Perform the indicated operation and simplify the result.

The correct statement regarding the equation is that A. the equation has no solution.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the equation will be illustrated thus:

-2x - y + 4 = 0 .... i

2x + y = 4 ... ii

From equation i

-2x - y = -4

2x + y = 4

Add both equation will give 0.

The equation has no solution.

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The probability of not rolling doubles on one roll of two fair six-sided dice is 5/6.

Hence, the probability of rolling doubles is 1/6. The probability of not rolling doubles in three rolls is (5/6)^3. So, the probability of rolling doubles on the third roll is 1 - (5/6)^3. This is the same as (1/6) (5/6)^2. So the correct answer is (d) (1/6) (5/6)^2.

The probability of rolling a specific number on one fair six-sided die is 1/6.

In this problem, we are looking for the probability of rolling doubles (i.e. getting the same number on both dice) in three rolls.

The probability of not rolling doubles in one roll is 5/6 (since there are five outcomes that are not doubles, out of a total of 6 possible outcomes).

The probability of not rolling doubles in three rolls is (5/6)^3, which represents the chance of not rolling doubles in three independent rolls, each with a 5/6 probability of not rolling doubles.

To find the probability of rolling doubles in three rolls, we subtract the probability of not rolling doubles in three rolls from 1:

P(rolling doubles in three rolls) = 1 - (5/6)^3 = (1/6) (5/6)^2

So, the correct answer is (d) (1/6) (5/6)^2.

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Answer:

The answer is point (4,8)

Step-by-step explanation:

The horizontal (x) distance between the given points is 6-1 = 5.

If the horizontal distance is 5, then because the ratio of the given points is 3 to 2, we can say that 3/5 of 5 is 3. The horizontal distance between (1,5) and (x,y) is 3, so x = 4.

We can do the same with the vertical (y) distance, which is 10-5 = 5.

Again, 3/5 of 5 is 3, so y = 5+3 = 8

Answer: the point is (4,8).

CHECK: We can check this result by finding the distances between the given points to (4,8), and calculating the distance.

Distance between (1,5) and (4,8) = √18 = 3√2

Distance between (6,10) and (4,8) = √8 = 2√2

The ratio between the distances is 3:2, so the solution checks out.

Answer:

Step-by-step explanation:

The given parameters are:

10% on the first $25,000 of income

20% on income above $25,000

The above means that;

T(x) = x * 10%, when x <= 25000

T(x) = x* 20%, when x > 25000

Evaluate the products

T(x) = 0.1x, when x <= 25000

T(x) = 0.2x, when x > 25000

In this case, x = 60000

60000 > 25000

So, we have:

T(60000) = 0.2 * 60000

Evaluate

T(60000) = 12000

Hence. if a person has income of $60,000, their income tax be under the proposal would be $12000

Answer:The problem says that income up to $25,000 will be taxed at 10%. This is the first tier (or bracket). People who make more than $25,000, will pay 10% of their initial $25,000, and the higher rate of 20% on any income above $25,000. This is the second tier.

Let's calculate the amount of tax in this particular case. For a person making $60,000, they'll pay 10% of the first $25,000, and then 20% of the additional $35,000. We have,

Total Income Tax=Tax from Tier 1+Tax from Tier 2=10100⋅$25,000+20100⋅($60,000−$25,000)=$2,500+$7,000=$9,500.

Under the proposal, this person will pay $9,500 in taxes.

The amount of  each type that should be mixed in order to have 20 pounds of coffee mixture that is worth ​$4.50 per​ pound is: 10  pounds $6.00 Gourmet coffee, 10 pounds $3.00 Cheap brand.

Gourmet coffee $6.00 ---- x pounds

Cheap brand $3.00 --- 20 - x pounds

Mixture $4.50 ---- 20

6 x + 3 ( 20 - x ) = 4.50 × 20

6 x + 3 ( 20 - x ) = 90

6 x + 60 - 3 x = 90

Collect like terms

6 x - 3 x = 90 -60

3 x = 30

x = 10

Cheap brand

20-x pounds

20-10

=10 pounds $3.00 Cheap brand

Therefore 10 pounds and 10 pounds should be mixed.

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Answer:

Step-by-step explanation:

[tex]altitude=\sqrt{8^2-4^2} =4\sqrt{2^2-1^2} =4\sqrt{3} \\area~of~triangle=\frac{1}{2} \times base \times altitude\\=\frac{1}{2} \times 8 \times 4\sqrt{3} \\=16\sqrt{3} \\\approx 27.7 ~in^2[/tex]

Part 1) Terry started at an elevation of 2,600 ft.

Part 2) The elevation is decreasing by 50 feet per second.

we have

E(t) = 2600 -50t

where

E(t) is Terry's elevation in feet

t is the time in seconds

Part 1) For t=0

substitute the value,

E(0) = 2600 -50(0)

E(0) = 2600

therefore

The equation says us that Terry started at an elevation of 2,600 ft

Part 2) we have

E(t)=2600−50t

This is the equation of the line in slope-intercept form.

The slope m is equal to, m = -50 ft/sec

The slope is negative because is decreasing

therefore

The elevation is decreasing by 50 feet per second.

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The solution set of the system of linear equations is (x1, x2, x3) = (3/2, 3/2, −1/4).

We can solve this system of linear equations using Gaussian elimination method.

Step 1: Add the first row to the second row:

leftbracket3.gif 2 1 −1 3 rightbracket3.gif

1 −1 1 0 2

0 1 2 1

Step 2: Subtract 2 times the second row from the third row:

leftbracket3.gif 2 1 −1 3 rightbracket3.gif

1 −1 1 0 2

0 0 4 −1

Step 3: Divide the third row by 4:

leftbracket3.gif 2 1 −1 3 rightbracket3.gif

1 −1 1 0 2

0 0 1 −1/4

Step 4: Subtract the third row from the first row:

leftbracket3.gif 2 1 −1 3 rightbracket3.gif

1 −1 0 −1/4 7/4

0 0 1 −1/4

Step 5: Add 4 times the second row to the first row:

leftbracket3.gif 2 0 −5/4 3 rightbracket3.gif

1 0 1 −1/4 −1/4

0 0 1 −1/4

This echelon form gives us the solution:

x3 = −1/4

x2 = 7/4 + x3 = 7/4 − 1/4 = 3/2

x1 = 3 − x2 = 3 − 3/2 = 3/2

So, the solution set of the system of linear equations is (x1, x2, x3) = (3/2, 3/2, −1/4).

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The point of intersection of the lines given is (1,4,2) and the plane determined is -3y +2z+8 = 0.

Let us first define the lines as -

L1 = x=3t+1, y=4t+4, z = 6t + 2

L2 = X=s+2 y=2s+6, z = 3s - 1

We have to find the intersection so -

= 3t+1 = s+2 ⇒ 3t - s - 1 = 0

= 4t+4 = 4t+4 ⇒ 4t - 2s - 2 = 0

= 6t + 2 = 3s - 1 ⇒ 6t - 3s + 3 = 0

Now, if we input the values of t and s as given in the question i.e., t = 0 and s = -1, we get -

= x = 1

= y = 4

= z = 2

These are the points of intersections of the given lines.

Now, the direction vector of L1 = (3,4,6) and L2 = (1,2,3)

So, the normal vector to the plane can be calculated using the determinant method.

[tex]\left[\begin{array}{ccc}i&j&k\\3&4&6\\1&2&3\end{array}\right][/tex]

On solving this, we get  = -3j + 2k

The equation of the plane is -

= 0(x-1) - 3(y-4) + 2(z-2) = 0

= -3y +2z+8 = 0

The complete question that you might be looking for is given below -

Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0<t< 0 X=s+2 y=2s+6 2 = 3s - 1 , C < 5 < 0

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The relation {(a, b), (b, c), (c, c)} does not represent a function because for the input value "c", there are two possible output values, "c" and "c". In a function, for each input value, there can only be one output value.

The vertical line test may be used to assess whether or not a relation is a function by looking at its graph.

If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.

To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.

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The compound inequality for the graph shown above include the following:

x < -2.

x > 5.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Since the point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.

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Answer:

In order in which the boxes appear in the sentences

[tex]\textsf{y-intercept \;\;\boxed{28000}}\\\\\textsf{this represents dollar value for a car that is $\boxed{0}$ years old}\\\\\textsf{Slope of the regression line is $\boxed{-4900}$}[/tex]

Step-by-step explanation:

The Range is the first component of the formula in parentheses.

What is Range

The range in statistics is the difference between the highest and lowest values for a specific data collection. For instance, if the given data set has the values 2, 5, 8, 10, and 3, the range will be 10 - 2 = 8.

It is possible to think of the range as the distance between the highest and lowest observation as a result. The consequence is known as the scope of observation. The breadth of statistics reflects the diversity of observations.

The first component of a sum or count calculation that is enclosed in the parenthesis is the Range.

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The Cartesian, or rectangular, coordinate system is composed of an x-axis that runs horizontally and a y-axis that goes vertically.

The rectangular coordinate system of the Cartesian plane, which bears Rene Descartes' (1596–1650) name, assigns each point in the plane a pair of integers.

An x-axis that runs horizontally and a y-axis that runs vertically make up the Cartesian, or rectangular, coordinate system. The origin is the place where the two axes meet. Any point can be characterized by its distance from the origin along the x-axis and along the y-axis, and this distance is represented by the symbol (x, y).

A two-dimensional coordinate plane produced by the intersection of the x- and y-axes is known as the cartesian plane in mathematics. At the location known as the origin, the x- and y-axes cross perpendicularly.

Therefore, the correct answer is option D. A graph used in mathematics to plot points.

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The area of the shaded region is given as follows:

70 cm².

The area of a triangle is given by half the multiplication of the base and of the height of the triangle.

For the triangle, the area is of 30 cm², while the height is of 6 cm, hence the base is obtained as follows:

0.5 x 6 x b = 30

3b = 30

b = 30/3

b = 10 cm.

Considering the side length of 10 cm², the area of the square is given as follows:

10² = 100cm².

The area of the shaded region is given by the subtraction of the area of the square by the area of the triangle, hence:

100 - 30 = 70 cm².

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Answer:

2620

Step-by-step explanation:

The batting average and percentage hits for the players will be Albert Pujois= 0.356 and 35.6%, Stan Musial=0.376 and 37.6% and Rogers Honsby=0.402 and 40.2%.

What is average?

In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4.  Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/Number of Values

Also

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+xn)/n

Now,

The batting averages and percentage of hits/bats for the players will be

Albert Pujois=187/524=0.356 and 35.6%

Stan Musial=230/611=0.376 and 37.6%

Rogers Honsby=203/504=0.402 and 40.2%

So I will put these in the order 1.Rogers Honsby 2.Stan Musial 3.Albert Pujois.

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The volume of the solid is 1789.33

For a circle of radius 11, we have the following equation:

x²+y²=11²

x²+y²=121

Now, making it explicit for x:

[tex]x=\sqrt{121-y^2}[/tex]

Then, if we consider that for a height y, the length x is double, we have that the length of each cross-section is given by:

[tex]s=\sqrt[2]{81-y^2}[/tex]

With this, we can propose the following integral to obtain the volume that they are asking us:

[tex]\int\limits^1_0 {s^2} \ \, dy \\\int\limits^1_0 ({\sqrt[2]{121-y^2})^2 } \, dy\\\\\int\limits^1_0 {4*(121-y^2)} \, dy\\\\4*(121y-\frac{y^3}{3} )[/tex]

Finally, calculating, we have that the volume is V=1789.33

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The other way of representing the given function is f(x) = 2 - 8/(x+4).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, rational function f(x)=2x/x+4

Using Long division:

x + 4) 2x      ( 2

         2x + 8

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

                -8

The remainder is -8.

Since the Degree of the remainder is less than the degree of the divisor then we are done.

Now using,

Dividend = divisor* quotient + remainder

=> 2x = 2 * (x+4) -8

Thus, f(x) = 2 - 8/(x+4)

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A method of accounting known as the double declining balance (DDB) maintenance method entails depreciating some assets at a rate that is twice that of straight-line depreciation. As a result, depreciation increases during the initial year of possession and decreases thereafter.

When to apply the twofold decreasing balance technique of depreciation When you buy assets that depreciate more rapidly in the first few years, the optimal scenario for using double reducing balance depreciation is that situation. The asset that lost value the most in the first few years of ownership is a car.

a) Straight-Line Depreciation Percent = 100% / 4 years = 25% / year

Depreciation Rate = 2 x 25% = 50% / year

b) Depreciation for a Period = 50% x Book Value at Beginning of the Period

Depreciation for Period 1 = 50% x $107,600 = $53,800

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The reconciled balance would be:

$2,314.22 (bank statement balance) + $35.50 (interest earned) - $504.13 (checks outstanding) - $25.00 (monthly service charge) = $1,820.59

The amount of money that is compounded monthly for 30 years will be $17,153.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

If $10,000 is deposited into a savings account that pays 1.8% annual interest.

Then the rate is given as,

r = 1.8% / 1200

r = 0.0015

Then the number of years is given as,

n = 30 x 12

n = 360

Then the amount of money that is compounded monthly for 30 years is given as,

A = $10,000 × (1 + 0.0015)³⁶⁰

A = $10,000 × (1.0015)³⁶⁰

A = $10,000 × 1.715

A = $17,153

The amount of money that is compounded monthly for 30 years will be $17,153.

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Circle Detection Algorithm is a highly efficient and effective solution to finding the most number of points that lie on any one circle in a 2D real plane.

The algorithm to solve this problem is known as the "Circle Detection Algorithm." This algorithm starts by considering three points randomly selected from the given N points.

Next, the algorithm checks the number of points that lie on this circle. If this number is greater than the current maximum, then this circle becomes the new candidate for the circle that contains the most number of points.

To ensure that the algorithm is efficient, it is important to choose the points randomly, as this reduces the chances of getting stuck in a local maximum.

The mathematical formula to calculate the center and radius of the circle that passes through three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:

x = ( (y₂ - y₁)(y₃² - y₁² + x₃² - x₁²) - (y₃ - y₁)(y₂² - y₁² + x₂² - x₁²) ) / (2 * (x₃ - x₁)(y₂ -y₁) - 2 * (x₂ - x₁)(y₃ - y₁) )

y = ( (x₂ - x₁)(x₃² - x₁² + y₃² - y₁²) - (x₃ - x₁)(x₂² - x₁² + y₂² - y₁²) ) / (2 * (y₃ - y₁)(x₂ -x₁) - 2 * (y₂ - y₁)(x₃ - x₁) )

r = √(x₁ - x)² + (y₁ - y)²

Once the center and radius have been calculated, the algorithm can easily check the number of points that lie on the circle by calculating the distance of each point from the center and checking if it is equal to the radius.

Complete Question:

Given N points on the 2D real plane, what is the most efficient algorithm to find the most number of points that lie on any one circle?

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The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.

A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.

In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.

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Answer:

Just add 5 to the other side

Step-by-step explanation:

x < 9

The linear equation for this scenario will be 2(x + x/4)=190 where x=Length.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Perimeter of rectangle=2 (length + Breadth)

Given Perimeter=190

Let length=x

then Breadth will be = x/4

Hence, the perimeter will form linear equation given below

          2(x + x/4)=190

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a. f(x) = 1.8x.

b. f(x) = 1.35x.

c. f(150) = 1.35×150 ⇒ f(150) = 202.5.

d. The order in which the adjustments are applied doesn't make any difference.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.

Let, 'x' be the price of the merchandise.

So, After adding 80% to its cost it becomes [(100 + 80)/100]×x = 1.8x.

Later it decreases by 25% the price of items that don't sell quickly.

So, It has a value of (75/100)×1.8x = 1.35x.

a. A function f(x) to represent the price after the 80% markup is.

f(x) = 1.8x.

b. A function g(x) to represent the price after the 25% markdown is,

f(x) = 1.35x.

c. A composition function to find the price of an item after both price adjustments that originally the boutique $150 is,

f(150) = 1.35×150.

f(150) = 202.5.

d. Let, The price of the item be $100, after 80% makeup it would be

$180 and after 25% markdown it would be $135.

Again 25% markdown on $100 is $85 and an 80% markup is

75×1.8 = $135 hence no difference.

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Answer:614

Step-by-step explanation:

The maximum number of boxes that can fit in the trailer can be calculated by dividing the volume of the trailer by the volume of each box.

First, we need to convert the dimensions of the boxes and the trailer to the same unit, such as cubic feet. The volume of each box is given by:

V_box = (1 1/2 ft)^3 = (1.5 ft)^3 = 3.375 ft^3

Next, we calculate the volume of the trailer:

V_trailer = 28 ft * 8 1/2 ft * 9 1/6 ft = 2070 ft^3

Finally, we divide the volume of the trailer by the volume of each box to find the maximum number of boxes:

N_boxes = V_trailer / V_box = 2070 ft^3 / 3.375 ft^3 = 614.07 boxes

Since we can only fit whole boxes in the trailer, the maximum number of boxes that will fit is 614.