what are the properties of rational exponents and how are they used to solve problems

(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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The x-coordinate of the solution of the system of equations is x = 20/3

Here we have a system of equations below:

3x - y = 6

3x + y = 34

And we want to find the x-cordinate of the solution, so we need to solve this for x.

We can use the elimination method, you can see that if we add both equations we will get:

(3x - y) + (3x + y) = 6 + 34

6x = 40

x = 40/6

We can simplify that fraction to get:

x = 20/3

That is the x-coordinate of the solution.

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The measure of the exterior angle of the triangle is 139°.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

From the two given angles are 75° and 64° and exterior angle is 2.

Now, ∠2=75°+64°

∠2=139°

Therefore, the measure of the exterior angle of the triangle is 139°.

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An investor writes a s&p 100 Jan. 185 put at $6 on May 4. In this situation, his function maximum potential benefit is $600.

We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.

A benefit is a positive outcome or advantage that results from something. It can refer to the positive aspects or advantages of a product, service, or action, and can be tangible or intangible. Benefits can include increased efficiency, cost savings, improved safety, increased customer satisfaction, and many other positive outcomes.

Here,

As a put buyer, the most you may lose is the premium you previously paid to purchase the put option.

The option price must be reduced to equal the strike price less any already-paid premium in order to break even.

The strike price less the premium is your maximum gain as a put buyer. The most bullish option strategy is thought to be purchasing call options.

This tactic allows the buyer of the call option the choice, but not the responsibility, to purchase the stock at a certain price at a precise moment.

Whenever the price of the security increases using this approach, the buyer benefits. A long position is one in which a call or put option is purchased or held.

Investors have the option of purchasing from or selling to the other investor at a predetermined price.

On the other hand, a short position is when you sell a call or put option. Writers must purchase from people holding long positions or buying options.

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On May 4th an investor writes on s&p 100 Jan 185 put at $6. his function maximum potential gain in this position is $600.

We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.

Your maximum loss as a put buyer is the premium already paid to buy the put option. To break even the option price must be lowered to cover the strike price minus the premium already paid. Your maximum profit as a put buyer is the strike price minus the premium. Buying call options are considered the most bullish options strategy.

This strategy gives the call option buyer the right but no obligation to buy the security at a specific price at a specific time. With this strategy, the buyer benefits when the price of the security rises. Buying or holding a call or put option is a long position. Investors have the right to buy or sell to the writing investor at a specified price. Conversely selling or selling a call or put option is a short position. Writers must buy or sell from long position holders or option buyers.

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The constant of variation for the given data is 1/4.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Given that the data in the table is,

x        f(x)

-8       -2

-4       -1

0        0

4         1

8        2

The constant of proportionality will be calculated as,

F(x) = kx

-2 = k x -8

k = -2 / -8

k = 1 / 4

Here, the proportionality constant will be 1/4.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

Answer:

yes!

Step-by-step explanation:

the y axis vertical, and the x axis is horizontal!

Answer:

Step-by-step explanation:

because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,

we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD

The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.

A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.

Option a. there are a greater number of older students is also correct, but it is not complete.

Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.

Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.

Option e. not enough information is not correct as the question is providing enough information to make a conclusion.

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To solve a function, you must determine the value of the function for a given input. This requires finding the equation for the function and then plugging in the given input to find the output. For example, if the function is f(x) = x2 + 2x - 5, and the given input is 3, then the output of the function is f(3) = 12.

1. Substitute the given input, x = 3, into the equation.

2. Simplify the equation:  f(3) = 32 + 2(3) - 5

3. Solve the equation:  f(3) = 9 + 6 - 5

4. Simplify the equation: f(3) = 12

5. Therefore, the output of the function is f(3) = 12.

To solve a given function, you must first determine the equation for the function. Then, you must substitute the given input into the equation and solve it. In this example, the given input was 3 and the equation for the function was f(x) = x2 + 2x - 5. After plugging in the input of 3, the equation was simplified to f(3) = 9 + 6 - 5, which was further simplified to f(3) = 12. Therefore, the output of the function is f(3) = 12.

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Answer:

do it

Step-by-step explanation:

Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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The solution for 3x 2y 5 is x = 0 and y = -2.5

The solution for 3x 2y 5 can be found by first rewriting the equation in standard form, which is ax + by = c. In this case, the standard form would be 3x + 2y = -5.

Next, we can calculate the value of y in terms of x by using the following formula:

y = (c - ax) / b

Substituting in the values, we get:

y = (-5 - 3x) / 2

Now, we can substitute this expression for y into the original equation to solve for x:

3x + 2((-5 - 3x) / 2) = -5

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

6x + -5 = -5

6x = 0

x = 0

Finally, substituting x = 0 into the expression for y, we get:

y = (-5 - 3(0)) / 2

y = (-5 - 0) / 2

y = -5 / 2

y = -2.5

The solution for 3x 2y 5 is x = 0 and y = -2.5

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Answer:

(20/3,0) is your x-intercept

Step-by-step explanation:

To find x-intercept, let y = 0

[tex] \displaystyle{3x = 20}[/tex]

Solve for x, divide both sides by 3:

[tex] \displaystyle{ \dfrac{3x}{3} = \dfrac{20}{3}} \\ \\ \displaystyle{ x = \dfrac{20}{3}}[/tex]

Hence, the x-intercept is (20/3,0). We write in order pair since it's x-intercept and x = 20/3 at y = 0

The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.

The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.

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Answer:

SSS

Step-by-step explanation:

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle it is known was SSS congruence

For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.

Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication

Given the polynomial:

p(x) = -3x² + 10 - 4x

Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:

p(x) = -3x² - 4x + 10

The degree is 2 (x²) and the leading coefficient is -3(-3x²)

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Answer:

A) 9.1%

B) 7.4%

Step-by-step explanation:

Part A

Because you are replacing each marble before selecting the next, the probability of choosing one red marble remains the same, so choosing 3 red marbles with replacement would mean the probability gets multiplied by itself 3 times:

[tex]\displaystyle P(\text{Red+Replace})=\biggr(\frac{9}{20}\biggr)^3=\frac{9}{20}*\frac{9}{20}*\frac{9}{20}=\frac{729}{8000}\approx9.1\%[/tex]

Part B

[tex]\displaystyle P(\text{Red+No Replace})=\frac{C(9,3)C(4,0)C(7,0)}{C(20,3)}=\frac{\frac{9!}{3!(9-3)!}}{\frac{20!}{3!(20-3)!}}=\frac{\frac{9*8*7}{3*2*1}}{\frac{20*19*18}{3*2*1}}=\frac{9*8*7}{20*19*18}=\frac{7}{95}\approx7.4\%[/tex]This can also be calculated with [tex]\frac{P(9,3)}{P(20,3)}[/tex] because the order does matter in which you pick the 3 red marbles with no replacement.

Answer:

9.1%

7.4%

Step-by-step explanation:

A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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by splanation, in be clearly what he taking about. the hamburger, usually. is 1/4 p.1/2 p. in triple hamburger on 4 by 4

The number of used hamburgers that is 80% lean is = 500

and the number of used hamburgers that is 88% lean is = 300.

Let the number of hamburger that is 80% lean be = x.

So the number of hamburger that is 88% lean is = 800 - x

According to question after the mixing all these the total percentage of lean in 800 ponds of burgers is 83%.

So, the suitable mathematical equation is,

80% of x + 88% of (800 - x) = 83% of 800

(80/100) x + (88/100) * (800 - x) = (83/100) * 800

80x + 88 (800 - x) = 83 * 800 [Multiplying 1000 with both sides]

80x + 88 * 800 - 88x = 83 * 800

88x - 80x = 88 * 800 - 83 * 800 = 800 (88 - 83) = 5 * 800

8x = 800 * 5

x = (800 * 5)/8 = 100 * 5 = 500

Hence the number of hamburger with 80% lean is 500 and the number of hamburger with 88% lean is = (800 - 500) = 300.

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Consequently, y-1 = 2 is the point-slope form linear equation for the line passing through (1, 3) and having a slope of 2. (x-3).

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Y = mx + c in this instance.

(y- y₁) = m(x - x₁)

where,

The coordinate for the x-axis is x and x1,

The coordinate for the y-axis is y and y1.

The slope of the line is m, and

The y-intercept can be represented by the letter c.

Replace the value of the slope and the point in the general equation to obtain the equation for the line passing through (1, 3) and having a slope of 2.

y-1 = 2(x-3) (x-3)

Consequently, y-1 = 2 is the point-slope form equation for the line passing through (1, 3) and having a slope of 2. (x-3).

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A range of fundamental, unchanging values may exist in the world, according to ethical pluralism.

According to ethical pluralism, the world may contain a variety of essential and unchangeable values. There may be more, but happiness and respect for people are two possible ones.

The notion of ethical plurality holds that there are various beliefs about what is "good" and "wrong" (moral norms), some of which may be incompatible and/or out of line with your own personal moral standards. Working in foreign societies, where you could encounter varying norms, is a component of international involvement.

The conviction that there are various viewpoints on a subject, each of which has some truth, but none of which contains the complete truth the conviction that while each moral theory somewhat captures the essence of what it means to live morally, none has the whole picture.

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Lawrence Hinman does not have a clear statement on the best baseball stat for determining the best player in a given year.

Statistics are a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In baseball, statistics are used to measure the performance of individual players, teams, and even entire leagues. Some common baseball statistics include batting average, home runs, runs batted in, earned run average, and wins. These statistics are used to evaluate the performance of players, compare them to other players, and even predict future performance.

Baseball statistics are a set of metrics used to measure the performance of individual players and teams in baseball. Some common baseball statistics include:

It is likely that different analysts and experts would have different opinions on which stat is the most important for determining the best player in a given year. Some might argue that traditional stats like batting average, home runs, and RBIs are the most important, while others might argue that newer stats like on-base percentage, slugging percentage, and WAR are more informative.

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Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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The  set of equations correctly representing x are as follows:

(x + 1/2) and (x = 7/2).

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one that has two equations as well as two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

Systems of equations in mathematics are a collection of relationships between different unknown variables that can be stated in terms of algebraic expressions. They are also known as simultaneous equations. Graphing, substitution, as well as elimination by addition, are methods that can be used to find the solutions to a basic system of equations.

Sum means addition (+).

Given that sum of a number, x and 1/2 is 4.

This means the adding  two numbers

x+1/2=4

Now make x the subject of formula,

x=4-1/2

Finding the L.C.M  = 8-1/2

                        x=7/2

                     ∴ x=3 1/2

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The total number of cookies baker sold in all are 350 cookies.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.

Let the total number of cookies be x.

Now, 38% of x=133

38/100 ×x=133

x=13300/38

x=350

Therefore, the total number of cookies baker sold in all are 350 cookies.

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Answer:

x) = 1 + 2(0.94)*

The y-intercept = (0, [?])

For x ≥ 0, the horizontal as

Answer:

Step-by-step explanation:

Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

What is a Ratio?

This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.

Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Answer:

Step-by-step explanation:

the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning

================================================

Explanation:

The x and y are placeholders for numbers.

Think of them as boxes so to speak, and we fill each box with a number.

In this case we will plug in x = 6 and y = 2.

The steps are shown below.

[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]

The final answer is choice B

-----------

This means,

[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]

Put another way

[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]

In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]

Step-by-step explanation:

I have to assume the equations are

4x + y = 13

(1/2)y = -2x + 5

let's bring both of them into a "y = ..." form :

y = -4x + 13

y = -4x + 10

now we see that both equations are lines with the same slope but different y-intersect.

so, they are parallel but not identical.

therefore, there are 0 solutions. the lines will never intersect and have no point in common.

Answer:

i do not not the answer of this question

Answer: i need your help, XD

Step-by-step explanation: