A leasing agreement is for 5 years. A sum of £10,000 must be paid at the beginning of the first year, to be followed by four equal payments of £x at the beginning of years two, three, four and five. At a discount rate of 8 per cent, the present value of the four equal payments is £26,496. Compute the total amount to be paid during the lease period.

Tan P expressed as a fraction in simplest terms is 15/29

Trigonometric Identities are defined as equalities involving trigonometry functions and also holds true for all the values of variables given in the equation.

There are five types of trigonometric identities;

From the information given, we have that;

Opposite side = 15

Adjacent side = 29

But the tangent trigonometric identity is;

Tan P = opposite/adjacent

Substitute the value

Tan P = 15/29

Hence, the value is 15/29

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Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.

We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08.  The unit price for each bottle will be: The bottle having the lower price will be:-

30-ounce bottle = $6.00

One ounce bottle = 30 / 6.00 = $5.00

and

24-ounce bottle = $4.08

One ounce bottle = $24/ 4.08 = $5.88

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

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The measurement of all the angles in the given geometrical image are mentioned below.

Given is a figure as shown in the image.

We can write the following equations -

∠1 + ∠2 + (8x - 8)° + (3x + 17)° = 360°

and

(8x - 8)° = (3x + 17)°                               {Vertically opposite angles}

8x - 3x = 17 + 8

5x = 25

x = 5

So -

8x - 8 = 8 x 5 - 8 = 32°

3x + 17 = 3 x 5 + 17 = 32°

So -

∠1 + ∠2 + (2 x 32) = 360°

2∠1 + 64 = 360

2∠1 = 296

∠1 = 148° = ∠2                                   {Vertically opposite angles}

∠6 = ∠1 = 148°

∠3 = 32°

∠5 = (180 - 148) = 32°

∠4 = 148°

∠6 = 148°

∠5 = 32°

Now -

(4y + 44) + (6y + 46) = 180°

10y + 90 = 180

10y = 90

y = 9

So -

(4y + 44) = 4 x 9 + 44 = 36 + 44 = 80

∠8 = 80°

Now -

6y + 46 = 6 x 9 + 46 = 100°

∠10 = 100°

∠11 = 80°

∠7 = ∠10 = 100°

∠7 = 100°

∠11 = ∠12 = 80°

∠12 = 80°

Therefore, the measurement of all the angles in the given geometrical image are mentioned above.

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All solutions of the following system of linear inequalities are given-

B (6, 2), C (9, 9), D (8, 2)

For the stated question,

Therefore, the solutions of the following system of linear inequalities are-

B (6, 2), C (9, 9), D (8, 2).

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Confidence interval for the mean score of all students is (91.679, 98.321)

Given:

Sample mean = 95

Standard deviation = 6.6

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

We have to construct a 99% confidence interval for the mean score of all the students.

Sample Standard Error =

[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]

= 1.205

t-value for the 99% confidence interval = 2.756

(use the t-tables for this)

Margin of error = 2.756 x 1.205 = 3.321

If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.

So, for the 99% confidence interval:

(95 - 3.321, 95 + 3.321) = (91.679, 98.321)

This is the final confidence interval.

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Answer:

3

Step-by-step explanation:

on edge

Answer:

  x = 3

Step-by-step explanation:

You want the root of the polynomial equation x(x -2)(x +3) = 18.

A graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.

There are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.

Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...

  x = 18/((x -2)(x +3))

This can be graphed as two equations:

  y = x

  y = 18/((x -2)(x +3))

This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)

__

Additional comment

Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.

The number of minutes that will be used for commercials will be 20 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

If the radio program plays 40 minutes of music.

Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,

⇒ 60 - 40

⇒ 20 minutes

The number of minutes that will be utilized for plugs will be 20 minutes.

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Answer:

B

Step-by-step explanation:

2x + 2 + 5x + 3 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25°

The triangle ABC is an isosceles triangle because AB = BC = √73

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

A(0, 0), B(3, 8), and C(6,0).

An isosceles triangle is any triangle that has two of its sides to be equal

So, we start by calculating the lengths of the sides using the distance equation represented as follows

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute the known values in the above equation, so, we have the following representation

AB = √[(0 - 3)² + (0 - 8)²]

AB = √73

AC = √[(0 - 6)² + (0 - 0)²]

AC = 6

BC = √[(3 - 6)² + (8 - 0)²]

BC = √73

Because AB = BC = √73, then the triangle is an isosceles triangle

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Answer:

Some points that are on this line are:

(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)

Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.

The maximum force on the rectangular floor tile is 32 N.

Force is the product of mass and acceleration.

To calculate the maximum force, we use the formula below

Formual:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the maximum force is 32 N.

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It takes 5 years for the population to decrease to 46785 from the current population of 48500 of a small city whose population is decreasing by an average of 325 people per year.

It is given that,

Current population = 48500 people

Rate of decrease = 325 per year

Number of years = x

decreased population after x years  = 46785

Then, the equation is

46785 = 48500 - 325x

On simplifying the obtained equation, we get

46785 = 48500 - 325x

⇒ 325x = 48500 - 46785 = 1625

⇒ x = 1625/325 = 5 years

So, the people become 46785 after 5 years.

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The corresponding trigonometric ratios are -6/√61,  5/√61, -6/5, -5/6,  √61/5, -√61/6

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant  (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

First of all we need to find the distance between the point (5,-6) and origin (0,0)

Distance (r) = √(5-0)²+(-6-0)²

= √25+36

= √61

Now, P(5,-6) is compared with (x,y)

Now, sin Ф = y/r = -6/√61

cos Ф = x/r = 5/√61

tan Ф = y/x = -6/5

cot Ф = 1/tan Ф = -5/6

sec Ф = 1/cos Ф = √61/5

cosec Ф = 1/sin Ф = -√61/6

The corresponding trigonometric ratios are -6/√61,  5/√61, -6/5, -5/6,  √61/5, -√61/6

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Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.

Given

Equation

x²-3x + 7 = 0

Using quadratic formula,

x = -b±√b² - 4ac/2a

x = -(-3) ± √((-3)² - 4×1×7/2×1

x = 3/2± √19 1/2i

x = 3 + √19/2 and 3 - √19/2

Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.

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Answer:

Look at the image

Step-by-step explanation:

You can solve the problem like in the image

The conditional statement that must also be true is given as follows:

If Stacie does not like pizza, then Amir does not like soda.

A conditional statement has the format defined as follows:

p -> q.

It is read as follows:

If p then q.

In which:

The statement in this problem is given as follows:

If Stacie likes pizza, then Amir likes soda.

Then the parameters are given as follows:

When the conditional statement is true, the inverse statement must also be true, that is:

~p -> ~q.

The symbol ~ represents negation.

Thus the inverse statement is given as follows:

If Stacie does not like pizza, then Amir does not like soda.

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The original number is, if The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number is 52.

An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.

Given:

The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number,

Assume the original number is x then, according to the condition,

10x + 9 + 2x = 633

12x = 633 - 9

x = 624 / 12

x = 52

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In the current year, Bonnie sells stock valued at $60,000 to Linda for $15,000. Later that year, Bonnie gives Linda $25,000 in cash. Bonnie's taxable gifts from these transfers total a) $55,000.

Shares, also known as stocks, are securities that represent partial ownership of the issuing company. A unit of stock is called a "share" and allows the holder to receive a portion of the company's assets and profits equal to the number of shares held.

shares are traded primarily on stock exchanges and form the basis of many individual investor portfolios. Stock trading must comply with government regulations designed to protect investors from fraud.

Taxable Gifts:

Gifts valued at $75 or more are taxable.

Non-cash gifts of small value (less than $75 annually) to employees. Holiday turkeys are tax exempt.

tax-free value is capped at $1,600 for all her awards for one year.

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Answer:

Step-by-step explanation:

Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7

Step-by-step explanation:

x = second number

first number = x - 6

third number = 4x

x - 6 + x + 4x = 96

6x - 6 = 96

6x = 102

x = 102/6 = 17

first number = x - 6 = 17 - 6 = 11

second number = x = 17

third number = 4x = 4×17 = 68

Mindy needs to place the painting at 2.125 feet away from each side of the wall.

The horizontal distance of two side of a wall is defined as width and the vertical distance is called length of wall.

We need to place the paint at an equal distance from each side of wall (horizontal distance).

suppose Mindy will place the paint at x feet away from each side of wall.

for both side she counts 2x feet

width of wall =12.25 feet

width of painting= 8 feet

now, 8+ 2x = 12.25

   2x= 4.25

  x=2.125 feet

hence, Mindy will place the paint at 2.125 feet away from each side horizontally.

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Answer:

D. x=4

Step-by-step explanation:

32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles

m<2=m<RQP

m<1=m<SQP

m<RQP+m<SQP=m<SQR

m<2+m<1=m<SQR

m<2+m<2=m<SQR

(2+7x)+(2+7x)=16x-4

2+7x+2+7x=16x-4

2+2+7x+7x=16x-4

4+14x=16x-4

4-4+14x=16x-4+4

4+4+14x=16x-4+4

14x+8=16x

14x-14x+8=16x-14x

8=2x

x=8/2

x=4 ==> D

The area of square is 100 square centimeter.

What is square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

Given:

A square has sides 10 centimeters long.

We have to find the area of square.

Since,

Area of square = (side)^2

Here side of square is 10cm

So,

Area of square = (10 cm)^2

Area of square = 100 cm^2

Hence, the area of square is 100 square centimeter.

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In order for mn to be even, m must be even or n must be an even number.

The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.

Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:

Let n and m be equal to 2a +1  and 2b + 1 respectively, then their product is:

                 (2a +1) (2b + 1) = 4ab + 2a + 2b + 1

                                       = 2(2ab +a + b) + 1

This shows that the expression 2(2ab +a + b) + 1  is of the form 2n +1,  thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.

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The value of 'x' in the expression 20/x = 2 is 10.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A numerical expression in the form of fraction 20/x = 2.

Now, To make 'x' in the numerator we'll move it to the other side which is,

2x = 20.

x = 20/2.

x = 10

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Answer:

Step-by-step explanation:i'm pretty sure that y=x^2+14x+49=625.

The percent change in the speed of Brian is found as 15%.

For the stated question-

Initial speed = 68 mph

Final speed =  80 mph.

Difference = Final speed - Initial speed

Difference = 80 - 68

Difference = 12 mph

Percent change = Difference/Initial speed x 100

Percent change =  12/80 x 100

Percent change = 15%

Thus, the percent change in the speed of Brian is found as 15%.

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