x + 5y +3z = 4
4y – z=3
6x – 2y + 4z = 0
Answer:
x = \(\frac{1}{4}\)
y = \(\frac{3}{4}\)
z = 0
Step-by-step explanation:
You first need to solve for a variable, it won't be as easy as x = 3, you are looking to replace a variable with another equation.
For example, the second equation, 4y-z=3, I can either solve for y or z. It won't be a numerical value but it will get you a step closer.
4y-z=3
4y=z+3
y = \(\frac{z}{4} +\frac{3}{4}\)
Then you are able to use substitution to negate one of the variables and solve for the other two variables. I won't type that but I think you get the idea.
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next time we will say t e e h e e
Answer:
teeheee
Step-by-step explanation:
Answer:
t e e h e e
Step-by-step explanation:
solve the given differential equation by using an appropriate substitution. the de is homogeneous. y dx = 2(x y) dy
The given differential equation y dx = 2(x y) dy is homogeneous, which can be solved by using the substitution y = ux. This leads to a separable differential equation in x and u, which can be integrated to obtain a general solution in terms of u. Finally, substituting back to y = ux gives the general solution to the original differential equation.
The given differential equation y dx = 2(x y) dy is homogeneous, which means that it is possible to solve it by using a substitution of the form
y = ux.
This yields the following differential equation in x and u:
u dx + x du = 2u du.
We can simplify this equation by rearranging the terms:
(x - 2u) du + u dx = 0. This equation is separable, which means that we can separate the variables and integrate both sides to solve for u.
To do this, we divide both sides by (x - 2u) u, which gives:
(1/u) du / (x - 2u) = -dx / u. Integrating both sides yields:
-ln|x - 2u| = ln|u| + C, where C is a constant of integration.
Exponentiating both sides and solving for u gives:
u = ±(Cx) / sqrt(4x^2 + C^2).
Substituting y = ux gives the general solution to the original differential equation: y = ±(Cx^2) / sqrt(4x^2 + C^2).
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a train is moving at a uniform speed of 80 kilometre per hour.
a) how far will it travel in 15 minutes
b) find the time required to cover a distance of 250 km. { as per direct and inverse propositions}.
A train is moving at a uniform speed of 80 kilometre per hour.
a) how far will it travel in 15 minutes
b) find the time required to cover a distance of 250 km. { as per direct and inverse propositions}.
Explanation -:a)
Given that the train is moving at a uniform speed of 80 km/h.
Time taken = 15 minutes
First we will convert the time
\( \small \sf Time \: taken = 15 min = \dfrac{ \cancel{15}}{ \cancel{60}}hr = \dfrac{1}{4}hr \)
Now we will calculate the distance
We know,
\( ✪ \: \small\boxed{ \frak{ {Distance }= {Speed} × Time }}\)
Substituting the values in the given formula
\( \small\sf{ Distance = \cancel{ 80} \: \: 20 \: km/ \cancel{ hr} × \dfrac{1}{ \cancel{4}} \cancel{hr} =20km }\)
Distance covered in 15 minutes = 20 km
\( \rule {40mm}{2pt}\)
b)
Given that the train is moving at a uniform speed of 80 km/h.
Distance covered = 250 km
Calculating the time
We know,
\( ✪ \: \small\boxed{ \frak{ Time = \dfrac{Distance}{Speed}}}\)
Substituting the values in the given formula
\( \small\sf{ Time = \dfrac{250 km}{80 km/hr} =3 \: hrs \: 20 \: mins }\)
\( \star \: \small\sf{ Final \: Answer }\)
Distance = 20 kmTime = 3 hrs 20 minutes\( ••═════════════••══════\)
The table shows the shoe sizes of women of different ages.
Which best describes the strength of the model?
A. a weak positive correlation
B. a strong positive correlation
C. a weak negative correlation
D. a strong negative correlation
Answer: A.
A weak positive correlation
Step-by-step explanation:
x² - 2x - 2 x 5 =
Show your work.
Your answer would be 2(x+1)
Express the following fraction into a decimal
- 5/9
Answer:
5/9 = 0.5
Step-by-step explanation:
hope it helps leme know if u hab doubts
Please help!! 1/6+1/3+1/6
Answer:
2/3
Step-by-step explanation:
1/6+1/6= 2/6, both divided by 2 gives you 1/3
1/3+1/3= 2/3
Good luck luv
Hope this helps
Answer:
2/3
Step-by-step explanation:
To add fractions with different denominators, change the denominator to the least common multiple of the denominators.
The denominators here are 6, 3, and 6. The least common multiple of these three numbers is 6. Now, convert each of the fractions into fractions with a denominator of 6, specifically only 1/3.
1/6+2/6+1/6
Now add up the numerators,
1/6+2/6+1/6 = 4/6
Simplify.
4/6 = 2/3
Getaway Travel Agency surveyed a random sample of 45 4545 of their clients about their vacation plans. Of the clients surveyed, 21 2121 expected that they would go on 3 33 vacations in the next year. There are 516 516516 Getaway Travel Agency clients. Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 33 vacations in the next year?
Answer:
241
Step-by-step explanation:
Given the following :
Number of random samples surveyed = 45
Of the random samples surveyed, 21 expected to go on 3 vacations in the next year:
Total number of clients = 516
Percentage of random sample surveyed who intend to go 3 vacations in the next year :
(21 / 45) * 100
0.4666667 * 100 = 46.7%
That is 46.7% of surveyed sample intend to go on 3 vacations in the next year.
Therefore using these to make inference about the number of total client who will go on 3 vacations in the next year:
46.7% of total clients
(46.7 / 100) * 516
= 240.8
= 241 ( to the nearest whole number)
A student is deriving the quadratic formula. Her first two steps are shown.
Step 1: –c = ax2 + bx
Step 2:
Which best explains or justifies Step 2?
division property of equality
factoring the binomial
completing the square
subtraction property of equality
Answer:
b
Step-by-step explanation:
i got it right
Answer: b
Step-by-step explanation:
its correct
Part A
Which angles are congruent to ∠5 ? Select all that apply.
∠1
∠2
∠3
∠4
∠6
∠7
Part B
I m∠6 = 85° what is the measure of ∠3?
m∠3 =
°
Express f(θ)=2cosθ−9sinθ in the form of Rcos(θ+α), where R>0 and 0<α< 2
π
. Hence, state the maximum value of −3+12cosθ−54sinθ
1
. Determine the values of θ in the interval 0≤θ≤2π where the maximum occurs. [11 marks] b) By using the substitution t=tan( 2
x
), show 4cosecx−2cotx= t
3t 2
+1
. Hence, solve the equation 4cosecx−2cotx=−5 for 0≤x≤2π
The equation 4cosecx−2cotx=−5 for 0≤x≤2π. state the maximum value of −3+12cosθ−54sinθ
Express f(θ)=2cosθ−9sinθ in the form of Rcos(θ+α), where R>0 and 0<α< 2
π
. Hence, state the maximum value of −3+12cosθ−54sinθ1
. Determine the values of θ in the interval 0≤θ≤2π where the maximum occurs. [11 marks] b) By using the substitution t=tan( 2
x
), show 4cosecx−2cotx= t
3t 2
+1
. Hence, solve the equation 4cosecx−2cotx=−5 for 0≤x≤2π
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Will give crown helo
Answer:
\(-\frac{3}{5}\)
Step-by-step explanation:
Your points on this line are:
(4, -1) and (-1, 2)
To find slope we will use the slope formula.
\(\frac{y2-y1}{x2-x1}\)
Substitute:
\(\frac{2+1}{-1-4}\)
\(\frac{3}{-5}\)
This means the slope is
\(-\frac{3}{5}\)
A coin lands on heads 300 times. The relative frequency of heads is 0.6. How many times was the coin flipped?
Answer: Number of times the coin is flipped =500
Step-by-step explanation:
Relative frequency of head = \(\dfrac{\text{Number of times heads occur}}{\text{Total number of times coin is flipped}}\)
Let x= Number of times the coin is flipped, then
\(0.6=\dfrac{300}{x}\\\\\Rightarrow\ x=\dfrac{300}{0.6}\\\\\Rightarrow\ x=\dfrac{3000}{6}\\\\\Rightarrow\ x=500\)
Hence, Number of times the coin is flipped =500
What is the electron geometry chart
The Electron Geometry Chart is a visual representation of the arrangement of electrons in a molecule. It is used to predict the molecular shape and the bond angles of a molecule based on its electron-group geometry.
Electron geometry is a term used to describe the arrangement of electron groups around a central atom in a molecule. This arrangement is important in determining the molecular shape and the bond angles of the molecule, which can affect its physical and chemical properties.
The Electron Geometry Chart provides a simple and visual way of understanding the arrangement of electrons in a molecule. It shows the number of electron groups surrounding a central atom and the shape that they form.
The chart also shows the bond angles between the electron groups and the central atom, which can be used to predict the molecular shape of the molecule.
The value of the Electron Geometry Chart lies in its ability to help students and scientists understand the relationship between the electron arrangement in a molecule and its molecular shape and bond angles.
By using the chart, students can develop a deeper understanding of molecular geometry and its impact on the physical and chemical properties of a molecule.
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Explain Polynomials I don't understand.
A particular sale involves four items randomly selected from a large lot that is known to contain 10% defective. Let Y denote the number of defective among the four sold. The purchaser of the items will return the defective for repair, and the repair cost is given by C = 3Y2 + Y + 2. Find the expected repair cost.
The expected repair cost is $39.60 calculated by using the function repair cost C = 3Y2 + Y + 2.
The probability of selecting a defective item is 0.10, so the probability of selecting Y defective items out of 4 is given by the binomial distribution: P(Y) = (4 choose Y) * (0.10)^Y * (0.90)^(4-Y).
The expected value of Y is E(Y) = ΣY * P(Y) = 0(0.6561) + 1(0.2916) + 2(0.0486) + 3(0.0036) + 4(0.0001) = 0.6.
Plug E(Y) into the repair cost equation to find the expected repair cost: C = 3(0.6)^2 + 0.6 + 2 = $39.60.
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DO THESE TWO YOU WILL GET 100 POINTS
Answer: first one is 25
Step-by-step explanation: second one i 6 gal
1 11. this table shows the input and output values for a linear function f(x). what is the difference of outputs for any two inputs that are one value apart? -15 30 15 -30
The difference of outputs for any two inputs that are one value apart in the given linear function is 15.
A linear function represents a straight line on a graph and can be expressed in the form of f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, we are given a table of input and output values for the linear function f(x). By examining the given values, we can observe that for any two inputs that are one value apart, the outputs differ by 15.
Let's consider the given input and output values: -15, 30, 15, -30. We can calculate the difference of outputs for inputs that are one value apart.
For input -15, the corresponding output is 30.
For input 15, the corresponding output is -30.
The difference between the outputs (-30 - 30) is -60. However, since we are interested in the absolute difference, we take the absolute value of -60, which is 60.
Hence, the difference of outputs for any two inputs that are one value apart in this linear function is 15 (the absolute value of -60). This indicates that for every increase of one unit in the input, the output decreases by 15, demonstrating a constant rate of change in the linear function.
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Carol's book collection contains 12 mysteries, 8 biographies, and 5 plays.
The ratio that compares the number of biographies to the total number of books is_______ to ______
Answer:
8:25
Step-by-step explanation:
Theres 8 biography books and 25 books in total. 8:25
:D
a. a basis for the row space b. a basis for the null space c. the rank of the matrix
⎣
⎡
1
0
−2
4
1
−8
2
1
−4
1
−1
−2
⎦
⎤
The rank of the matrix is equal to the number of nonzero rows in its row-echelon form. In this case, the rank is 2, as there are 2 nonzero rows.
To find the basis for the row space, we can row reduce the matrix. Performing row operations, we can obtain the row-echelon form.
row-echelon form
⎣ 1 0 -2 ⎦
⎡ 0 1 0 ⎤
The nonzero rows of the row-echelon form (1 0 -2) and (0 1 0) form a basis for the row space.
To find the basis for the null space, we need to solve the system of equations Ax = 0, where A is the given matrix. By setting up the augmented matrix and row reducing, we have:
⎣ 1 0 -2 | 0 ⎦
⎡ 4 1 -8 | 0 ⎤
Row reducing further, we obtain:
⎣ 1 0 -2 | 0 ⎦
⎡ 0 1 0 | 0 ⎤
The basic solutions of the system are x = (-2t, 0, t), where t is a parameter. Hence, the basis for the null space is {(−2t, 0, t)}, where t is a nonzero scalar.The rank of the matrix is equal to the number of nonzero rows in its row-echelon form. In this case, the rank is 2, as there are 2 nonzero rows.
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PLEASE HURRY Question 5 Multiple Choice Worth 4 points)
(06.01)A scatter plot is shown:
7
6
5
4
3
.
1
o
0 1
2
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
linear positive association
Step-by-step explanation:
The scatter plot's are going at an upwards slant which makes it positive.
The type of correlation shown in the scatter plot is a linear positive correlation
What is correlation?Correlation is a statistical tool that is used to determine the relationship between two variables.
The types of correlation that we have are:
Positive correlationNegative ccorrelationZero or no correlationThe type of correlation shown in the scatter plot is a positive correlation since it moves upwards towards the positive side of the graph in a straight line
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2 3/5 * 3 1/3
Just answer please
Answer: 8.66666666667
Step-by-step explanation:
Answer:
26/3 in the simplest fraction.
Use the diagram to find the angle measures that satisfy each case. Find m∠1, m∠3, and m∠4 if m∠2=117°.
Answer:
angles 1 & 3: 63 angle 4: 117
Step-by-step explanation:
fo this all you'd do, is look at the diagram in front of you (assuming you have one), and you'll soon figure out that two of the components are the same size.
2 is parrallel to 4, which means 4 is 117.
now, the whole circle is equal to 360 degrees.
this mean that your equation should look like:
x + x + 117(2) = 360
2x + 117(2) = 360
2x + 234 = 360
-234 -234
2x = 126
x = 63
now since we've already figured out 2 & 4, since we found the number 63 with the variable "2x", that means there are 2 angles. therefore angles 1 & 3 would be equal to 63.
lets check!
63 (2) + 117(2) = 360 or not?
126 + 234 = 360
so theres your answer. : D
-7th grade math-
The measure of angle 1 and angle 2 is 63 degrees and the measure of angle 4 is 117 degrees.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
The missing figure is attached in the picture.
From the figure
Angle 2 = 117 degrees
As we know,
From the definition of the vertically opposite angles:
Agle 1 = Angle 3
Angle 2 = Angle 4
Angle 2 = Angle 4 = 117
Let
Angle 1 = Angle 3 = x
x + x + 117(2) = 360
2x + 234 = 360
2x + 234 = 360
2x = 360 - 234
2x = 126
x = 126/2
x = 63 degrees
Angle 1 = Angle 3 = 63
Thus, the measure of angle 1 and angle 2 is 63 degrees and the measure of angle 4 is 117 degrees.
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A farmer has 30 boxes of eggs.
There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form.
The ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b". Then their ratio will be formed as;
\(\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}\)
where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.
Thus, a = px, b = qx
We have given that farmer 30 boxes of eggs. and there are 6 eggs in each box.
Thus, we know that the total number of eggs is the same as the number of eggs given in 30 boxes.
Hence, the ratio will be;
2: 30,
then divide both sides by 2 ;
1: 15
Therefore, the ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
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Choose whether or not the series converges. If it converges, which test would you use? ∑ n=1
[infinity]
n 3
10 n
(−3) 2n
Diverges by the divergence test. Converges by the integral test. Converges absolutely by the ratio test Converges, but not absolutely, by the alternating series test.
The series ∑ n=1 to infinity \((n^3 / (10^n) * (-3)^{2n})\) converges by the ratio test.
The given series is ∑ n=1 to infinity \((n^3 / (10^n) * (-3)^2n).\)
To determine if the series converges or diverges, we can use the ratio test. Let's apply the ratio test to the series:
lim(n→∞) |(a_{n+1}) / (a_n)|
= lim(n→∞)\(|[((n+1)^3) / (10^(n+1)) * (-3)^2(n+1)] / [(n^3) / (10^n) * (-3)^2n]|\)
= lim(n→∞) \(|(n+1)^3 / (n^3) * (1/10) * (9/4)|\)
= lim(n→∞) \(|(1 + 1/n)^3 * (1/10) * (9/4)|\)
As n approaches infinity, \((1 + 1/n)^3\) approaches 1, so we have:
lim(n→∞)\(|(1 + 1/n)^3 * (1/10) * (9/4)|\)
= (1/10) * (9/4)
The absolute value of this limit is less than 1, which means the series converges by the ratio test.
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When testing the differences between means, the null hypothesis suggests that any observed difference is due to?
When testing the differences between means, the null hypothesis suggests that any observed difference is due to random error.
What is hypothesis testing?
Hypothesis testing is a form of interference that uses data from a given data set or sample to derive meaningful results or conclusions about population distribution.
What is a Null hypothesis?
A null hypothesis is a type of assumption in statistics that proposes that for a given set of data or observations, there is no statistical significance or it shows that there is no difference.
It is a quantitative analysis. It is denoted by H0.
What is mean?
The mean is the average for a given number of samples in the sample solution. The mean can also be derived from the normal distribution graph.
Hence when testing the differences between means, the null hypothesis suggests that any observed difference is due to random error.
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This is probably rly easy but need help asap
Answer:
x = 16
y = 14.8
Step-by-step explanation:
hope that helped
can someone help me solve D, a, or/and b
Answer:
\(slop = (175 - 125) \div (2 - 1) = 50 \\ y - 125 = 50 \times (x - 1) \\ y = 50x - 50 + 125 \\ y = 50x + 75\)
you can solve problems by this equation
Marian Plunket owns her own business and is considering an investment. if she undertakes the investment, it will pay $28,000 at the end of each of the new 3 years. the opportunity requires an initial investment of $7,000 plus an additional investment at the end of the second year of $35,000. what is the NPV of this opportunity if the interest rate is 8% per year? Should Marian take it?
The NPV is positive, it is worth taking the Investment.
Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.
This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:
NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.
The given problem can be solved by using the following steps:
Calculate the present value (PV) of the expected cash inflows:
Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82
Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39
Since the NPV is positive, it is worth taking the investment.
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