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You can hold qualified investments like cash, stocks, bonds, mutual funds in a TFSA and can withdraw contributions as well as the interest, capital gains, and dividends earned in the account at any time1, without paying taxes

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Janice donated 20 pants and 80 t-shirts of clothing to the Salvation Army.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, Janice donates 100 items of clothing to the Salvation Army and the number of t-shirts were 4 times the number of pants.

Therefore, If the number of pants is 'x' then the number of t-shirts are '4x'.

So, x + 4x = 100.

5x = 100.

x = 20.

So, The number of pants are 20 and the number of t-shirts are 80.

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Sum of the series will be (19/30)

Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.

An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.

Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.

Using partial fractions, we have

[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]

Put n=-8,

we have 6=0+2B=>B=3

Put n=-10,

we have 6=-2A =>A=-3

[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]

other terms will be cancelled out

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The correct question should be:

Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]

Answer:

Fraction of fruit or vegetable cans = 13/28

Step-by-step explanation:

The fraction of the cans that are either fruit or vegetables is the sum of the fractions of the cans that are fruit and the cans that are vegetables. Since the fractions are for mutually exclusive categories, we can add the fractions of cans of fruit and the cans of vegetables to find the total fraction of cans that are either fruit or vegetables.

Fraction of fruit cans: 6/7

Fraction of vegetable cans: 1/4

Therefore,

Fraction of fruit or vegetable cans = 6/7 + 1/4 = (6 + 7)/(7*4) =13/28

So on solving the provided question, we can say that n the graphs we have A at origin; B at origin; C in 3rd quadrant; D in the 2nd quadrant

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here in the graphs we have

A at origin

B at origin

C in 3rd quadrant

D in the 2nd quadrant

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MNOP is a rhombus then, the length of the segment MP = 49 unit.

One kind of parallelogram is the rhombus, which has four sides and four vertices.

The length of each side is the same as the length of the opposing angle.

Given:

A rhombus is given in the attached image.

In rhombus,

every side is equal in length.

That means,

the parallel sides are equal.

9x - 77 = 3x + 7

6x = 84

x = 14

So,  3(14) + 7 = 42 + 7 unit

That means, the side in rhombus = 49 unit.

Therefore, MP = 49 unit.

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The complete question is given in the attached image.

Answer: The discount percentage is 23.4%

Step-by-step explanation:

The discount percentage can be calculated by taking the difference between the original price and the sale price, dividing that by the original price, and then multiplying by 100 to get a percentage.

Answer:

  29°

Step-by-step explanation:

In given parallelogram LMNQ, you want the measure of angle LMQ when angle MQN is given as 29°.

Angles LMQ and MQN are alternate interior angles where transversal MQ crosses parallel lines LM and NQ. As such, they are congruent.

  m∠LMQ = 29°

Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)

The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.

The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.

It will be an exponential growth if the base is greater than 1.

It will be an exponential decay if the base is less than 1.

There won't be any exponential growth or decay if the function's exponent is zero.

Therefore: Decay exponential (base less than 1:

W = 9/8(3/5)t

f(t) = (3/4)t

L = 4.2(0.6)t

Exponential Growth (base larger than 1:

L = 0.25(12)t

W = 0.5(2.1)t

f(t) = 2/3(6)t

Not exponential growth or decay (no exponent):

G(x)=1.3(x)

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The length of measurement would be in a scale drawing of 180 m is 24 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the scale is 2 cm = 15 m.

So, 1 m =2/15

A scale drawing of 180 m

Now, 180 m = 2/15 ×180

= 2×12

= 24 cm

Therefore, the length of measurement would be in a scale drawing of 180 m is 24 cm.

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An object O is displayed in front of a plane mirror in the figure. The image of the object is visible from locations B and C.

An object's image is created by a plane mirror by reflecting light rays that originate from the object. The object and its image appear to be equally distant from the mirror because the image created by a plane mirror is imaginary, upright, and the same size as the object.

As light from the object enters the plane mirror, it reflects each beam in accordance with the Law of Reflection. At the intersection of the reflected beams' extensions, the image is visible.

Therefore, the location must be on the reflected ray's path for the image to be visible. Here, locations B and C are on the path of the reflected ray. So the image is visible in these locations. But not in locations A and D.

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Answer:

A mary go round I'm sorry I am middle school

The perimeter of Δ BUG with sides BG = 105, BU = 16 and UG = 30 is 151 units.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

It is given that ΔTOP ~ ΔBUG.

The lengths of sides of ΔTOP is - TO = 16, TP = 20, OP = 30.

The length of one side of ΔBUG is BG = 105.

Since ΔTOP is same as ΔBUG, so sides BU and UG will same as sides TO and OP respectively.

So, BU = 16 and UG = 30.

The formula for the perimeter of a triangle is -

P = a + b + c

Where, P is the perimeter and a, b, c are the sides of the triangle.

For ΔBUG -

P = BU + BG + UG

P = 16 + 105 + 30

P = 151

Therefore, the perimeter of ΔBUG = 151 units.

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Without the specific function it is not possible to give you the exact solution and also without knowing the specific limits of the integral, it is not possible to evaluate the definite integral.

The solid in the figure is a rectangular prism with a cutout, the cutout is a cylinder with radius 2. The volume of the solid can be found by using a double integral.

The first integral represents the volume of the rectangular prism, and the second integral represents the volume of the cylinder cut out of it. The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder.

The volume of the rectangular prism = (x-coordinate max - x-coordinate min) * (y-coordinate max - y-coordinate min) * (z-coordinate max - z-coordinate min)

The volume of the cylinder = ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <= 2.5] dA

The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder

The x-coordinate min is 0, x-coordinate max is 4, y-coordinate min is 0, y-coordinate max is 6, z-coordinate min is 0, and z-coordinate max is 6.

The volume of the solid

= (4 - 0) * (6 - 0) * (6 - 0) - ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <=2.5] dA

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Therefore , the solution of the given problem of set A when A= {5, 6, 7, 8, ..., 35}.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

Here,

The set A contains integers between 5 and 35, inclusive. So, the cardinality of set A is the number of integers between 5 and 35, which is 35-5+1 = 31.

b. A when A= {xEZ: -2 ≤ x ≤ 90}.

The set A contains all integers between -2 and 90, inclusive. So, the cardinality of set A is the number of integers between -2 and 90, which is 90-(-2)+1 = 93.

c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}

The set A contains all the natural numbers less than or equal to 31. The set B contains all the prime numbers less than or equal to 31. There are 15 prime numbers less than or equal to 31: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. So, the cardinality of set B is 15.

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Answer: D

Step-by-step explanation:

Answer:

No it is not

Step-by-step explanation:

In an additive relationship, two quantities can be expressed as related to each other through addition. It can be written as y = x + a, where y is related to x through the addition of a constant, “a”.

In this scenario, the "a" is not constant

1+2=3, 5+3=8, and 9+4=13

the number is increasing by one each time

Answer:

y= 60+ 2x  and if he spent 19.5 hours then he would pay $99 for that month

Step-by-step explanation:

$60 PER MONTH + $2 per hour of boxing classes

X represents the total hours he had the boxing classes

equation: y= 60+ 2x

if he spent 19.5 hours in boxing class

plug in 19.5 hours to X

99 = 60+ 2(19.5)   = 60 + 39

The limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined.

We can see that the denominator [tex]x^2[/tex][tex]y^2[/tex] goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.

The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.

Therefore, the limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.

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The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We should know that a circle is a set of points on a circle that are equal from a fixed point

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)² = b=r²

where; (a, b) is the center of the circle

r is the radius of the circle

Given the following

Diameter = 12 units

radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Therefore, Substituting into the formula, we will have (x-0)² + (y-3)² = 6² which is equivalent to x²+ (y-3)² = 36

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Answer: c

Step-by-step explanation:

Answer:

$1688.40

Step-by-step explanation:

1% of 1608 = 16.08

16.08 (5) = 80.40

1608+ 80.40= 1688.40

The value of the z is 6√6 units. The triangles follow similar triangle property.

What are similar triangles?

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Consider △BDC and △ABC:

∠C = ∠C

∠ABC = ∠BDC = right angle

If two angles of a triangle are equal to two angles of another triangle, then third angle of the triangles also equal.

∠BAC =∠DBC

According to A-A-A rule △BDC and △ABC are similar to each other.

Thus the ratio of corresponding sides is also equal.

Therefore:

AB/BD = BC/DC = AC/ BC

Consider the last two ratios:

BC/DC = AC/ BC

z/12 = z/18

z² = 12 × 18

z² = 6×2×6×3

z = 6√6

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An inequality to determine at what times the car will be ahead of the truck is; 63x > 55x + 30

The graph of the inequality is attached and the solution is (3.75, 236.25).

We are told that;

x represent the number of hours that the car and truck travel

The truck is traveling at an average rate of 55 mph. Thus, the expression 55x represents the distance the truck travels in x hours.

The car is traveling at a rate of 63 mph. Thus, the expression 63x represents the distance the car travels in x hours.

In the beginning, the truck was 30 miles ahead of the car. So, we need to solve the inequality:

63x > 55x + 30

Use technology to graph y = 63x and y = 55x + 30 gives us;

The intersection point is (3.75, 236.25)

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The perimeter of a rectangle is given by the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width.

We know that the perimeter of the parking lot is 354 m, and the width of the parking lot is 83 m. We can use this information to find the length of the parking lot.

Substituting the known values into the formula, we get:

354 = 2(L + 83)

Simplifying the equation:

354 = 2L + 166

Subtracting 166 from both sides:

188 = 2L

Dividing both sides by 2:

L = 94

The length of the parking lot is 94 m.

Answer:

Step-by-step explanation:

Formula for perimeter = (2 * length) + (2* width) = Perimeter

2l + (83 * 2) = 354

2l + 166 = 354

2l = 354 - 166

2l = 188

l = 188/2

l = 94 m

Evelyn’s enlarged photo will not retain the same proportions as the original one.

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Given,

Length of the original photograph L = 5''

Width of the original photograph W = 7''

Ratio between length and width of original photograph

L/W = 5/7

Length of the enlarged photograph L' = 16''

Width of the enlarged photograph W' = 20''

Ratio between length and width of enlarged photograph

L'/W' = 16/20 = 4/5

Comparing both ratios

L/W = L'/W'

5/7 ≠ 4/5

so, proportion is not same.

Hence, proportion of the enlarged photo is not same as the original photo.

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Answer: x = 15

Step-by-step explanation: Combine like terms

7 x plus 4 x plus x equals 180

12 x equals 180

2

Divide both sides by the same factor

12 x equals 180

the fraction with numerator 12 x and denominator 12 end fraction equals the fraction with numerator 180 and denominator 12 end fraction

3

Simplify

Solution

x equals 15

Answer:

A

Step-by-step explanation:

Answer: y = (3/4)x - (7/4).

Step-by-step explanation:

Subtract 3x from both sides of the equation. Divide both sides of the equation by -4. Simplify. We get that solving 3x - 4y = 7 for y gives y = (3/4)x - (7/4).