Annual high temperatures in a certain location have been tracked for several years. Let
X
represent the year and
Y
the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).

x y
2 20.35
3 21.6
4 21.45
5 22.8
6 23.25
7 20.6
8 20.95
9 22.1
10 18.85
11 21.1
12 17.75
13 19.5
14 19.25
15 17.1

Answer:

3-4i

Step-by-step explanation:

Since A, B and C are collinear, they lie on a straight line. From the information given,

AB + BC = AC

AB = x + 6

BC = 3x - 5

AC = 36 - x

Thus,

x + 6 + 3x - 5 = 36 - x

x + 3x + 6 - 5 = 36 - x

4x + 1 = 36 - x

4x + x = 36 - 1

5x = 35

x = 35/5

x = 7

Option D is correct

Answer:

C & D

Step-by-step explanation:

A. p = 29

B. p= 29

C. p = 0

D. p = 0

E. p = 29

________

9514 1404 393

Answer:

  a(bc) = (ab)c

Step-by-step explanation:

The associative property of multiplication says the product is the same regardless of how the factors are grouped. That is demonstrated by the equality ...

  a(bc) = (ab)c

When a function is plotted, the domain and the range of the function are the x-coordinate and the y-coordinate respectively. The domain and range of the assumed function for Melissa's garden are: \(x = (2,\infty]\) and \(p(x) = (0,\infty]\), respectively.

The function for Melissa's garden is not given. So, I will give a general explanation to calculate domain and range.

The domain is all possible values the independent variables of a function can take while the range is all possible values the dependent variables of a function can take

Assume the function of Melissa's garden is:

\(p(x) = x(x - 2)\)

Start by equating the function to 0

\(x(x - 2) = 0\)

Split

\(x = 0\ or\ x - 2 = 0\)

Solve

\(x = 0\ or\ x = 2\)

The above values of x will give \(p(x) = 0\)

Because it is a garden, the length of the garden cannot be 0 or less.

So, the domain of the function is:

\(x = (2,\infty]\)

This means that the domain starts from a value greater than 2 (e.g. 3) and ends at infinity

To calculate the range, we substitute \(x = (2,\infty]\) in the function

\(x = 2\) means

\(p(2) = 2 \times ( 2- 2) = 0\)

\(x = \infty\) means

\(p(2) = \infty \times (\infty- 2) = \infty\)

So, the range of the function is:

\(p(x) = (0,\infty]\)

This means that the domain starts from a value greater than 0 (e.g. 1) and ends at infinity

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Answer:

The range is 0, infinity and the domain is 0,12

Step-by-step explanation:

Answer:

2812 people

Step-by-step explanation: There are 38 buses and each holds 74 people so 38 x 74= 2812

Hope this helps :)

Answer:

56

Step-by-step explanation:

28x2=56

multiply 56x2=112

Add 112+124=236

Add 236+124=360

The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)

Answer:

0.0071164

Step-by-step explanation:

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Answer:

210

Step-by-step explanation:

Answer:

The answer is 197

Step-by-step explanation:

I saw this on another question so I hope you trust that this is the right answer

Answer:

$1781.53

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

Step 1: Define variables

Principle amount P = 1500

Rate r = 0.035

Years n = 5

Step 2: Substitute and Evaluate for A

A = 1500(1 + 0.035)⁵

A = 1500(1.035)⁵

A = 1500(1.18769)

A = 1781.53

Answer:

See attached graph

Step-by-step explanation:

We need to convert the polar coordinates into Cartesian coordinates using the rules \(x=r\:cos\theta\) and \(y=r\:sin\theta\) (see table in attached file).

The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation \(r=4\:cos\theta\).

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

0.6

Step-by-step explanation:

probability of choosing a composite number, since all composite numbers from 12 are, 2,4,6,8,10,12 (might have left some out) but those are 6 chances you can pick a composite number :)

20,000 ten thousand equals 2000 Hundred thousand.

As per the question statement, we are provided with a value: "20,000 ten thousand".

We are required to calculate how many hundred thousand are equal to 20,000 ten thousand.

To solve this question, let us first write down 20,000 ten thousand into the numerical format, i.e, \((20000*10,000)=200000000\).

As we know, a hundred thousand when written down in the numerical format becomes 100,000, let us assume that 20,000 ten thousand equals to "x" number of Hundred thousand.

Therefore, we can form a linear equation in one variable "x" based on the condition, in the above-mentioned statement, which goes as  \((100,000*x)=200000000\)

\(or, (100,000x)=200000000\\or,x=\frac{200000000}{100,000}\\or,x=\frac{2*10^{8} }{10^5\\}or,x=(2*10^3)\\or,x=2000\)

Hence, 20,000 ten thousands equals 2000 Hundred thousands.

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Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

The true statements are

The value of f(–10) = 82

The graph of the function is a parabola.

The graph contains the point (20, –8).

A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).

The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.

Here we have

The quadratic function f(x) = x²/5 – 5x + 12

Now check each option as follows

1. The value of f(–10) = 82

To check this find f(-10) as follows

f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82

Hence, The value of f(–10) is equal to  82

2. The graph of the function is a parabola.

As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c

Hence, the quadratic function represents a parabola

3. The graph of the function opens down.

In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.

Hence, The graph of the function opens down is false

4. The graph contains the point (20, –8).

To check this substitute the point in f(x)

=> –8 = 1/5(20)²– 5(20) + 12

=> –8 = 80 – 100 + 12

=> –8 = –8   [ Which is true ]

Hence, The graph contains the point (20, –8).

5. The graph contains the point (0, 0).

=>  0 = (0)²– 5(0) + 12

=>  0 = 12   [ which is not true ]

Hence, The graph doesn't contain the point (0, 0).

Therefore,

The true statements are

The value of f(–10) = 82

The graph of the function is a parabola.

The graph contains the point (20, –8).

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Answer:

16 ft

Step-by-step explanation:

Each edge of wall = √256 ft = 16 ft

The original number of the equation for the sum of numbers is found to be 1/3.

For the stated question-

Let the number be 'x'.

Then,

−2 5/6 + 1/3 x = −1 7/9

Solving mixed fractions;

-17/6 + 1/3 x = -16/9

1/3 x = -16/9 + 17/9

1/3 x =  1/9

x = 1/3

Thus, the original number of the equation for the sum of numbers is found to be 1/3.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

Step-by-step explanation:

The two purchases can be described by the equations ...

  50r +70p = 258

  90r +60p = 372

Rewriting these equations in general form facilitates the use of the cross-multiplication method of solving them.

  50r +70p -258 = 0

  90r +60p -372 = 0

According to the cross-multiplication method, we need three cross-products:

  ∆1 = (50)(60) -(90)(70) = -3300

  ∆2 = (70)(-372) -(60)(-258) = -10560

  ∆3 = (-258)(90) -(-372)(50) = -4620

The solutions are the solutions to the equations ...

  1/∆1 = t/∆2 = p/∆3

  r = ∆2/∆1 = -10560/-3300 = 3.20

  p = ∆3/∆1 = -4620/-3300 = 1.40

The cost per foot of the redwood was $3.20; of the pine, $1.40.

_____

Additional comment

Here's how this version of the "cross-multiplication" method works. For equations ...

a coefficient array can be written as ...

  \(\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right]\)

The cross-products of interest are formed from adjacent columns:

  \(\Delta1=ac-db\\\Delta2=bg-ec\\\Delta3=cd-ga\)

and the solutions are ...

  \(x=\dfrac{\Delta2}{\Delta1},\quad y=\dfrac{\Delta3}{\Delta1}\)

Using this method requires no more arithmetic operations than solving by substitution or elimination, and may require fewer: 6 products, 3 sums, and 2 quotients are needed.

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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Answer:

True

Step-by-step explanation:

When you distribute the 3, you get x(2x3)-(12x3)

2x3=6

12x3=36

so 6x-36

and that is equivalent to the first expression.

An estimate for the number of pet dogs and cats in the United States based on a recent survey, written as a single digit times an integer power of 10 is 2 x 10⁸.

An estimate is a rough calculation or judgment arrived at when the details are not required or available.

We can apply number approximation, rounding, and scientific notations in estimation, as above.

First, the number, 183,900,000, can be approximated to 200 million pet dogs as an estimate.

Then, 200,000,000 can be written in a standard form or scientific notation by using an integer that indicates the place value in the power of 10.

Thus, 183,900,000 pet dogs can be estimated as 2 x 10⁸.

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The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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