Paul wants to buy a new car, but rather than take out a loan, he decides to save $150 a month in an account that earns 2.5% interest, compounded monthly. How much will he have saved up after three years have passed?

The equation of the line of given slope and point is y = 2x + 12. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is the line with m as its slope and b as its y-intercept. The slope-intercept form of the linear equation is used when the values of m and b are real integers.

We are given the slope as 2 and which is passing through the point (6,24).

We need to first find the y-intercept using y = mx + b

⇒y = mx + b

⇒24 = 2(6) + b

⇒24 = 12 + b

⇒b = 12

The equation in the slope-intercept form is

y = mx + b

This gives equation as y = 2x + 12.

Hence, the equation of the line of given slope and point is y = 2x + 12.

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Answer: X and Y values

Step-by-step explanation:

The function f(x-3) is simplified to have x² - 6x + 13

Given the following quadratic function below

f(x) = x² + 4

We need to determine the value of the function f(x-3). Replace x with x -3 in f(x) to have:

f(x-3) = (x-3)² + 4

Expand the equivalent expression

f(x-3) = x² - 6x + 9 + 4

f(x-3) = x² - 6x + 13

Hence the simplified form of the expression is x² - 6x + 13

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Answer:

1/7

Step-by-step explanation:

Absolute value is the distance from zero. 7 and -1/7 and their distance from zero is not the same, but the distance from zero with the numbers -1/7 and 1/7 are the same. The absolute value, the distance from zero, is both 1/7.

In the following option n log n seems to grow the fastest amongst all according to the size of inputs.

In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.

In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.

Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.

1. n grows linearly with n, so it takes more time as the size of the input grows.

2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.

3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.

4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.

5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.

So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.

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The better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory.

Given that, a can of Tab costs R7, 20 at Timber City.

Then 6 packs will cost = 6(720) = R4320

At promotion the cost is R3960 the discount offered is:

D = R4320 - R3960

D = R360

At campus Canteen a can of tab is for R7, 50.

6 packs = 6(750) = R4500

Discount = 4500 - 3900 = R600

Hence, the better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.

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The values of t that satisfy the inequality are less than 1.25

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

8 > 3+ 4t​

Evaluate the like terms

So, we have

5 > 4t

Divide both sides by 4

So, we have the following representation

1.25 > t

Rewrite as

t < 1.25

This means that the values of t that satisfy the inequality are less than 1.25

None of the options are applicable

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Complete question

Which of the t-values satisfy the following inequality?

8 > 3+ 4t​

Choose all answers that apply:

(Choice A) t = 12

(Choice B)t = 16

(Choice C)t = 20

The surface area of rectangular prism above is 2738 in².

At the picture above is a rectangular prism with the sides 29 in, 36 in and 5 in.

The question is want to know The are

The surface area of a rectangular prism is given by this formula: 

A = 2 (lh +wh + lw )

Substitute the sides of the shapes to the formula

A = 2 (lh +wh + lw )

A= 2( 36.5 + 29.5 + 36.29)

A= 2(180+145+1044)

A= 2(1369)

A=2738 in²

Therefore the surface area is 2738 in².

A right-angle prism is a three-dimensional shape with six faces, where all faces of the prism (top, bottom, and sides) are rectangular and all pairs of opposing faces are congruent. Like all three-dimensional shapes, right-angled prisms have a volume and a surface area. A right angle prism is also called a cuboid 

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Answer: Account 1 earns a higher return over 3 years, with a total of $515.64.

To calculate the return of Account 1:

$500 * (1 + 0.012/12)^(12*3) = $515.64

To calculate the return of Account 2:

$500 * (1 + 0.013/2)^(2*3) = $515.16

Therefore, Account 1 earns a higher return of $515.64 compared to Account 2's return of $515.16.

Step-by-step explanation:

The equations for the amount of ingredients is

The amount of pasta = 33 parts pasta

The amount of tomato = 16 parts tomato

The amount of cucumber = 10.5 parts cucumber

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of pasta , tomato and cucumber required to make 6 servings be represented as P , T and C respectively

Now , the equation will be

The amount of pasta for 1 servings = 5 1/2

The amount of pasta for 6 servings P = 6 x ( 5 1/2 )

On simplifying the equation , we get

The amount of pasta for 6 servings P = 33 parts pasta

And ,

The amount of tomato for 1 servings = 2 2/3

The amount of tomato for 6 servings T = 6 x ( 2 2/3 )

On simplifying the equation , we get

The amount of tomato for 6 servings T = 16 parts tomato

And ,

The amount of cucumber for 1 servings = 1 3/4

The amount of cucumber for 6 servings C = 6 x ( 1 3/4 )

On simplifying the equation , we get

The amount of cucumber for 6 servings C = 10.5 parts cucumber

Hence , the equations are solved

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The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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The image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.

The coordinates W(-2, 1), X(-1, 3), Y(3, 3), and Z(3, 3) can be plotted to form the quadrilateral's graph as follows:

code is as follows:

     |

     | Y(3,3)

     |

     |

------Z(3,-3)

------

     |

     |

     |

     | X(-1,3)

     |

     |

     |

W(-2,-1)

We may use the following transformation on each vertex to determine the image of this quadrilateral following a 180-degree rotation of the origin:

(x, y) -> (-x, -y) (-x, -y)

As a result, the picture quadrilateral's new vertices are:

W' = (-(-2), -(-1)) = (2, 1) (2, 1)\sX' = (-(-1), -(3)) = (1, -3) (1, -3)\sY' = (-3, -3) = (-3, -3) (-3, -3)\sZ' = (-3, 3) = (3, -3) (3, -3) (3, -3)

To create a quadrilateral image, we can plot these points on the same coordinate plane:

code

     |

     | Y'(3,-3)

     |

     |

------

Z'(3,-3)

------

     |

     |

     |

     | X'(1,-3)

     |

     |

     |

W'(2,1)

It should be noted that the image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.

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The expression for the number of sundaes shop owner needs to sell in September is 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.

If the ice cream shop owner sold x sundaes in August, then she will sell

3×x=3x sundaes in September.

Therefore, number of sundaes shop owner sold in September is 3x.

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The quadratic regression equation is y = 2x^2 + 16x - 0.75

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

x 0 2 4 6 8

f(x) 2 31 54 71 82

Using a graphing calculator, we have the following summary:

The equation is represented as

y = ax^2 + bx + c

So,, we have

y = 2x^2 + 16x - 0.75

Hence, the equation is y = 2x^2 + 16x - 0.75

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The area of the given  figure is, 123ft²  .So option c  is correct

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The given figure can be assumed as a trapezoid with the two parallel sides being the bottom side (20.5 feet) and the top side (from the perpendicular to the right vertex to the perpendicular to the left vertex

= 18.4 + 2.1

= 20.5 feet

The height of the trapezoid is given as 6 feet.

The formula for the area of a trapezoid is:

Area = (sum of the parallel sides) * height / 2

So, in this case, the area of the trapezoid would be:

Area = (20.5 + 20.5) x 6 / 2

        = 41 x 3

        = 123 square feet

Therefore, the answer is 123 square feet.

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For Ф=-π/3 it is found in second quadrant, Ф=-π/4 is also found in second quadrant and Ф=-5π/6 in fourth quadrant.

What exactly are quadrants?

A quadrant is an area specified by the coordinate system's two axes (x and y). When the two axes, x and y, cross at 90 degrees, the four areas generated are known as quadrants. These areas include both positive and negative x- and y-axis coordinate values. The coordinates reflect a point's location in a quadrant.

In the Coordinate Plane, there are four quadrants.

Based on such values, the graph is split into parts or four quadrants.

The first quadrant is located in the upper right-hand corner of the graph. Both x and y values are positive in this quadrant.

The second quadrant is located in the upper left-hand corner of the graph. The value of x in this quadrant is negative, whereas the value of y is positive.

The third quadrant is located in the graph's lower left-hand corner. It has negative values for both x and y.

Fourth Quadrant: Finally, the fourth quarter is in the lower right-hand corner, with a positive x and a negative y value.

Now,

For quadrants, upto value of π/2 angles are in first qudrants

and upto -π/2 and π/2 to π are in second quadrant

and -π/2 to -π are in fourth quadrant.

Hence,  

          For Ф=-π/3 it is found in second quadrant, Ф=-π/4 is also found in second quadrant and Ф=-5π/6 in fourth quadrant.

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Answer:

96cm

Step-by-step explanation:

scale of 4cm : 1'    

actual: length 3 feet,  width is 2 feet.

so 12 cm & 8 cm

so area. = 12*8 = 96cm

Answer:

A: No solution

B: Unique Solution: (0, 0)

Step-by-step explanation:

In System A, you may notice that in both equations the two equations have variables with the same coefficient, and this is ideal for the elimination method of solving the equation. We want to add the equations in a way that cancels out variables. So let's multiply the top equation by negative one: [tex]-1(2x+3y)=-(9)\implies -2x-3y=-9[/tex]

Now from here we want to add the two equations:

[tex]\ \ -2x-3y=9\\+2x+3y=4\\0+0=13[/tex]

And the statement provided is clearly not true, 0 is never equal to 13, meaning the systems of equation has no solution, which occurs when you have two parallel lines.

In this case, we can easily solve this using substitution, since y is equal to 7x that means we can substitute in 7x for y in the second equation:

[tex]y=x\implies 7x=x[/tex]

And from here we subtract x from both sides, and divide by 6 giving us:

[tex]x=0[/tex]

And now we can take this value and plug it into either equation to solve for our y value, and it's most convenient to plug it into the y = x equation... since there's nothing to solve, we just get:

y = 0

So x = 0, and y = 0, meaning there is a unique solution of (0, 0)

The probability values are obtained as -

P(X + Y > 3) = 0.45

P(XY = 2) = 0.10

P(XY > 1) = 0.55

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The joint probability mass function XX and YY is given as -

p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1.

The first operation is -

P(X + Y > 3)

Substitute the values in the equation -

P(X + Y > 3) = P(3,1) + P(2,2) + P(3,2) + P(1,3) + P(2,3) + P(3,3)

P(X + Y > 3) = 0.05 + 0.1 + 0.1 + 0.05 + 0.05 + 0.1

P(X + Y > 3) = 0.45

Therefore, the value is obtained as 0.45.

The second operation is -

P(XY = 2)

Substitute the values in the equation -

P(XY = 2) = P(2,1) + P(1,2)

P(XY = 2) = 0.05 + 0.05

P(XY = 2) = 0.10

Therefore, the value is obtained as 0.10.

The third operation is -

P(XY > 1)

Substitute the values in the equation -

P(XY > 1) = 1 - [P(XY ≤ 1)]

P(XY > 1) = 1 - [P(1,1)]

P(XY > 1) = 1 - 0.45

P(XY > 1) = 0.55

Therefore, the value is obtained as 0.55.

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The joint probability mass function of XX and YY is given by

p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1

Compute the following probabilities:

P(X+Y>3)=

P(XY=2)=

P(XY>1)=

The number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

Cubic form is defined as the shape of a cube. Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped.

According to the prism, the cube at the center has no stickers.

Stickers on 0 side = 1

The face of the prism contains cube that would have stickers on one side. The center cubes on each face will have stickers on one side:

Stickers on 1 side = 6

The edges of the prism will have cubes at the center that contain stickers on both sides:

Stickers on 2 side = 4 (3) = 12

Every vertices on the prism will have sticker on three sides.

Sticker on three side = 8

Hence, the number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

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The correct question is:

the equation of the Linear function will be f(x) = -19x + 14.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a data set of a linear function

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (the value of y, at x = 0)

since, slope = (y - y')/(x -x')

In our case,

Slope = (128 -90)/ (-6 + 4)

Slope = 38/-2

Slope = -19

And b = 14 (Given)

Thus,

The equation of Line:

y = -19x + 14

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The expression 5(AB)+3(AB) = 8(A^2)(B^2)​ are not equal

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

5(AB)+3(AB) = 8(A^2)(B^2)​

The left side of the equation represents the sum of two products of A and B, while the right side represents the product of 8 and A^2 times B^2,

These are two completely different expressions and their values are unlikely to be equal unless A, B, and the specific values involved are known.

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The total sales when the farm stands have 410 customers will be $4326.

To predict the total sales when the farm stand has 280 customers, we need to interpolate between the data points for 254 and 316 customers. First, we can calculate the average growth rate between these two data points:

Average growth rate = (ln(2606) - ln(1995)) / (ln(316) - ln(254)) = 0.3763

Using this average growth rate, we can predict the sales for 280 customers as follows:

ln(y) - ln(1995) = 0.3763 x  (ln(280) - ln(254))

ln(y) = 7.5835

[tex]y = e^{7.5} = 1961.36[/tex]

Rounding to the nearest whole number, we predict that the total sales when the farm stands have 280 customers will be $1961.

To predict the total sales when the farm stands have 410 customers, we need to extrapolate beyond the data points. We can use the same average growth rate calculated above to make this prediction:

ln(y) - ln(2606) = 0.3763 x (ln(410) - ln(316))

ln(y) = 8.4256

[tex]y = e^{8.4256}[/tex] = 4326.46

Rounding to the nearest whole number, we predict that the total sales when the farm stands have 410 customers will be $4326.

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Answer:

the income affect is changed drastically as now for every person they loose $3.00

The equation of line is y = -2x + 9

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 7 )

The slope of the line is m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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The factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression. A factor is a number that evenly divides the inputted number or expression.

Algebraic expressions can be factored by identifying two or more expressions whose product is the provided expression, which is known as finding the factors of the given expression.

Given that:

9x^5+x^2

Factor x^2 out of 9x^5.

= x^2 (9x^3 ) + x^2

= x^2 (9x^3 + 1)

Therefore, we can conclude that the factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

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Answer:

D

Step-by-step explanation:

ROA, ROE, and ROIC are important metrics for comparing the performance of different companies and can provide valuable insights into a company's financial health and competitiveness.

Return on assets (ROA), return on equity (ROE), and return on invested capital (ROIC) are among the most commonly used metrics for comparing the performance of different companies. These metrics are widely used by investors, analysts, and other stakeholders to evaluate a company's financial performance and to compare it with other companies in the same industry.

Return on assets (ROA) is a measure of a company's efficiency in using its assets to generate profits. It is calculated by dividing the company's net income by its total assets. A higher ROA indicates that a company is generating more profits from its assets, while a lower ROA suggests that the company is not using its assets as efficiently.

Return on equity (ROE) is a measure of how much profit a company generates in relation to the equity invested by its shareholders. It is calculated by dividing the company's net income by its total equity. A higher ROE indicates that a company is generating more profits for its shareholders and is a sign of a well-managed company.

Return on invested capital (ROIC) is a measure of how much profit a company generates in relation to the capital it has invested in its business. It is calculated by dividing the company's net income by its invested capital. A higher ROIC indicates that a company is generating more profits from its invested capital, while a lower ROIC suggests that the company is not using its capital as effectively.

In summary, ROA, ROE, and ROIC are important metrics for comparing the performance of different companies and can provide valuable insights into a company's financial health and competitiveness.

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Answer:

$57.02

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the values into the simple interest formula and solve for I:

[tex]\implies I=850 \cdot 0.0575 \cdot \dfrac{14}{12}[/tex]

[tex]\implies I=57.0208333...[/tex]

Therefore, the amount of interest is $57.02 (nearest cent).

The volume of the trapezoidal prism shown is 168 in³

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The volume of the figure is the product of its base area and height. Hence:

Volume = area of base * height

The base is a trapezoid with parallel sides 3 in and 9 in, hence:

Area of base = 3 in * 9 in = 24 in²

Volume = area of base * height = 24 in² * 7 in = 168 in³

The volume of the figure is 168 in³

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