Set up fitting the least squares line through the points (1, 1), (2, 1), and (3, 3). Find R of the fitted line.

The correct match of each ordered pair with each function is:

(-9, 74) for y = -8x + 2

(2,-6) for y = -4x + 2

(9, 70) for y = 7x + 7

(-4, 23) for y = -7x - 5

To match each function with the correct ordered pair, we need to substitute the x-values from the ordered pairs into each function and see which one gives the corresponding y-value.

Substitute the x value of (-9, 74) into y = -8x + 2:

y = -8(-9) + 2

y = 74

Substitute the x value of (2,-6) into y = -4x + 2:

y = -4(2) + 2

y = -6

Substitute the x value of (9, 70) into y = 7x + 7:

y = 7(9) + 7

y = 70

Substitute the x value of (-4, 23) into y = -7x - 5:

y = -7(-4) - 5

y = 23

Therefore, the correct matching is:

(-9, 74) for y = -8x + 2

(2,-6) for y = -4x + 2

(9, 70) for y = 7x + 7

(-4, 23) for y = -7x - 5

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Answer:

Step-by-step explanation:

Comment

The first thing you ought to notice is that the original shape is a rectangle, with 2 of the y coordinates of the 4 points of 1. What that statement means is that two of the points (1,1) and (3,1) both sit on the line y = 1. they don't move. The other two points do move and they form a circular shape. So what you are going to get is a cylinder.

Answer: cylinder

Answer: 345

Step-by-step explanation: the alls

Answer:

Probability is the mathematical term for the likelihood that something will occur, such as drawing an ace from a deck of cards or picking a green piece of candy from a bag of assorted colors. You use probability in daily life to make decisions when you don't know for sure what the outcome will be.

Step-by-step explanation:

Answer: x=12

Step-by-step explanation: 10(x−3)=90

(10)(x)+(10)(−3)=90 (Distribute)

10x+−30=90

10x−30=90

Step 2: Add 30 to both sides.

10x−30+30=90+30

10x=120

Step 3: Divide both sides by 10.

x=12

Answer:

D

Step-by-step explanation:

Answer:

answer choice C.

Step-by-step explanation:

complementary angles are 2 angles that add up to 90 degrees

90=58+x

90-58=x

x=32

The average value of the function over the given solid is given by Volume = 4/3 and Average value is 3/2.

The average is determined by adding up all the numbers and dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value.

In plain English, an average is a single number chosen to represent a group of numbers. This average is often the arithmetic mean, which is the total of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 (which add up to 25) is, for instance, 5. An average might be another statistic like the median or mode depending on the situation.

f(x, y, z) = x + y + z on over tetrahedron in the first octant with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0) and (0, 0, 2),

The volume is given by,

\(V=\int\limits^2_0 {((2-x)^2-\frac{(2-x)^2}{2} )} \, dx\)

V = 4/3

Now average value of f(x,y,z) on solid region Q is given by,

Average value = 1/V ∫∫∫f(x, y, z)dV.

\(=\frac{3}{4} \int\limits^2_0 {\frac{x^3}{6} -2x+\frac{8}{3} } \, dx\)

= 3/2.

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The documentation provided with the procedure states that the procedure will display the value of (x + y) / x.

This means that the result of the calculation will be shown to the user, and it will be the value obtained by adding x and y, then dividing the result by x.

However, the documentation also includes a very important requirement for the parameter x: it must not be 0. This is because dividing by zero is not a valid mathematical operation, and will result in an error. Therefore, it is crucial to ensure that the value of x passed to the procedure is a non-zero integer.

To summarize, the "calculate" procedure takes two integer parameters, x and y, and displays the value of (x + y) / x.

It is important to note that the value of x must not be 0, as dividing by zero is not a valid mathematical operation.

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The length and width of the rectangle with perimeter 254 yards are 57 and 70 yards respectively.

Perimeter of rectangle is 2(Length + width)

Given,

Perimeter of rectangle = 254 yards

Width = Length+ 13

Consider the Length of the rectangle as "x". Thus, width of the rectangle is x+13 ( as it is 13 yards more than the Length ).

Put the value in the formula.

=> 254 = 2(x+x+13)

=> 254 = 2(2x+13)

=> 254 -26 = 4x

=> 228= 4x

=>  x = 57 (length)

=>  x+13= 70( width)

Therefore, we get length = 57 yards and width = 70 yards.

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Answer:

18 miles per gallon

Step-by-step explanation:

We get this by taking 2,250 (the distance traveled) divided by 125 (the amount of gas used)

Answer:

Three gallons will be enough to make 128 servings.

Step-by-step explanation:

In Three gallons there are 64 cups. if 5 cups makes 10 servings, that is 1/2 cup per serving. So 64 cups will make 128 servings.

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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To find the expected value of the question, we need to find the probability of having a card with a value less or equal to 5, and the probabilities greater than 5. We are told that the aces are considered the highest card in the deck. So, this card is not part of the group less or equal to 5.

Then, we have in a standard deck of cards 52 cards.

• Those cards that are equal or less than 5 are 16 cards.

• Those cards that are greater than 5 are 36 cards.

The probability of having a card equal to or less than 5 is equal to:

The probability of having a card greater than 5 is equal to:

When we pay someone, we have a "loss" in a game. Then, if we pay $22, we need to write this value as -$22.

Therefore, the expected value of the proposition is as follows:

If we round the result to two decimal places, we have that the expected value is equal to E(V) = $ -3.23.

Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

Answer:

  see attached

Step-by-step explanation:

You want a clock face with an angle of 240° between the hour and minute hands.

There are 22 possible locations for the minute hand such that the long arc between the hour and minute hands is 240°. The two of these that do not involve fractions of a second are 4:00 and 8:00.

The next occurrence will be 21 minutes 49 1/11 seconds later. And the one after that will be 43 minutes 38 2/11 seconds later, or 1 hour 5 minutes and 27 3/11 seconds after the first occurrence of the pair.

A clock face illustrating 8:00 is attached. You may need to scale it to your desired radius.

You can set your compass to 2" and draw the clock face circle. The points for 12 and 8 can be located by using the 10:00 position as the center of arcs with the same radius. Where those arcs intersect the original circle are the locations of 12 and 8.

Given statement solution is:-The bearing of City C from City B is approximately 76.14°.

To solve this problem, we can use the law of cosines and trigonometry to find the distance and bearing between City B and City C.

Let's start with calculating the distance between City B and City C.

i. Distance between City B and City C:

We can form a triangle ABC with sides AB, BC, and AC.

Given:

AB = 22m (distance between City A and City B)

AC = 33m (distance between City A and City C)

To find BC (distance between City B and City C), we can use the law of cosines:

\(BC^2 = AB^2 + AC^2 - 2 * AB * AC *\) cos(angle BAC)

Angle BAC can be found by subtracting the bearing of City A from City C (018°) from 180° since they are on opposite sides of City B:

Angle BAC = 180° - 018° = 162°

Now, let's calculate BC using the law of cosines:

\(BC^2 = 22^2 + 33^2 - 2 * 22 * 33 *\) cos(162°)

Using a calculator, we can evaluate the right side of the equation:

\(BC^2\) ≈ 484 + 1089 + 1452.43 ≈ 3025.43

Taking the square root of both sides, we get:

BC ≈ √3025.43 ≈ 55.01m

Therefore, the distance between City B and City C is approximately 55.01m.

ii. Bearing of City C from City B:

To find the bearing of City C from City B, we need to determine the angle formed by the line connecting City B and City C with respect to the north direction.

Since we know the distances AB and BC, we can use trigonometry to find the angle.

tan(angle B) = BC / AB

Let's calculate the angle:

angle B ≈ arctan(BC / AB) ≈ arctan(55.01 / 22)

Using a calculator, we find:

angle B ≈ 68.86°

However, this gives us the bearing of City C from City B. To find the bearing of City C from City B, we need to subtract this angle from the bearing of City B.

Bearing of City C from City B = 145° - 68.86°

Bearing of City C from City B ≈ 76.14°

Therefore, the bearing of City C from City B is approximately 76.14°.

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The expected gain or loss of an experiment over the long run is called the expected value.

The expected value is the weighted average of all possible outcomes, where the weights are the probabilities of those outcomes occurring. It is calculated by multiplying each possible outcome by its probability of occurring and then adding up these products. The expected value can be used to make decisions and assess risk in various fields, including finance, economics, and gambling. If the expected value is positive, it means that, on average, the experiment will result in a gain, while a negative expected value indicates a loss.

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In sharecropping contracts, the landlord receives a fixed share of the output, while in fixed rent contracts, the landlord receives a fixed amount. On the other hand, in sharecropping contracts, the tenant receives a fixed share of the output, whereas in fixed rent contracts, the tenant receives a fixed amount.

Sharecropping and fixed rent contracts are two different arrangements between landlords and tenants in agricultural settings. In a sharecropping contract, the landlord's compensation depends on the output of the land. Specifically, the landlord receives a fixed share or proportion of the output produced by the tenant. This means that if the tenant's effort leads to a high output, the landlord's share will be larger, and if the output is low or zero, the landlord's share will be correspondingly smaller. The tenant, in turn, receives a fixed share of the output as their compensation.

On the other hand, in a fixed rent contract, the landlord's compensation is predetermined and does not depend on the output. The landlord receives a fixed amount of rent regardless of the output produced by the tenant. This fixed amount ensures that the landlord's income remains stable and is not influenced by the variability of agricultural output. In this case, the tenant also receives a fixed amount as their compensation, which is unaffected by the output.

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The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.

Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.

Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.

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The geometric description of the subspace W of R³ is a line. This can be observed from the given set W, which consists of three-dimensional vectors of the form (5t, t, t), where t is a real number.

All the vectors in W have the same x-component (5t), indicating that they lie on a line parallel to the y-z plane. The y-component and z-component (both t) vary freely, but they are always equal. Therefore, W forms a one-dimensional subspace, which can be visualized as a line in three-dimensional space.(b) To find a basis for the subspace W, we need to identify linearly independent vectors that span the subspace. In this case, a suitable basis for W would be {(5, 1, 1)}. This single vector is sufficient to generate all other vectors in W through scalar multiplication.

(c) The dimension of the subspace W of R³ is 1. This can be determined by the number of linearly independent vectors in the basis for W, which is only one. The subspace W is one-dimensional, consisting of all vectors that can be obtained by scaling the basis vector {(5, 1, 1)} with a real number.

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In order to cross the bridge, the seven cars can form groups of four to cross the bridge in 35 combinations.

The process of combination is used to calculate in how many ways seven cars can form groups of four in order to cross the bridge.

Combination formula is given by:

\(nCr = n!/ (n! * (n-r)!)\)

The number of combinations of seven cars taken four at a time can be given by the equation:

C(7,4) = 7!/(4! * (7-4)!)

C(7.4) = 5040/(24*6) = 5040/144 = 35.

Therefore, the seven cars can cross the bridge in groups of four in 35 different combinations.

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The MLE of σ² is a biased estimator of σ²

The maximum likelihood estimator (MLE) of σ² is a biased estimator, we need to demonstrate that its expected value is different from the true population variance, σ².

Let's start with the definition of the MLE of σ². In the context of simple linear regression, the MLE of σ² is given by:

MLE(σ²) = SSE/n

where SSE represents the sum of squared errors and n is the number of observations.

The expected value of the MLE, we need to take the average of all possible values of MLE(σ²) over different samples.

E(MLE(σ²)) = E(SSE/n)

Since the expectation operator is linear, we can rewrite this as:

E(MLE(σ²)) = 1/n × E(SSE)

Now, let's consider the expected value of the sum of squared errors, E(SSE). In simple linear regression, it can be shown that:

E(SSE) = (n - k)σ²

where k is the number of predictors (including the intercept) in the regression model.

Substituting this result back into the expression for E(MLE(σ^2)), we get:

E(MLE(σ²)) = 1/n × E(SSE)

= 1/n × (n - k)σ²

= (n - k)/n × σ²

Since (n - k) is less than n, we can see that E(MLE(σ²)) is biased and different from the true population variance, σ².

Therefore, we have shown that the MLE of σ² is a biased estimator of σ².

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The question is incomplete the complete question is :

Show that σ² = SSE/n, the maximum likelihood estimator of σ² is a biased estimator of σ²?

Note that the sum of the angles in a triangle is always 180 degrees.

So it follows that :

The triangle has a right angle at G, and a right angle measures 90 degrees.

angle F = 4x + 15

and

angle H = 3x + 12

Substitute the angle values to the formula and solve the value of x :

Now we have the value of x, substitute this value to the angles.

Therefore, the angles are :

F = 51 degrees

G = 90 degrees

H = 39 degrees

The petrol cost for Anne's journey of 120km is $16.236

Her car has a fuel consumption of 8.2 litres per 100 km .

Therefore,

100 km = 8.2 litres

120 km = ?

cross multiply

volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres

Therefore,

1 litres = 1.65 dollars

9.84 litres = ?

cross multiply

cost of fuel used = 1.65 × 9.84 / 1

cost of fuel used = $16.236

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Answer:

1564

Step-by-step explanation:

1564

6/9384

-6

_____

33

-30

____

38

- 36

______

24

-24

__________

0

Answer:

1564

Step-by-step explanation:

attached........

The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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Answer:

(x-3) (x-2)

Step-by-step explanation:

\(x^{2}\) - 5x + 6

How to break down the equation and factorise it:

-3 x -2 = 6

-3 + -2 = -5

Final Answer:

(x-3) (x-2)

1a. The interest that Thato will pay equals to R3,840.

1b. The final amount he will pay for the bicycle will be R 11 840.

a) To calculate the interest that Thato will pay, you can use the following formula:

Interest = Principal * Rate * Time

Interest = R 8,000 * 0.14 * 3

Interest = R3 840

Final amount = Principal + Interest

Final amount = R 8,000 + R 3,840

Final amount = R 11,840

Cost price per rose = Total cost of roses / Number of roses

Cost price per rose = R 900 / 200

Cost price per rose = R 4.50

Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet

Selling price per rose = R 35 / 5

Selling price per rose = R 7.00

Profit per rose = Selling price per rose - Cost price per rose

Profit per rose = R 7.00 - R 4.50

Profit per rose = R 2.50

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