To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
A. because the system of equations actually has only one solution
B. because the system of equations actually has no solution
C.because the graphs of the two equations overlap each other
D. because the graph of one of the equations does not exist
Answers
9514 1404 393
Answer:
C. because the graphs of the two equations overlap each other
Step-by-step explanation:
When a system of linear equations has an infinite number of solutions, the equations are "dependent." That means they both describe the same line. The graph will appear to be one line because the lines overlap each other.
__
Additional comment
The Desmos graphing calculator lets the texture of the graph be varied, so we can see that the two lines overlap. In the attached, one equation is graphed as a dotted red line, the other as a solid blue line.
Related Questions
Sport Chek conducts customer satisfaction surveys by having its customers complete questionnaires regarding their customer service experience. Their computer system automatically sends surveys to customers who spend more than $100 at their store. What type of bias might result?
a) Response Bias
b) Sampling Bias
c) Both response bias and sampling bias
d) Neither response bias or sampling bias
Answers
Answer:
b
Step-by-step explanation:
Because only the customers who spend more than $100 get to complete the form. The other customers wont be able to complete it(people who spent less than $100). thats why the answer would be sampling bias.
Please help with this question
Answers
9514 1404 393
Answer:
dy/dx = 2x +1
Step-by-step explanation:
The power rule can be used.
d/dx(x^n) = n·x^(n-1)
Then the derivative of x² is 2x¹ = 2x, and the derivative of x = 1x⁰ = 1.
The derivative of the function is ...
dy/dx = 2x +1
Mark bought seeds, 5 packets of carrot seeds, 2 packets of
bean seeds, and 3 packets of pea seeds. If he randomly
selects 4 packets to plant, what is the probability that he
selects 2 packets of carrots, 1 packet of beans, and 1 packet
of peas?
Answers
Answer:
4/10=2/5 therefore the answer to 2/5
write the equation of the graph, y=? SOMEBODY PLEASE HELP
Answers
Answer:
[tex]y=\left(6\right)^{x}\ -3[/tex]
Step-by-step explanation:
You flip a coin that is not fair, the prbability of heads on each flip is 0.7. if the coin shows heads, you draw a marble from urn h with 1 blue and 4 red marbles. if the coin shows tails, you draw a marble from urn t with 3 blue and 1 red marble. Find the following probabilities:
a. The probability of choosing a red marble.
b. The probability of choosing a blue marble, given that the coin showed heads.
c. The probability that the coin showed tails, given that the marble was red.
Answers
Solution :
P(H) = 0.7 ; P(T) = 0.3
If heads, then Urn H, 1 blue and 4 red marbles.
If tails, then Urn T , 3 blue and 1 red marbles.
a).
P ( choosing a Red marble )
= P (H) x P( Red from Urn H) + P (T) x P( Red from Urn T)
[tex]$=0.7 \times \frac{4}{5} + 0.3 \times \frac{1}{4}$[/tex]
= 0.56 + 0.075
= 0.635
b). If P (B, if coin showed heads)
If heads, then marble is picked from Urn H.
Therefore,
P (Blue) [tex]$=\frac{1}{5}$[/tex]
= 0.2
c). P (Tails, if marble was red)
[tex]$=P (T/R) = \frac{P(R/T)}{P(R)} \ P(T)$[/tex]
Where P (R/T) = P ( red, if coin showed tails)
[tex]$=\frac{1}{4}$[/tex]
= 0.25 (As Urn T is chosen)
P (R) = P (Red) = 0.635 (from part (a) )
P (T) = P (Tails) = 0.3
∴ [tex]$P(T/R) = \frac{0.25 \times 0.3}{0.635}$[/tex]
= 0.118
Alejandro wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he likes: a male and female puppy from each of the four breeds of and Labrador. The puppies are each so cute that Alejandro cannot make up his mind, so he decides to pick the dog randomly. Find the probability that Alejandro chooses a .
Answers
Answer:
Hence the required probability is, 3/4
Step-by-step explanation:
At the shelter, he likes :
a male coolie, a female coolie, a male boxer, a female boxer, a male beagle, a female beagle, a male Labrador, and a female Labrador.
Let, A denote the event of selecting a male coolie and B denote the event of selecting a male Labrador.
P(A) = 1/8 = P(B)
Here the probability of selecting a puppy except A & B is,
P(AUB)c = 1 - P(AUB) = 1 - { P(A) + P(B) } = 1 - 1/8 - 1/8 = 3/4
The quadratic equation x^2 + 3x + 50 = 0 has roots r and s. Find a quadratic equation whose roots are r^2 and s^2.
Answers
Answer:
x^2 + 91x + 2500
-----------------------------------------------------------------------------
x^2 + 3x + 50
(x-r)(x-s)
-> x^2-(r+s)x+rs
rs = 50, r + s = -3
-> (rs)^2 = 2500
(r+s)^2 = 9
-> r^2 + 2rs + s^2 = 9
-> r^2 + 2(50) + s^2 = 9
-> r^2 + s^2 + 100 = 9
-> r^2 + s^2 = -91
(x-r^2)(x-s^2)
-> x^2-(r^2+s^2)x+(rs)^2
-> x^2 - (-91)x + 2500
x^2 + 91x + 2500
Drag each equation to the correct location on the table.
Match the equations with the value of x that makes them true.
5x - 2x - 4 = 5
5x - (3x - 1) = 7
x + 2x + 3 = 9
2(2x - 3) = 6
4x - (2x + 1) = 3
5(x + 3) = 25
x = 2
X = 3
Answers
Answer:
The answer to your questions are given below.
Step-by-step explanation:
To answer the question given above, we shall determine the value of x in each equation. This can be obtained as follow:
5x - 2x - 4 = 5
3x - 4 = 5
Collect like terms
3x = 5 + 4
3x = 9
Divide both side by 3
x = 9/3
x = 3
5x - (3x - 1) = 7
Clear the bracket
5x - 3x + 1 = 7
2x + 1 = 7
Collect like terms
2x = 7 - 1
2x = 6
Divide both side by 2
x = 6/2
x = 3
x + 2x + 3 = 9
3x + 3 = 9
Collect like terms
3x = 9 - 3
3x = 6
Divide both side by 3
x = 6/3
x = 2
2(2x - 3) = 6
Clear the bracket
4x - 6 = 6
Collect like terms
4x = 6 + 6
4x = 12
Divide both side by 4
x = 12/4
x = 3
4x - (2x + 1) = 3
Clear the bracket
4x - 2x - 1 = 3
2x - 1 = 3
Collect like terms
2x = 3 + 1
2x = 4
Divide both side by 2
x = 4/2
x = 2
5(x + 3) = 25
Clear the bracket
5x + 15 = 25
Collect like terms
5x = 25 - 15
5x = 10
Divide both side by 5
x = 10/5
x = 2
SUMMARY:
x = 2
x + 2x + 3 = 9
4x - (2x + 1) = 3
5(x + 3) = 25
x = 3
5x - 2x - 4 = 5
5x - (3x - 1) = 7
2(2x - 3) = 6
Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 99% confidence; n=23, s=0.28 mg.
df = (Type a whole number.)
χ2L = (Round to three decimal places as needed.)
χ2R = (Round to three decimal places as needed.)
The confidence interval estimate of σ is __ mg < σ < __ mg. (Round to two decimal places as needed.)
Answers
Answer:
χ²R = 8.643
χ²L = 42.796
0.20 < σ < 0.45
Step-by-step explanation:
Given :
Sample size, n = 23
The degree of freedom, df = n - 1 = 23 - 1 = 22
At α - level = 99%
For χ²R ; 1 - (1 - 0.99)/2= 0.995 ; df = 22 ; χ²R = 8.643
For χ²L ; (1 - 0.99)/2 = 0.005 ; df = 22 ; χ²L = 42.796
The confidence interval of σ ;
s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]
0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)
0.2008 < σ < 0.4467
0.20 < σ < 0.45
Find the sum of -3x^2-4x+3 2x^2+3
Answers
find the area of the shaded region
Answers
Answer:
22 cm²Step-by-step explanation:
Shaded area is the difference of the bigger circle and two smaller ones:
A = π(3²) - 2π(1²) = 7π = 7*3.14 ≈ 22 cm²Use the graph of ƒ to find ƒ(2).
0.5
–8
–0.5
Does not exist
Answers
Answer:
Step-by-step explanation:
When you're looking to find things like f(2) and f(4) and f(-3000), etc. the number inside the parenthesis is an x value. Look to the graph, find that x value, and locate the y value that corresponds to it. f(2) = -8. f(-1) = 4. f(1) = -4. See?
Answer:
does not exist
Step-by-step explanation:
that what i put hope it helps
Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answers
Answer:
-
Step-by-step explanation:
-
Find the circumference of the circle.
10.1 in
Hint: C = xxd
x= 3.14
A.15.857 in
B.31.714 in
C.63.428 in
D.13.24 in
Answers
Step-by-step explanation:
c=3.14×3.14×10.1
=99.58196
What is the slope, m, and the y-intercept of the line that is graphed below?
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Answers
Answer:
Slope: 1
Y-intercept: (0,3)
Step-by-step explanation:
The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.
Y intercept: (0, 3)
For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]
From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.
Slope: 1
Hope this helped.
Answer: 1
Step-by-step explanation: got it right on edge
HELP ASAP
What is the area of this polygon on a coordinate plane?
Answers
Answer:
Step-by-step explanation:
One way to find the area of any polygon is to find areas of all of its inside sections and then adding them together. For example, if I had a polygon made of a square stuck to a triangle, I could calculate the area of the polygon by adding the area of the square to the area of the triangle.
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Answers
9514 1404 393
Answer:
AC = 2.0 mm = 41.3 kgStep-by-step explanation:
The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.
__
a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).
The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)
These are equal, so we have ...
16(AC -1.5) = 7(3 -AC)
16AC -24 = 21 -7AC . . . . . eliminate parentheses
23AC = 45 . . . . . . . . . . . add 7AC+24
AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC
AC ≈ 2.0 meters . . . . rounded to 1 dp
__
b) The torques in this scenario are ...
M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m
M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M
M = 41.3 kg . . . . rounded to 1 dp
_____
Additional comment
Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.
What is the slope of a line perpendicular to line A?
Answers
Hope your day is going well
The slope equation is y2- y1/ x2-x1
Y2 = 5
Y1 = 0
X2= 3
X1= -7
5-0/ 3 - -7
5/10 5 divided by 10 is 2
Your slope is 2
Hope this helps *smiles*
please give me correct answer
Answers
Answer:
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disha
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8ઈઘુઘ
Trish's punch recipe calls for 8 liters of lemon-lime soda and 4 liters of cranberry juice, Jenny's punch recipe requires 7
liters of lemon-lime soda and 6 liters of cranberry juice. Which recipe has a higher ratio of lemon-lime soda to cranberry
juice?
( A, neither, the ratios are equivalent
B. Trish's recipe
c. Jenny's recipe
D. not enough information
Answers
Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Answers
Answer:
The answer is "0.340".
Step-by-step explanation:
[tex]n = 500\\\\x = 170[/tex]
Using formula:
[tex]\to \hat{p} = \frac{x}{n} = \frac{170}{500}=\frac{17}{50} =0.340[/tex]
The average weekly assignment score of students in a statistics class is 7 out of 10 points. The professor proposes new incentives to boost the score of the students (like providing internship contacts etc.) He hopes that the results of running this incentives plan for a trial during the next couple of weeks will enable him to conclude that the incentives he offers increase the average weekly assignment score of students. What is the null hypothesis.
A. The average weekly score is strictly more than or equal to 7.
B. The average weekly score is less than our equal to 7.
C. The average weekly score is strictly less than 7.
D. The average weekly score is strictly more than 7.
Answers
Answer:
B. The average weekly score is less than or equal to 7.
Step-by-step explanation:
The average weekly assignment score of students in a statistics class is 7 out of 10 points. Test if it has increased.
This means that at the null hypothesis it is tested that the mean score of the students has not increased, that is, it still is of at most 7, so:
[tex]H_0: \mu \leq 7[/tex]
And thus, the correct answer is given by option b.
Find the missing segment in the image below
Answers
Answer:
x = 12
Step-by-step explanation:
Missing length of the segment is the altitude of the right triangle.
Based on the geometric mean theorem, we would have the following:
h = √(ab)
Where,
h = x
a = 16
b = 9
Plug in the values:
x = √(16*9)
x = √144
x = 12
A computer is selling for $883 the finance value is $1077.26 under an 11% simple interest loan what is the length of the loan
Answers
Answer:
The length of the loan was 2 years.
Step-by-step explanation:
Given that a computer is selling for $ 883, and the finance value is $ 1077.26 under an 11% simple interest loan, to determine what is the length of the loan, the following calculation must be performed:
883 x 0.11 = 97.13
(1077.26 - 883) / 97.13 = X
194.26 / 97.13 = X
2 = X
Therefore, the length of the loan was 2 years.
A randomized study compared two drugs that are designed fo lower a person's serotonin level. It was found that over a 1-year period, those receiving Drug A decreased their serotonin level by a mean of 36 nanograms per millimeter. Those receiving Drug B decreased their serotonin level by a mean of 20 nanograms per millimeter. To determine whether the results are significant, the data are randomized and the difference of the means is shown in the dot plot. What is the best conclusion to make based on the data?
A. The difference of the means is significant because the rerandomizations show that it is outside the range of what likely happens by chance.
B. The difference of the means is not significant because the rerandomizations show that it is outside the range of what likely happens by chance.
C. The difference of the means is not significant because the rerandomizations show that it is within the range of what likely happens by chance.
D. The difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance.
Answers
The best conclusion to make based on the data is: The difference of the means is significant because the re-randomizations show that it is outside the range of what could happen by chance.
Difference of meansGiven:
Drug A= Decrease serotonin level by means of 36 nanograms per millimeter
Drug B= Decrease serotonin level by means of 20 nanograms per millimeter
Hence,
When we take a look at the difference of means data that was given, we would see that the different of means is significant between the means of Drug A and Drug B due to chance or random variation.
Based on the fact that the re-randomizations indicate that it is outside the range of what could happen by chance.
Therefore the correct option is A.
Learn more about difference of mean here:https://brainly.com/question/6281520
#SPJ1
Answer:
The difference of the means is NOT significant because the rerandomizations show that it is within the range of what likely happens by chance
Step-by-step explanation:
Took the test and this is 100% the answer. Hope it helps.
Can somebody help me solve this ?
Answers
Step-by-step explanation:
volume of sphere = 288
based on formula, V = 4/3πr³
288 = 4/3(3.14)r³
288 = 4.187(r³)
r³ = 288/4.187
r =
[tex] \sqrt[3]{68.78} [/tex]
r = 4.09
= 4.1
What type of line is PQ?
A. angle bisector
B. median
C. altitude
D. side bisector
Answers
Answer:
D
Step-by-step explanation:
RS is a side.
RQ = QS They are both equal to seven.
That means that the answer is A or D
Since the word side is in D, it must be the answer.
Look at images below. : ]
Answers
Answer:
1) A
B) 5.818 stops
Step-by-step explanation:
Number One is less than or equal to 21 because the person only has 21 dollars, so she can't spend more than 21.
B can be solved through the equation by first subtracting $5, and then dividing 2.75 by 16.
Write A linear equation in standard form the passes through the points (4,-2) and (2,6)
Answers
Answer:
Step-by-step explanation:
4 x + y =
14
The 3rd and 6th term of a geometric progression are 9/2 and 243/16 respectively find the first term, common ratio, seventh term
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]
