what is the mistake below? solve the system equations by substitution: {4x − y = 20−2x − 2y = 10

From the line of the best fit y = 5.2x -0.4 for the considered data, the residual for x = 5 is given by: Option A: -1.6

Suppose the given input output pair be (x,y) (actual data point)

Then suppose the prediction be y' from the line of best fit for that input x.

Then the residual value will be calculated for that point as:

Residual value = Actual value - Predicted value

Residual = y - y'

Here, we're given the data as:

         x                         y

         1                          8

         2                        13

         3                        18

         4                        23

         5                        24

The line of best fit for this data is \(y= 5.2x -0.4\)

For x = 5, the real corresponding y value is 24, and the predicted value is:

\(5.2(5) -0.4 = 25.6\)

Thus, the residual for x=5 is: y - y' = 24 - 25.6 = -1.6

Thus, from the line of the best fit y = 5.2x -0.4 for the considered data, the residual for x = 5 is given by: Option A: -1.6

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Answer:

The answer is A: -1.6

Step-by-step explanation:

Doing the assignment on edge rn and got the question right

When importing a matrix and calculating the determinant using eliminations, it is important to ensure that the matrix is correctly formatted. If you are receiving an error, there may be a formatting issue with the matrix. Here are some steps to check and fix the issue:

Step 1: Check the matrix dimensions. Make sure the matrix is square, meaning that it has an equal number of rows and columns. If it is not square, you will not be able to calculate the determinant.

Step 2: Check the syntax of the matrix. Make sure the matrix is formatted correctly using brackets or parentheses. For example, if you are using MATLAB, the matrix should be entered in the following format: matrix = [1 2 3; 4 5 6; 7 8 9]

Step 3: Check for any missing or extra elements in the matrix. Make sure that each row and column of the matrix has the same number of elements. If there are any missing or extra elements, you will not be able to calculate the determinant.

Step 4: Check the syntax of the determinant calculation. Make sure that you are using the correct syntax to calculate the determinant. In MATLAB, you can use the "det" function to calculate the determinant of a matrix. For example, if you have a matrix called "A", you can calculate the determinant using the following syntax: det(A)If you follow these steps and still receive an error, try searching for the specific error message to see if there are any other solutions to the problem.

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To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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The equation for the Bowler world is c = $1.1g + $5,

The equation for the Lucky spares is c = $1.5g + $3.

and the cost is the same for 5 games and the cost is $10.5.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the Bowler, World charges $5.00 to rent shoes and $1.10 per game. Lucky Spares charges $3.00 for shoes and $1.50 per game.

Part A

using g for the number of games and c for the cost

for Bowler World

charges for shoes = $5

cost for per game = $1.1

cost for g games = $1.1g

total cost c =  $1.1g + $5 ..........(1)

for Lucky spares

charges for shoes = $3

cost for per game = $1.5

cost for g games = $1.5g

total cost c =  $1.5g + $3 ..........(2)

B. if the cost used in both places is equal then equation 1 equals equation 2

so $1.1g + $5 = $1.5g + $3

1.5g - 1.1g = 5 - 3

0.4g = 2

g = 2/0.4

g = 5

and cost is c =  $1.1g + $5

c = 1.1*5  + 5

c = 5.5 + 5

c = $10.5

Hence equations are  c =  $1.1g + $5 and  c =  $1.5g + $3,

and the cost is same for 5 games and the cost is $10.5.

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Answer:

Could be

Just to increase word count

x = 30

Step-by-step explanation:

Given,

y = 10, x = ?

2y+y = x → Equation no. (1)

Substitute the value of y in Equation no. (1) then,

2(10)+10 = x

20+10 = x

30 = x (OR) x = 30.

Answer:

The probability that event B will occur is 0.45

Step-by-step explanation:

Given;

probability that event A occurs, P(A) = 0.4

the probability that events A and B both occur, P(A ∩ B) = 0.25

the probability that either event A or event B occurs, P(A ∪ B) = 0.6

To determine the probability that event B will occur, we use probability addition rule;

P(A) + P(B) = P(A ∩ B) + P(A ∪ B)

0.4 + P(B) = 0.25 + 0.6

0.4 + P(B) = 0.85

P(B) = 0.85 - 0.4

P(B) = 0.45

Therefore, the probability that event B will occur is 0.45

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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A function T:Rn -- > Rm that meets the criteria listed below is said to be linear (or to be a linear map). T(x+y)=T(x)+T(y)

T(x+y)=T(x)+T(y)

T(ax)=aT(x) for any vectors x, y, and any scalar a.

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.

The volume of the solid is 1.5 cubic units. From the solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4

To find the volume of the solid by subtracting two volumes, we need to find the limits of integration for x, y, and z.

From the given information, we know that the solid is in the first octant and is enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4. Thus, the limits of integration for x and y are 0 to 2 since the radius of the circle x2 + y2 = 4 is 2.

Next, we need to find the limits of integration for z. To do this, we need to set the two given equations equal to each other:

xy = x + y

xy - x - y = 0

Using partial fraction decomposition:

xy - x - y = (x - 1)(y - 1) - 1

So, we have:

(x - 1)(y - 1) = z - 1

Thus, the limits of integration for z are 1 to 3.

Now, we can set up the integral to find the volume:

V = ∫∫∫ dV

V = ∫0^2 ∫0^(2 - x) ∫1^(x + y) dz dy dx

Evaluating this integral, we get the volume of the solid as 1.5 cubic units.

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The party cost for 19 guests is 95 dollars.

We assume there is a proportional relation between the number of guests and the cost.

y is the cost and x the number of guests, then we can write:

y = k*x

k is the unit rate.

We know that it costs $20 to invite 4 people, then:

20 = k*4

20/4 = k

5 = k

Then the relation is:

y = 5*x

So, if x = 19 we will have:

y = 5*19 = 95

The cost for 19 guests is $95.

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Answer:

Step-by-step explanation:

hello : here is an solution

The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

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To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:

1. Start with the initial B&B tree, where the root node represents the original problem.

2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for

\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)

3. At each node, perform the following steps:

  - Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.

  - If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.

  - If the LP solution is integer, update the current best solution if the objective value is higher.

  - If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.

4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.

5. The node with the highest objective value among the integer feasible solutions is the optimal solution.

6. Optionally, backtrace through the tree to retrieve the optimal solution variables.

Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.

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Answer:

45/56

Step-by-step explanation:

We have,

Numerator = 45 L

Denominator = 56 L

We need to find the ratio as a fraction in simplest form. So,

\(\dfrac{N}{D}=\dfrac{45}{56}\)

As there is no common factor between 45 and 56. It means the simplest fraction is 45/56.

The function formula will be

G= 50 + 125x

Since we have given that

Charges per each magical broom he makes for his customers = 125 gold pieces

Charges of one-time fees = 50 gold pieces

Let the number of magical brooms he makes be 'x'.

Let the total number of gold pieces be 'G'.

According to the question, it becomes

G= 50 + 125x

Hence, the function formula will be

G= 50 + 125x

A formula is a fact or rule written in mathematical symbols. An equal sign usually connects two or more quantities. If you know the value of one quantity, you can use a formula to find the value of the other.

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Answer:

Step-by-step explanation:

P = F/a

Pa = F

a = F/P

Answer:

a = \(\frac{F}{p}\)

Step-by-step explanation:

P =\(\frac{F}{a}\)  multiple both sides by a

aP = \(\frac{F}{a}\) \(\frac{a}{1}\)  On the right side of the equal sign, the a's cancel each other out

aP = F  Divide both sides by P

\(\frac{aP}{P}\) = \(\frac{F}{P}\)  The P's cancel out on the left side of the equal sign.

a = \(\frac{F}{P}\)

The answer that I got for your answer was 396 ask me more questions if you need help

Answer:

8

Step-by-step explanation:

Answer:

8 Km

Step-by-step explanation:

         Use Pythagorean theorem to find the length of the lake.

     \(\sf \boxed{leg_1^2 + leg_2^2=hypotenuse^2}\)

Let the length of Swan Lake = x Km

          6² + x²  = 10²

        36 + x²   = 100

                 x²  = 100 - 36

                 x²  = 64

                x = √64

                x = 8 km

Length of Swan Lake = 8 Km

Answer:

negative slope.............

Answer:

c

Step-by-step explanation:

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

Margin of error: $776.56Construct the 80% confidence interval: $45,353.44 < μ < $46,906.56

Margin of error (E) can be calculated as:

Where; z is the z-score corresponding to the level of confidence, σ is the population standard deviation, n is the sample size, and E is the margin of error.

So, for an 80% confidence interval, z = 1.282. Putting the values in the above formula, we get:

E = $776.56 (rounded off to the nearest dollar)Construct the 80% confidence interval:The lower limit of the confidence interval can be calculated as:And, the upper limit of the confidence interval can be calculated as:

So, the 80% confidence interval for the true population mean annual salary for office managers is:$45,353.44 < μ < $46,906.56 (rounded off to the nearest dollar)

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A minutes to decimal chart is a table that shows the equivalent decimal representation of minutes. It is commonly used in various fields, such as finance and payroll, to calculate the number of hours worked or the amount of pay earned.

Here's a sample minutes to decimal chart:

Minutes   Decimal

0        0.0

15         0.25

30          0.5

45           0.75

60             1.0

To use the chart, simply find the number of minutes you want to convert, and look up its equivalent decimal representation. For example, if you have worked 30 minutes, you would look up 0.5 on the chart.

It's important to understand the concept of minutes to decimal chart and how to use it, as it is a useful tool in various industries and applications.

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Answer:

\( x = \dfrac{-1 \pm \sqrt{11}}{2} \)

Step-by-step explanation:

(2x - 3)² - 14 = 2x(x - 7)

4x² - 12x + 9 - 14 = 2x² - 14x

2x² + 2x - 5 = 0

\( x = \dfrac{-2 \pm \sqrt{2^2 - 4(2)(-5)}}{2(2)} \)

\( x = \dfrac{-2 \pm \sqrt{4 + 40}}{4} \)

\( x = \dfrac{-2 \pm 2\sqrt{11}}{4} \)

\( x = \dfrac{-1 \pm \sqrt{11}}{2} \)

Answer:

6 weeks

Step-by-step explanation:

end goal = $76

how much he has in the bank = $30

how much he earnes per week = $8

first, subtract 30 from 78 to figure out how much he has left to ear:

$78 - $30 = $48

then take the difference and divide it by 8 since he earned $8 per week:

48 ÷ 8 = 6

It will take him 6 remaining weeks to complete his end goal.

∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

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