The solution to the linear system of equation is x = 3, y = 5, and z = -0.5
What is a linear system of equation?A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together
The system of linear equation is presented as follows;
2·x - 3·y + 6·z = -12...(1)
5·x + 2·y - 8·z = 29...(2)
7·x + 6·y + 4·z = 49...(3)
Multiplying equation (1) by 5 and equation (2) by 2, we get;
5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)
2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)
Subtract equation (4) from equation (5), to get;
10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118
19·y - 46·z = 118...(6)
Multiplying equation (1) by 7 and equation (3) by 2, we get;
7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)
2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)
Subtracting equation (7) from equation (8), we get;
14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182
33·y - 34·z = 182...(9)
Multiplying equation (6) by 33 and equation (9) by 19, we get;
627·y - 1,518·z = 3,894...(10)
627·y - 646·z = 3,458...(11)
Subtracting equation (10) from equation (11), we get;
627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436
872·z = -436
z = -436 ÷ 872 = -0.5
z = -0.5
From equation (6), we have;
19·y - 46·z = 118
19·y - 46 × (-0.5) = 118
19·y - 46 × (-0.5) = 118
19·y = 118 + 46 × (-0.5) = 95
y = 95 ÷ 19 = 5
y = 5
From equation (1), we get;
2·x - 3·y + 6·z = -12
2·x - 3 × 5 + 6 × (-0.5) = -12
2·x = -12 + 3 × 5 - 6 × (-0.5) = 6
x = 6 ÷ 2 = 3
x = 3
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redo the probability calculation for pits in [1,3] and [2,2], assuming that each square contains a pit with probability 0.01, independent of the other squares. what can you say about the relative performance of a logical versus a probabilistic agent in this case?
The pit [2, 2]'s prior probability tends to be 0 and its posterior probability tends to be 1.
Compute the probabilities of Pits Each square in the Wumpus world do consist of a pit with the probability of 0.01 and consist of independent contents of the squares.
As suppose there are total of N/2 pits that are scattered randomly among the total of N squares. To compute the probabilities of the pits in [1, 3] and [2,2], consider that the probabilities of the assignments to complete where the other assignments doesn't gets off.
Thus, the total number of the 3-pit assignment rather remains consistent with the three assigned partial assignments here P 1,3 =true.Thus, in 21 assignment completes when the P 1,3 =true. Next the 55 assignment completes when the
P 1,3, = false.
Thus, it gives P(P 1.3 ) = a' (0.01(0.0001+0.0099+0.0099), 0.99(0.0001+ 0.0099)) = (0.1674, 0.8326)
While when the value of Pay = true, then there are basically four assignments that are partialenough with the total value of 0.0001, 0.0099, 0.0099, 0.9801, through the assignment gets completed.
Next when the value of Pa, = false, then there is only a single assignment that is partial with the value of 0.0001 that completes the assignments. Thus, then the final value of P (P2.2 ) is given asP(P2.2) = a' (0.01(0.0001+ 0.0099+0.0099+0.9801), 0.99x 0.0001) = (0.9902, 0.0098
Thus, the prior probability of the pit [2, 2] tends to be 0 and the posterior probability tends to be one (1).
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find y when x=17 if y varies directly as x, and y=43 when x=11
The value of y when x = 17 is 66.5
How to determine the value of y?From the question, we understand that:
The variation is a direct variation
The equation of a direct proportion can be represented as
y = kx
Where:
y = independent variablek = constant of proportionalityx = independent variableFrom the question, we have
When x = 11, we have = 43
So, we have
11k = 43
Make k the subject
k = 43/11
Substitute k = 43/11 in y = kx
y = 43/11x
When x = 17, we have
y = 43/11 x 17
This gives
y = 66.5
Hence, the value of y is 66.5
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a publisher reports that 45% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 300 found that 37% of the readers owned a particular make of car. determine the p-value of the test statistic. round your answer to four decimal places.
The test statistic's p-value is -2.785.
According to A publisher, 45% of its readers own a particular make of car.
Claim: An executive in marketing would like to test the claim that the percentage is different from what is reported.
[tex]H_{o}[/tex]: p = 0.45
[tex]H_{a}[/tex]: p ≠ 0.45
a random sample of 300 found that 37% of the readers owned a particular make of car.
= 37% × 300
= (37 ÷ 100) × 300
X = 111
n= 300
One sample proportion test should be used.
p-vector = x ÷ n,
p-vector = 111 ÷ 300
p-vector = 0.37
The test statistic's formula,
= [tex]\frac{p-q}{\sqrt{\frac{pq}{n} } }[/tex]
test statistic = [tex]\frac{0.37- 0.45}{\sqrt{\frac{0.45(1-0.45)}{300} } }[/tex]
≈ -2.7851
thus, the p-value of the test statistic is -2.7851.
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The figure shows two parallel lines, j and k, cut by two transversals, t₁ and t₂.
What is the value of m<3, in degrees, if m<5 = 70° and m<2 = 60°?
the figure for m3 in the above question is 50
Expand and simplify (x + 3)(x + 5)
Answer:
expanded: x^2+8x+15
Step-by-step explanation:
(x+3)(x+5)
x^2+5x+3x+15
A point has the coordinates (0, k).
Which reflection of the point will produce an image at the same coordinates, (0, k)?
The reflection of point produce an image at the same coordinates, (0, k) is a reflection of the point across the y-axis.
What is Reflection?A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a figure in a line or a point.
Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line.
Given:
A point has the coordinates (0, k).
The rule for a reflection of a point across the x-axis is:
(x, y) ----> (x, -y)
and, the reflection is (0 , -k)
The rule for a reflection of a point across the y-axis is:
(x, y) ----> (-x, y)
and, the reflection is (-0 , k) or (0, k).
The rule for a reflection of a point across the line y = x is:
(x, y) ----> (y, x)
and, the reflection is (k, 0).
and, The rule for a reflection of a point across the line y = -x is:
(x, y) ----> (-y, x)
and, the reflection is (-k, 0)
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which hypothesis or hypotheses about the relation between life satisfaction and job satisfaction has received the most empirical support?
Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.
According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.
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Y'all someone PLEASE help me!!! This is due tonight!!!!!!!!!!!!!
The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.
What is the AAS Congruence Theorem?The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.
In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.
Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.
Statements Reasons
1. ∠Z ≅ ∠C 1. Given
AK bisects ∠ZKC
2. ∠ZKA ≅ ∠CKA 2. Definition of bisection
3. AK ≅ AK 3. Reflexive property
4. ΔAKZ ≅ ΔAKC 4. AAS
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Given that D( x ) = 2 x , select all of the following that are true statements.
D( x ) is a direct variation.
D( x ) is a function.
D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4)
x is the dependent variable.
D(6) = 3
Gaste el 30% de lo que no gaste, si hubiera gastado el 40% de lo que no hubiera gastado, entonces ahora tendría 30 dólares menos de los que tengo
Veremos que originalmente tenias $300, y el valor de la compra fue de $90
¿Cuanto dinero tenía originalmente?Definamos X como la cantidad original de dinero. Ahora trabajaremos con porcentajes.
Sabemos que tu gastaste 30% de esto, entonces lo que te sobra es:
0.7*X
Sabemso qe si hubieras gastado el 40% (en este caso te sobra 0.6*X), te sobrarian 30 dolares menos, entonces podemos escribir:
0.7*X = 0.6*X + $30
Resolviendo para X
0.7*X - 0.6*X = $30
0.1*X = $30
X = $30/0.1 = $300
Originalmente tenias $300 dolares, y gastaste:
$300*0.3 = $90
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please help!!!!! math functions
Answer:
A and C
Step-by-step explanation:
For every x value, there should be at most 1 y value.
B and D violate that constraint.
Tiara, a quality assurance inspector at a chocolate factory, checks for product quality using a random sample of 18 pieces of chocolate from a batch of 60, with 17 white chocolates and 43 dark chocolates. Let p be the proportion of white chocolates in the sample
The 10% criterion is not followed in Part A. The typical condition is not satisfied in component B.
What is proportion?A proportion is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.
Here,
The chocolate chunks' data are as follows:
The sample size (n = 18) of chocolates
The batch contains 17 pieces of white chocolate.
The batch contains 43 dark chocolates.
Given the percentage of white chocolates in the sample, we have;
p = 17/60 = 0.28, the proportion of white chocolates in the batch
Part A
Because sampling samples without replacing them does not result in independent Bernoulli trials, the 10% condition stipulates that the sample size should be less than or equal to 10% of the population.
Because the stated sample size, n = 18, is 18/60100 = 30% > 10% of the batch, the 10% condition is not satisfied in the current case.
Part B
The normal approximation can be assumed when we have;
n·p > 10 and n·p·(1 - p) > 10
By plugging in the values for 'n' and 'p', we have;
p = 0.28 = 17/60
n·p = 18 × 17/60 = 5.1 < 10
n·p·(1 - p) = 18 × 17/60 × (1 - 17/60) = 3.655 < 10
Therefore the normal condition is not met.
Part A does not adhere to the 10% requirement. Component B does not meet the normal condition.
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Martina purchased a prepaid phone card for 45.50$ calls cost 10 cents a minute using this card. The credit, C (in dollars) , left on the card after it is used for x minutes of calls is given by the following function
Answer:
Credit (C) = $45.50 - 0.10x
Step-by-step explanation:
Since you are wanting the credit (C) that is the y variable.
The prepaid phone card starts off with a balance of $45.50.
Every minute a call is made $0.10 is deducted (subtracted) from the card.
The unknown number or 'x' represents the number of minutes the calls lasted.
Carter is hooked on a new book series, The Galaxy. Each book in the series is the same
length and chronicles a different year in the Waka Waka Galaxy. Carter has cleared off the top
shelf of his bookcase to leave room for each of the books as they come out.
There is a proportional relationship between the number of books on the shelf, x, and how
much shelf space the books take up (in inches), y.
The proportional relationship between the number of books on shelf and how much shelf space the books takes up is 1 inch
What is proportionality?
The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.
When two or more parameters are directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k.
As we know [tex]\frac{y}{x}[/tex] = constant of proportionality
So, [tex]\frac{y}{x}[/tex] will be
[tex]\frac{2}{2} = \frac{11}{11} = \frac{13}{13} = \frac{16}{16}[/tex] = 1
∴ it is 1 inch per book
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AB has endpoints at A(-4, 4) and B(5, -1).
Find the coordinates
(x, y) of the midpoint.
Answer:
(0.5, 1.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (- 4, 4 ) and (x₂, y₂ ) = B (5, - 1 ) ,then
M = ( [tex]\frac{-4+5}{2}[/tex] , [tex]\frac{4-1}{2}[/tex] ) = ( [tex]\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = (0.5, 1.5 )
Answer:
The midpoint is at ( 1/2, 3/2)
Step-by-step explanation:
Midpoint
To find the x coordinate of the midpoint
Add the x coordinates of the endpoints and divide by 2
( -4+5)/2 = 1/2
To find the y coordinate of the midpoint
Add the y coordinates of the endpoints and divide by 2
( 4+-1)/2 = 3/2
The midpoint is at ( 1/2, 3/2)
each law firm in one state registers its phone number with the state court system. an employee of the state court system uses a computer to select 500500500 random registered phone numbers, and the law firms associated with those numbers will be selected for an audit. what type of sample is this?
In this "Simple Random Sample" scenario, 500500500 selected randomly registered phone numbers were chosen.
Define the term Simple random sample?A subset of either a population is chosen at random in a basic random sampling. Each individual in the population has had an exact equal probability of getting selected using this sampling technique.Among all of the probability sampling techniques, this one is the easiest to understand because it only includes one random selection and little prior population knowledge. Any research conducted on this sample must have excellent validity both internally and externally because it uses randomization.For the given data in the question.
Every law firm in a state registers it phone number only with state court system as a result.Thus, 500500500 random registering phone numbers are randomly chosen by a state court employee using a computer, and the law firms connected to all those numbers are randomly chosen for an audit.
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hello can someone help me pls
Answer:
sum= 1080
Step-by-step explanation:
Answer:
The sum of an octagon is always 1080 degrees. The interior angles are usually all equal to 135 degrees, but this is an irregular octagon, making that not the case. Because the angles are not all equal, that does not mean that the octagon's sum is any different. Thus, the sum of the interior angles is 1080 degrees.
Hope this helps!
The difference between a big shot and a little shot is that a big shot is just a little shot that kept on shooting. what do you think about this quote? answer and ill give you a lot of points 100 for free
Answer:
The quote seems to have a little to much shooting. Don’t you think?
Step-by-step explanation:
Answer:
lair lair
Step-by-step explanation:
During 75 days, rain fell on 3/5 of the day. On how many days did rainfall?
Answer:45
Step-by-step explanation:
75*3/5
Cube root of 426 give your answer to the nearest integer
Answer:
3
Step-by-step explanation:
what is the answer to this equation? 20=v+9-16
Answer:
Step-by-step explanation:
20=v+9-16
So first, we combine like terms
20=v-7
Then we want to add 7 on each side
20=v-7
+7 +7
Then we are left with
27=v
Step-by-step explanation:
Subtract the numbers
20=v+9-16 =20=v-7
Add 7 to both sides
20=v-7
20+7=v-7+7
Then simplify P.S if you dont know how to comment on the answer
ANSWER v=27
Please Help me with this (ASAP) 20 POINTS
The value of y when x = -2, 0,2 is 1/49, 7, 49.
Simplification is an algebraic expression is when we utilize a range of approaches to make algebraic expressions more efficient and compact - in their simplest form - without changing the value of the original expression.
Given function y =[tex]7^{x}[/tex]
We have to determine the y values when x = -2, 0, 2
Now substitute the x values in the given function
If x = -2 then
Y = 7(-2)
Y = 1/49
If x = 0 then
Y = 7(0)
Y = 1
If x = 2 then
Y = 7(2)
Y = 49
Therefore the value of y when x = -2, 0 ,2 is 1/49, 7 , 49
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if they are 180 percent of people not satisfied with there car and there is 820 people somewhat satisfied, and 1500 people are completely satisfied. what is the percent of people who are completely satisfied with their car
Answer:
Completely satisfied with their car: 60.00%
Step-by-step explanation:
I'll assume that "180 percent of people not satisfied . ." is meant to read "180 people not satisfied . . ."
Add the people in the groups to find a total. Then divide the numeber of people in each group by the total. This will provide a decimal number which can be multiplies by 100% to give the breakdown requested.
Group Count Percent(%)
Not S. 180 7.20
Somewhat S. 820 32.80
Completely S. 1500 60.00
Total People: 2500 100.00%
a police car is located 70 feet to the side of a straight road. a red car is driving along the road in the direction of the police car and is 90 feet up the road from the location of the police car. the police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. how fast is the red car actually traveling along the road?
The speed of 213.25 mph is the red car actually traveling along the road.
What is speed?
The definition of speed is the pace of movement of an object (covering a particular distance). It defines only the magnitude and not the direction, making it a scalar quantity.
The meter per second (m/s) unit of speed is taken from the SI.
let distance between the police and red cars = h
distance from the red car to a point horizontal to the police car = a
distance from from the road to the police car = b
=>[tex]h^2=a^2+b^2[/tex]
take the derivative with respect to time
=>hh' = aa' + bb' b'=0
=>174.64(75) = 90a'
=>a' = 174.64(75)/90 = 145.4ft/sec
=>145.4ft/sec = 145.4(5280)/60^2 = about 213.25 mph
Here ,1 mile = 5280 feet
=>1 hour = 60 minutes x 60 seconds = 3600 seconds
=>1 mile per hour = 5280 feet per 3600 seconds
=>1 foot per second = 5280/3600 mph = 1.4666...mph
=>145.4x 1.4666... = 213.25 mph
Hence 213.25 mph speed is the red car actually traveling along the road.
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Explain how the distributive property cam be used to eliminate the fractions in the equation 1/5x +8 = 1/10x + 9
We will use the distributive property to take a common factor in the next step:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Using that we will see that the solution is x = 10.
How can we use the distributive property?The distributive property can be written as:
A*(B + C) = A*B + A*C
Now we have the equation:
(1/5)*x + 8 = (1/10)*x + 9
If we group like terms we get:
(1/5)*x - (1/10)*x = 9 - 8
Here we apply the property, we can rewrite the left side as:
(1/5)*x - (1/10)*x = (1/5 - 1/10)*x
Then we can write:
(1/5)*x - (1/10)*x = 9 - 8
(1/5 - 1/10)*x = 1
(1/10)*x = 1
x = 10*1
x = 10
And that is the solution.
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help!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.
Jonshelle is developing a new bread recipe. The relationship between cups of water, w, and cups of flour, f, is a=2/5b. What is the scale factor of flour to
water?
Answer: the i8 49
Step-by-step explanation:98493
A school needs to buy new notebook and desktop computers for its computer lab. The
notebook computers cost $200 each, and the desktop computers cost $400 each.
How many total computers would someone buy if they get 12 notebooks and 15
desktop computers? How many total computers would someone buy if they get n
notebooks and d desktop computers?
Total computers, 12 notebooks and 15 desktop computers:
Total computers, n notebooks and d desktop computers:
Answer: 27
Step-by-step explanation:
Well we already know that n is 12 and d is 15
So based on what I see we do n + d which would equal 27.
Which expression equals 9/10 ?
O 5√10+4√10
O5 10+4 10
O 5√10+43/10
O 5 10+4 10
Answer:
The second answer:
5cubrt10 + 4cubrt10
Step-by-step explanation:
In order to get a cubrt10 answer you have to add cubrt10's.
The first answer has squareroots, so that's a no.
The last two have cubrt + sqrt, which cannot be simplified.
5cubrt10 + 4cubrt10 = 9cubrt10
I am stuck on this. Can someone help me with my math homework
Answer: -5,5 = B
Step-by-step explanation:
