an arm wrestler is the champion for a period of 75 hours. (here, by an hour, we mean a period starting from an ex- act hour, such as 1 p. m ., until the next hour.) the arm wrestler had at least one match an hour, but no more than 125 total matches. show that there is a period of consec- utive hours during which the arm wrestler had exactly 24 matches.

Answer:

(a - 1)(3p - 2)

Step-by-step explanation:

3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term

= (a - 1)(3p - 2)

The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.

The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.

Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.

Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.

Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.

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The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.

         Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.

Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.

If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.

We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].

            By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]

Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.

Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.

Multiplying both sides by e + fi, we get:

          [tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]

Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]

Multiplying both sides by the conjugate of (e + fi), we get:

           [tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]

Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and

so    [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).

             We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.

            Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed

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Answer:

<D = 130°

Step-by-step explanation:

Supplementary = 180°

<C = 50°

<D = ?

<C + <D = 180°

180° - 50° = 130°

<D = 130°

In response to the stated question, we may state that The scatter plot indicates a clustering pattern in the data, and as elevation increases, temperature drops.

"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."

"A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection."

Because the graph is a scatter plot, the data displays a clustering pattern.

We may deduce from the figure that as height increases, temperature falls.

As a result, C and E are the proper choices.

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The correct question is -

The scatter plot shows the relationship between elevation and temperature on a certain mountain peak in North America. Which statements are correct?

A. The data shows one potential outlier

B. The data shows a linear association

C. The data shows a clustering pattern

D. The data shows a negative association

E. As elevation increases, temperature decreases

The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.

The formula for the probability that a truck drives between 99 and 128 miles in a day is:

[tex]Z = (X - \mu) /\sigma[/tex]

where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:

[tex]Z = (99 - 120) / 11 = -1.91[/tex]

The value of Z for 128 miles driven per day is:

[tex]Z = (128 - 120) / 11 = 0.73[/tex]

Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:

[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]

Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

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The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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The required perimeter is 25+√61 units.

We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.

Using the distance formula, the distance between points A and B is:

[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]

Similarly, the distances between the other pairs of points are:

[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]

[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]

[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]

Therefore, the perimeter of the polygon is:

[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]

= 25+√61

Thus, required perimeter is 25+√61.

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By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

We can use the formula:

rate = distance / time

Let's calculate Ivanna's rate for the first part of her journey:

rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour

Let us now compute Ivanna's rate for the second leg of her journey:

rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour

As a result, Ivanna's overall rate is the average of these two rates:

rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour

As a result, Ivanna's average speed is approximately 2.311 miles per hour.

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The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.

The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.

We are given the following system of two equations with two variables:

11x + 9y = -20 (equation 1)

x = -5y - 6 (equation 2)

To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:

x = -5y - 6

Now we can substitute this expression for x into equation 1, and solve for y:

11x + 9y = -20

11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)

-55y - 66 + 9y = -20

-46y = 46

y = -1

Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:

x = -5y - 6

x = -5(-1) - 6

x = 1

Therefore, the solution to the system of equations is (x, y) = (1, -1).

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Answer:

  (A)  10e^(i7π/4)

Step-by-step explanation:

You want the exponential form of 5√2 -5i√2.

There are numerous ways a complex number can be written in "polar form".

The usual choices are ...

  a +bi . . . . . . . . . . . . . rectangular form

  A(cos(θ) +i·sin(θ)) . . . . a sort of hybrid form

  A·cis(θ) . . . . . . . . . . an abbreviation of the above

  A∠θ . . . . . . . . . . . . polar form

  A·e^(iθ) . . . . . . . . . using Euler's formula

The conversion from rectangular form to any of the others makes use of trig identities and the Pythagorean theorem.

  A = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention to quadrant

For the given number, ...

  A = √((5√2)² +(-5√2)²) = (5√2)√(1 +1) = 5·2

  A = 10

  θ = arctan(-5√2/(5√2)) = -1 . . . in the 4th quadrant

  θ = 7π/4

Then the desired exponential form of the complex number is ...

  10e^(i7π/4)

__

Additional comment

Spreadsheets and some calculators have an ATAN2(x, y) function that performs a quadrant-sensitive angle conversion.

Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

By using addition calculation, we determine that Angela will end up making 42 cards in total.

Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.

So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:

23 + 19 = 42

Therefore, Angela will make 42 cards in all.

By using simple arithmetic calculation of basic addition, we find that  Angela will make 42 cards in all.

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Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.

Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.

A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.

by applying the binomial theorem:

[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]

where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]

The first few terms of this expansion are:

[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:

[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Equating coefficients of [tex]x^3[/tex] on both sides, we get:

[tex]c = n(n-1)(n-2)(a^3/6)[/tex]

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The Z-score of the interval within standard deviations of the mean for a normal distribution contains 87% of the probability is 1.11 (rounded to two decimal places).

To find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we need to use the standard normal distribution table (Z-table) or a calculator that has the inverse normal function.

The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. It is denoted by the letter Z. Z-scores measure the number of standard deviations a data point is from the mean of the data set. A positive Z-score indicates a data point is above the mean, while a negative Z-score indicates a data point is below the mean.

To find the Z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we first need to find the probability that is outside the interval. Since the interval is within standard deviations of the mean, we can use the empirical rule or the 68-95-99.7 rule to find the probability that is outside the interval.

The 68-95-99.7 rule states that 68% of the probability lies within 1 standard deviation of the mean 95% of the probability lies within 2 standard deviations of the mean 99.7% of the probability lies within 3 standard deviations of the mean. Since we are interested in the interval within standard deviations of the mean that contains 87% of the probability, we can assume that the interval is 1 standard deviation away from the mean.

Using the 68-95-99.7 rule, we can find the probability that is outside the interval:

100% - 68% = 32%

Since the probability that is outside the interval is 32%, we want to find the Z-score that corresponds to the probability of 16% on either side of the mean. We use the Z-table or a calculator that has the inverse normal function to find the Z-score that corresponds to a probability of 0.16.

From the Z-table, the Z-score that corresponds to a probability of 0.16 is 1.11 (rounded to two decimal places).

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False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.

This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.

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The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².

Here,

a. [tex]125^{2/3}[/tex]

radical form:

[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]

[tex]125^{1/2}[/tex] = √125

= 5√5

Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]

= [tex](5^3)x^{2/3}[/tex]

= [tex]5x^{3*2/3}[/tex]

= 5²

= 25

b. √16

In radical form:

√16 = 4

Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]

= 4

c. [tex]16^{1/2}[/tex]

In radical form:

1/√16 = 1/4

Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]

= 1/4

d.[tex]\sqrt[4]{81}[/tex]

In radical form:

[tex]\sqrt[4]{81}[/tex] = √(√81)

= √9

= 3

Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]

= 1/3

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a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.

ii. For mothers who smoke is 6.82 pounds.

iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:

Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.

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The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.

To find the new population of the city after a 2% increase from 20000, we need to use the following formula:

New population = Old population + (Percentage increase x Old population)

Substituting the given values into the formula, we get:

New population = 20000 + (2/100 x 20000)

New population = 20000 + 400

New population = 20400

It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.

Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.

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The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:

H' (4, -1).

I' (2, -3).

J' (-4, 1).

K' (-2, 3).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).

By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:

(x, y)                                   →         (y, -x)

Ordered pair H (1, 4)        →    Ordered pair H' (4, -(1)) =  (4, -1).

Ordered pair I (3, 2)        →    Ordered pair I' (2, -(3)) =  (2, -3).

Ordered pair J (-1, -4)        →    Ordered pair J' (-4, -(-1)) =  (-4, 1).

Ordered pair K (-3, -2)        →    Ordered pair K' (-2, -(-3)) =  (-2, 3).

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Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.

Step-by-step explanation:

We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].

Now to solve for c

[tex]c-34=21\\[/tex]

add 34 to both sides

[tex]c=55[/tex]

In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:

25 students times 210 millilitres each equals 5250 millilitres.

Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.

5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.

We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:

6 bottles in 5.25 bottles

In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

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The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.

To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.

The times for the remaining cyclists were as follows:

We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:

Adding up all of the times and dividing by four, we get an average of 00:06:07.

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Answer:

One solution

Step-by-step explanation:

I added a photo of my solution

Answer:

The system has one solution: (0, 4).

The correct answer is graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9.

Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph. In a line graph, the x-axis is the horizontal line and the y-axis is the vertical line.

The first graph shows a relationship between the number of side dishes and the total cost of the special that does not match the data given in the table.

The second graph does not reflect the data given in the table, as the total cost of the special increases from $5.25 to $9.00 when the number of side dishes increases from 0 to 5.

The third graph also does not reflect the data given in the table, as the total cost of the special increases from $6.75 to $8.25 when the number of side dishes increases from 0 to 4.

The fourth graph also does not reflect the data given in the table, as the total cost of the special increases from $5.75 to $7.25 when the number of side dishes increases from 0 to 1.

Therefore, the correct answer is mentioned above. This graph accurately reflects the relationship between the number of side dishes and the total cost of the special.

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The correct answer is "graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0,6 and 75 hundredths through the point 3,9".

Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph.

This graph correctly illustrates the relationship between the number of side dishes and the total cost of the special as shown in the table.

The line starts at 0 side dishes and $6.75

and ends at 4 side dishes and $8.25, both of which are in the table.

The graph accurately reflects this by having a line that starts at 2 side dishes and $6.75 and ends at 5 side dishes and $9.00.

This shows that as the number of side dishes increases, the cost also increases.

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.

The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.

Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.

Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.

Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.

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Answer:

Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression

Answer:

Step-by-step explanation:

is 8,15,24