The data set is 12, 46, 32, 18, 26, 41, 46. the mean is 31.6 and the median is 32. if we add another 12, what affect does this have on the mean and median?

Step-by-step explanation:

Use the Distributive Property for the left side of the equation.

\(a( b+ c) = ab + ac\)

Use the Distributive Property:

\(3x + 6 + 8x = 11x + 7\)

\(11x + 6 = 11x + 7\)

x has no solution.

Answer:

option b is the correct one l

Mean of the data = 83.92  

The term "mean" refers to the average of the data and is derived by dividing the total number of data observations in the data by the total number of observations.

It is a data point that represents the average of all the data points in the collection. The most popular and commonly applied approach in statistics for determining the middle of a data collection is the mean.  

Here given data is

No of students(f\(_{i}\))         4        3       9         2       3        3          4  

Score (x\(_{i}\))                     70      75     80       85      90      95      100        

f\(_{i}\) x\(_{i}\)                          280       225    720    170     270    285    400      

The formula for the mean of the data is given by

=>  ∑ f\(_{i}\) x\(_{i}\) = 280 + 225 + 720 + 170 + 270 + 285 + 400 = 2350

=>  ∑f\(_{i}\)   = 4 + 3 + 9 + 2 + 3 + 3 + 4 = 28

=> Mean of the data = 2350/28 = 83.92  

Therefore,

The Mean of the data = 83.92

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\(\large{\color{red}{\rightarrow{-\:0.2}}}\)

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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The graph of Stewart's assignment added as an attachment

From the question, we have the following parameters that can be used in our computation:

This means that the equation of the scenario is

Number of assignments remaining = Initial number of assignments - Rate of assignment per day * Number of days

Represent the number of assignments remaining with y and the number of days with x

So, we have the following representation

y = Initial number of assignments - Rate of assignment per day * x

Substitute the known values in the above equation, so, we have the following representation

y = 36 - 4 * x

Evaluate the products

y = 36 - 4x

So, the equation is y = 36 - 4x and the graph is added as an attachment

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Hope it helps.

Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.

Answer:

Hence the simplified form has has 1 term and a degree of 4

Step-by-step explanation:

Given the expression

3j⁴k - 2jk³+jk³-2j⁴k+jk³

Collect like terms

= 3j⁴k-2j⁴k- 2jk³+jk³+jk³

= j⁴k- 2jk³+jk³+2jk³

= -j⁴k-2jk³+2jk³

= - jk⁴

Hence the simplified form has has 1 term and a degree of 4

Answer:

It has 1 term and a degree of 5.

Step-by-step explanation:

(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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(a) The dot product of A and B is given by: A · B = (2î + 3ĵ + 4k) · (î - 2ĵ + 3k)= 2(1) + 3(-2) + 4(3)= 2 - 6 + 12 = 8

Therefore, A · B = 8.

(b) The angle between two vectors A and B is given by:

θ = cos^(-1)((A · B) / (|A| |B|))

In this case, |A| is the magnitude of vector A and |B| is the magnitude of vector B. The magnitude of a vector is given by the square root of the sum of the squares of its components.

|A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29

|B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14

Plugging in the values:

θ = cos^(-1)(8 / (√29 √14))

(c) The scalar component of vector A in the direction of vector B is given by:

A_B = (A · B) / |B|

Plugging in the values:

A_B = 8 / √14

(d) The cross product of vectors A and B is given by:

A x B = (2î + 3ĵ + 4k) x (î - 2ĵ + 3k)

= (3(3) - 4(-2))î + (4(1) - 2(3))ĵ + (2(-2) - 3(3))k

= 17î - 2ĵ - 13k

Therefore,AXB = 17î - 2ĵ - 13k.

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Answer:   3^4 · 3^-9 = 3^4 · 1/3^9

Step-by-step explanation:

The final solution of the given problem is X = 2.82, Y = 1.04 for an Optimal solution Value of -16.93.

Given the optimization problem in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 8, we have to find the minimum solution to the given problem.

Solution To find the solution to the given optimization problem, we need to use the Lagrange multiplier method. Using this method, we have the following system of equations: 2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 8Solving the above equations, we get the following solutions:x = 3, y = 1, λ = 6

The optimal solution is X = 3, Y = 1, for an optimal solution value of -17. If the right-hand side of the constraint is increased from 8 to 9, the objective function would change by -2.29. (Decrease by 2.29)Now, we have to resolve the problem with a new right-hand side of 9.

The new optimization problem will be in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 9

Using the same method as above, we have the following system of equations:2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 9Solving the above equations, we get the following solutions:x = 2.82, y = 1.04, λ = 6.07

The objective function value is -16.93 so the actual increase/decrease is only -0.07 rather than -2.29. Hence, the actual change is very different from the estimated change.

Therefore, the final solution of the given problem is X = 2.82, Y = 1.04 for an optimal solution value of -16.93.

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in an election debate, two candidates for governor are debating about whether to raise the general sales tax from 5 to 7 percent, so candidate a assumes that the price effect would be larger than the quantity effect.

When a tax is added on a good or service at the point of sale and is financed by the client, it is known as general sales tax. The store is then obligated to transmit, or remit, the tax to the government.

Candidate a contends that revenue will rise along with the sales tax as it rises from 5 to 7 percent. This suggests that the price impact is greater than the quantity effect since, when the tax is raised, the price would rise and the quantity would fall. As a result, the tax revenue would only rise if the price effect is more than the quantity effect.

Additionally, Candidate b claims that the tax will harm consumers and merchants, slow the economy, and reduce tax revenue. However, this claim can only be supported if the quantity effect outweighs the price effect.

Candidate a assumes that the price effect would be larger than the quantity effect.

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Answer:

Equation 1: y = 7x + 6

Equation 2: y = -7x + 8

Step-by-step explanation:

Isolate the y variables in both equations

Equation 1:

y - 7x = 6

y = 7x + 6

Equation 2:

y + 7x = 8

y = -7x + 8

So, the equations in slope intercept form are:

Equation 1: y = 7x + 6

Equation 2: y = -7x + 8

Answer:

Find the value of b using the formula for the equation of a line. y = mx + b

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer: 0.286 i think

Step-by-step explanation:

In parallelogram ABCD, what is the relationship between angle a° and angle b° is: a° = b°.

Correct answers of given question are given below:

1. The correct relationship between angle a° and angle b° in parallelogram ABCD is: a° = b°. In a parallelogram, opposite angles are congruent, meaning they have the same measure. Therefore, angle a° and angle b° have equal measures.

2. The area of rectangle FGHK can be calculated by multiplying the length and width. However, the width is not given in the information provided. Therefore, it is not possible to determine the area of the rectangle based on the given information. The correct answer cannot be determined.

3.In rectangle FGHK, FC = CH = 8.5 cm. Since FC and CH are equal, they represent the width of the rectangle. The length of the rectangle is not provided in the information. Therefore, it is not possible to determine the length of GK based on the given information. The correct answer cannot be determined.

4. The correct relationship between angle e and angle g in parallelogram EFGH is: e° = g°. In a parallelogram, opposite angles are congruent, meaning they have the same measure. Therefore, angle e° and angle g° have equal measures.

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The values of x, y, and z are 25,15 and, 7 respectively.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. 

Given that,

x=y+10................(i)

y=z+8..................(ii)

x+y+z=47............(iii)

Solving these equations to find the values of x,y, and z.

Putting The value of x from the first equation in the third equation:

we get,

y+10+y+z=47

Solving this equation further, we get,

=>2y+z=47 -10=37

=>2(z+8)+z=37

=>2z+16+z=37

=>3z=37-16=21

=>z=21/3=7

=>y=z+8=7+8=15

=>x=y+10=15+10=25

Thus, The values of x, y, and z are 25,15 and, 7 respectively.

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Your current age is 13 years.

Five times my age 4 years ago is the same as 3 times my age in 2 years.

let

x = current age.

Therefore, the expression can be represented as follows

5(x - 4) = 3(x + 2)

open the bracket

5(x - 4) = 3(x + 2)

5x - 20 = 3x + 6

subtract 3x from both sides

5x - 3x - 20 = 3x - 3x + 6

2x - 20 = 6

add 20 to both sides

2x - 20 + 20 = 6 + 20

2x  = 26

divide both sides by 2

2x / 2 = 26 / 2

x = 13

Therefore, your current age is 13 years.

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Answer:

x=7.8

Step-by-step explanation:

use Pythagoras

a^2+b^2=c^2

6^2+5^2=c^2

36+25=61

square root 61

x=7.8102496759066

to the nearest tenth

x=7.8

Answer:

$37.26

Hope this helps.

Answer:

118

Step-by-step explanation:

Answer:

118⁰

Step-by-step explanation:

37⁰+25⁰= 62 ⁰

180⁰-62⁰= 118⁰

The division of the given complex numbers in rectangular form is approximately 1/3 (cos10° - isin10°).

To divide the complex numbers [2(cos25° + isin25°)] and [6(cos35° + isin35°)], we can apply the division rule for complex numbers in polar form.

In polar form, a complex number can be represented as r(cosθ + isinθ), where r is the magnitude and θ is the argument (angle) of the complex number.

First, let's express the given complex numbers in polar form:

[2(cos25° + isin25°)] = 2(cos25° + isin25°)

[6(cos35° + isin35°)] = 6(cos35° + isin35°)

To divide these complex numbers, we can divide their magnitudes and subtract their arguments.

The magnitude of the result is obtained by dividing the magnitudes of the given complex numbers, and the argument of the result is obtained by subtracting the arguments.

Dividing the magnitudes, we have: 2/6 = 1/3.

Subtracting the arguments, we have: 25° - 35° = -10°.

Therefore, the division of the given complex numbers [2(cos25° + isin25°)] and [6(cos35° + isin35°)] can be written as 1/3 (cos(-10°) + isin(-10°)).

In rectangular form, we can convert this back to the rectangular form by using the trigonometric identities: cos(-θ) = cos(θ) and sin(-θ) = -sin(θ).

So, the division of the given complex numbers in rectangular form is approximately 1/3 (cos10° - isin10°).

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                                "Complete question"

         Divide And Write Answer In Rectangular Form[2(Cos25+Isin25)]•[6(Cos35+Isin35]

The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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So x/1 + y/-2 = 1 and x/1 + y/-2 = 1 are the slope intercept forms of graphs 1, respectively.

The optimal angle in geometry is where the line's incline contacts the y-axis. a point where a line or curve's y-axis crosses it. This is demonstrated using the equation and for straight line, Y = shifting from traditional, where m denotes the slope and c the en la. The line's slope (m) as well as y-intercept (b) are highlighted in the analytic form of the equation. The slope is feet and the y-intercept is b when an equation has to have the intercept form (y=mx+b). It is also reasonable to rewrite some equations so that they appear to be slope intercepts. For example, the inclination and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0.

given

The slope intercept form = x/a + y /b = 1

1) for graph 1

The intercept form is  x/1 + y/-2 = 1

2) for graph 2

The intercept form is x /-1 + y /1 = 1

So x/1 + y/-2 = 1 and x/1 + y/-2 = 1 are the slope intercept forms of graphs 1, respectively.

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Answer:

6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

x+16=4x-5

slove for x

The standard equation of the line is:

\(3x - 4y = 20\), option B.

------------------------------

In slope-intercept form, the equation of a line is given by:

\(y = mx + b\)

In which:

In standard form, the equation of the line is:

\(y - mx = b\)

Without fractions.

In this problem:

Thus, the equation is:

\(y = mx + b\)

\(y = \frac{3}{4}x - 5\)

Multiplying everything by 4:

\(4y = 3x - 20\)

\(4y - 3x = -20\)

\(3x - 4y = 20\), option B.

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Answer:

6

Step-by-step explanation:

180 - 90= 90

180 - 90= 90

16 x - 6 = 90

16x = 90+6

16x = 96

x =96/19

x = 6