Solve the equation 6p=2(5-2p).
First, divide both sides by 2 and simplify.
6p=2(5-2p)
2p)
6p 2(5-2p)
2
2
p=5-2p

Answer:

The correct answer is: 2. t=0.45a

Step-by-step explanation:

Let t be the price of apples

and a be the number of apples

The price and quantity are directly proportional

\(t \propto a\)

Removing the proportionality symbol introduces a proportionality constant in the equation

\(t = ka\)

So far we know that cost of 6 apples is $2.70

Putting in the equation

\(2.70 = k (6)\\k = \frac{2.70}{6}\\k = 0.45\)

Putting the values of k will give us:

\(t = 0.45a\)

Hence,

The correct answer is: 2. t=0.45a

This a question that has to do with a Rotation about the origin. It is to be noted that T: \(\mathbb{R}^{2}\) → \(\mathbb{R}^{2}\) As given in the question. See the explanation below.

First Case:

T (R1, R2) = (+r1, -r2)

Let Bl = {(1,0), (0,1)} Standard Bases

⇒ (T(1, 0) = (+1, 0)

T (0, 1) = (0, -1)

Then matrix is:

A1 = \(\begin{bmatrix} +1& 0\\0 & -1\end{bmatrix}\)  and A1 R1 = \(\begin{bmatrix} r1\\y2\end{bmatrix}\)

Second Case

T (1, 0) = (0, 1)

T (0, 1) = (1, 0)

The Matrix is:

A2 = \(\begin{bmatrix} 0& 1\\1 & 0\end{bmatrix}\)

Hence,

TA2 (TA1(r1))  = \(\begin{bmatrix} 0& 1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix} r1\\r2\end{bmatrix}\)  = \(\begin{bmatrix} -r2\\r1\end{bmatrix}\)

Thus

(TA2 * TA1) (r) = \(\begin{bmatrix} 0& -1\\1 & 0\end{bmatrix}\) \(\begin{bmatrix} r1\\r2\end{bmatrix}\)

The standard Matrix is:

\(\mathbb{A} = \begin{bmatrix} 0& -1\\1 & 0\end{bmatrix}\)

In this case,

T (0, 0) = (0, 0)

⇒ Transformation is rotation about the origin.

Hence Rotation Matrix is given as:

Tθ = \(\begin{bmatrix} Cos \theta & - Sin \theta\\Sin \theta & Cos\theta\end{bmatrix}\) ⇒ θ  = π/2

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High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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Answer:

x = 7

Step-by-step explanation:

Substitute y = 4 into the equation and solve for x

8x - 2(4) = 48

8x - 8 = 48 ( add 8 to both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Answer:

x = 7

Step-by-step explanation:

8x - 2y = 48

y = 4

First, let's substitute y for it's actual value as we know it.

8x - 8 = 48

Next, add 8 on both sides. (When doing these sort of questions you must do the inverse.)

8x = 56

Divide both sides by 8 to get x.

x = 7

Hope this helps and I hope you have a good day!:)

The point-slope formula of a line can be expressed by the following equation:

Where m is the slope and (y1, x1) is a point that belong to the line. For this problem we were given a line with slope 5/2 and a point (-4,-8). By replacing these values on the general expression above we have:

Answer:

discriminant =b^2 -4ac

= (12)^2 -4(-4)(-9)

=0

Answer:

Step-by-step explanation:

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1)

so it would be

11-(-1)/12--4)

which would be

12/16

to simplify that it is 3/4

The value of the given iterated integral is -(1/14) [1 + 2π^(3/2)].

The iterated integral can be evaluated step by step. We start with the innermost integral:

∫₀^(xz) 5x² sin(y) dy.

Integrating sin(y) with respect to y gives -5x² cos(y) evaluated from y = 0 to y = xz:

= -5x² [cos(xz) - cos(0)]

= -5x² (cos(xz) - 1).

Next, we integrate the result with respect to z:

∫₀^(7x) [-5x² (cos(xz) - 1)] dz.

Integrating -5x² (cos(xz) - 1) with respect to z gives:

= -5x² [∫₀^(7x) cos(xz) dz - ∫₀^(7x) dz]

= -5x² [sin(7x²) - 7x].

Finally, we integrate with respect to x:

∫₀^(√π) [-5x² (sin(7x²) - 7x)] dx.

To evaluate this integral, we substitute u = 7x², du = 14x dx, and adjust the limits of integration:

= -∫₀^(7π) (sin(u) - 7√(u/7)) du/14

= -(1/14) ∫₀^(7π) (sin(u) - 7√(u/7)) du.

Now, we can evaluate the integral using antiderivatives:

= -(1/14) [-cos(u) - 2(√(u/7))³] evaluated from u = 0 to u = 7π

= -(1/14) [-(1 - cos(7π)) - 2(√(7π/7))³]

= -(1/14) [1 + 2π^(3/2)].

Hence, the value of the given iterated integral is -(1/14) [1 + 2π^(3/2)].

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Answer:

answer is 24_/3.

......................

The statement about the hyperbola is true is D. the point (−2, 0) is a vertex.

It should be noted that a hyperbola simply means an open curve that has two branches and usually symmetric.

In this case, the statement about the hyperbola is true is that the point (−2, 0) is a vertex.

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Answer:

\( {(x + 2)}^{2} + {(y - 8)}^{2} = 16\)

Answer:

333 cars

Step-by-step explanation:

Assuming among 6 agents, the working efficiency is the same and constant. Fixing number of agents:

    6 agents can sell 333 cars in 3 months.

=> 6 agents can sell 333/3 cars in 3/3 month.

=> 6 agents can sell 111 cars in 1 month.

Fixing number of months:

=> 6/2 agents can sell 111/2 cars in 1 month.

=>  3 agents can sell 111/2 cars in 1 month.

Then considering that 3 agents worked in 6 months:

=> 3 agents can sell 6 x 111/2 cars in 6 x 1 months.

=> 3 agents can sell 333 cars in 6 months.

Data:

Loan=$278 at 10%

A simple interest is calculated for payments on the initial capital.

If the total interest was $174.12.

If the interest is on a year. You calculated the interes of one year. The 10% of $278:

In a year the interest is $27.8.

Then, $174.12 divided into $27.8 is the number of years of the loan:

Answer:

Step-by-step explanation:

Calculating the average speed during this time interval is the same as calculating how many km he traveled per hour.

\(\frac{km}{hr}:\frac{250}{2.5}\)

This is also the same thing as the unit rate. Do that division and find that he traveled 100 km/hr.

Answer:

Step-by-step explanation:

Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.

a³/b³=1001/1024+45*sqrt(23)/1024*i

b³/a³=1001/1024-45*sqrt(23)/1024*i

Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!

If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.

It is -2c=-2*1001/1024=-1001/512, and

c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.

The coordinates for each point would be:

M': (2,-2)

N': (4, 2)

O': (8, -1)

If the rule is (x, y) = (x + 2, y - 6), this is how you solve this problem...

M to M': (0 + 2, 4 - 6), then (2, -2)

N to N':  (2 + 2, 8 - 6), then (4, 2)

O to O': (6 = 2, 5 - 6), then (8, -1)

Answer:

A

hope this helps :)

Answer:

2 2/3

Step-by-step explanation:

absolute value means the distance between a number and 0 so therefore the absolute value s 2  2/3

If the motorist wants to complete the journey in 4 hours, he must travel at the speed of 71.11 km/hr

We can calculate the speed in the following way,

We will first have to calculate the distance that the motorist has to travel to reach his destination

Since we know distance = speed / time

We have been given the following values,

time = 4.5 hours

speed = 80 km/hr

substituting the know values in the formula we get,

distance = 80/4.5 = 17.77 km

Therefore distance the motorist has to travel is 17.77 km to reach his destination

Now we need to find the speed he must travel to complete the journey in 4 hours.

Now the known values are,

time = 4 hours

distance = 17.77 km

speed = distance * time

speed = 17.77 * 4

speed = 71.11 km/hr

Therefore, to complete his journey in 4 hour, the motorist must travel at the speed of 71.11 km/hr.

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We have to find the time required for an object to cool from 300°F to 260°F by evaluating the following where t is time in minutes:t = 10/ln 2 ∫260300 (1/T - 100) dT.

To find the time t, let's first evaluate the integral using integration by substitution: Let u = T, then du/dT = 1 dT= du

Now we have,\(t = 10/ln 2 ∫260300 (1/T - 100) dT= 10/ln 2 ∫260300 (1/u - 100) du= 10/ln 2 ln|u| - 100u |_260^300= 10/ln 2 [ ln|300| - ln|260| - 100(300) + 100(260) ]= 10/ln 2 [ 5.7038 -  3000 + 2600 ]= 10/ln 2 ( - 94.6913 ) ≈ 133.4775\)

minutes.

Therefore, the time required for the object to cool from 300°F to 260°F is approximately 133.4775 minutes.

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Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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The product of the radical expression is  - 49 + 13√7. option B is the correct answer

From the question, we have

(7-√7)(-6+√7)

= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)

= -42 - 7 + 6√7 + 7√7

= - 49 + 13√7

The product of the radical expression is  - 49 + 13√7

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The left right hand derivative is 3.

The left hand derivative is 2.

The function is not differentiable at x = 1.

When x < 1,

given that the function is, f(x) = 2x² - 2x - 1

Differentiating with respect to 'x' we get, f'(x) = 4x - 2

When x \(\geq\) 1,

given the function is, f(x) = 3x - 3

Differentiating with respect to 'x', f'(x) = 3

Now, left hand derivative,

f'(1 -) = (4x - 2) at 1 = 4*1 - 2 = 4 - 2 = 2

f'(1+) = 3

Since, left hand derivative and right hand derivative for given function at x =  1 is not equal, so the function is not differentiable at x = 1.

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approximately 23 child tickets were sold on Saturday at the movie theater.

To find the number of child tickets sold at the movie theater on Saturday, we can follow these steps:

1. Let's assume the number of child tickets sold is "x". Since the child admission is $5.60, the total revenue from child tickets would be 5.60x dollars.
2. Given that three times as many adult tickets were sold, the number of adult tickets sold would be 3x. Since the adult admission is $8.90, the total revenue from adult tickets would be 8.90 * 3x dollars, which can be simplified to 26.70x dollars.
3. The total sales for the day is given as $742.90. Therefore, the sum of the revenues from child and adult tickets should equal $742.90:
  5.60x + 26.70x = 742.90
4. Combining like terms, we get:
  32.30x = 742.90
5. To isolate x, the number of child tickets sold, we divide both sides of the equation by 32.30:
  x = 742.90 / 32.30
6. Evaluating the division, we find that x is approximately equal to 23.0078.
7. Since we can't sell a fraction of a ticket, we round down to the nearest whole number. Therefore, approximately 23 child tickets were sold on Saturday at the movie theater.

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Arithmetic overflow error converting numeric to data type numeric can be solved by increasing the precision and the scale, storing number in different data type or use user-defined datatype.

An "arithmetic overflow error converting numeric to data type numeric" error occurs when you try to store a number in a numeric column that is too large to be represented by the specified precision and scale. To resolve this error, you have a few options:

Increase the precision and scale of the numeric column, you can increase the precision and scale of the numeric column so that it can store larger numbers.

If you don't need the precision and scale of a numeric column, you can store the number in a different data type, such as float or big int.

 If the number is too large to be represented in the numeric column, you can round it to a smaller value before inserting it into the database.

 If the number is still too large to be represented in a numeric column or a different data type, you can create a custom data type in SQL Server to store the number.

It's important to choose the right solution based on your requirements and the specific use case. You may also need to consider the performance implications of each solution, especially if the data being stored is very large or complex.

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The total surface area of the can is 61.23 square inches

The total surface area of can S = 2πr(r+h)

where:

h is the height

r is the radius

A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth.

Given

h = 5in

r = 1.5in

S = 2(3.14)(1.5)(1.5 + 5)

S = 6.28(1.5)(6.5)

S = 61.23 square inches

Hence the total surface area of the can is 61.23 square inches

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