Reason corp just issued a series of 24 year maturity bonds with a oar value of 1000 and a 5 % coupon, paid semianually the bonds can sell in the open market for 1175. Flotation costs on the new bonds

a. Finding equation of line passing through A and parallel to BC.

[tex]\quad[/tex]

Since our line is parallel to BC, slope of the line is,

[tex]\longrightarrow\rm{m_a=\dfrac{y_B-y_C}{x_B-x_C}}[/tex]

[tex]\longrightarrow\rm{m_a=\dfrac{7-4}{2-(-10)}}[/tex]

[tex]\longrightarrow\rm{m_a=\dfrac{1}{4}}[/tex]

Since our line passes through A, the equation will be,

[tex]\longrightarrow\rm{y-y_A=m_a(x-x_A)}[/tex]

[tex]\longrightarrow\rm{y-(-2)=\dfrac{1}{4}(x-5)}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{x-4y-13=0}}\quad\quad\dots(1)}[/tex]

[tex]\quad[/tex]

b. Finding equation of line passing through B and perpendicular to AC.

[tex]\quad[/tex]

Since our line is perpendicular to AC, slope of the line is,

[tex]\longrightarrow\rm{m_b=-\dfrac{x_A-x_C}{y_A-y_C}}[/tex]

[tex]\longrightarrow\rm{m_b=-\dfrac{5-(-10)}{-2-4}}[/tex]

[tex]\longrightarrow\rm{m_b=\dfrac{5}{2}}[/tex]

Since our line passes through B, the equation will be,

[tex]\longrightarrow\rm{y-y_B=m_b(x-x_B)}[/tex]

[tex]\longrightarrow\rm{y-7=\dfrac{5}{2}(x-2)}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{5x-2y+4=0}}\quad\quad\dots(2)}[/tex]

[tex]\quad[/tex]

c. Finding point of intersection of the above two lines.

[tex]\quad[/tex]

From (1),

[tex]\longrightarrow\rm{x=4y+13}[/tex]

Putting this value of x in (2),

[tex]\longrightarrow\rm{5(4y+13)-2y+4=0}[/tex]

[tex]\longrightarrow\rm{18y+69=0}[/tex]

[tex]\longrightarrow\rm{y=-\dfrac{23}{6}}[/tex]

Then,

[tex]\longrightarrow\rm{x=4\left(-\dfrac{23}{6}\right)+13}[/tex]

[tex]\longrightarrow\rm{x=-\dfrac{7}{3}}[/tex]

Hence the intersection point is [tex]\bf{\left(-\dfrac{7}{3},\ -\dfrac{23}{6}\right)}.[/tex]

For two variable inequalities which has equal to inequal sign is shown in the graph as a solid line.

An algebraic expression of two variables having equal to inequal sign or inequal sign with it.  such as ≥ and ≤ are equal to inequal sign and < and > are inequal sign.

The way we solve linear equation is similar to solve the inequalities. The inequalities which have equal to inequal sign ≤ or ≥ is plotted on the graph and identify the boundary with solid line.

hence, we indicate an equal to inequality on a graph for variables by solid line.

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The value of x in the equation x² = 16 is  ± 4

        Here, x² = 16

        Taking square root on both sides,

        [tex]\sqrt{x^{2} } =\sqrt{16}\\[/tex]

        Simplifying the radicals,

         x = ± 4

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Fraction (3x)/(x-3) + 5/(x²-9) after simplifying is  (3x²+9x+5) / (x²-9).

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than its denominator.

Given, fraction expression;

(3x)/(x-3) + 5/(x²-9)

Simplifying,

(3x)/(x-3) + 5/(x²-9)

= (3x)/(x-3) + 5/(x-3)(x+3)

Taking LCM,

= {3x(x+3)+5} / {(x-3)(x+3)}

= (3x²+9x+5) / (x²-9)

Therefore, fraction's simplification is (3x²+9x+5) / (x²-9).

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Answer: 28

Step-by-step explanation:

   First, we will write what the first line of text represents:

3x + 5 = 7

   Then, we will solve:

3x + 5 = 7

3x = 2

x = [tex]\frac{2}{3}[/tex]

   Lastly, we will substitute this value of x into the expression and simplify:

12x + 20

12([tex]\frac{2}{3}[/tex]) + 20

8 + 20

28

Only when we can map one figure onto the other using stiff transformations can we say that two figures are congruent.

While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

Only when we can map one figure onto the other using stiff transformations can we say that two figures are congruent. All related sides and angles are congruent because stiff transformations maintain the measure of both distance and angle.

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Answer:

Step-by-step explanation:

The number of events is 5 (since there are 5 red marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

To arrange the data points in ascending order for a small data set, count the number of data points (n).

To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

The expressions which are equivalent to 35 + 30s - 45t are:

The correct answer options are options B and C

35 + 30s - 45t

Check all options

A. 7⋅(5+30s−45t)

= 35 + 210s - 315t

False

B. 5(7+6s−9t)

= 35 + 30s - 45t

True

C. (−35−30s+45t)×(−1)

= 35 + 30s - 45t

True

D. 10×(3.5+3s−4.5)

= 35 + 30s - 45

False

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

= (17.5 - 15s + 22.5t) (-2)

= -35 + 30s - 45t

False

Therefore, the equivalent expression is an expression which has an equal value to each other.

Complete question:

Which expressions are equivalent to 35 + 30s - 45t?

A. 7⋅(5+30s−45t)

B. 5(7+6s−9t)

C. (−35−30s+45t)×(−1)

D. 10×(3.5+3s−4.5)

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

choose 2 answers

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(a) If your entire portfolio is now composed of stock a and you can add some of only one stock to your portfolio, you would choose stock D of corr(a, d) = .45.

(b) No, the answer to (a) would not change.

(c) No, you would not change your answers to parts a and b if the T-Bill rate is 8%.

A- Since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in the lowest risk. This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D.
B- The answer to (a) would not change, at least as long as investors are not risk lovers.

C- Treasury Bills (T-bills) 1.3 Treasury bills or T-bills, which are money market instruments, are short-term debt instruments issued by the Government of India. Treasury bills are zero coupon securities and pay no interest.

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A- Since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in the lowest risk. This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D.

B- The answer to (a) would not change, at least as long as investors are not risk lovers.

C- Treasury Bills (T-bills) 1.3 Treasury bills or T-bills, which are money market instruments, are short-term debt instruments issued by the Government of India. Treasury bills are zero coupon securities and pay no interest.

The discriminant of the equation 3x² - 6x + 5 = 0 is -24

Given,

The equation; 3x² - 6x + 5 = 0

We have to find the discriminant of the equation;

Discriminant of equation;

Any equation with the formula ax2 + bx + c = 0 and an alpha value of 0 is a quadratic equation. The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not.

Here,

a = 3

b = -6

c = 5

Then,

Discriminant, D = b² - 4ac

D = -6² - 4 × 3 × 5

D = 36 - 60

D = -24

That is,

The discriminant of the equation is -24

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The slope of the graph determines if a graph is positive or negative.

The slope is the ratio of change of the dependent variable with respect to the change in the independent variable.

It is calculated for both straight lines as well as curves.

for example, let us say , we have a straight line y = mx +c , then the coefficient of the dependent variable 'm' is the slope of the line. It is also calculated by (y2-y1)/ (x2-x1) where y2, x2 are the final positions and y1,x1 are the initial positions.

For curves, since the graph is not linear, the slope changes everywhere and hence we take the differential of y w.r.t. x i.e. dy/dx.

for example, we have a parabola  , y^2 =4ax .

So , here 2ydy= 4adx , so dy/dx = 4a/2y.

Hence , we can say that is the slope is positive, i.e. the graph extends upto right , its a positive graph; if the slope is negative, i.e. the graph extends down to y , its a negative graph .

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Answer: 3.14 means pi

The Median is calculated because it helps us determine where a dataset's "center" is, the median is a crucial measure to compute. It also helps us determine what a dataset's "typical" value is.

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change. The median is the mean of any two numbers that fall in the middle of a dataset.

What are Mean, Median, and Mode?

Different measures of the center in a set of numerical data include mean median and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.

Mean = The result of summing all the data points and dividing by the total number of data points is the "average" value.

Median = Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

Mode = The number that appears the most frequently, or the one that does so most frequently.

So, we can say that the Median is generally calculated to find the center of the given dataset.

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Answer:

Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer:

(x - 3) ( 2x+1)

Step-by-step explanation:

(x - 3) ( 2x+1)

2x^2 + x - 6x -3

2x^2 - 5x -3

So, my answer is right!

No, 8 is  real number.

Real numbers are those that can be expressed in decimal form, can be represented on number lines, and include positive or negative numbers. Real numbers do not include imaginary numbers because they cannot be expressed on number lines.

Given to find 8 is real or not,

non real numbers: The numbers which are not genuine and are Fanciful are known as not genuine or non-genuine numbers. The number line cannot be used to represent non-real numbers.

Number lines assume a significant part in deciding if a number is genuine or non-genuine as the genuine numbers can be shown on the number lines while non-genuine numbers can't be addressed on the number lines as they are fanciful.

Examples of real number  −1, 4, 8, 9.5, −6, 3, etc.

example of non real number  √-2, √-6

Hence, 8 is real number.

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The probability to get tails is 0.50.

What is rounding 2decimal place?

The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

The probability of an event is the ratio of the number of outcomes of the required event to the number of total outcome.

In a coin, there are two parts in coins that are tails and heads.

The total number of possible outcomes is 2.

The number of tails of a coin is 1.

The probability to get tails is = 1/2

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Answer:

Natalie has $1.11 right now.

Step-by-step explanation:

1. Create an equation that represents Natalie's situation. Let x = the money Natalie has right now.

        [tex]x+ 10 = 9(x)^2[/tex]

2. This equation is a quadratic, so we need to factorise to solve for x, the amount of money Natalie has right now.

3. [tex]x + 10 = 9x^2[/tex]

4. [tex]0 = 9x^2 -x - 10[/tex]

5. [tex]0 = 9x^2 + 9x -10x - 10[/tex]

6. [tex]0 = 9x(x+1) -10(x+1)[/tex]

7. [tex]0 = (9x-10) (x+1)[/tex]

8. [tex]x+ 1 = 0\\\\x = -1[/tex]

9. [tex]9x - 10 = 0\\9x = 10\\x = 10/9, 1.11[/tex]

10. The amount of money Natalie has now cannot be negative. Therefore, Natalie has $1.11 right now.

Answer:

C

Step-by-step explanation:

3 [tex]\frac{1}{8}[/tex] ÷ 1 [tex]\frac{5}{8}[/tex] ( change mixed numbers to improper fractions )

= [tex]\frac{25}{8}[/tex] ÷ [tex]\frac{13}{8}[/tex]

to perform the division

leave first, change ÷ to × , turn second fraction ' upside down '

= [tex]\frac{25}{8}[/tex] × [tex]\frac{8}{13}[/tex] ( cancel 8 on numerator/ denominator )

= 25 × [tex]\frac{1}{13}[/tex]

= [tex]\frac{25}{13}[/tex]

= 1 [tex]\frac{12}{13}[/tex]

Customers pay an amount of $259 for the tents. which is the correct answer would be an option (C).

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

To find the price that the customers pay for the tents, we need to first calculate the markup on the tents.

The markup is 40% of the purchase price, which is $185. So the markup is: ⇒ 40/100 × $185 = $74.

Now we can add the markup to the purchase price to find the selling price of the tents.

The selling price is :

$185 + $74 = $259.

Therefore, the customers pay $259 for the tents.

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Approximately 19.8% of the students have grade point averages that are greater than 1.66.

We can use the empirical rule to calculate that approximately 68% of the students have grade point averages that are within one standard deviation of the mean. So, the remaining 32% of the students have grade point averages that are either less than 1.66 or greater than 3.46.

To find the percentage of students with grade point averages greater than 1.66, we need to subtract the percentage of students with grade point averages less than 1.66 from 32%. To do this, we need to find the z-score corresponding to 1.66.

To find the z-score we can use the formula:

z = (x - μ) / σ

Where x is the value we are trying to find the z-score for (in this case, 1.66), μ is the mean of the distribution (in this case, 2.56), and σ is the standard deviation of the distribution (in this case, 0.45).

Plugging in the values, we get:

z = (1.66 - 2.56) / 0.45 = -1.22

We can use a z-table to find the percentage of values less than -1.22 in a standard normal distribution. The percentage is approximately 12.2%. So, the percentage of students with grade point averages greater than 1.66 is 32% - 12.2% = 19.8%.

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Answer:

2x² - 3x - 6 = 0

Step-by-step explanation:

the standard form of a quadratic equation is

ax² + bx + c = 0 ( a ≠ 0 )

here a = 2 , b = - 3 and c = - 6 , then

2x² - 3x - 6 = 0 ← in standard form

Answer:

C. Subtraction Property of Equality

Step-by-step explanation:

The equation is

m<1 + m<2 = m<2 + m<4

m<1 = m<4

We see that is subtraction property, so the answer is C

Counting numbers are another name for natural numbers. These are 1, 2, 3, and so forth.

Natural numbers plus zero are whole numbers.

Natural numbers, whole numbers, and the opposites of whole numbers are all considered integers. These numbers range from -3 through -2, -1, 0, 1, 2, 3, etc.

Integers, whole numbers, rational numbers, and numbers that may be expressed as fractions are all considered rational numbers. In this case, fraction [tex]\frac{a}{b}[/tex], where; a and b must both be integers.

All non-rational numbers are categorized as being irrational. These figures cannot be expressed as fractions. This includes decimals like [tex]\pi[/tex], [tex]\sqrt{2}[/tex], and 3.2576352417942 that doesn't end or repeat.

The collection of all rational and irrational numbers, as well as their subsets, is known as the Real Number System.

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To find your target heart rate, multiply the percentage of how hard you want to work by your Maximum heart rate and then add your Resting heart rate

To find your target heart rate, you will need to calculate your maximum heart rate and resting heart rate. Maximum heart rate is calculated by subtracting your age from 220. Resting heart rate is your heart rate when you are completely at rest. Once those two values are calculated, you can use the following formula to find your target heart rate:

Target Heart Rate = [(Percentage of How Hard You Want to Work X Maximum Heart Rate) - (Maximum Heart Rate - Resting Heart Rate)] + Resting Heart Rate

For example, if you are 35 years old, your maximum heart rate is 220 - 35 = 185. If your resting heart rate is 60, you can use the following formula to find your target heart rate if you want to work at 70% of your maximum heart rate:

Target Heart Rate = [(0.7 X 185) - (185 - 60)] + 60

Target Heart Rate = 153 bpm

In summary, to find your target heart rate, you will need to calculate your maximum heart rate and resting heart rate and then use the above formula to determine your target heart rate. Knowing your target heart rate will help you monitor your exercise intensity and ensure that you are working out at the appropriate level for your fitness goals.

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A linear equation, with five variables, has an infinite number of solutions.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let linear equation:

5 =  x + a + b + c + y

In this equation,

there are five variables, x, a, b, c and y.

And the number of equation is one.

That means,

the number of unknowns > the number of equation

5>1.

Substitute the value of 4 variables to find the value of one variable.

Let, we have to find solutions as subject to y.

We so obtain varied values of y when preserving distinct values of x, a, b, c.

Therefore, infinitely many solutions are possible.

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To know it's AAS or ASA check, In ASA, the side is in between the two angles on the triangle i.e Its included side. In AAS, the S is listed at the end to indicate that the side is not in between the angles i.e it's not include side.

AAS stands for "Angle, Angle, Side" and means that there are two triangles whose two angles and sides that are not included are known to be equal. Triangles are congruent if two angles and not included sides of a triangle are equal to the corresponding angles and sides of another triangle.

ASA (Angle, Side, Angle) :

If two triangles are congruent, all three corresponding sides are congruent and all three corresponding angles are congruent. Triangles are congruent if two corresponding pairs of angles and the sides between them are known to be congruent. A triangle is congruent if two pairs of corresponding angles are congruent and the sides involved are also congruent. This criterion is known as Angle Side Angle (ASA). Another criterion is the angle-angle-side (AAS), which is known to congruent two pairs of angles and an absent side.

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The complete question should be: What is the per capita personal income for a given state in 2004, represented by the value [?] on the vertical axis of the state table?

The missing value on the vertical axis represented by [?] must be $21,200.

In order to determine the missing value on the vertical axis represented by [?], we need to consider the per capita personal income for each of the states listed in the table. The states are listed in order from highest income to lowest income. The highest-earning state is listed first with a per capita personal income of $52,000. The next-highest-earning state has a per capita personal income of $21,200. Therefore, the missing value on the vertical axis represented by [?] must be $21,200.

To enter this answer, first identify the numerical keypad on the calculator. Then, enter the numerical value of $21,200 (21200) using the keypad. Finally, press the “enter” or “equals” key to submit the answer. This will cause the missing value on the vertical axis to be displayed on the calculator screen.

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answer- 5 watches

- you divide 1,500 by 300