The null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
To find the null space of a matrix, we need to solve the equation \( Ax=0 \), where \( x \) is a vector in the null space.
For matrix \( A \), we can set up the following system of equations:
\begin{align*}
x-2y &= 0 \\
x+2z &= 0
\end{align*}
Solving for \( x \) and \( y \) in terms of \( z \) gives us:
\begin{align*}
x &= -2z \\
y &= -z
\end{align*}
So the null space of \( A \) is the set of all vectors of the form \( \left[\begin{array}{c}-2z \\ -z \\ z\end{array}\right] \), where \( z \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right] \), so the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \).
For matrix \( B \), we can set up the following system of equations:
\begin{align*}
x+3y+4z &= 0 \\
2y+4z+4w &= 0 \\
x+y-4w &= 0
\end{align*}
Solving for \( x \), \( y \), and \( z \) in terms of \( w \) gives us:
\begin{align*}
x &= 4w \\
y &= -2w \\
z &= w
\end{align*}
So the null space of \( B \) is the set of all vectors of the form \( \left[\begin{array}{c}4w \\ -2w \\ w \\ w\end{array}\right] \), where \( w \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right] \), so the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
Therefore, the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
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Liam wants to run 10 more runs what is the equations
the answer is x+10 i think bye
Find the y intercept and slope of the linear equation x+y=-6 1/2
The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
To find the y-intercept and slope of the linear equation x +y=-6 1/2, we
need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y by subtracting x from both sides of the equation:
x + y = -6 1/2
y = -x - 6 1/2
Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.
Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
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a line segment is drawn between (4,8) and (8,5). find it’s gradient.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3 }{ 4 }[/tex]
It takes 4 minutes for the wheel to make one complete rotation. Put a star at Bo’s location after riding the wheel for 21 minutes
After 21 minutes the location of BO in the wheel is EO
How to find BO after 21 minutesThe location of BO after 21 minutes is solved using the data:
It takes 4 minutes for the wheel to make one complete rotation
hence in 21 minutes the rotation covered is
= 21 / 4
= 5.25
This is 5 complete rotations and 0.25 (a quarter rotation).
0.25 rotation is
=0.25 * 360
= 90
Each gap in the wheel is
360 / 12 = 30 degrees
hence three steps from B which is EO
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Question 10 of 10 6 st Answer here 5 E Given the two similar triangles above, what is the measure of side DE?
Answer:
DE = 3
Step-by-step explanation:
What is a scale factor?A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of [tex]\frac{1}{2}[/tex] means that the new shape is half the size of the original.
To solve for a missing length, we can use this expression:
[tex]a^{2} +b^{2} =c^{2}[/tex]Inserting our numbers into the expression:
[tex]8^{2}+ b^{2} =10^{2}[/tex][tex]64 + b^{2} = 100[/tex]Subtract 64 from each side:
[tex](64 - 64) + b^{2} =(100-64)[/tex][tex]b^{2} =36[/tex][tex]\sqrt{36} =6[/tex]Therefore, the missing side length is 6.
Looking at the side CB, it is 10 units long. If the new shape is 5 units long, that means that the scale factor from shape 1 to 2 is [tex]\frac{1}{2}[/tex], meaning it is half its size. If the new shape is half its size, we can use this expression to solve for the missing length:
6 × [tex]\frac{1}{2}[/tex] or 6 ÷ 2 = 3Therefore, the measure of DE is 3.
Jeff and Ella use a payment plan to buy new furniture. Jeff writes the equation y = –108x + 2240 to represent
the amount owed, y, after x payments. The graph shows how much Ella owes after each payment.
Whose furniture costs more, Jeff's or Ella's? Explain
Therefore, after 10 payments, Jeff owes $1160.
Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.
What roles do equations play?A mathematical equation, such as 6 x 4 = 12 x 2, can be used to compare two amounts or values. a significant noun. An equation is employed when it's required to integrate two or more elements in order to understand or fully explain a situation.
To determine whose furniture costs more, we need to compare the amounts owed by Jeff and Ella for the same number of payments.
Jeff's equation is y = -108x + 2240, which gives the amount owed after x payments.
Ella's graph does not have an equation provided, but we can see that after 10 payments, she owes approximately $2200.
To compare the amounts owed after 10 payments, we can substitute x = 10 into Jeff's equation:
y = -108(10) + 2240
y = -1080 + 2240
y = 1160
Therefore, after 10 payments, Jeff owes $1160.
Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.
Answer: Ella's furniture costs more than Jeff's.
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Babe and Ruth are 675 miles apart and headed straight toward each
other. If Babe is traveling at 40 mph and Ruth is traveling at 35
mph, how many hours will it be before the two meet?
Babe and Ruth are 675 miles apart and headed straight toward each
other. If Babe is traveling at 40 mph and Ruth is traveling at 35
mph, it will take 9 hours before they meet.
To determine the time it will take for Babe and Ruth to meet, we need to use the formula:
time = distance / rate
Since they are traveling towards each other, we can add their speeds to get the combined speed at which they are approaching each other.
combined speed = Babe's speed + Ruth's speed
combined speed = 40 mph + 35 mph
combined speed = 75 mph
Now we can plug in the values we have into the formula:
time = distance / combined speed
time = 675 miles / 75 mph
time = 9 hours
Therefore, it will take 9 hours before Babe and Ruth meet.
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What is the coordinate point of the red dot on the graph?
(3, 2)
(-2, 3)
(2, -3)
(3, -2)
Answer:
(2,-3)
Step-by-step explanation:
Give an example of a linear function that has a minimum value but no maximum value. Specify the domain and whether the function is increasing or decreasing.
Select all linear functions with a minimum value but no maximum value.
The decreasing function f(x)=10−3x over the domain x≤9 has a minimum value but no maximum value .
The decreasing function f(x)=5x−1 over the domain x≥−7 has a minimum value but no maximum value.
The increasing function f(x)=2x+5 over the domain x≥ 5has a minimum value but no maximum value .
The increasing function f(x)=7−2x over the domain x≥10 has a minimum value but no maximum value .
The two linear functions that have a minimum value but no maximum value are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
Determining linear functions that have minimum value but no maximum valueFrom the question, we are to determine the linear function that have minimum value but no maximum value
The decreasing function f(x) = 10 - 3x over the domain x ≤ 9 has a minimum value but no maximum value.
Domain: x ≤ 9
This function is decreasing since the slope is negative.
The minimum value occurs at x = 9, where f(9) = 10 - 3(9) = -17.
Since the slope is negative, the function continues to decrease without bound as x approaches negative infinity.
The decreasing function f(x) = 5x - 1 over the domain x ≥ -7 has a minimum value but no maximum value.
Domain: x ≥ -7
This function is increasing since the slope is positive.
The minimum value occurs at x = -7, where f(-7) = 5(-7) - 1 = -36.
Since the slope is positive, the function continues to increase without bound as x approaches positive infinity.
Hence, the functions are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
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4. IQ (intelligence) tests are usually specified so that scores are normally distributed with a mean of 100 over the entire population. Suppose that a certain IQ test is designed to have a mean of 100 and standard deviation of 10. (a) What is the probability that a randomly selected individual from the population will score between 90 and 110 on this test? (b) An employer wishes to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, what is the score the employer will use to decide job offers?
The probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826. The score the employer will use to decide job offers is 123.3 to decide job offers for potential "high flyers."
The IQ test is designed to have a mean of 100 and a standard deviation of 10. This means that the test follows a normal distribution with a mean of 100 and a standard deviation of 10.
(a) The probability that a randomly selected individual from the population will score between 90 and 110 on this test can be found using the standard normal distribution table. We need to find the z-scores for 90 and 110 and then use the table to find the corresponding probabilities.
The z-score for 90 is (90 - 100) / 10 = -1
The z-score for 110 is (110 - 100) / 10 = 1
Using the standard normal distribution table, we find that the probability for a z-score of -1 is 0.1587 and the probability for a z-score of 1 is 0.8413.
The probability that a randomly selected individual will score between 90 and 110 is the difference between these two probabilities:
0.8413 - 0.1587 = 0.6826
So the probability that a randomly selected individual will score between 90 and 110 on this test is 0.6826.
(b) The employer wants to identify potential "high flyers" and intends to do this using the outcome of the IQ test. If the employer offers these positions to people with IQs in the top 1% of the population, we need to find the z-score that corresponds to the top 1% of the population.
Using the standard normal distribution table, we find that the z-score that corresponds to the top 1% of the population is 2.33.
Now we can use the z-score formula to find the corresponding IQ score:
z = (x - mean) / standard deviation
2.33 = (x - 100) / 10
Solving for x, we get:
x = (2.33 * 10) + 100 = 123.3
So the employer will use a score of 123.3 to decide job offers for potential "high flyers."
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Amanda has $200 in her lunch account. She spends 25$ each week on lunch. The
equation y=200-25x represents the total amount in Amanda's school lunch accou
y for x weeks of purchasing lunches.
The x intercept and y intercept of the equation is 8 and 200 respectively.
What are x Intercepts and y Intercepts?x intercept is the point on the line where it touches the X axis.
y intercept is the point on the line where it touches the Y axis.
Given equation is,
y = 200 - 25x
where y is the total amount in Amanda's school lunch account after purchasing lunches for x weeks.
x intercept is the point on X axis. Any point on x axis has y coordinate 0.
So x intercept is the x coordinate when y coordinate is 0.
0 = 200 - 25x
25x = 200
x = 8
This means that the amount in the account will become 0, after purchasing lunch for 8 weeks.
y intercept is the y coordinate when x coordinate = 0.
y = 200 - (25 × 0)
y = 200
This indicates the amount in the account at the start before purchasing any lunch.
Hence the x intercept is 8 and y intercept is 200.
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Your question is incomplete. The complete question is as follows.
Amanda has $200 in her lunch account. She spends 25$ each week on lunch. The equation y=200-25x represents the total amount in Amanda's school lunch account, y for x weeks of purchasing lunches.
Find the x and y intercepts and interpret their meaning in the context of the situation.
What is most likely true about the melting times of these two types of chocolates
It can be inferred that milk chocolate does have a lower melting point than dark chocolate and that the rate at which chocolate melts is influenced by a number of variables, including composition, temperature, as well as humidity.
According to the facts provided, it is anticipated that within 64 seconds, half of the milk chocolate brands will melt. According to their composition as well as melting point, different milk chocolate brands may melt sooner or later than 64 seconds.
However, it is believed that none of the dark chocolate brands are expected to melt before 64 seconds have passed and that their melting time actually begins after 200 seconds.
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Equilateral triangle properties solve for x and y
The value of x and y are
x=100° y=100°
In an equilateral triangle,
Each angle = 60°
∴ a + a + 100° = 180°
⇒ 2a + 100° = 180°
⇒ 2a = 180° – 100° = 80°
∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°
And y = 60° + 40° = 100°
What is an equilateral triangle?An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.
An equilateral triangle has a predictable shape. By combining the words "Equi" (which means equal) and "Lateral," which refers to sides, the word "Equilateral" is created. Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.
from the question:
In an equilateral triangle,
Each angle = 60°
Let each base angle = a
∴ a + a + 100° = 180°
⇒ 2a + 100° = 180°
⇒ 2a = 180° – 100° = 80°
∴ a = 80°/2 = 40° ∴ x = 60° + 40° = 100°
And y = 60° + 40° = 100°
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complete question
Apply the properties of equilateral triangles and find the values of x and y in the given figure
Assume that A is a matrix with three rows. Find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B=
The matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].
Assuming that A is a matrix with three rows, we can find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= by following these steps:
1. Start with the identity matrix, I, which is a matrix with ones along the main diagonal and zeros everywhere else:
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
2. Apply the first row operation, 3R3+R1⇒R1, to the identity matrix by adding three times the third row to the first row:
I = [[1+3(0), 0+3(0), 0+3(1)], [0, 1, 0], [0, 0, 1]]
I = [[1, 0, 3], [0, 1, 0], [0, 0, 1]]
3. Apply the second row operation, −7R2⇒R2, to the identity matrix by multiplying the second row by -7:
I = [[1, 0, 3], [0*(-7), 1*(-7), 0*(-7)], [0, 0, 1]]
I = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]
4. The resulting matrix, I, is the matrix B that we are looking for:
B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]
Therefore, the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3+R1⇒R1−7R2⇒R2B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].
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Given the population growth model 12000/3+e^−.02(t) , what is
the initial population and what is the maximum population?
The initial population is 4001 and the maximum population is 4000
The given population growth model is [tex]12000/3+e^{-0.02(t)}.[/tex]
To find the initial population, we need to plug in t=0 into the equation.
[tex]12000/3+e^{-0.02(0)}[/tex]
= [tex]12000/3+1[/tex]
= [tex]4000+1[/tex]
= [tex]4001[/tex]
So the initial population is 4001.
To find the maximum population, we need to find the limit of the equation as t approaches infinity.
= [tex]12000/3+0[/tex]
= [tex]4000[/tex]
So the maximum population is 4000.
In conclusion, the initial population is 4001 and the maximum population is 4000.
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If the values of A and B make the equation 35x – 29/x^2-3x+2 = A/x-1 +b/x-2 true for all values of x for which it is defined, find A+B. (A) 6 (B) 29 (C) 35 (D) 47 (E) None of these
If the values of A and B make the equation 35x – 29/x²-3x+2 = A/x-1 +b/x-2 true for all values of x for which it is defined, A+B is 35.
The given equation is 35x - 29/(x² - 3x + 2) = A/(x - 1) + B/(x - 2).
We can simplify the denominator of the second term on the left hand side by factoring it:
35x - 29/[(x - 1)(x - 2)] = A/(x - 1) + B/(x - 2)
Now, we can multiply both sides of the equation by (x - 1)(x - 2) to get rid of the fractions:
35x(x - 1)(x - 2) - 29 = A(x - 2) + B(x - 1)
Expanding the left hand side gives us:
35x³ - 70x² + 35x - 29 = A(x - 2) + B(x - 1)
Now, we can compare the coefficients of x on both sides of the equation to find the values of A and B. The coefficient of x on the left hand side is 35, and on the right hand side it is A + B. Therefore, A + B = 35.
Therefore, the values of A and B make the equation 35x – 29/x^2-3x+2 = A/x-1 +b/x-2 true for all values of x for which it is defined is 35.
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Consider the polynomial P(x)=kx^(3)-4x^(2)+x+4. Find the value of k such that the remainder is -6 when P(x) is divided by x+1. k
The value of k that makes the remainder of the polynomial equal to -6 when divided by x + 1 is k = 5.
To find the value of k that makes the remainder of the polynomial P(x) = kx3 - 4x2 + x + 4 equal to -6 when divided by x + 1, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by x - a, the remainder is P(a).
In this case, we are dividing by x + 1, so we can rewrite this as x - (-1). Therefore, a = -1 and we can plug this value into the polynomial to find the remainder:
P(-1) = k(-1)3 - 4(-1)2 + (-1) + 4
Simplifying this equation gives us:
P(-1) = -k - 4 - 1 + 4
P(-1) = -k - 1
Since we want the remainder to be -6, we can set P(-1) equal to -6 and solve for k:
-k - 1 = -6
-k = -5
k = 5
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A store manager adjusts the price of an item each week that the item goes unsold. The price of the unsold item, in dollars, after x weeks can be modeled by the exponential function f(x)=320(0.90)^x
: The initial price of the store item before the store manager made any price adjustments were: _________
Can someone help me solve this?
Thanks!
Answer:
The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.
Plugging x=0 into the given function, we get:
f(0) = 320(0.90)^0 = 320(1) = 320
Therefore, the initial price of the store item was $320.
A piece of timber 0.72 m long is cut evenly into smaller pieces of 0.03 m each. How many of these pieces can be cut?
Answer:
24
Step-by-step explanation:
This is a division problem.
0.72/0.03 = 7.2/0.3 = 72/3 = 24
I want to be done with this
The equation which represents exponential growth is y = (1.2)* and equation which represents exponential decay is y = (.71)*, y = 0(6.3)* represents a constant function.
What is exponential growth or decay function?Consider the function:
[tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is plus sign, then there is exponential growth happening by r fraction or 100r %
If there is negative sign, then there is exponential decay happening by r fraction or 100r %
We are given that;
c. y = (1.2)*
d. y = 0(6.3)*
e. y = (.71)*
a.) The equation and graph that show exponential growth is y = (1.2)x. This is because the base of the exponent (1.2) is greater than 1, so as x increases, the value of y increases at an increasing rate. The graph of y = (1.2)x is an upward-curving curve that gets steeper as x increases.
b.) The equation and graph that show exponential decay is y = (0.71)x. This is because the base of the exponent (0.71) is between 0 and 1, so as x increases, the value of y decreases at a decreasing rate. The graph of y = (0.71)x is a downward-curving curve that flattens out as x increases.
Therefore, exponential growth shows y = (1.2)* whereas y = (.71)* show exponential decay.
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Please help me with this math problem!! Will give brainliest!! :)
According to a recent survey of students about the juice they preferred, 20% of the students preferred cranberry juice, 40% preferred orange juice, 20% preferred grapefruit juice, and the remaining students preferred tomato juice. If each student preferred only 1 juice and 250 students preferred tomato juice, how many students were surveyed?
Answer: 1250 students
Step-by-step explanation:
20% + 40% + 20% = 80%
100% - 80% = 20%
If 250 is 20%, then it's just 250 x 5 = 1250
How to find a height of a trapezoid with phythagorean theorem
Height of a trapezoid with Pythagorean theorem is = √{Hypotenuse ^2 - Base ^2}
Trapezoid has two parallel sides and two non parallel sides. The length of the parallel sides are unequal but the length of the non parallel sides are equal.
Thus the trapezoid can be divided into three parts where one is rectangle ( which has length equal to the shortest length of the parallel sides) and two triangles which are equal ( having equal base, height and hypotenuse).
The Pythagoras theorem on the triangular part of the trapezoid can be stated as ,
Hypotenuse ^2 = Base ^2 + Height ^2
⇒ Height ^2 = Hypotenuse ^2 - Base ^2
⇒ Height = √{ Hypotenuse ^2 - Base ^2}
where, Height of the triangle is equal to that of the trapezoid it belongs to;
Hypotenuse of the triangle is the non parallel but equal side of the trapezoid;
Base of the triangle is = {(length of the longest side of parallel sides of trapezoid) - (length of the shortest side of parallel sides of trapezoid) }/2
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A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.
Outcome Frequency
A, A 15
A, B 12
A, C 10
B, A 18
B, B 15
B, C 17
C, A 11
C, B 13
C, C 14
Based on the table, for what probability can you expect the spinner to not land on A?
0.66
0.47
0.33
0.10
The probability of the spinner not landing on A is 0.47.
How to find the probability you can expect the spinner to not land on A?To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):
Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) + Frequency(C,B) + Frequency(C,C)
Frequency of not landing on A = 15 + 17 + 13 + 14 = 59
The total number of outcomes is 125, so the probability of not landing on A is:
P(not A) = Frequency of not landing on A / Total number of outcomes
P(not A) = 59 / 125 = 0.47
Therefore, the probability of the spinner not landing on A is 0.47.
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Jimmy is paying for a meal with group of friends. They received great service, so he is giving a 20% tip. The meal came to 166.60 before sales tax. How much will he leave as a tip?
Tip=$
Jimmy will leave a $33.32 tip for the great service.
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):
20% of 166.60 = 0.20 x 166.60 = 33.32
Therefore, Jimmy will leave a $33.32 tip for the great service.
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Mr stoves is investing $1500 on a bank account that would give him 3. 7% compounded monthly. What would be his final balance after 10 years?
Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37
What would be his final balance after 10 years?A = P(1 + r/n)^nt
Where
P = $1500
r = 3.7% = 0.037
n = monthly = 12
t = 10 years
So,
A = P(1 + r/n)^nt
A = 1,500.00(1 + 0.037/12)^(12×10)
A = 1,500.00(1 + 0.0030833333333333)¹²⁰
A = $2,170.37
Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.
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26. G(9, 12), H(−2, −15), J(3, 8) and
G'(9, -2), H'(-2, 25), J'(3, 2)
The transformation between the points is (x, y) = (x, -y + 10)
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
G(9, 12), H(−2, −15), J(3, 8) and
G'(9, -2), H'(-2, 25), J'(3, 2)
We can see that the x coordinates of the image and the preimage are equal
However, the relationship between the y-coordinates is
y' = -y + 10
This means that
(x, y) = (x, -y + 10)
The above rule is a translation transformation
Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.
Hence, the transformation is (x, y) = (x, -y + 10)
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Complete question
26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)
Write out the transformation rule from GHJ to G'H'J'
Can anybody please help me with this question
Answer:
(a) 8 : 3
(b) 1 7/8 cups
Step-by-step explanation:
Given a recipe that calls for 2 cups of flour and 3/4 cup of water, you want to know the ratio in simplest terms, and the amount of water for 5 cups of flour.
Simplified ratioThe ratio can be written and simplified as a fraction. Fractions are divided in the usual way.
2/(3/4) = 2 ÷ 3/4 = 2 × 4/3 = 8/3 = 8 : 3
5 cups flour
If we multiply each term in this ratio by 5/8, we can find the recipe that uses 5 cups of flour:
(5/8)·8 : (5/8)·3 = 5 : 15/8 = 5 : 1 7/8
Naomi uses 1 7/8 cups of water with 5 cups of flour.
Answer:
Step-by-step explanation:
[tex](a)[/tex]
[tex]2:\frac{3}{4}[/tex]
Multiply both sides by 4 to remove fraction:
[tex]2\times4:\frac{3}{4} \times 4[/tex]
[tex]8:3[/tex] (this is simplest form because no number goes into both 8 and 3)
[tex](b)[/tex]
5 cups of flower:
[tex]8 \times \frac{5}{8} : 3 \times \frac{5}{8}[/tex] (I chose [tex]\frac{5}{8}[/tex] to turn the 8 into 5)
[tex]5:\frac{15}{8}[/tex]
5 cups flour needs [tex]\frac{15}{8}[/tex] ([tex]=1\frac{7}{8}[/tex]) cups water
What is the volume of the composite solid?
The volume of the composite solid is 5104 cubic ft.
What is triangular prism?A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.
The area of a triangular prism is given as:
V = 1/2(bhl)
Here, h = 22 - 12 = 10 ft.
Substituting the values we have:
V = 1/2(13)(10)(32)
V = 2080 cubic ft.
The volume of the rectangular prism is given as:
V = lwh
V = (28)(9)(12)
V = 3024 cubic ft.
The volume of the composite solid is:
V = V1 + V2
V = 2080 + 3024
V = 5104 cubic ft.
Hence, the volume of the composite solid is 5104 cubic ft.
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Which of the following proves these triangles as congruent?
Answer:
AAS
Step-by-step explanation:
Answered this question before on Acellus.
solve the problem with simplex method , and verify using graphical method
Extra Credit Min Z = -X1 + 2X2 St. -X1 + X2 >= -1 4X1 + 3X2 + <= 12
2X1 <= 3
Xi >= 0
In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.
To solve the problem using the simplex method, we first need to convert the inequalities to equations by adding slack variables. Then we can set up the initial tableau and use the simplex method to find the optimal solution. Finally, we can verify the solution using the graphical method.
Convert inequalities to equations by adding slack variables
-X1 + X2 >= -1 becomes -X1 + X2 + S1 = -1
4X1 + 3X2 <= 12 becomes 4X1 + 3X2 + S2 = 12
2X1 <= 3 becomes 2X1 + S3 = 3
Set up the initial tableau
| -1 | 2 | 1 | 0 | 0 | 0 |
| -1 | 1 | 1 | 0 | 0 | -1 |
| 4 | 3 | 0 | 1 | 0 | 12 |
| 2 | 0 | 0 | 0 | 1 | 3 |
Use the simplex method to find the optimal solution
We first need to choose the pivot column, which is the one with the most negative coefficient in the objective row. In this case, it is the first column. Then we need to choose the pivot row, which is the one with the smallest positive ratio of the right-hand side to the pivot column coefficient. In this case, it is the third row. We can then use the pivot element to eliminate the other coefficients in the pivot column and repeat the process until we have no negative coefficients in the objective row.
After performing the simplex method, we get the following final tableau:
| 0 | 5/4 | 1 | 1/4 | 0 | 3 |
| 0 | 7/4 | 1 | 1/4 | 0 | 3 |
| 0 | 3/4 | 0 | 1/4 | 0 | 3 |
| 1 | 0 | 0 | 0 | 1/2 | 3/2 |
The optimal solution is X1 = 3/2, X2 = 0, and Z = -3/2.
Verify the solution using the graphical method
We can graph the constraints and find the feasible region. Then we can graph the objective function and find the point where it intersects the feasible region that gives the maximum or minimum value. In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.
Extra Credit:
To solve the problem using the simplex method, we first need to convert the inequalities to equations by adding slack variables. Then we can set up the initial tableau and use the simplex method to find the optimal solution. Finally, we can verify the solution using the graphical method.
Convert inequalities to equations by adding slack variables
-X1 + X2 >= -1 becomes -X1 + X2 + S1 = -1
4X1 + 3X2 <= 12 becomes 4X1 + 3X2 + S2 = 12
2X1 <= 3 becomes 2X1 + S3 = 3
Set up the initial tableau
| -1 | 2 | 1 | 0 | 0 | 0 |
| -1 | 1 | 1 | 0 | 0 | -1 |
| 4 | 3 | 0 | 1 | 0 | 12 |
| 2 | 0 | 0 | 0 | 1 | 3 |
Use the simplex method to find the optimal solution
We first need to choose the pivot column, which is the one with the most negative coefficient in the objective row. In this case, it is the first column. Then we need to choose the pivot row, which is the one with the smallest positive ratio of the right-hand side to the pivot column coefficient. In this case, it is the third row. We can then use the pivot element to eliminate the other coefficients in the pivot column and repeat the process until we have no negative coefficients in the objective row.
After performing the simplex method, we get the following final tableau:
| 0 | 5/4 | 1 | 1/4 | 0 | 3 |
| 0 | 7/4 | 1 | 1/4 | 0 | 3 |
| 0 | 3/4 | 0 | 1/4 | 0 | 3 |
| 1 | 0 | 0 | 0 | 1/2 | 3/2 |
The optimal solution is X1 = 3/2, X2 = 0, and Z = -3/2.
Verify the solution using the graphical method
We can graph the constraints and find the feasible region. Then we can graph the objective function and find the point where it intersects the feasible region that gives the maximum or minimum value. In this case, the point (3/2, 0) is the optimal solution, which matches the solution we found using the simplex method.
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