Describe the relationship between precalculus and calculus. List three precalculus concepts and their corresponding calculus counterparts.

Step-by-step explanation:

If we use direct substitution, we will get

[tex] \frac{0}{0} [/tex]

Which is intermediate from so we must use.algebraic manipulation

Let's divide everything by x

We would get

[tex] \frac{x + 1}{1} [/tex]

So the limit as x approaches 0 is

[tex]1[/tex]

Proof using a graph:

As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.

Raul made a mistake in evaluating the expression 3 - (-5) - 7 in B) Step 2 by not following PEMDAS.

PEMDAS means Parentheses, Exponents, Multiplication and Division, Addition and Subtraction from left to right.

PEMDAS refers to the correct order for evaluating mathematical expressions.

The expression 3 - (-5) - 7 should be evaluated as follows:

3 - (-5) - 7

= 3 + 5 - 7

= 8 - 7

= 1

Thus, if Raul did not make a mistake in Step 2, he would have valued the expression as 1.

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Raul tried to evaluate an expression step by step.

3 - (-5) - 7

Step 1: 3 + 5 - 7

Step 2: 3 + 2

Step 3: 5

Find Raul's mistake.

A) Step 1

B) Step 2

C) Step 3

D) Raul did not make a mistake.

Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.

The parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.

This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.

The correct option is C.

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The number of guests that shared one platter is 10.

A. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.

If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.

B. Landon's reasoning is incorrect.

While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.

Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.

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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning

The value of sin(tetha/2) is ±√½(1-8/√113)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.

if tan(tetha) = 7/8

this means that 7 is the opposite and 8 is the adjacent

hyp² = opp² +adj²

hyp² = 49+64

hyp = √113

sin(tetha/2) = ±√1-cos(tetha))/2

= ±√1-(8/√113))/2

therefore the value is sin(tetha)/2

= ±√1-(8/√113))/2 or ±√½(1-8/√113)

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Yes, It intersect at positive x-coordinates.

The equation of line in point-slope form which passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Given that;

The function f (x) is defined in graph.

Now, The function g (x) is defined as,

⇒ y - 5 = (10 - 5) / (2 - 1) (x - 1)

⇒ y - 5 = 5 (x - 1)

⇒ y - 5 = 5x - 5

⇒ y = 5x

Clearly, By the graph of functions f (x) and g (x), both intersect at positive x - coordinate.

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Answer:

1.02n or 51/50n

Step-by-step explanation:

n + 2% raise = 1.02n and 50/51n

Answer: undefined

Step-by-step explanation: can’t raise a negative number to a integer exponent

Answer:

If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.

Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:

V = Bh

3/8 = (1/4)h

Multiplying both sides by 4, we get:

3 = h

So the height of the prism is 3 inches.

Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.

a) Two different ways.

x = ln(32)/ln(2)

2^x = 2^5

b) Only the natural logarithm way can be used.

c) x = 3.58

We want to solve:

2^x = 32

in two ways.

The first way is trivial, apply the natural logarithm to both sides:

ln(2^x) = ln(32)

x = ln(32)/ln(2)

The second way is the next one:

2^x = 32

The right number can be written as:

4*8 = 32

Now we can factorize the left side:

4*8 = (2*2)*(2*2*2) = 2^5

Replacing that we get:

2^x = 2^5

So we know that x = 5.

b) The second way can't be used to solve:

2^x = 12

Because 12 has a factor different than 2.

c) Using the natural logarithm  way:

x = ln(12)/ln(2) = 3.58

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The value of x is equal to 8, in the equation 14x -22.

An equation is a mathematical statement consisting of two expressions joined by an equal sign. 

Solution:

The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.

setting the displayed dimensions correspond to 90° angular dimensions.

14x -22 = 90

You can solve this two-level linear equation in the usual way.

14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x

x = 112/14 = 8 . . . Step 2, divide by the factor of x

Hence, the value of x is 8. 

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From  transitive property of equality, RT = SU.

Given:

RS = TU

What is Segment addition postulate  ?

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC

Since , from Segment addition postulate

ST = ST

What is addition property of equality ?

The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation. if a-b=c,then a−b+b=c+b, or a=c+b. The same goes with the subtraction property of equality.

Now , by addition property of equality

SU = ST + TU

Similarly,

RT = RS + ST

Now , Using transitive property of equality,

RT = SU

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The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.

The system of equations that represents the question is:

f + s = 168 equation 1

2.41f + 1.57s = (1.66 x 168)

2.41f + 1.57s = 278.88 equation 2

Where:

The elimination method would be used to determine the required values

Multiply equation 1 by 2.41

2.41f + 2.41s = 404.88 equation 3

Subtract equation 2 from equation 3

126 = 0.84s

s = 126 / 0.84

s = 150

Substitute for s in equation 1

f + 150 = 168

f = 168 - 150

f - 118 gallons

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Answer:

Step-by-step explanation:

Here's a step-by-step solution to finding the probabilities of the time between customer arrivals:

a. less than 20 seconds:

To find the probability that the time between arrivals is less than 20 seconds, we need to find the cumulative distribution function (CDF) of the time between arrivals and evaluate it at 20 seconds. The CDF for a uniform distribution is given by:

F(x) = x/b - a/b, where a is the lower bound and b is the upper bound of the distribution

For this problem, the lower bound a is 0 and the upper bound b is 120, so the CDF of the time between arrivals is:

F(x) = x/120

Now, we can evaluate the CDF at 20 seconds to find the probability that the time between arrivals is less than 20 seconds:

F(20) = 20/120 = 1/6

So, the probability that the time between arrivals is less than 20 seconds is 1/6.

b. between 10 and 30 seconds:

To find the probability that the time between arrivals is between 10 and 30 seconds, we need to find the difference between the CDFs at 30 seconds and 10 seconds:

F(30) - F(10) = 30/120 - 10/120 = 3/12 - 1/12 = 2/12 = 1/6

So, the probability that the time between arrivals is between 10 and 30 seconds is 1/6.

c. more than 35 seconds:

To find the probability that the time between arrivals is more than 35 seconds, we need to subtract the CDF at 35 seconds from 1:

1 - F(35) = 1 - 35/120 = 85/120 = 7/12

So, the probability that the time between arrivals is more than 35 seconds is 7/12.

d. Mean and standard deviation:

The mean of the time between arrivals is given by the average of the lower and upper bounds of the distribution:

mean = (a + b)/2 = (0 + 120)/2 = 60

The standard deviation of the time between arrivals for a uniform distribution is given by:

standard deviation = (b - a)/(2 * sqrt(3))

For this problem, the standard deviation is:

standard deviation = (120 - 0)/(2 * sqrt(3)) = 60/sqrt(3) ≈ 34.64101615

So, the mean time between arrivals is 60 seconds and the standard deviation is approximately 34.64 seconds.

a. The less than 20 seconds 0.1667.

b. The between 10 and 30 seconds 0.1667.

c.  The more than 35 seconds 0.7083.

d.  The mean and standard deviation of the time between arrivals 34.64 seconds.

To solve the probability questions, to find the probability density function (PDF) of the uniform distribution for the time between customer arrivals. In a uniform distribution, the probability density is constant within the given range.

Given:

Time between arrivals follows a uniform distribution between 0 to 120 seconds.

a. Probability of time between arrivals being less than 20 seconds:

Since the probability density is constant within the given range, we can calculate the probability by dividing the time range of interest (20 seconds) by the total time range (120 seconds).

Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667

b. Probability of time between arrivals being between 10 and 30 seconds:

Similar to part (a), the probability for this interval can be found by dividing the time range of interest (30 - 10 = 20 seconds) by the total time range (120 seconds).

Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667

c. Probability of time between arrivals being more than 35 seconds:

In this case, we need to calculate the probability of the time between arrivals being in the range from 35 to 120 seconds (as it is more than 35 seconds).

Probability = (Time of interest) / (Total time range) = (120 - 35) / 120 = 85 / 120 ≈ 0.7083

d. Mean and standard deviation of the time between arrivals:

In a uniform distribution, the mean (μ) can be calculated as the average of the minimum and maximum values in the range.

Mean (μ) = (Minimum value + Maximum value) / 2 = (0 + 120) / 2 = 60 seconds

The standard deviation (σ) for a uniform distribution can be calculated using the formula:

Standard deviation (σ) = (Maximum value - Minimum value) / √12

Standard deviation (σ) = (120 - 0) / √12 ≈ 34.64 seconds

So, the mean time between arrivals is 60 seconds, and the standard deviation is approximately 34.64 seconds.

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On solving the provided question, we can say that quadratic equation is 46.

A quadratic equation is x ax² +bx +c = 0, which is a quadratic polynοmial in a single variable. a 0. The Fundamental Theοrem of Algebra ensures that it has at least οne solution since this polynomial is of second οrder. Solutions may be simple or cοmplicated.

An equation that is quadratic is a quadratic equatiοn. This indicates that it has at least οne word that has to be squared. The fοrmula "ax² + bx + c = 0" is one of the often used solutions for quadratic equatiοns. where are numerical cοefficients or constants a, b, and c. where the variable "X" is unidentified.

Quadratic equatiοn is



R(d) = d³ +3d² -8

R(3) = (3)³ +3(3)² - 8

R(3) = 27 + 27 - 8

R(3) = 46

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Answer:

162π - 324 (exact) or 184.938

Step-by-step explanation:

You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.

Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2

√648 = c (this is exact) so radius is √648/2

Area of square = lw = 324

Area of circle = (√648/2)^2π = (648/4)π = 162π

Area of shaded region = 162π - 324 (exact) or 184.938

The correct option regarding the domain of the reflected absolute value function is given as follows:

All real numbers.

The domain of a function is the set that contains all possible input values for the function.

The absolute value function is defined for all real numbers, and the reflection does not change the domain, hence the domain is all real numbers.

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Answer: the correct choice is b

Step-by-step explanation:

The linear function for the amount of store credit he will have left after purchasing x video games is given as follows:

f(x) = 299 - 60x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

f(x) = 299 - 60x.

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Answer:

              In order from least to greatest, the numbers would be organized as such:  [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.

Step-by-step explanation:

              At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.

            Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

BEF

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).

Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.

KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.

Answer:

BEF and ADE

Step-by-step explanation:

These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.

a) The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

b) For 4 years, the mass of the element is, 19.95 milligrams

c) No, the mass of the radioactive element will never be 0 milligrams.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The function that represents this situation is,

⇒ y = 35 (1 - 12.9%)ⁿ

Where, 'n' is number of years and 'y' is mass of element.

Now, For 4 years, the mass of the element is,

⇒ y = 35 (1 - 12.9%)ⁿ

⇒ y = 35 (1 - 12.9%)⁴

⇒ y = 35 (1 - 0.129)⁴

⇒ y = 35 (0.87)⁴

⇒ y = 35 × 0.57

⇒ y = 19.95 milligrams

No, the mass of the radioactive element will never be 0 milligrams.

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The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5

Number of bowls= 6

Quantity of stew in each bowl > 2.5

Quantity of stew Finn made = x

The inequality

Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl

x/6 > 2.5

Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.

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A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.

A cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.

A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.

A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

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Answer:

Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:

Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.

Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.

Simplify the equation: On simplifying the equation, we get: y = 2x - 2.

Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.

Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.

Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.

That's it! You have successfully graphed the equation -3y + 6x = 6.

Answer:



Step-by-step explanation:

75

Step-by-step explanation:

I think this is the answer I'm not sure I hope this helps

The explanation 3 is the path that tells us that the interlopers would have to come between the men in the story.

The summary here is that the men are faced with a face off. That is they were to fight themselves till they killed themselves.

But while they were to fight they are met with the interloper which is a more ferocious danger that they are facing.

This tells us that they both have more on their plate at the moment.

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In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen

The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

The total  dozen = 8 dozen eggs

The total price of the 8 dozen eggs $2,800.00

The price per dozen = $2,800.00/ 8 dozen

=$350 per dozen

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Answer:

For --    (1.)   38 / 1 ( apples and baskets)

It is 304 apples distributed evenly among 8 baskets.

For --    (3.)  42 / 1 (apples and baskets)

It is 294 apples distributed evenly among 7 baskets.

Step-by-step explanation:

For the 2nd one, I don't see an answer relating to it. Are there more options when you scroll down?

I hope the other 2 answers helped.