 2\)
The slope is:
\(m=3\)
Hence, (c) cannot make a consistent and independent system with \(y =3x -2\)
\((d)\ 6x - 2y = 4\)
Make y the subject
\(2y = 6x -4\)
Divide by 2
\(y = 3x -2\)
The slope is
\(m =3\)
Hence, (d) cannot make a consistent and independent system with \(y =3x -2\)
\((e)\ 3y - x = -2\)
Make y the subject
\(3y = x -2\)
Divide by 3
\(y = \frac{1}{3}x -\frac{2}{3}\)
The slope is:
\(m = \frac{1}{3}\)
Hence, (e) can make a consistent and independent system with \(y =3x -2\)
2)
3)
Х
у
시
Lカー
-10
O
-7
4
5
13
Answer:
I agree sir
Step-by-step explanation:
perform each step to solve for x
3x-6+x-2
Based on the given expression representing each angle, the value of x is 47 and each angles are 135° and 45° respectively.
How to solve supplementary angles?Based on the given diagram; the angles represented by the expression are referred to as supplementary angles.
So, we can find the unknown variable x by adding the expressions and equating it to 80°
(3x - 6) + (x - 2) = 180
3x - 6 + x - 2 = 180
combine like terms
3x + x - 6 - 2 = 180
4x - 8 = 180
Add 8 to both sides
4x = 180 + 8
4x = 188
divide both sides by 4
x = 188/4
x = 47
Therefore, the respective angles are;
3x - 6
= 3(47) - 6
= 141 - 6
= 135°
x - 2
= 47 - 2
= 45°
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A SPORTS CAR CAN DRIVE 240 MILES IN 2 HOURS.
HOW MANY MILES CAN IT DRIVE IN 1 HOUR?
Answer:
120 Miles in 1 hour.
Step-by-step explanation:
Sorry if I'm wrong but, that's my calculation.
Which pair of triangles must be similar?
A.Triangles 1 and 2 are equilateral.
B.Triangles 3 and 4 each have an 80 degree angle.
C.Triangle 5 has a 80 degree angle and a 30 degree angle, and Triangle 7 has a 70
degree angle
D.Triangle 7 has 2 50 degree angle, and Triangle 8 has a 50 degree angle and a 100
degree angle
Answer:
Step-by-step explanation:
This question involves the concept of similar triangles.
The pair of triangles that are similar are "B and D".
A pair of triangles is termed as similar triangles if the two angles of both the triangles are equal to each other. Hence, we will check this condition for each pair given in the question.
A.
Only one angle is given to be equal for both the triangles, while the other two angles are unknown. Hence, this pair can not be termed as similar.
B.
For an isoceles triangle, two sides and two angles of the triangle are equal. Considering the 40° angle to be the equal angle, we can safely conclude that the two angles of both the triangles in the pair are the same. Hence, this pair can be termed as similar.
C.
Triangle 5 has angles: 30°, 90° and (180°-30°-90°) = 60°. While triangle 6 has angles: 30°, 70°, and (180°-70°-30°) = 80°. Since all the angles of both the triangles are different. Therefore, they can not be termed as similar.
D.
Triangle 7 has angles: 50°, 20° and (180°-50°-25°) = 105°. While triangle 6 has angles: 50°, 105°, and (180°-50°-105°) = 25°. Since all the angles of both the triangles are equal. Therefore, they can be termed as similar.
8. Beth doesn’t begin to receive commission until she reaches $50,000 in sales. Once she does, her commission rate is 12%. If she sells cars totaling $115,000, how much money does she make in commission?
A.$13,800
B.$6,000
C.$7,800
D.$8,400
PLEASE HELP ME
Answer:
The Answer Is A. $13,800
Step-by-step explanation:
what is the answer for this, I have to solve the proportion,
n/18 = 12/7.5
Answer:
n = 28.8
Step-by-step explanation:
\(\frac{n}{18} =\frac{12}{7.5}\)
n × 7.5 = 18 × 12
7.5n = 216
7.5n ÷ 7.5 = 216 ÷ 7.5
n = 28.8
8
Marcus surveyed 100 people who went to a movie yesterday.
He recorded the time of day each person went to the movie and
whether or not they bought a snack. His results are shown in this
two-way table.
MOVIE SURVEY
Time
Got a Snack
Yes
No
Day
14
26
Night
36 24
What is the relative frequency of people who saw a movie at night
and got a snack to all people who saw a movie at night?
A
0.36
(В)
0.5
© 0.6
D
0.67
Relative frequency are used to represent frequency in percentages or decimals
The relative frequency of people who saw a movie at night is
How to determine the relative frequencyFrom the table, we have:
\(Night = 36 + 24\)
Evaluate the sum
Night = 60
The relative frequency (RF) is then calculated as:
RF = 60/100
Evaluate the quotient
RF = 0.60
Hence, the relative frequency of people who saw a movie at night is 0.60
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The following data represent the number of student athletes visiting a physio therapist per day during last three weeks at the Bridgewater High School. 3,3,3,4,5,5,5,7,7,8,8,9,9,919 Construct a frequency distribution table for this data. Once complete, scan or take a picture and upload here.Previous question
The frequency distribution table for number of student athletes visiting a physio therapist per day during last three weeks at the Bridgewater High School is attached.
What is a frequency distribution table?A frequency distribution table can be defined as a table which is used to organize data for effective and efficient interpretation. It usually consists of two or more columns.
3, 3, 3, 4, 5, 5, 5, 7, 7, 8, 8, 9, 9, 9, 1, 9
Class interval. Frequency
0 - 3. 4
4 - 7. 6
8 - 11. 6
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