Answer:
80cm
Step-by-step explanation:
i worked it out like this
2x4=8
then that means
20x4=80
Answer:
80 is the answer
a discount voucher offering 15% off is used to pay a bill. after using the voucher the bill is reduced to £36.72.
how much was the bill before applying the voucher discount?
Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length.
What is the height of the pennant? Recall the formula
A = bh.
Answer:
Height of the pennant is 30 inches.
Step-by-step explanation:
Given that:
Area of pennant = 180 sq inches
Base of pennant = z inches
Height of pennant = (2z + 6) inches
Also, it is a triangular pennant and area of a triangle can be given as:
[tex]A = \dfrac{1}{2} \times Base\times Height[/tex]
Putting the values in above formula:
[tex]180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15[/tex]
Value of z can not be negative, so value of Base, z = 12 inches.
Height is given as 2z + 6 so, height = 2[tex]\times[/tex]12 +6 = 30 inches
Answer:
C.30 inches
Step-by-step explanation:
The weight of oranges growing in an orchard is normally distributed with a mean weight of 6 oz. and a standard deviation of 0.5 oz. Using the empirical rule, determine what interval would represent weights of the middle 95% of all oranges from this orchard.
Answer:
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 0.5
Middle 95% of weights:
By the Empirical Rule, within 2 standard deviations of the mean.
6 - 2*0.5 = 5
6 + 2*0.5 = 7
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
The Empirical Rule states that for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
What is the empirical rule?The empirical rule says that, in a standard data set, virtually every piece of data will fall within three standard deviations of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 0.5
Middle 95% of weights
By the Empirical Rule, within 2 standard deviations of the mean.
6 - 2*0.5 = 5
6 + 2*0.5 = 7
The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
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If A = (0, 0) and B = (6, 3) what is the length of overline AB ?
Answer:
A= (0,0) and B = (6,3)
We can find the length AB with the following formula:
[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]
And replacing we got:
[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]
So then the length AB would be [tex] 3\sqrt{5}[/tex]
Step-by-step explanation:
For this case we have the following two points:
A= (0,0) and B = (6,3)
We can find the length AB with the following formula:
[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]
And replacing we got:
[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]
So then the length AB would be [tex] 3\sqrt{5}[/tex]
Answer:6.71
Step-by-step explanation: awesomeness
Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?
Answer:
Area of rectangle = [tex]196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
Step-by-step explanation:
Given:
Perimeter of rectangle is 56 m
To find: the maximized area of a rectangle and the length and width
Solution:
A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]
Let x, y denotes length and width of the rectangle.
Perimeter of rectangle = 2( length + width )
[tex]=2(x+y)[/tex]
Also, perimeter of rectangle is equal to 56 m.
So,
[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]
Let A denotes area of rectangle.
A = length × width
[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]
Differentiate with respect to x
[tex]\frac{dA}{dx}=28-2x[/tex]
Put [tex]\frac{dA}{dx}=0[/tex]
[tex]28-2x=0\\2x=28\\x=14[/tex]
Also,
[tex]\frac{d^2A}{dx^2}=-2<0[/tex]
At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]
So, x = 14 is a point of maxima
So,
[tex]y=28-x=28-14=14[/tex]
Area of rectangle:
[tex]A=xy=14(14)=196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
2x + y + 4z = 16
5x - 2y + 2z = -1
X + 2y - 32 = -9
a. (-1, 2, 22)
c. (-1, 2, 4)
b. (-10, 22, 42)
d. (-10, 2, 22)
The solution to the system of equations is (-1, 2, 4), which is equal to choice (c) (-1, 2, 4).
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
To solve the system of equations, we can represent it in an augmented matrix and use row operations to find its reduced row-echelon form.
The augmented matrix for the system is:
[ 2 1 4 | 16 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
We want to get the matrix in reduced row-echelon form.
We can start by using row operations to get a 1 in the upper left corner:
R(1/2) -> R1:
[ 1 1/2 2 | 8 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
Now we want to get zeros in the first column below the pivot element (1). We can do this by subtracting 5 times the first row from the second row, and subtracting the first row from the third row:
-5R1 + R2 -> R2:
-R1 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 3/2 -5 | -17 ]
R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 -3 -13 | -58 ]
We can continue with row operations to get a 1 in the second row, second column:
(-2/9)R2 -> R2:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 -3 -13 | -58 ]
3R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 -23/3 | -92/3 ]
Finally, we can get a 1 in the third row, third column:
(-3/23)R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 1 | 4 ]
Now the matrix is in reduced row-echelon form.
We can read the solution directly from the last column:
x = 8 - (1 + 8) = -1
y = 82/9 - (16/9)(4) = 2
z = 4
Therefore, the solution to the system of equations is (-1, 2, 4).
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Boxes A and B contained 112 pencils. When 1/5 of the pencils in box A were transferred to box B, both boxes combined the same number of pencils. How many more pencils were there in box A than in Box B at first?
Answer:
The number of pencils in the box A is 70
The number of pencils in the box B is 42
Step-by-step explanation:
The number of pencils in the box A is a
The number of pencils in the box B is b
We have:
a + b = 112
a - (1/5)a = b + (1/5)a
or
a + b = 112
a - (2/5)a = b
or
a + b = 112
(3/5)a = b
or
a + (3/5)a = 112
or
(8/5)a = 112
or
a = 112*(5/8)
or
a = 70
=> b = 112 - 70 = 42
Hope this helps!
Use slopes and y-intercepts to determine if the lines y=5x+5 and 5x−y=−5 are parallel.
Answer: They are not parallel, they are coincident
Step-by-step explanation:
If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.
We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:
5x - y =-5
5x - y -5x = -5 - 5x (adding -5x to both sides)
-y = -5 - 5x
Multiplying by -1
y = 5x + 5
Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 64 months and a standard deviation of 7 months. Using the empirical (68-95-99.7) rule, what is the approximate percentage of cars that remain in service between 43 and 50 months?
Answer:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
Step-by-step explanation:
For this case we have the following parameters from the variable number of motnhs in service for the fleet of cars
[tex] \mu = 64, \sigma =7[/tex]
For this case we want to find the percentage of values between :
[tex] P(43< X< 50)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{X-\mu}{\sigma}[/tex]
In order to calculate how many deviation we are within from the mean. Using this formula for the limits we got:
[tex] z =\frac{50-64}{7}= -2[/tex]
[tex] z =\frac{43-64}{7}= -3[/tex]
We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%
And then the final answer for this case would be:
[tex] 2.5 -0.15 = 2.35\%[/tex]
Select all statements below that are true about the binomial distribution shown on the right. The bar for any number k represents the probability of getting k successes in 5 flips. The number of successes, k, can range from 0 (no success) to 5 (all successes). Each coin flip is independent; it is not affected by any other coin flip. For 5 coin flips, P(2 heads) = P(3 heads). The sum of the probabilities shown in the binomial distribution is p.
Answer:
Step-by-step explanation:
Hello!
Distribution in attachment.
The variable of interest is:
X: Number of successes after flipping a coin 5 times.
If you check the binomial criteria:
The number of trials is fixed: n=5
There are only two possible outcomes "success" or "failure"
Each flip of the coin is independent of the others.
The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5
The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)
Statements:
1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.
2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)
3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.
4) For 5 coin flips, P(2 heads) = P(3 heads). Correct
Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.
5) The sum of the probabilities shown in the binomial distribution is p.
Incorrect.
For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.
For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.
I hope this helps!
Answer:
Lets make this easier for you guys. The correct answers are 1 through 4.
The bar for any number k represents the probability of getting k successes in 5 flips.
The number of successes, k, can range from 0 (no success) to 5 (all successes).
Each coin flip is independent; it is not affected by any other coin flip.
For 5 coin flips, P(2 heads) = P(3 heads
Step-by-step explanation:
Correct on edge :))
A nurse’s aide earns $375 per week for 50 weeks of the year. What are her total earnings for the year?
Answer:
$18,750
Step-by-step explanation:
Take the earnings per week times the number of weeks
50 * 375
18,750
Answer:
$18,750
Step-by-step explanation:
If we want to find the nurse's aide's earnings for the year, we have to multiply her weekly salary by the number of weeks she worked.
weekly salary * number of weeks
She earns $375 per week and she worked for 50 weeks.
$375*50 weeks
375*50
Multiply the 2 numbers
18,750
Her total earnings for the year are $18,750
In a certain area an average of 13 new swarms of honeybees are seen each spring. If the number of swarms stays constant each year, what is the probability of observing between 9 and 15 (inclusive) swarms?
Answer:
The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
Step-by-step explanation:
The random variable X can be defined as the number of swarms of honeybees seen each spring.
The average value of the random variable X is, λ = 13.
A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.
For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.
So, the random variable X follows a Poisson distribution with parameter λ = 13.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]
Compute the the probability of observing between 9 and 15 (inclusive) swarms as follows:
P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)
[tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]
Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
Suppose that x has a binomial distribution with n = 201 and p = 0.45. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.
Answer:
a) It can be used because np and n(1-p) are both greater than 5.
Step-by-step explanation:
Binomial distribution and approximation to the normal:
The binomial distribution has two parameters:
n, which is the number of trials.
p, which is the probability of a success on a single trial.
If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.
In this question:
[tex]n = 201, p = 0.45[/tex]
So, lets verify the conditions:
np = 201*0.45 = 90.45 > 5
n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5
Since both np and n(1-p) are greater than 5, the approximation can be used.
The ice cream shop has 7 types of toppings available, and you decide to add 4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5 scoops of ice cream and 4 toppings are possible
Answer: 35
Step-by-step explanation:
The number of combinations of r things selected out of n things is given by
[tex]^nC_r= \dfrac{n!}{r!(n-r)!}[/tex]
Given , the total number of types of toppings available = 7
The number of toppings needed to be selected = 4
Then, the number of ways to do this would be
[tex]^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35[/tex]
Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.
what do you think 40×40 is
And tell how you got your answer
Answer:
1600
please see the attached picture for full solution
Hope it helps...
Solve the equation 4c=3
c =
Answer:−2x=−8
4sin2(x)−1=0
2x+3=3
Step-by-step explanation:
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
260
20
Step-by-step explanation:
speed of plane= p
speed of wind =w
(p+w)*3=840 p+w=840/3=280and
(p-w)*3.5=840p-w= 840/3.5= 240added up the 2 equations we get:
2p= 280+240p=260 mphthen
w= 20 mphPlease answer this correctly
Answer:
B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.
Step-by-step explanation:
The first option is an opinion, not a fact.
Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?
Answer:
Solve -x2+11xandg+6x-6 = 0
Step-by-step explanation:
Suppose 221 subjects are treated with a drug that is used to treat pain and 51 of them developed nausea. Use a 0.10 significance level to test the claim that more than 20% of users develop nausea.
Answer:
[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]
The p avlue for this case is given by:
[tex]p_v =P(z>1.152)=0.125[/tex]
The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%
Step-by-step explanation:
Information provided
n=221 represent the random sample taken
X=51 represent the people with nausea
[tex]\hat p=\frac{51}{221}=0.231[/tex] estimated proportion of people with nausea
[tex]p_o=0.21[/tex] is the value to test
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to check if the true population is higher than 0.20, the system of hypothesis are.:
Null hypothesis:[tex]p \leq 0.2[/tex]
Alternative hypothesis:[tex]p > 0.2[/tex]
The statistic is given:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]
The p avlue for this case is given by:
[tex]p_v =P(z>1.152)=0.125[/tex]
The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%
Budget
8.) If Peter Gower paid $650 for rent
monthly for an entirely year, how
much should he budget for rent
each month?
Answer:
I
(a) $108.33
(b) $54.17
(c) $7.800
(d) $650
A cereal box is an example of a____ a0___ a1.
Answer:
rectangular prism
Step-by-step explanation:
A rectangular prism has 6 sides that are rectangles.
Which statement accurately describes chemical rocks?
Answer:
Chemical rocks form when minerals dissolve in a solution and crystalize.
Answer:
Chemical rocks don't form from solidification from a melt
Step-by-step explanation:
Salid bought 30 feet of window trim at a hardware store. The trim cost $1.75 per foot including sales tax. If Salid paid with a $100.00 bill, how much change should he have received?
Answer:
47.50
Step-by-step explanation:
According to the question above Salid bought 30 feet of window at a hardware trim store
The trim cost of each window is $1.75 per foot with an inclusion of sales tax added to this amount
= $1.75×30
= 52.5
Since Salid paid for the trim service with a cash of $100.00, his change is calculated as follows
=$100-52.5
= $47.50
Hence Salid change is $47.50
How many strings can be formed by ordering the letters MISSISSIPPI which
contain the substring of MISS?
Answer:
1680 is the answer.
Step-by-step explanation:
Here, we have 11 letters in the word MISSISSIPPI.
Repetition of letters:
M - 1 time
I - 4 times
S - 4 times
P - 2 times
As per question statement, we need a substring MISS in the resultant strings.
So, we need to treat MISS as one unit so that MISS always comes together in all the strings.
The resultant strings will look like:
xxxxMISSxxx
xxMISSxxxxx
and so on.
After we treat MISS as one unit, total letters = 8
Repetition of letters:
MISS - 1 time
I - 3 times
S - 2 times
P - 2 times
The formula for combination of letters with total of n letters:
[tex]\dfrac{n!}{p!q!r!}[/tex]
where p, q and r are the number of times other letters are getting repeated.
p = 3
q = 2
r = 2
So, required number of strings that contain MISS as substring:
[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]
So, 1680 is the answer.
14d+21 and 7 (2d+3) choose yes or no to see if the expression is equivalent
Answer:
Yes- these answers are equivalent.
Step-by-step explanation:
In the expression 7(2d+3), the 7 is outside the parentheses, meaning everything inside the parentheses is multiplied by 7.
2d X 7 = 14 d
3 X 7 = 21
7(2d+3) = 14d + 21
Yes, the expressions are equivalent.
What is expression ?By combining numbers, variables, functions in mathematics we get an expression.
Example : 4p+2, 3x-4y etc
What is the required result ?Given expressions are 14d+21 and 7(2d+3)
Here, simplifying the expression 7(2d+3) we get,
7(2d+3) = (7×2d)+(7×3) = 14d+21
Therefore, the given two expressions are equal to each other, i.e same.
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In performing a chi-square goodness-of-fit test with multinomial probabilities, the ___________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.
Answer:
Step-by-step explanation:
The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.
A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon. It was felt that gasoline price in Texas was significantly lower than the national average. A study of 37 different suburbs in Dallas, Texas, found the average price of gasoline to be $1.192 a gallon with a standard deviation of $0.0436. What is the alternative hypothesis
Answer:
alternative hypothesis : H₁ :
Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average
Alternative Hypothesis : H₁: μ < $1.298 a gallon
Step-by-step explanation:
Explanation:-
Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon
Population average μ= $1.298 a gallon
sample size 'n' = 37
Sample mean (x⁻) = $1.192 a gallon
Sample standard deviation 'S' = $0.0436
Null hypothesis :H₀ : μ = $1.298 a gallon
Alternative Hypothesis : μ < $1.298 a gallon
Degrees of freedom : ν = n-1= 37-1=36
t₀.₀₂₅ = 1.688
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }[/tex]
t = -14.8044
|t| = |-14.8044| > 1.688
Null hypothesis is rejected
Alternative hypothesis is accepted
Recent Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average
I can’t figure this out it’s difficult for can anyone help me Plz
Answer:
the correct option is D
Step-by-step explanation:
JK IS longer than JL
A square matrix AA is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A)s(A) and is called the magic sum of the matrix AA. Let VV be the vector space of 2×22×2 half-magic squares.
A) Find an ordered basis BB for VV.
B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]
Answer:
A) [tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]
B) [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]
Step-by-step explanation:
Let [tex]A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right][/tex] where a, b, c and d are real numbers
Since A is said to be a half magic square matrix, a = d, b = c.
The matrix A therefore becomes [tex]A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right][/tex] where [tex]a,b \epsilon R[/tex]
A can therefore be manipulated as:
[tex]A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
The matrices [tex]\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex] are apparently linearly independent and therefore form a basis B for V
[tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]
B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]
[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right][/tex]
[tex]M[/tex] can be written in the form [tex]M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]
The coordinate vector is therefore, [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]