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The account's balance after 5 years is given as follows:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

In which:

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

Quarterly compounding means that the value of n is given as follows:

n = 4.

Then the balance of the account after 5 years, when t = 5, is given as follow:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

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From the given data points, about 50% of the data points are above the point 34.

Percentage defines the parts of a number per fraction of 100 or a part per 100. It is usually denoted by the symbol '%'.

Percentage of a number is calculated by dividing the number with the whole and then multiply with 100.

Given are a set of data points.

20  22  24  26  28  30  32  34  36  38  40  42  44  46  48  50

The numbers are in ascending order.

Total number of data points = 16

Data points above 34 are,

36  38  40  42  44  46  48  50

Number of data points which are above 34 = 8

Percent of numbers above 34 = (8 / 16) × 100 = 50%

Hence the percent of the data falls after 34 are 50%.

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The area of the triangle PQR is 12 square units

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

J(–2, 2), K(–2, 6), and L(–8, 2),

Reflection and rotation are rigid transformation

This means that

Area of PQR = Area of JKL

So, we have

Area = 1/2 * |x1y2 - x2y1 + x2y3 - x3y2 + x3y1 - x1y3|

So, we have

Area = 1/2 * |-2 * 6 + 2 * 2 + -2 * 2 + 8 * 6 - 8 * 2 + 2 * 2|

Evaluate

Area = 1/2 * |24|

So, we have

Area = 12

Hence, the area is 12 square units

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The amount in the college fund is $16,899.66

In order to determine the amount in the college fund, we need to find the  future value of the money.

The formula for the future value of money is:

FV = PV * (1 + r)^t

where:

FV = future value

PV = present value (initial amount)

r = interest rate (as a decimal)

t = time (in years)

PV = $5000, r = 7% = 0.07, t = 18

FV = PV * (1 + r)^t

FV = 5000 * (1 + 0.07)¹⁸

FV = 5000 * (1.07)¹⁸

FV = $16,899.66

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Complete Question

When a new baby is born to the Johnsons, the family decides to invest $5000 in an account that earns 7% interest as a way to start the baby's college fund. If they do not touch that investment for 18 years, how much will there be in the college fund?

Answer: obtuse scalene triangle

Step-by-step explanation:

A scalene triangle has three different sides.

An isosceles triangle has 2 of the same sides and 1 different side.

Answer:

Its a obtuse scalene triangle!

If the slope of a staircase is 0. 95 and rises with 210, then the run is:

221.05 units.

In this problem, we can use the formula for the slope of a staircase, which is given by:

where "rise" is the vertical height of the staircase and "run" is the horizontal distance of the staircase.

We are given the slope of the staircase as 0.95 and the rise as 210. We can substitute these values in the formula and solve for the run:

Multiplying both sides by run, we get:

Dividing both sides by 0.95, we get:

Simplifying the expression, we get:

Therefore, the run of the staircase is approximately 221.05 units.

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To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.

Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial.  The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.

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The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.

What is Graph?

In mathematics, a graph is a collection of points, called vertices or nodes, and a collection of lines, called edges, that connect pairs of vertices. Graphs are used to represent relationships between objects, such as the connections between different parts of a network or the dependencies between different variables in a system. They are commonly used in fields such as computer science, operations research, and engineering to model and solve problems involving complex systems.

The correct transformations are:

The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.

The graph is translated up 2 units. This is because there is a constant term of +2 added to the function, which means the function has a vertical shift upwards by 2 units.

Therefore, the correct answers are:

The graph is translated to the right 2 units.

The graph is translated up 2 units.

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The cups of milk required for the  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.

Here,

( 2 / 5 ) of a gallons is equal to 0.4 gallons.

( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.

Total gallons left after coffee is equal to

= ( 0.4 ) - ( 0.25 )

= ( 0.15 )gallons

Conversion of gallons to cups is given by :

1 gallon = 16 cups

⇒  ( 0.15 )gallons = 0.15 × 16 cups

⇒  ( 0.15 )gallons = 2.4 cups of milk used.

Therefore, the 2.4 cups of milk is used when  ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.

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The pole is 34.93 feet tall. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is the branch of mathematics that focuses on the study of the sides, angles, and connections of the right-angle triangle.

We are given that Leon is standing 67 feet from a telephone pole. Leon's angle of sight up to the bird is 24° and his eyes are 5.1 feet above the ground.

From this, a figure is obtained which is attached below.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = x/67

Here, θ = 24°

So,

⇒tan 24° = x/67

⇒x = 67 tan 24°

⇒x = 67 * 0.4452

⇒x ≈ 29.83

The height of the pole = 29.83 + 5.1 = 34.93 feet

Hence, the pole is 34.93 feet tall.

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The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.

Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.

If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:

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make brainalist keep smiling dude..!

Answer: 20

Step-by-step explanation:

58-38=20

Answer:

C. it decreases the removal of carbon dioxide from the atmosphere

Answer:

Step-by-step explanation:

it decreases the production of ozone in the atmosphere

Since the diameter of this circle is 14 cm, a measurement of the circumference of this circle to the nearest tenth is 43.96 centimeters.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 14

Circumference of circle, C = 43.96 centimeters.

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Answer:

a)  See the attachment for the completed Venn diagram.

b)  The number of people who liked to watch television only is 20.

c)  The total number of people who took part in the survey was 200.

Step-by-step explanation:

Draw a Venn diagram with two overlapping circles.

Label one circle "Radio" and the other circle "TV".

Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.

Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:

Therefore, place the number 70 in the part where the two circles overlap.

Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:

Therefore, place the number 60 in the area outside the two circles.

Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:

Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.

Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:

Therefore, there was a total of 200 people who took part in the survey.

The probability of getting one club and one heart is 0.127.

p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.

An expression is combination of variables, numbers and operators.

Given that Marcia's cost, in dollars, to wash her car can be calculated using the expression

0.25m +1.50

Zero point two five plus one point five.

In the expression m represents the number of minutes the car wash will run.

We need to find the value of expression when m is 20

0.25(20)+1.50

5+1.50

6.5

When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.

Hence, Marcias cost $6.5 to wash her car for 20 minutes.

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The distance from point A to point B is 1496 ft.

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

Given that, a boat is at point A which at 724 ft distance from a lighthouse making an angle of elevation to the lighthouse’s beacon-light of 16°, when moved to some distance B making an angle of elevation to the lighthouse’s beacon-light of 5°, we need to find the distance from point A to point B.

Refer to the figure attached,

The whole scene is creating two right triangles, rt Δ CDA and rt Δ CDB

Using the trigonometric functions, in rt Δ CDA,

We have,

tan 16° = CD/DA

CD = tan 16° × 724

CD = 207.6

Therefore, the height of the lighthouse is 207.6 ft

Now,

tan 5° = CD/DB

DB = CD / tan 5°

DB = 2373

The distance between A and B = DB-DA = 2373 - 724 = 1496

Hence, the distance from point A to point B is 1496 ft.

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the solution is where they intercept; (2,-4)

The vector in component form is given as follows:

v = (6.9, 1.2).

Considering a vector with a magnitude of M and an angle of x, the component form notation for the vector is given as follows:

v = (Mcos(x), Msin(x)).

The parameters for this problem are given as follows:

Hence the components are given as follows:

Hence the vector is of:

v = (6.9, 1.2).

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Hi there, here's your answer:

Given, a basketball team averaged 68 points per game in the last season and averaged 77 points per game in the present season.

To find:

The approximate percentage of increase.
Solution:

If 68 points was the average last season, and 77 points was the increase this season, then the number of increase in points is 9.

Also we have that % increase = [tex]\frac{Difference}{Original}[/tex] × 100

Which is [tex]\frac{9}{68}[/tex] × 100 = 0.1323 × 100 = 13.23%

Therefore, the approximate percent increase is 13%.

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Answer: The total amount paid for shoes = $63.75

Step-by-step explanation:

The original price of the shoes = $ 80

Sale Discount = 25 %

So, the discount offered = 25 % of 80 = 20

So, the Discounted Price  = Marked price - discount

= $ 80 -$ 20 = $ 60

Now, we need to calculate the sale tax of 6.25 % on $ 60.

Also, we know that  Sales Tax = Sales Tax rate x Sale Price

= $ 60 x 0.0625  = $ 3.75

Total Cost = Sale Price + Sales Tax

=  $ 60 + $ 3.75  = $63.75

Hence, the total amount paid for shoes = $63.75 included sales tax

The dilated points are:

W': (-1, 2)

X': (2.5, 0)

Y': (-0.5, -2).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

Given:

Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).

And the scale factor is 1/4.

So, the image points are,

W': (-4/4, 8/4) = (-1, 2)

X': (10/4, 0/4)  = (2.5, 0)

Y': (-2/4, -8/4) = (-0.5, -2)

Hence, the image points are given above.

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The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.

Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.

The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.

But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.

The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.

So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.

Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.

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With given features we can definably say that Both triangles are congruent under ASA Criteria.

A triangle is a closed polygon made up of three line segments that intersect at three different angles.

If the sides and angles of two triangles are the same length, the triangles are said to be congruent. As a result, two triangles can be superimposed side by side and angle by angle. Congruence is the term used to describe the relationship between an object and its mirror image. When two objects or shapes superimpose on one another, they are said to be congruent. They are identical in terms of shape and size. Line segments of the same length and angles of the same measure are congruent in the context of geometric figures.

Given far opposites angle are same = 25°

Given intersected line makes equal line

Intersecting angles are equal due to vertically opposite angle theorem.

Then we have,

Angle = Angle

Side = Side

Angle = Angle

With this features we can definably say that Both triangles are congruent under ASA Criteria.

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a) Sin2θ = 22/20 = 11/10

b) cos 2θ = 2(17/20) = 17/10

c)tan 2θ = 2(11/17) = 22/17

The trigonometric ratios are six functions that relate the angles of a right triangle to the lengths of its sides. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

If sin θ = 11/20

The missing side of the triangle is;

b = √20^ - 11^2

b = 17

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Considering AB=BC, the matrices A, B, and C are square matrices such that matrix B is invertible.

Now, post-multiply both sides of 

[tex]AB=BC by  {B}^{−1} [/tex]

[tex] {ABB}^{−1} = {BCB}^{−1} [/tex]

Solving the obtained equation for A by using the properties

[tex]AI= {BCB}^{−1} \\ A= {BCB}^{−1} [/tex]

Therefore, the required matrix A is BCB−1

A matrix, also known as matrices, is a rectangular array or table of letters, numbers, or other symbols arranged in rows and columns that is used to represent a mathematical object or a characteristic of one.

In linear algebra, matrices represent linear maps and enable explicit computations. Since most properties and operations of abstract linear algebra can be expressed in terms of matrices, the study of matrices constitutes a significant portion of linear algebra.

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a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8

b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5

In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint

Highest common factor is the highest factor that is common to two or more numbers:

Factors of 24 = 1,2,3,4,6,8,12 and 24

Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.

Common factors of 24 and 40 = 1, 2, 4, 8

Therefore, the highest common factor is 8.

The number of paintbrushes in each package:

= Number of brushes / number of package

= 24/8

= 3 brushes

The number of tubes of paint:

= number of tubes of paints / number of package

= 40 / 8

= 5 tubes of paints

Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?​".

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