Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5
years was 5.6% per year. If that growth rate were maintained, how many years would it take for
Thomson's EPS to triple? (Note: EPS is calculated annually.)
a. 23 years
b. 25 years
c. 21 years
d. 15 years
e. 22 years

To solve the equation √6x+3 = x-2, we can start by squaring both sides of the equation:

(√6x+3)² = (x-2)²

Simplifying the left side of the equation, we get:

6x+3 = (x-2)²

Expanding the right side of the equation, we get:

6x+3 = x² - 4x + 4

Moving all the terms to one side, we get a quadratic equation:

x² - 10x + 1 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = -10, and c = 1. Plugging these values into the formula, we get:

x = (10 ± √(100 - 4))/2

x = (10 ± √96)/2

x = 5 ± 2√6

Therefore, the solutions to the equation √6x+3 = x-2 are x = 5 + 2√6 and x = 5 - 2√6.

The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division)

An equation is a claim that two alternatives are equal in mathematics. The equals sign (=) is generally used to denote this claim. It is a mathematics assertion that two expressions are equal. Variables, constant, coefficients, and mathematical operations like addition, subtraction, multiply, and dividing can all be found in an equation. Finding the value(s) of both the variable(s) that render the equation true is the aim of an equation's solution.

given

Each of the five pears Kylie has is divided into thirds. She must therefore distribute the following quantity of pear slices to her teammates:

5 pears cut into 3 slices each equals 15 slices.

The two equations that can be applied to the issue are as follows: A. 5 × 3 Equals 15 (multiplication) (multiplication) . B. 1/5 × 3 Equals 3/5 (multiplication and division) (multiplication and division) .

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Answer: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. So, we set each denominator equal to zero and solve for x:

(x-3)(x-1)² = 0

x = 3 or x = 1

Therefore, the vertical asymptotes of the function occur at x = 3 and x = 1.

To find the horizontal asymptotes, we need to look at the degree of the numerator and denominator. Since both the numerator and denominator are degree 2, we can find the horizontal asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator. In this case, the leading coefficient of both the numerator and denominator is 1, so the horizontal asymptote is y = 1/1 = 1.

Therefore, the vertical asymptotes are x = 3 and x = 1, and the horizontal asymptote is y = 1.

Step-by-step explanation:

Answer: 144

Step-by-step explanation:

60/100 times x/240

Cross multiply!!!

I hope this helps, have a nice day!!

The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55. Suppose that 44 randomly selected lunch patrons are o

population mean is 6.45

population standard deviation is 2.55.

sample size is 44.

z-score is indicated because you are using population standard deviation and sample size is greater than 30.

The z-score formula is [tex](x - m) / s[/tex]

in this case, x is the sample mean, m is the population mean, s is the standard error.

[tex]standard error = standard deviation / sqrt(sample size0 = 2.55 / sqrt(44) = .3844[/tex] rounded to 4 decimal places.

z-score formula becomes [tex]z = (x - 6.45) / .3844[/tex]

solve for x to get:

[tex]x = .3844 * z + 6.45[/tex]

since you don't have a z-score, you can't find x.

the best you can do is find the critical z-scores, and hence, the critical raw scores.

In order to do that you need to to know the confidence level.

if you know that, you can find the critical z-scores and, from that, the critical x-scores.

we'll compare two confidence levels.

the first is at 99% confidence level.

the second is at 90% confidence level.

with a 99% two-tail confidence level, the critical z-scores are plus or minus 2.5758 rounded to 4 decimal places.

the critical raw scores are found by using the z-score formula.

you get [tex]x = .3844 * 2.5758 + 6.45 = 7.4401[/tex] for the high score.

you get x = [tex].3844 * -2.5758 + 6.45 = 5.4599[/tex] for the low score.

the 99% two-tail confidence level tells you that 99% of your samples of size 44 will have the sample mean between 5.4599 and 7.4401.

that's your 99% confidence interval.

with a 95% two-tail confidence level, the critical z-scores are plus or minus 1.9600 rounded to 4 decimal places.

the critical raw scores are found by using the z-score formula.

you get [tex]x = .3844 * 1.9600 + 6.45 = 7.2034[/tex] for the high score.

you get[tex]x = .3844 * -1.9600 + 6.45 = 5.6966[/tex] for the low score.

the 95% two-tail confidence level tells you that 95% of your samples of size 44 will have the sample mean between 5.6966 and 7.2034.

that's your 95% confidence interval.

the higher the confidence level, the wider the confidence interval when you are dealing with the same population mean and population standard deviation and same sample size.

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Correct and complete question:

The average amount of money spent for lunch per person in the college cafeteria is $6.45 and the standard deviation is $2.55.

Suppose that 44 randomly selected lunch patrons are observed.

Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

b. What is the distribution of x?

x-N(6.45,_________________)

By responding to the prompt, we may deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the points D, E, and F.

A circle, which appears to be a 2D component, is made up of all the points in a jet that are uniformly spaced out from the hub. The capital "O" for the centre and the bottom component "r" for the radius stand for the distance from the origin to any point on a circle, respectively.

The formula πr², where (pi) is a proportionality constant roughly equal to 3.14159, determines the girth (the distance from the centre of the circle). The formula 2πr is used to determine a circle's circumference.

To recreate the original triangle using just two of its sides and the included angle, follow these steps:

Locate the location where the circle and the ray cross. Draw an arc that twice intersects the circle starting at point E on the compass. The point that is adjacent to point B on side AC should be designated as point F.

Create a polygon that passes across points D, E, and F to finish the copied triangle.

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Triangle DEF should be congruent with triangle AED because they share two sides and the included angle.

A circle looks to be a two-dimensional component described as the collection of all equidistant points in a jet from the hub. A circle is usually represented by a capital "O" for the centre and a lower section "r" for the Radius, which refers to the distance between the origin and any point on the circle.

Based on your directions, it appears that you are constructing a triangle using the SAS (side-angle-side) method. The stages are as follows:

Draw a line segment DE of the length determined in component B.

Draw a circle with a radius equivalent to the length of DE using point E as the centre.

Draw an angle equivalent to the measure of angle AED using line segment ED as one of its sides and point E as the vertex. To expand this angle, draw ray EF from vertex E.

Find the spot of intersection of ray EF and the circle and label it F.

Draw a line section connecting points E and F.

Finally, connect the locations D, E, and F with line segments to form the triangle DEF.

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Image is attached below,

Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

If x is your data point, is the mean, and is the standard deviation,

z = (x - ) /

Hence, Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation, it is significant.

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Step-by-step explanation:

pi * d  = total 360° circumference....you want 210/360 ths of this total

                pi * 10   *   210 / 360 =   calculate this.....

To solve for the missing value, we need to first find a common denominator for the fractions on the left side of the equation. The common denominator is (m - n)(m + n)(m - 1). Thus, we can write:

[(m - n) - ?]/[(m - n)(m + n)(m - 1)] = 2m/(m^2 - n^2)

Next, we can cross-multiply to eliminate the fractions:

[(m - n) - ?](m^2 - n^2) = 2m[(m - n)(m + n)(m - 1)]

Simplifying the right side of the equation:

2m[(m - n)(m + n)(m - 1)] = 2m(m - n)(m + n)(m - 1)

= 2m(m^2 - n^2)(m - 1)

Expanding the left side of the equation:

[(m - n)(m + n) - ?](m^2 - n^2) = (m - n)(m + n)(m - 1)

Distributing the left side of the equation:

(m - n)(m^2 - n^2 + ?) = (m - n)(m + n)(m - 1)

Canceling out the common factor (m - n):

m^2 - n^2 + ? = (m + n)(m - 1)

Expanding the left side of the equation:

? = (m + n)(m - 1) - (m^2 - n^2)

Simplifying the right side of the equation:

? = m^2 - m + n^2 + n - m^2 + n^2

= 2n^2 - m + n

Therefore, the missing value is ? = 2n^2 - m + n.

The answer of the given question based on the  confidence interval is , it suggests that the drug treatment has significantly reduced the mean wake time , the drug appears to be effective in treating insomnia in the older subjects.

Mean is a statistical measure of central tendency that represents the average of a set of numerical values. It is also referred to as the arithmetic mean or simply "the average." To calculate the mean, we add up all the values in the set and divide the sum by the number of values.

To construct the 99% confidence interval estimate of the mean wake time for a population with the treatment, we can use the following formula:

CI = x⁻ ± tα/2 (s/√n)

where x⁻ is the sample mean (94.9 min), s is the sample standard deviation (24.3 min), n is the sample size (19), and tα/2 is the critical t-value with α = 0.01/2 and degrees of freedom (d f) = n - 1.

The degrees of freedom for this sample is d f = 19 - 1 = 18. Using a t-table or a t-distribution calculator, we find that t0.005,18 = 2.878, where 0.005 is the tail probability for a 99% confidence interval (α/2 = 0.005).

Plugging in the values, we get:

CI = 94.9 ± 2.878 * (24.3/√19) = (80.36, 109.44)

Therefore, we can say with 99% confidence that the mean wake time for a population with the drug treatment falls between 80.36 and 109.44 minutes.

Regarding the mean wake time of 104.0 min before the treatment, we can compare it with the lower bound of the confidence interval (80.36 min). Since the lower bound is much lower than 104.0 min, it suggests that the drug treatment has significantly reduced the mean wake time.

Therefore, based on the confidence interval estimate, the drug appears to be effective in treating insomnia in older subjects.

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Answer:

8:15

Step-by-step explanation:

Answer: p=50 h=2

Step-by-step explanation:

so its 50 x 2=100 is the answer then u add 3

Answer:

Space explorer A traveled about 77,000 miles in roughly 10 hours.

Step-by-step explanation:

space traveler b travels about 155 miles faster per hour than space traveler A

Answer:

1. Decay of 51%

2. Growth of 51%

3. Decay of 49%

4. Growth of 49%

Step-by-step explanation:

Look at the number in the parentheses raised to the power t.

In the formula, you have (1 + r)^t.

The number in parentheses is 1 + r.

Set each number in parentheses equal to 1 + r and solve for r.

If r is positive, it is growth.

If r is negative, it is decay.

1.

1 + r = 0.49

r = 0.49 - 1

r = -0.51

Decay of 51%

2.

1 + r = 1.51

r = 1.51 - 1

r = 0.51

Growth of 51%

3.

1 + r = 0.51

r = 0.51 - 1

r = -0.49

Decay of 49%

4.

1 + r = 1.49

r = 1.49 - 1

r = 0.49

Growth of 49%

The length of the hypotenuse is approximately 10.63 inches.

What is hypotenuse?

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. In other words, the hypotenuse is the side that connects the two acute angles of the triangle. The hypotenuse is always opposite the right angle in a right triangle and is also the side that has the largest length compared to the other two sides of the right triangle.

The length of the hypotenuse can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the right triangle.

According to the question:
We can use the Pythagorean theorem to find the hypotenuse of a right triangle given the lengths of its other two sides. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the length of the opposite side is 7 inches and the length of the adjacent side is 8 inches. Let's label the hypotenuse as c. Then, we can set up the equation:

[tex]c^2 = 7^2 + 8^2[/tex]

[tex]c^2 = 49 + 64[/tex]

[tex]c^2 = 113[/tex]

To solve for c, we take the square root of both sides of the equation:

[tex]c = \sqrt(113)[/tex]

[tex]c \approx 10.63[/tex]

Therefore, the length of the hypotenuse is approximately 10.63 inches.

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Answer:

Step-by-step explanation:

let l = the length of the rectangle

area of the rectangle (A) = 13 * l

Cost of Products Sold is equal to $111,100 minus $97,400, or 13,700 as the formula for Net Income, the amount is $74,100.

The word "amount" in mathematics typically denotes the number or size of something that can be counted, measured, or computed. It is applicable to several fields, including geometry, arithmetic, algebra, statistics, and calculus. An amount, for instance, can also be used to describe the sum of a group of numbers after addition. An unknown number or value that needs to be factored into an equation in algebra is referred to as an amount.

given

(a) Gross Profit = Sales Revenue - Cost of Items Sold ($83,00)

When provided, Gross profit equals $32,700, therefore

Cost of Goods Sold is equal to $83,000 - $32,700 ($50,300).

Running Costs = $18,300

Operational costs minus Gross Profit gives you Net Income.

$32,700 - $18,300 = $14,400 is the net income.

Sales revenue equals $111,100 in (b).

Sales revenue minus gross profit equals cost of goods sold.

When provided, Operational Costs = $23,300, yet there is no gross profit, so:

Sales revenue minus costs of goods sold equals gross profit.

Total Revenue = $111,100 - Selling Prices for Items

Operational expenses minus gross profit equals $74,100 in net income.

Using the formula for Net Income, the amount is $74,100: Gross Profit - $23,300

Gross Profit: $97,400 ($74,100 + $23,300).

Cost of Products Sold is equal to $111,100 minus $97,400, or 13,700 as the formula for Net Income, the amount is $74,100.

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Answer:

---------------------------------

See the attached, where the given distance is copied over each option. Since the whole distance is 4 times the 1/4 of the distance, the correct choice is C.

To find the probability that a given tree has between 270 and 330 apples, we need to calculate the area under the normal curve between the z-scores corresponding to 270 and 330.

First, we need to convert the values of 270 and 330 to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation.

For x = 270, we get:

z = (270 - 300) / 30 = -1

For x = 330, we get:

z = (330 - 300) / 30 = 1

Using the 68-95-99.7 rule, we know that approximately 68% of the area under the normal curve is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations.

Since the z-scores for 270 and 330 are within one standard deviation of the mean (i.e., they are both less than 1 standard deviation away from the mean of 300), we can use the 68% rule to estimate the probability that a given tree has between 270 and 330 apples.

According to the 68% rule, approximately 68% of the trees will have between 270 and 330 apples.

Therefore, P = 68%.

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Therefore , the solution of the given problem of equation comes out to be (-x² + 3x + 2) / (x² - 18x - 12) = -x + 15.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of another algorithm that can analyze data given by y + 7, split 12 to two parts, and produce y + 7, leveling produces b + 7 in this instance.

Here,

We can use long division to determine the quotient of the given polynomial division problems. Let's begin with the initial issue:

    2x² - 5x

-6x | 6x³ - 18x² - 12x + 0

      - (6x³ - 18x²)

      ----------------

                   0 - 12x²

                   - (-12x² + 0x)

                   ---------------

                                0 - 12x

                                - (0 - 12x)

                                ----------

                                         0

As a result, 2x2 - 5x is the result of (6x3 - 18x2 - 12x) / (-6x).

Let's now turn our attention to the second issue:

     -x + 15

x² - 18x - 12 | -x² + 3x + 2

               x² - 15x

               --------

                       18x + 2

                       18x - 270

                       --------

                              272

As a result, -x + 15 is the result of (-x² + 3x + 2) / (x² - 18x - 12).

Thus, the ultimate responses are:

(6x³ - 18x² - 12x) / (-6x) = 2x² - 5x

(-x² + 3x + 2) / (x² - 18x - 12) = -x + 15

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Ed's total monthly expenses for each loan option includes:

The lists of banks and their annual interest rates are as follows:

Because the interest rate at the first bank is 7.5%, the total interest:

= 7.5% of $20000

= 0.075 * $20000

= $1500.

Since the interest rate at City Bank is 8.2%, the total interest:

= 8.2% of $20000

= 0.082 * $20000

= $1640.

Because the interest rate at Star Bank is 9%, the total interest:

= 9% of $20000

= 0.09 * $20000

= $1800.

The annual loan plus interest for banks is:

First bank:

= $20,000 + $1500

= $21,500

City bank:

= $20000 + $1640

= $21640

Star Bank:

= $20000 + $1900

= $21900

The banks' monthly payments are as follows:

First bank = $21500 / 12 months = $1,792.

City bank = $21640 / 12 months = $1,803

Star bank = $21800 / 12 months = $1,817

Now, since monthly cost of running the gym is $5,000. Ed's total monthly expenses for each loan option are equal to the monthly payments plus the cost for each month. It is calculated as follows:

First bank = $5000 + $1792 = $6792.

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817

Full question "Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best loan option, Ed wants to know the percent profit he will make each month. Part A The cost to run the gym each month is $5,000. Find Ed's total monthly expenses for each loan option.

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Answer:

- 2x + 6

Step-by-step explanation:

Expand

5(x+1)-7(x-1) = 5x + 5 - 7x + 1 and upon adding, = - 2x +6

- 2x + 6 can also be written as 6 - 2x

The randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

The range οf a data set is the difference between the highest and lοwest value in a given set.

The range οf a data set is the difference between the largest and smallest values in the set.

In this case, the smallest value is 38 and the largest value is 65. Therefοre, the range οf the data set is:

Range = Largest value - Smallest value

Range = 65 - 38

Range = 27

Sο, the randοm variable in this case is the range οf the 12 data values, which is equal tο 27.

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After answering the provided question, we can conclude that  To circle complete the copied triangle, draw a polygon through points D, E, and F.

A circle appears to be a two-dimensional component that is defined as the collection of all points in a jet that are equidistant from the hub. A circle is typically depicted with a capital "O" for the centre and a lower section "r" for the radius, which is the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which refers to the amount of space inside the circle.

Follow these steps to duplicate the original triangle using only two of its sides and the included angle:

Find the point where the ray and the circle intersect. Place the tip of the compass at point E and draw an arc that intersects the circle twice. Label the point that is on the same side of side AC as point B as point F.

To complete the copied triangle, draw a polygon through points D, E, and F.

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The name of shape A is right trapezoid

The congruent shapes are B and D

A right trapezoid is a trapezoid (a four-sided polygon with two parallel sides) in which one of the angles formed by the non-parallel sides is a right angle (90 degrees).

The parallel sides of a right trapezoid are called the bases of the trapezoid, and the other two sides are called the legs. The perpendicular distance between the bases of a right trapezoid is called the height of the trapezoid.

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Answer:

Multiply the given numbers by a factor of 2.5, then find the perimeter by adding up all 4 of the sides.

Step-by-step explanation:

While there isn't a picture given, it can be assumed that the shape given is a rectangle.

Then, simply multiply all 4 sides by a factor of 2.5, since that's the number it is being enlarged by.

Then to find the "framing" of said rectangle, add up all 4 of the sides that you just calculated to find the perimeter.

The residual of the data for this new baby is 0.7

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Here, we have

Given: A clinic has recorded the age, x, versus weight, y, of many babies for their first 12 months of life, and claims the line of best fit is ŷ = 0.60x + 3.3, where y is in kg, and x is in months.

ŷ = 0.60x + 3.3

Substitute, x=10

ŷ = 0.60(10) + 3.3   = 9.3

Residual =  y - ŷ  = 10 – 9.3 = 0.7

Hence, the residual of the data for this new baby is 0.7

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