345.00 divided by .072

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: (f + g)(x)\)

\(\qquad \sf  \dashrightarrow \: f(x) + g(x)\)

\(\qquad \sf  \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)\)

\(\qquad \sf  \dashrightarrow \: 7 {x}^{2} + x - 4\)

The train is traveling along the tracks at a speed of 15 miles per hour (rounded to two decimal places).

To solve this problem, we can use the concept of relative velocity. The velocity of the gang of outlaws will be subtracted from the velocity of the train to determine the train's effective velocity along the tracks.

Given:

Velocity of the outlaws in the west direction = 10 miles per hour

Velocity of the outlaws in the north direction = 30 miles per hour

Now, let's determine the effective velocity of the train along the tracks.

The ratio of westward distance to northward distance along the tracks is given as 15 miles west for every 100 miles north. This ratio can be simplified to 3 miles west for every 20 miles north.

Considering the velocity of the outlaws, we can say that for every 20 miles north traveled by the outlaws, they close the distance by 10 miles west. Therefore, the effective velocity of the train along the tracks is 10 miles per 20 miles north, which can be simplified to 0.5 miles per 1 mile north.

Now, let's convert this effective velocity to miles per hour. Since the outlaws' velocity is given in miles per hour, we can say that the train's effective velocity is 0.5 times the velocity of the outlaws in the north direction.

Effective velocity of the train = 0.5 * 30 miles per hour

                            = 15 miles per hour

Therefore, rounding to two decimal places, the train is moving along the rails at a speed of 15 miles per hour.

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The null hypothesis (H0) is that the proportion of clients who have high-risk stocks is equal to or greater than 15%, while the alternative hypothesis (H1) is that the proportion of clients who have high-risk stocks is less than 15%. In other words, the null hypothesis assumes that p >= 0.15 and the alternative hypothesis assumes that p < 0.15.

To Test These hypotheses, the brokerage firm can collect a sample of clients and determine the proportion of those clients who have high-risk stocks in their portfolio. If the sample proportion is significantly lower than 15%, the firm can reject the null hypothesis and conclude that there is evidence to suggest that the true proportion of clients with high-risk stocks is less than 15%.

If the sample proportion is not significantly lower than 15%, the firm fails to reject the null hypothesis and cannot conclude that the true proportion of clients with high-risk stocks is less than 15%.

It is important for the brokerage firm to accurately determine the proportion of clients with high-risk stocks, as this information can help them manage their clients' portfolios more effectively and reduce the overall risk of their business.

By testing these hypotheses, the firm can gain a better understanding of the risk level of their clients' investments and make informed decisions about how to allocate their resources.

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In my opinion, Darrin's inference is wrong because according to given question, "Darrin surveyed a random sample of 10 students from his science class about their favorite types of TV shows."

This line provides the information that the survey is taken randomly. Also, if Darrin had taken some other students, then the ineference of other new students compared with previously surveyed students will be different.

This frankly tells that the probability is different always.

Therefore, Darrin's inference is wrong or invalid.

The expression x - 4 is a factor of the polynomial f(x) = 4x³ - 21x² + 26x - 24 as f(4) = 0. And (x - 4)(4x² - 5x + 6) is the product of two factors for f(x).

The factor theorem states that: if f(x) is divisible by x - a if and only if f(a)=0.

We shall evaluate f(4) to know if x - 4 is a factor of the polynomial f(x) as follows;

f(4) = 4(4)³ - 21(4)² +26(4) - 24

f(4) = 256 - 336 + 104 - 24

f(4) = 360 - 360

f(4) = 0

The first row of the synthetic division is derived as follows:

4x³ divided by x equals 4x²

x - 4 multiplied by 4x² equals 4x³ - 16x²

subtract 4x³ - 16x² from 4x³ - 21x² + 26x - 24 will result to -5x² + 26x - 24

Thus x - 4 is a factor and we will divide the polynomial expression 4x³ - 21x² + 26x - 24 exactly to get the quotient 4x² - 5x + 6.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

167,225.472ft³

Step-by-step explanation:

1/2 × 8ft × 5ft = 609.6ft² [base area]

609.6ft² × 3ft = 55,741.824ft³ [volume of the bottom half]

(8 × 5 × 3)÷3 = 111,483.648ft³ [volume of pyramid]

111483.648ft³ + 55,741.824ft³ = 167,225.472ft³ [entire volume]

Answer:

11 1/4

Step-by-step explanation:

2 5/4 = 3 1/4

3 5/1 = 8

8 + 3 1/4 = 11 1/4

Answer:

(x2 +16)⋅(x+3)

Step-by-step explanation:

Answer:

1/3 or 1:3

Step-by-step explanation:

since there is a 10/30 chance

to simplify divide by 2

10/30 ÷ 2/2 = 5/15

then divide by 5

5/15 ÷ 5/5 = 1/3

your answer is 1/3

another simple way to simplify

since there is a zero (0) in both the ones (1s) spot on both the numerator and denominator in 10/30, you may just cross out both zeros (0s) to simplify the value

10/30 simplified/taken away 0s = 1/3

hope this helps:)

Answer:

The answer is B. (4) Because a coeffecient is the number next to the letter.

Answer:

Its 4

Step-by-step explanation:

A coefficient is the quantity placed before the multiplier aka in this case "x"

Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

An estimate of DEF Company's cost of equity is 7.14%.

To estimate the cost of equity, we can use the dividend growth model. The formula for the cost of equity (Ke) is: Ke = (Dividend per share / Current share price) + Growth rate

Given data:

The cost of equity iss:

Ke = ($0.55 / $16) + 0.037

Ke ≈ 0.034375 + 0.037

Ke ≈ 0.071375.

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Both the cost of equity and the cost of preferred stock play important roles in determining a company's overall cost of capital and the required return on investment for different types of investors.

To estimate DEF Company's cost of equity, we need to calculate the dividend growth rate and use the dividend discount model (DDM). The cost of preferred stock can be found by dividing the fixed dividend by the current price of the preferred stock.

The calculations will provide the cost of equity and cost of preferred stock as percentages.

To estimate DEF Company's cost of equity, we use the dividend growth model. First, we calculate the expected dividend for the next year, which is given as $0.55 per share.

Then, we calculate the dividend growth rate by taking the expected growth rate of 3.7% and converting it to a decimal (0.037). Using these values, we can apply the dividend discount model:

Cost of Equity = (Dividend / Current Share Price) + Growth Rate

Plugging in the values, we get:

Cost of Equity = ($0.55 / $16) + 0.037

Calculating this expression will give us the estimated cost of equity for DEF Company as a percentage.

To calculate the cost of preferred stock, we divide the fixed dividend per share ($1.8) by the current price per share ($27.6). Then, we multiply the result by 100 to convert it to a percentage.

Cost of Preferred Stock = (Fixed Dividend / Current Price) * 100

By performing this calculation, we can determine DEF Company's cost of preferred stock as a percentage.

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Answer:

$12.50

Step-by-step explanation:

First, find the exact cost of all the things she bought:

3.75 + 1.5 + 2.25

= 7.5

Then, subtract this from 20:

20 - 7.5

= 12.5

So, she received $12.50 in change

There is insufficient evidence to support that bolts are too long or too short.

What is Mean and Standard Deviation?

Mean: Dividing the sum of all values in a data set by the number of values.

Standard Deviation: The standard deviation is a measure that summarizes how far away from the mean each observation is.

Given:

mean: 0.94cm

standard deviation = 0.31cm

Alright, so a manufacturer must test that these bolts are long as they come off the manufacturing line and he must readjust the machines if they're too long or too short. Consequently, sample 121V and sample mean are 0.94 cm. So we want to test whether or not these are actually equal to two, so are no hypothesis is that the mean is too and our alternative hypothesis, because it says that we have to recalibrate if they're too short or too long, is that the mean is not too we could probably go with the left tail test here because the sample mean is under but we'll be safer with a two tail test um just because the standard deviation may sway things.

So what we want to do next is compute the test statistic and that's gonna be a Z score and that's just supplied by X bar minus population mean over standard deviation over squared event. And we're using Z here because we have a high sample size and since we know the population standard deviation.

Hence, There is insufficient evidence to support that bolts are too long or too short.

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Answer:

A bee flaps its wings about 3 times faster than a hummingbird.

Answer:

I think c?

Step-by-step explanation:

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

\(NK \approx 7.001\), \(MK = 2\), \(MF \approx 7.001\), \(A_{AMNFD} = 49.007\)

Step-by-step explanation:

According to the statement, we find the following inputs:

\(\angle MDK = \angle DMF = 45^{\circ}\) (Due to the condition of isosceles trapezoid)

\(MD = 9\)

\(NF = 5\)

Given than longer base and shorter base are parallel to each other, we conclude that:

\(\angle KND = 180^{\circ} -\angle NKD - \angle KDN\)

\(\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}\)

\(\angle KND = 45^{\circ}\)

\(\angle FND = 90^{\circ}-\angle KND\)

\(\angle FND = 45^{\circ}\) (By definition of complementary angles)

\(\angle FND = \angle NFM = 45^{\circ}\) (Due to the condition of isosceles trapezoid)

\(\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}\)

\(\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}\) (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

\(MO = DO = \frac{\sqrt{2}}{2}\cdot MD\) (By theorem for 45-45-90 Right Triangle)

\(NO = OF = \frac{\sqrt{2}}{2}\cdot NF\) (By theorem for 45-45-90 Right Triangle)

If we know that \(MD = 9\) and \(NF = 5\), then we find that:

\(DO = MO \approx 6.364\)

\(NO = OF \approx 3.536\)

The value of MK is obtained from the following relationship:

\(MK = \frac{MD-NF}{2}\)

\(MK = \frac{9-5}{2}\)

\(MK = 2\)

And the value of KD is calculated from this expression:

\(KD = MD-MK\)

\(KD = 9-2\)

\(KD = 7\)

Now by the Pythagorean Theorem we find that:

\(NK = \sqrt{(NO+DO)^{2}-KD^{2}}\)

\(NK = \sqrt{9.9^{2}-7^{2}}\)

\(NK \approx 7.001\)

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

\(MF = NO + DO \approx 7.001\)

Lastly, the area of the isosceles trapezoid is determined by the following formula:

\(A_{AMNFD} = NF\cdot NK + MK\cdot NK\)

\(A_{AMNFD} = NK\cdot (NF+MK)\)

If we know that \(NK \approx 7.001\), \(NF = 5\) and \(MK = 2\), then the area of the figure is:

\(A_{AMNFD} = (7.001)\cdot (5+2)\)

\(A_{AMNFD} = 49.007\)

\( \sf3m + 12 = 15 \\ \sf3m = 15 - 12 \\ \sf3m = 3 \\ \sf \: m = \frac{3}{3} \\ \sf \: m \: = \underline{ \bf \: 1}\)

-> Just move all the numbers from the left side to the right side until only the variable is left. Then you can solve the equation & find the required value.

3 m+ 12 = 15

⇔3 m=  3

⇔m=  1

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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The lines x - y = 2 and y = x - 1 are related as they are equations of two different lines that intersect at a single point. This is not a valid equation, indicating that the lines are parallel and do not intersect.

The equation x - y = 2 can be rewritten as y = x - 2, which represents a line with a slope of 1 and a y-intercept of -2. On the other hand, the equation y = x - 1 represents a line with the same slope of 1 but a y-intercept of -1.

When we compare the two equations, we can see that they have the same slope, indicating that the lines are not parallel. The lines intersect at a point where their y-coordinates are equal. To find the point of intersection, we can set the two equations equal to each other:

x - 2 = x - 1

By canceling out the x terms, we find:

-2 = -1

This is not a valid equation, indicating that the lines are parallel and do not intersect. Therefore, the two lines x - y = 2 and y = x - 1 are actually parallel lines and do not have a common point of intersection.

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In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

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Answer:

16

Step-by-step explanation:

-21x+121

x=5

substitute x

-21(5)+121=-105+121=16

If Martin's mass is initially m kilograms, his mass after gaining 7 kilograms would be:

m + 7 kilograms.

In the question, it's given that Martin's initial mass is m kilograms. This means that he weighs m kilograms at some point in time.

If Martin gains 7 kilograms, we need to add 7 to his initial mass to get his new mass. The formula for this is:

Martin's new mass = Martin's initial mass + the mass he gained

Martin's new mass = m + 7

So if Martin's initial mass is m kilograms, his mass after gaining 7 kilograms would be m + 7 kilograms. This means that he would weigh m + 7 kilograms at this point in time.

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The HDD for the month of January in State College, PA is 930.

To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.

HDD = 65°F - 35°F
HDD = 30°F

Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:

1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.

So, the HDD for the month of January in State College, PA is 930.

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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.

To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:

HDD = (65 - 35) x 31
HDD = 930

So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.

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Respuesta. La probabilidad de sacar um 3 seria de 16.66% osea un sexto ,de sacar un numero par es de tres sexto osea del 50% y de sacar un numero impar es de tres sexto osea 50% igual ke los pares y de sacar un numero menor k 7 es de 6 sobre 6 osea 100%.

El valor uno corresponde al suceso seguro: lanzamos un dado al aire y la probabilidad de que salga cualquier número del 1 al 6 es igual a uno (100%). El resto de sucesos tendrá probabilidades entre cero y uno: que será tanto mayor cuanto más probable sea que dicho suceso tenga lugar.

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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