The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;
to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.
A system of linear equations can be solved by three major methods which are;
- Elimination method
- Substitution method
- Graph method
Now, in this question we want to know how substitution method is done.
Let us say we have two simultaneous equations which are;
2x + 3y = 8 ----(eq 1)
x + 5y = 11 ----(eq 2)
Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.
In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;
x = 11 - 5y
In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.
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Use the Venn diagram to calculate probabilities.
Which probability is correct?
P(A|B)=1/2
P(B|A)=7/20
P(A|C)=6/23
P(C|A)=13/17
Answer: The correct probability is (D) [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Step-by-step explanation: We are given to select the option that gives the correct probability statements using the Venn-diagram in the figure.
From the figure, we can see that there are three events, A, B and C.
And,
[tex]n(A)=1+6+7+3=17,\\\\n(B)=1+6+4+9=20,\\\\n(C)=6+4+6+7=23,\\\\n(A\cap B)=1+6=7,\\\\n(A\cap C)=6+7=13,\\\\n(B\cap C)=6+4=10,\\\\n(A\cap B\cap C)=6.[/tex]
By the law of SET THEORY, we have
[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cup B\cup C)=17+20+23-7-13-10+6\\\\\Rightarrow n(A\cup B\cup C)=36.[/tex]
So, the total number of elements in the sample space 'S' will be
n(S) = 36 + 8 = 44.
Therefore,
[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\dfrac{n(A\cap B)}{n(S)}}{\dfrac{n(B)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{20}=\dfrac{7}{20},\\\\\\\\P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\dfrac{n(B\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{17}=\dfrac{7}{17},\\\\\\\\P(A/C)=\dfrac{P(A\cap C)}{P(C)}=\dfrac{\dfrac{n(A\cap C)}{n(S)}}{\dfrac{n(C)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{23}=\dfrac{13}{23},\\\\\\\\P(C/A)=\dfrac{P(C\cap A)}{P(A)}=\dfrac{\dfrac{n(C\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{17}=\dfrac{13}{17}.[/tex]
Thus, the correct probability is [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Option (D) is correct.
The probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
For the value of probability P(A|B):
We know that:
[tex]\rm P(A/B)=\frac{P(A\cap B)}{P(B)} \Rightarrow \frac{\frac{n(A\cap B)}{n(T)} }{\frac{n(B)}{n(T)} }[/tex]
From the Venn diagram:
n(A∩B) = 7, n(B) = 20, n(T) = 44
P(A/B) = (7/44)×44/20)
P(A/B) = 7/20
For P(B|A):
[tex]\rm P(B/A)=\frac{P(B\cap A)}{P(A)} \Rightarrow \frac{\frac{n(B\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(B∩A) = 7, n(A) =17
P(B/A) = (7/44)×(44/17)
P(B/A) = 7/17
For P(A|C):
[tex]\rm P(A/C)=\frac{P(A\cap C)}{P(C)} \Rightarrow \frac{\frac{n(A\cap C)}{n(T)} }{\frac{n(C)}{n(T)} }[/tex]
The value of n(A∩C) = 13, n(C) = 23
P(A/C) = (13/44)×(44/23)
P(A/C) = 13/23
For P(C|A):
[tex]\rm P(C/A)=\frac{P(C\cap A)}{P(A)} \Rightarrow \frac{\frac{n(C\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(C∩A) = 13, n(A) = 17
P(C|A) = (13/44)×(44/17)
P(C|A) =13/17
Thus, the probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
Learn more about the Venn diagram here:
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Marie decides to work all summer rather than going on vacation. She will be able to earn money and learn new skills but will not be able to spend much time with her friends. What is the opportunity cost in this scenario?
The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.
Explanation:The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.
Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.
What is 6 divided by 1/3
How do you write 230% as a fraction or mixed number in simplest form?
A quadrilateral has angle measures of 52°, 94°, and 97°.
What is the measure of the fourth angle?
Enter your answer in the box.
A quadrilateral has angle measures of 52°, 94°, and 97°.
What is the measure of the fourth angle?
Enter your answer in the box.
Answer: 117
Step-by-step explanation:
A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 ft/s. a. Substitute the values into the vertical motion formula h = −16t2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
f √6 is the geometric mean between 6 and another number, then the number is
HELLO!!! ^-^
The answer is 1.
If √6 is the geometric mean between 6 and another number, then the number is 1.
(I had the same question and got it right using this answer so yeah) ^-^
Have an amazing day!!! ^-^
Historical Fact:
Back in the older days, the word awful was a word used to praise someone! That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!
Just a short answer please help :( the top
A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (4, -9) and could have walked 10 miles in any direction since then. Which equation represents the area the hiker could be in?
A) (x - 4)2 + (y + 9)2 = 102
B) (x + 4)2 + (y - 9)2 = 102
C) (x + 4)2 + (y + 9)2 = 1002
D) (x - 4)2 + (y - 9)2 = 1002
What perfect squares divide into 337? I only need two!
The center of a circle is at (−2, −7) and its radius is 6.
What is the equation of the circle?
(x−2)2+(y−7)2=36
(x−2)2+(y−7)2=3
(x+2)2+(y+7)2=3
(x+2)2+(y+7)2=36
The equation of a circle is (x+4)2+(y−5)2=121.
What is the center and radius of the circle?
center: (4, −5); radius: 11
center: (−4, 5); radius: 121
center: (−4, 5); radius: 11
center: (−4, −5); radius: 121
Answer:
1. option D is correct; [tex](x+2)^2+(y+7)^2=36[/tex]
2. option C is correct; center: (-4, 5) and radius = 11 unit
Step-by-step explanation:
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] .....[1]
where,
(h, k) is the center of the circle and r is the radius of the circle.
1.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
⇒(h, k) = (-2, -7) and r = 6 units
Substitute these in [1] we have;
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
⇒[tex](x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]
2.
As per the statement:
The equation of a circle is:
[tex](x+4)^2+(y-5)^2 = 121[/tex]
We can write this as:
[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]
On comparing with equation [1] we have;
(h, k) = (-4, 5) and r = 11 units
Therefore, the center and radius of the circle is,
center: (-4, 5) and radius = 11 unit
1 question pleasee i need this asap!! thank you :D
In the graph below, find the coordinate of the image point, P(3, 0). O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.
Rx O,90: (3,0)
(0, 3)
(-3, 0)
(0, -3)
Answer:
Thus, (3,0) Rx O,90° changes to (0,-3)
Step-by-step explanation:
O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.Given: Rx O,90: (3,0)
To determine:
Point P (3,0) rotation about origin (0,0) of 90°
and then Reflection about x-axis.
Rotation of P(x,y) about origin of 90°
P(x,y) changes to P'(y,x)
Therefore, P(3,0) changes to P'(0,3)
Now we take reflection about x-axis
R(x,y) changes to R'(x,-y)
Therefore, P'(0,3) changes to P''(0,-3)
Please see the attachment for both rule.
Thus, (3,0) Rx O,90° changes to (0,-3)
Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?
Which of the following best describes the solutions to the inequality shown below?
4c + 5 < 4c + 3
A. All real numbers
B. c < 1/2
C. c > 1/4
D. No solution
Plot the data for the functions f(x) and g(x) on a grid
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 3 or 9?
A.1/6
B.1/13
C.1/18
D.1/162
[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]
If a fair coin is tossed 5 times what is the probability of getting 3 heads in a row
32 deanna bought a shirt that was on sale for 40% off the original price. she also used a coupon that gave her an additional 20% off the sale price of the shirt. the original price of the shirt was $54. what is the new price of the shirt before tax?
The birdwatching club has 27 members, 18 girls and 9 boys. What is the ratio of the girls to boys in the birdwatching club?
Can anyone please help
a doctor is using a treadmill to assess the strength of a patients heart. he sets the 48 inch long treadmill at an incline of 10 degrees. how high is the treadmill raised
In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:
[tex]h= 8.3[/tex]
So from the values initially given we can describe that the calculation for this triangle will be:
[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]
See more about triangles at brainly.com/question/25813512
Jessica is designing a large, circular garden for a neighborhood park. A part of the garden will be occupied by a fountain. If the diameter of the garden is 82 meters and the measure of the angle formed by the fountain is 126°, what will be the approximate length of the garden cover by the fountain?
How are experimental and theoretical probability alike?
Norma has an A-frame cabin.The back is shown below. How many square feet of paint will she need to cover the back of the cabin?
PLEASE HELP ME QUICKLY!!
TIME SENSITIVE
The range of [tex]y= \frac{4}{5} sinx[/tex] for [tex] \pi \leq x \leq \frac{3 \pi }{2} [/tex] is _____.
HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[tex]\sqrt{a}=b\iff b^2=a\\\\a\geq0\ \wedge\ b\geq0\\\\\text{therefore your answer is}\\\\\text{(A) The equation has no solutions.}[/tex]
show or describe two different ways to complete the comparison using < , > ,or =: 0.26 () 0.4
Multiply. −5m(−2m6+4m4+m−9) Express the answer in standard form. Enter your answer in the box.