Answers
Answer:
(2.83 , 1 , 4)
Step-by-step explanation:
[tex]2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\[/tex]
Rewrite these equations in matrix form
[tex]\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\[/tex]
we can write it like this,
[tex]AX=B\\X=A^{-1}B[/tex]
so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.
We get the inverse of matrix A,
[tex]A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\[/tex]
now multiply the matrix with B
[tex]X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\[/tex]
Related Questions
Garrett paid $20 for five movie tickets. Find the cost per ticket.
Write the unit rate rounded to the nearest hundredth
Answers
Answer:
4 is the unit rate
Step-by-step explanation:
Stephanie thinks of a positive number.
She squares the number and adds 7
The result is 43
What number did Stephanie think of?
Answers
Answer:
Step-by-step explanation:
If the number is 6 then square of 6 is 36 then adding 7 = 36 + 8 = 43
So the number is 6
Answer:
6
Step-by-step explanation:
Do the question backwards
43 - 7 = 36
[tex]\sqrt{36}[/tex] = 6
Stephanies number was 6
PLS HELP Which number has a product of -6/5 when multiplied by -12/5
A. -18/5
B -1/2
C 1/2
D 2/1
Answers
1/2 x -12/5 = -6/5
You multiple across the top and bottom so you would do 1 x -12, which equals -12 (the numerator) and then 2 x 5 = 10 (the denominator) so the answer is -12/10, this can be simplified to -6/5.
A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Answers
Answer:
1) The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
Step-by-step explanation:
1) Let [tex]A(x,y) = (2,3)[/tex] and [tex]B(x,y) = (8,11)[/tex]. From Analytical Geometry, we get that slope of AB ([tex]m_{AB}[/tex]), dimensionless, is determined by the following formula:
[tex]m_{AB} = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (1)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the slope of the line segment is:
[tex]m_{AB} = \frac{11-3}{8-2}[/tex]
[tex]m_{AB} = \frac{4}{3}[/tex]
The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB ([tex]l_{AB}[/tex]), dimensionless, can be calculated by the Pythagorean Theorem:
[tex]l_{AB} =\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex] (2)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the length of the line segment AB is:
[tex]l_{AB} = \sqrt{(8-2)^{2}+(11-3)^{2}}[/tex]
[tex]l_{AB} = 10[/tex]
The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{x_{A}+x_{B}}{2}[/tex] (3)
[tex]y_{M} = \frac{y_{A}+y_{B}}{2}[/tex] (4)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{2+8}{2}[/tex]
[tex]x_{M} = 5[/tex]
[tex]y_{M} = \frac{3+11}{2}[/tex]
[tex]y_{M} = 7[/tex]
The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:
[tex]m_{\perp} = -\frac{1}{m_{AB}}[/tex] (5)
If we know that [tex]m_{AB} = \frac{4}{3}[/tex], then the slope of a line perpendicular to AB is:
[tex]m_{\perp} = - \frac{1}{\frac{4}{3} }[/tex]
[tex]m_{\perp} = -\frac{3}{4}[/tex]
The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
Felipe sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit
$125, how many t-shirts did he sell?
Answers
Answer:
He sold 17 shirts at the festival.
The total number of t-shirts Felipe sold is 17 t-shirts.
Consider that the number of t-shirts Felipe sold be "x".
Since He made a profit of $5 for each t-shirt sold. Therefore, his profit from selling t-shirts is 5x. also made a profit of $40 from selling hats.
His total profit is given as $125.
So we can write the following equation:
5x + 40 = 125
Subtracting 40 from both sides;
5x = 85
Dividing both sides by 5, we get:
x = 17
Therefore, Felipe sold 17 t-shirts.
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HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answers
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
5/13 as a decimal rounded to the nearest hundredth
Answers
Answer:
0.40
Step-by-step explanation:
5/13 = 0.38461538461. Hundreths place is the 2nd number after decimal so if you round 8 it'll be .40
Answer:
5/13 as a decimal to the nearest hundredth is 0.39 or 0.40.
Step-by-step explanation:
You simply need to divide 5 by 13, and you get 0.384615, but round to the nearest hundredth gets you 0.40
I need your help pls help me I make u big brain\
Answers
4 or d object is moving away at an increasing speed
select the pair of perpendicular segments from the figure below
Answers
15.) whats the approximately measure of one interior angle of the regular polygon shown
16.) the shape in the figure is a square . Use the properties to determine the value of X
Answers
Answer:
15) For a regular polygon of N sides, the measure of one interior angle is:
A = (N - 2)*180°/N
In this case, the figure has 11 sides, then we have N = 11, and the measure of each interior angle will be:
A = (11 - 2)*180°/11
A = 9*180°/11 = 147.27°
Rounding to the first decimal after the decimal point, we get:
A = 147.3°
Then the correct option is B.
16) We know that the length of all the sides of a square is the same.
In the image, we can see that the length of the right side is 4, and the length of the top side is 2x + 4
And those lengths must be the same, then we have the equation:
2x + 4 = 4
subtracting 4 in each side of the equation we get:
2x + 4 - 4 = 4 - 4
2x = 0
The only solution for this equation is x = 0.
Then the correct option is C
Question 1
Mathematical Relationships
Part A
In general, what can you say about the relationship between health (life
expectancy at birth) and wealth? Mention possible reasons for this
relationship
Answers
someone with wealth without health is nobody
Step-by-step explanation:
when someone that is wealthy didn't give birth d Husband would say they should adopt a child or he should marry another wife
Solve the equation for x. 3x = 15
Answers
Answer:
x=5
Step-by-step explanation:
15/3=5 or 5x3=15
Answer:
So divide each term by -3 and simplify the answerr x=5
Step-by-step explanation:
If I litres of Paint cost R10,00
how many will 10 litres of paint
cost ?
Answers
Answer:
10000
hope it helps!
.....
Which expression is equivalent to -3(4x-0.50)?
PLEASEEEEEEEEEEEEE HELPPP
Answers
Final Answer: [tex]-12x + 1.5[/tex]
Steps/Reasons/Explanation:
Question: Which expression is equivalent to [tex]-3(4x - 0.50)?[/tex]
Step 1: Expand by distributing terms.
[tex]-3[/tex] × [tex]4x - 3[/tex] × [tex]-0.50[/tex]
Step 2: Simplify [tex]-3[/tex] × [tex]4x[/tex] to [tex]-12x[/tex].
[tex]-12x - 3[/tex] × [tex]-0.50[/tex]
Step 3: Simplify [tex]3[/tex] × [tex]-0.50[/tex] to [tex]-1.5[/tex].
[tex]-12x - (-1.5)[/tex]
Step 4: Remove parentheses and add.
[tex]-12x + 1.5[/tex]
~I hope I helped you :)~
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answers
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
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When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 10.
Answers
Answer:
1/7
Step-by-step explanation:
Steven needs to unload a truck containing boxes filled with video consoles. He wants to determine the time required to unload the truck. Which quantity will help Steven to determine the time required?
Answers
Answer:
the last one
Step-by-step explanation:
32. Sinead bought 2 shirts for $15.82 each and a pair of shoes for $42.37. If she
paid for the items with a $100 bill, how much change did she receive?
$25.99
$10.17
$74.01
$41.81
Answers
15.82x2=31.64
31.64+42.37=74.01
100-74.01=25.99
Sinead received $25.99 for change.
Answer:
Sinead received $25.99 for change.
Step-by-step explanation:
PLEASE HELP! WILL GIVE BRAINLIEST AND EXTRA POINTS
Answers
Answer:
1,3,4
Step-by-step explanation:
mean median mode range
Answers
Answer:
I think your question is the differences between these terms in mathematical explanation? Well, the median is the middle. You add and divide for the mean. The mode is the one that appears the most. And the range is the difference in between.
Other:
Brainliest? Thanks!
[tex]mean = \frac{sum \: \: of \: \:all \: \: obsevations}{no. \: \: of \: \: observations} [/tex]
[tex]median = middle \: \: most \: \: value[/tex]
[tex]mode = most \: \: occuring \: term[/tex]
[tex]range = highest \: \: observation \: - lowest \: \: observation[/tex]
A farmer conducted a hypothesis test to see if a new type of soybean would grow better on their land. The alternative hypothesis is the new seed will on average grow more than the old soybean type. The farmer runs a controlled experiment and finds a p-value of .345. The farmer comes to the conclusion that there is no evidence that the new soybean will lead to a larger harvest. What error(s) is it possible to commit
Answers
Answer:
Type 2 Error
Step-by-step explanation:
Null Hypothesis [H0] : New soybean has no impact on harvest
Alternate Hypothesis [H1] : New soybean leads to larger harvest
The farmer accepts the null hypothesis & concludes, that there is no impact of new soybean on harvest.
He could have committed Type 2 Error, which refers to accepting a null hypothesis when it is actually false.
Which box has a volume of 125 cubic feet?
4 feet
9 feet
5 feet
4 feet
3 feet
4 feet
5 feet
12 feet
2 feet
5 feet
5 feet
5 feet
Answers
Answer: Bottom left
5x5x5=125
The volume having 125 cubic, is a box which has dimensions, 5 feet, 5 feet, 5 feet. So Option D is correct
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
Given that,
4 boxes having different different dimensions
1. 4 feet, 9 feet, 5 feet
2. 4 feet, 3 feet, 4 feet
3. 5 feet, 12 feet, 2 feet
4. 5 feet, 5 feet, 5 feet
lets calculate the volume for all the four boxes
V = 4 feet × 9 feet × 5 feet = 180 feet³
V = 4 feet × 3 feet × 4 feet = 48 feet³
V = 5 feet × 12 feet × 2 feet = 120 feet³
V = 5 feet × 5 feet × 5 feet = 125 feet³
Hence, the volume of box having dimension 5 feet, 5 feet, 5 feet is 125 feet³
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Which represents the equation of the roll line?
Answers
Answer:
A) y=3x-4
Step-by-step explanation:
Please Help fast I don’t know
Answers
16 is what percent of 20?
Answers
Answer:
3.2
Step-by-step explanation:
0.8 * 100 = 80
Solution: 80%
Terence works as a carpenter and a blacksmith.He earns $30 per hour as a carpenter and $45
per hour as a blacksmith. Last week, Terence
worked a total of 55 hours and earned a total of
$2070. How long did Terence work as a carpenter
last week, and how long did he work as a blacksmith?
Answers
Answer:
he worked 69 hours
Step-by-step explanation:
if u do 2070 divided by 30 u will get 69 and theres your answer
(-25w^5+30w^2)/(-5w) =
Answers
Answer:
(-25w^5+30w^2)/(-5w) Simplified:
5w^4 - 6w
Can you guys help me find the answer, I’m in 6th grade?
Answers
What is the least common multiple of the two denominators 6/8, 4/32
Answers
Answer:
32
Step-by-step explanation:
What is the solution to the following system of equations?
3x - 6y = -12
x - 2y = -8
(1) Use the substitution method to justify that the given system of equations has no solution.
(2) What do you know about the two lines in this system of equations?
Answers
Answer:
1.) x=2y-4
2.) x=2y-4 :)
Answer:
[tex]3x - 6y = - 12 ..........i)\\ x - 2y = - 8............ii) \\ x = 2y - 8 \\ Substituting \: the \: value \: of \: x \:in \: equation \: i) \: we \: get \\ 3(2y - 8) - 6y = - 12 \\ 6y - 24 - 6y = - 12 \\ Here \: we \: can \: see \:that\: the \: value \: of \: y \: cannot \: be \: found \\ Equation \: is \: in \: form \: a \frac{}{1} x + b \frac{}{1} y + c \frac{}{1}= 0\:and \\ a \frac{}{2} x + b \frac{}{2} y + c \frac{}{2} = 0 \\ where, \: \: \frac{a \frac{}{1} }{a \frac{}{2} } = \frac{b \frac{}{1} }{b \frac{}{2} } \\ Therefore \: lines \: are \: parallel \: to \: each \: other \\ Lines \: have \: no \: solution.[/tex]