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The loan's future value A, or the total amount due at time t is equal to $3,720.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 3,000 × 6/100 × 5

S.I = 3,000 × 0.06 × 4

S.I = $720.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = $720 + $3,000

Future value, A = $3,720.

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the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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The maximum possible value of the result is 8.

How to solve Linear Equations?

We are given the linear equation;

4x - x = 0

From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;

The first step to solving the equation is to; C. add x to both sides

The second step  to solving the equation is to; C. cube both sides

Solving the equation for x initially yields; C. two possible values

Checking the solutions shows that; D. none are valid solutions

4x - x + x = 0 + x

4x = x

Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;

(4x)³ = x³

4³x = x³

64x = x³

Divide both sides by x to get;

x² = 64

Take square root of both sides to get;

x = ±√64

x = ±8

Hence, The maximum possible value of the result is 8.

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The area of the isosceles trapezoid is 281.25 square cm.

Let's denote the length of the base of the trapezoid as "b".

According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.

The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.

Therefore, we can write:

Perimeter = 2b + 2(b/2) = 3b

We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:

3b = 45

Solving for b, we get:

b = 15

Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:

Area = (1/2)h(b1 + b2)

where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.

Substituting these values, we get:

Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8

Substituting b = 15, we get:

Area = 15^2/8 = 281.25 sq cm

Therefore, the area of the isosceles trapezoid is 281.25 square cm.

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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.

Find the areae

Answer:

Step-by-step explanation:

18.) 19 - 3x = 14 + 2x

To solve for x, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side:

19 - 3x = 14 + 2x

19 - 14 = 2x + 3x

5 = 5x

x = 1

To check our solution, we can substitute x = 1 back into the original equation and see if it holds true:

19 - 3(1) = 14 + 2(1)

19 - 3 = 14 + 2

16 = 16

Since both sides of the equation are equal when x = 1, we have verified that x = 1 is the correct solution.

19.) 2(7 + 5y) - 3y = -35

We can start by simplifying the left-hand side of the equation by using the distributive property:

2(7 + 5y) - 3y = 14 + 10y - 3y = 14 + 7y

Now, we can solve for y by moving the constant term to the other side:

14 + 7y = -35

7y = -49

y = -7

To check our solution, we can substitute y = -7 back into the original equation and see if it holds true:

2(7 + 5(-7)) - 3(-7) = -35

2(7 - 35) + 21 = -35

-56 + 21 = -35

-35 = -35

Since both sides of the equation are equal when y = -7, we have verified that y = -7 is the correct solution

20.) 14 + 4(x - 5) = 6 - 2x

We can start by simplifying the left-hand side of the equation by using the distributive property:

14 + 4(x - 5) = 14 + 4x - 20 = 4x - 6

Now, we can solve for x by moving the constant term to the other side:

4x - 6 = 6 - 2x

6x = 12

x = 2

To check our solution, we can substitute x = 2 back into the original equation and see if it holds true:

14 + 4(2 - 5) = 6 - 2(2)

14 - 12 = 6 - 4

2 = 2

Since both sides of the equation are equal when x = 2, we have verified that x = 2 is the correct solution.

Answer:

Step-by-step explanation:

x inter for line a = 1

x inter for line B = -4

Line A is greater then Line B

This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.

The probability that none of the households are tuned to Pretty Betty is:

P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031

The probability that at least one household is tuned to Pretty Betty is:

P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969

The probability that at most one household is tuned to Pretty Betty is:

P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500

However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.

Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

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Applying the law of sines, the value of c is calculated as: c ≈ 11.8.

The Law of Sines, also known as the Sine Rule, is a theorem in trigonometry that relates the side lengths of a triangle to the sine of its angles.

Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be expressed as:

a / sin A = b / sin B = c / sin C

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Applying the law of sines, we have:

c/sin 105 = 7/sin 35

Cross multiply:

c * sin 35 = 7 * sin 105

c = 7*sin 105/sin 35

c ≈ 11.8

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The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

given that,

its angles , x, 102, x

now, we know,

The sum of the angles in a triangle add to 180

i.e.

x+ 102+x = 180

Combine like terms

so, we get,

102 + 2x = 180

Subtract 102 from each side

2x = 78

divide by 2, both sides,

x =39

Since we have a 102 degree angle it is a obtuse triangle.

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The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Answer:

The slope of the line that passes through (7,-4) and (11 -4) is 0, since it is a horizontal line.

To find the slope when given two points, use the formula:

y2-y1/x2-x1=m(-4- -4)/(11-7)=0/4=0

So the slope is 0 because 0 is the numerator. If 0 is the denominator, the slope will be undefined.

Hope this helped!

Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.

Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.

Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.

The percentage error of the student's estimated mass is 2.15%.

The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.

The estimated mass of the student = 82.0 kg

The actual mass of the student = 83.8 kg

Absolute error = Actual Value - Estimated Value

= 1.8 kg (83.8 - 82.0)

Percentage error = Actual Value - Estimated Value /Actual Value x 100

= 2.15% (1.8/83.8 x 100)

Thus, we can conclude that the student's estimate contains a 2.15% error.

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The function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

What are functions?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.

Given a function as follows:

[tex]y = -\sqrt[3]{11+8x}[/tex]

Consider two functions, f(x) and g(x).

Let f(x) = -∛x

g(x) = 11+8x

Then f(g(x) = f(11+8x) = [tex]-\sqrt[3]{11+8x}[/tex]

Therefore the function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

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The standard equation of a hyperbola centered at the origin and a vertical transverse axis values of a=8 and b=9 is  y²/64 - x²/81 = 1.

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The standard equation of a hyperbola centered at the origin and a vertical transverse axis is given by

y²/a² - x²/b² = 1

We are given that;

a = 8

b = 9

Now, putting the values of the variables into the equation;

y²/a² - x²/b² = 1

y²/8² - x²/9² = 1

y²/64 - x²/81 = 1

Therefore, the standard equation will be  y²/64 - x²/81 = 1.

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The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.

Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.

To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:

Assets                                    2017        2018        Change   % Change

Cash                                     $2,500 $3,900  $1,400  56%

Accounts receivable, net    $35,000 $40,000  $5,000     14%

Inventory                               $85,000 $122,000  $37,000   44%

Other current assets            $3,400      $4,110       $710        21%

Total current assets              $125,900  $170,010   $44,110    35%

PPE, net                                 $180,000  $230,000  $50,000  28%

Other assets                         $15,000    $26,000   $11,000    73%

Total assets                          $320,900   $426,010  $105,110 33%

Interpretation

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Therefore, the parameters of the binomial distribution in this scenario are:

p = 0.404

n = 21

Probability, or the probability that an event will occur, is calculated by dividing the number of favourable outcomes by the total number of potential possibilities. Indeed, a coin flip is the most simple illustration. When you flip a coin, only one of two outcomes—heads or tails—is possible.

A binomial distribution with p and n parameters is present in this situation.

The likelihood of making a free throw, p (a success).

The quantity n represents the attempted free throws.

p = 0.404, which is the probability of making a free throw.

1 - p = 0.596, which is the probability of missing a free throw.

n = 21, which is the total number of free throws attempted.

the probability that the player makes no more than 6 of the 21 free throws. This can be represented as P(X ≤ 6), where X is the number of successful free throws (or made free throws).

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Answer: |x + 4| = 3

Step-by-step explanation:

The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.

The mean of a binomial distribution is given by:

μ = np

Substituting n = 100 and p = 0.20, we get:

μ = 100 × 0.20 = 20

Therefore, the mean is 20.

The variance of a binomial distribution is given by:

σ²= np(1 - p)

Substituting n = 100 and p = 0.20, we get:

σ² = 100 × 0.20 × (1 - 0.20) = 16

Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.

The standard deviation of a binomial distribution is the square root of its variance:

σ =√Variance

=√16

= 4

Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

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To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:

6x²2 - 4xy = 2x(3x - 2y)

What is factorization?

Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.

For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):

x²2 - 4x - 21 = (x - 7)(x + 3)

This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.

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Inputting the values provided yields:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

A + B = 5 - sqrt (34)after simplifying and solving for a + b. 

As a result, we have established that a + b=  0.27.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.

Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:

[tex]CH^2 = CB^2 - BH^2[/tex]

Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:

[tex]CH^2 = AC^2 - x^2[/tex]

We can also use the given values of x and h to find AC:

[tex]AC^2 = x^2 + h^2[/tex]

Substituting this into the equation for [tex]CH^2[/tex], we get:

[tex]CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2[/tex]

Taking the square root of both sides, we get:

CH = h = 4

Therefore, we have found that CH = 4.

Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:

Area = (1/2) * CH * AB

Area = (1/2) * AC * BC

Setting these two expressions equal to each other and substituting the given values, we get:

(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5

Simplifying and solving for y, we get:

2x + 8 = 15 - 5/2 * y

2x + 13/2 = 5/2 * y

y = 2x + 13/5

Using the given value of x, we can find y:

y = 2(3) + 13/5 = 6.6

Therefore, we have found that y + h = 6.6 + 4 = 10.6.

Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:

[tex]AC^2 + BC^2 = AB^2[/tex]

Substituting the given values, we get:

[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]

Simplifying and solving for a + b, we get:

a + b = 5 - sqrt(34)

Therefore, we have found that a + b ≈ 0.27.

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Answer: Length = 7 and Width = 2

Step-by-step explanation:

Perimeter = 2(length + width)  
18 = 2(L+W)
[tex]\frac{18}{2}[/tex] = (L+W)  
9 = L+W  
Make width the subject.
w = 9-L ------Equation 1

  Area = Length × Width
⇒14 = L×(9-L)   | Substitute Eq.1 in place of Width
⇒14 = 9L - L²
⇒L² - 9L + 14 = 0
⇒L² -7L - 2L + 14 = 0
⇒L×(L-7) -2×(L-7) = 0
⇒(L-7)(L-2) = 0
∴ L=7(Answer) or L=2(Not Applicable since length can't be larger than width)

Substitute the value into eq.1
when L=7
W=9-7      
  =2      

Lenth=7
Width=2

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Answer:

Step-by-step explanation:

Let the length of the plank be "l" and the width be "w".

The perimeter of the plank is the sum of the lengths of all four sides, which is:

2(l + w) = 18

Simplifying the equation, we get:

l + w = 9

The area of the plank is given by:

lw = 14

We can solve for one of the variables in terms of the other by rearranging the equation:

l = 14/w

Substituting this expression for "l" into the equation for the perimeter, we get:

(14/w) + w = 9

Multiplying both sides by "w", we get:

14 + w^2 = 9w

Rearranging the terms, we get:

w^2 - 9w + 14 = 0

This is a quadratic equation that can be factored as:

(w - 7)(w - 2) = 0

Therefore, the possible values of "w" are 7 and 2.

If we take "w = 7", then using the equation l = 14/w, we get:

l = 14/7 = 2

Therefore, the length and width of the plank are 2 feet and 7 feet, respectively.

If we take "w = 2", then using the equation l = 14/w, we get:

l = 14/2 = 7

Therefore, the length and width of the plank are 7 feet and 2 feet, respectively.

In summary, the plank could have a length of 2 feet and a width of 7 feet, or a length of 7 feet and a width of 2 feet, given its perimeter of 18 feet and area of 14 square feet.

the expected value of the random variable with this probability distribution is 7.

Why it is?

To find the expected value of a discrete random variable with a probability distribution, you multiply each possible value of the random variable by its corresponding probability and then add up all of the products.

For example, for the probability distribution given:

X P(X)

2 1/36

3 1/18

4 1/12

5 1/9

6 5/36

7 1/9

8 1/12

9 1/18

10 1/36

The expected value, denoted by E(X), can be calculated as follows:

E(X) = (2)(1/36) + (3)(1/18) + (4)(1/12) + (5)(1/9) + (6)(5/36) + (7)(1/9) + (8)(1/12) + (9)(1/18) + (10)(1/36)

E(X) = 7

Therefore, the expected value of the random variable with this probability distribution is 7.

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Answer: -1/2

Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]

Answer:

Area = 380 square inch

Volume = 697 cubic inch

Step-by-step explanation:

Diameter = 11

=> radius = 11/2 = 5.5

A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch

V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch

Answer:

Account B will have the most after 10 years. It will be worth $21760

Step-by-step explanation:

Hope it helps! =D

Therefore, the value of the expression -2f(-6) - 7g(-7) is equal to -99.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

Using the function notations given in the problem, the statement can be read as follows:

-2 times the value of the function f evaluated at x = -6, minus 7 times the value of the function g evaluated at x = -7, is equal to:

-2f(-6) - 7g(-7) =

Substituting the expressions for f(x) and g(x) given in the problem, we get:

-2*(3*(-6)+1) - 7*(-2*(-7)+5) =

Simplifying this expression, we get:

-2*(-17) - 7*(19) = 34 - 133 = -99

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Answer:t= 1/4

Step-by-step explanation:

Divide both sides by -2/3, and simplify which would leave u with 1/4.