Prove that, for a, b, and c ∈ Z, a > b and c > 0 =⇒ ac
> bc (part 3 of Proposition 2)

The  general form of an explicit function for what the nth term of any arithmetic sequence would bean = a + (n-1)*d

An explicit function is a mathematical function containing only the independent variable or variables —opposed to an implicit function which is written in terms of both dependent and independent variables

The general arithmetic progression can be written as:

T₁ ,  T₂,   T₃,   T₄,   ......,  Tn.

Where n is any term

Now since a = 1 and d = common difference, The general arithmetic progression can be written as:

a, a+d,  a+2d,  a+3d, a+4d, a+(n-1)*d

Thus, the explicit function becomes a+(n-1)*d

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The function g(s) = 8s²/3 is an even function and its symmetry is y-axis symmetry.

The given function satisfies the condition g(-s) = g(s) which makes it an even function. This means that if we plug in the opposite value of s into the function, we will get the same result. For example, g(-2) = 8(-2)^2/3 = 8(4)/3 = 32/3 and g(2) = 8(2)^2/3 = 8(4)/3 = 32/3.

The symmetry of an even function is y-axis symmetry. This means that the graph of the function is symmetric with respect to the y-axis. In other words, if we fold the graph along the y-axis, the two halves will match up perfectly.

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Step-by-step explanation:

The price is $30.

please make me brainalist and keep smiling dude

Answer:See below

Step-by-step explanation:

answers from top left to top right, then bottom left to bottom right.

First one is alternate interior, because they are on the inside, and are on opposite sides.

the second one is supplementary, because they supplement each other, or add up to 180 degrees.

the third one is alternate exterior, because they are opposite to each other on the outside.

the last one is corresponding, because they are in the same position on each side, and are almost like a copy and paste.

I found a few images on the internet to help you understand.

Hope this helped!

The Equation to represent the amount she spend on the material

is y= 15 + 0.75 x.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

For First 10 pound the charges will be $1.50.

Each additional pound $0.75

let She bought x pounds then the price is 0.75x

Now, The Equation to represent the amount she spend on the material

y = 10 (1.5)+ 0.75x

y= 15 + 0.75 x

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The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective. However, if there are several broken eggs, the package design may need to be improved to provide better protection.

When testing a new package design, it is important to simulate real-world conditions as much as possible. In this case, dropping a carton of a dozen eggs from a height of 1 foot is a good way to simulate the types of impacts that the package may experience during shipping and handling.

To conduct the test, you will need to follow these steps:

The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective.

However, if there are several broken eggs, the package design may need to be improved to provide better protection.

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The value of a12 is 45.

The given matrix A = [aij] is a 2x3 matrix, which means it has 2 rows and 3 columns. The given condition is aij = 5(-i + 2j)^2. We need to find the value of a12, which means the element in the first row and second column.

To find the value of a12, we need to substitute i = 1 and j = 2 in the given condition.

a12 = 5(-1 + 2*2)^2
= 5(3)^2
= 5*9
= 45

Therefore, the value of a12 is 45.

So, the correct option is:

Select one:
a. 53
b. 59
c. 45
d. 56

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f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

A relation is a function if it has only One y-value for each x-value.

To find out how many times larger f(x) is than g(x), we need to divide the value of f(x) by the value of g(x).

Then we simplified the expression and found that it is always larger than g(x) except at two values of x where it is undefined.

To determine how much larger f(x) is than g(x), we looked at their leading coefficients and found that f(x) is always larger than g(x) for large positive or negative values of x.

Finally, we took the limit of f(x) / g(x) as x approaches infinity or negative infinity and found that it approaches -5/2.

Hence,  f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

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Using the %1RM to number of repetitions table, your client's estimated 1RM for the barbell back squat exercise would be 125 lbs, rounded to the nearest whole number.

To estimate the predicted 1RM (one repetition maximum) for the barbell back squat exercise, we can use the %1RM to number of repetitions table from the lecture. According to the table, performing 5 repetitions corresponds to 87% of the 1RM.

To find the estimated 1RM, we can use the following formula:

1RM = weight lifted / %1RM

Plugging in the values from the question:

1RM = 109lb / 0.87

1RM = 125.287lb

Rounding to the nearest whole number, the estimated 1RM for the barbell back squat exercise is 125lb.

Therefore, the answer is 125.

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To prove that |z+w| ≤ |z| + |w| for two complex numbers z and w, we can use an algebraic proof.

First, let's rewrite z and w in terms of their real and imaginary parts:

z = a + bi

w = c + di

Now, we can use the definition of the absolute value of a complex number to write:

|z+w| = |(a+c) + (b+d)i|

= √((a+c)² + (b+d)²)

Similarly, we can write:

|z| = |a + bi| = √(a² + b²)

|w| = |c + di| = √(c² + d²)

Now, we can use the triangle inequality to prove that |z+w| ≤ |z| + |w|:

√((a+c)² + (b+d)²) ≤ √(a² + b²) + √(c² + d²)

Squaring both sides of the inequality gives us:

(a+c)² + (b+d)² ≤ (a² + b²) + (c² + d²) + 2√((a² + b²)(c² + d²))

Expanding the left-hand side of the inequality gives us:

a² + 2ac + c² + b² + 2bd + d² ≤ a² + b² + c² + d² + 2√((a² + b²)(c² + d²))

Simplifying and rearranging terms gives us:

2ac + 2bd ≤ 2√((a² + b²)(c² + d²))

Dividing both sides of the inequality by 2 gives us:

ac + bd ≤ √((a² + b²)(c² + d²))

Squaring both sides of the inequality again gives us:

(a² + b²)(c² + d²) - (ac + bd)² ≥ 0

Expanding and simplifying gives us:

a²c² + a²d² + b²c² + b²d² - a²c² - 2abcd - b²d² ≥ 0

a²d² + b²c² - 2abcd ≥ 0

(a²d² - 2abcd + b²c²) ≥ 0

(a² - 2ab + b²)(d² - 2cd + c²) ≥ 0

(a - b)²(d - c)² ≥ 0

Since the square of any real number is always greater than or equal to zero, this inequality is always true. Therefore, |z+w| ≤ |z| + |w| for any two complex numbers z and w. This completes the algebraic proof.

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The number of bags of oranges that Ruth needs to sell on day 4 to have an average of 50 bags is 65.

Let the number of bags to be sold on day four be = x,

To have an average of 50 bags over 4 days,

The total number of bags Ruth sells in four days must be,

⇒ 4 days × 50 bags/day = 200 bags,

The total number of bags of oranges she sells in 3 days is,

⇒ 3 days × 45 bags/day = 135 bags,

So, to reach a total of 200 bags in 4 days, she needs to sell x bags on the fourth day, which is in equation form as :

⇒ x + 135 = 200

⇒ x = 200 - 135

⇒ 65

Therefore, Ruth needs to sell 65 bags on day four.

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The probability that a student surveyed was either a boy or had a bicycle is 0.62.

What is probability?

The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.

We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.

So, Total number of boys = 490

Total number of girls with bicycle = 130

Total number of students that was either a boy or had a bicycle is

490 + 130 = 620

The probability is

620 / 1000 = 0.62

Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.

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Considering the expression of a line, the gradient or slope is zero and the line is horizontal.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (4, 7) and (x₂, y₂)= (9, 7), the slope m can be calculated as:

m= (7 -7)÷ (9 -4)

m= 0÷ 5

m= 0

Finally, the gradient or slope is zero.

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Answer:130

Step-by-step explanation:

2×5+3= 13

10×13=130

Answer:

130/5

Step-by-step explanation:

10x13=130

130/5

ghyhf f yyhgf

20/325 is equivalent to 6.15% rounded off to one decimal place.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To express a fraction as a percentage, you need to multiply the fraction by 100. Therefore, we have:

20/325 = 0.0615

Multiplying by 100, we get:

0.0615 x 100 = 6.15%

So, 20/325 is equivalent to 6.15% rounded off to one decimal place.

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As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.

The vertex of the angle is the common endpoint shared by two rays or line segments that make up an angle in geometry. The sides or limbs of the angle are the rays or line segments that make up the angle. Angles are used to describe the amount of spin or turn between two lines or objects. They are usually measured in degrees or radians. Numerous areas of mathematics, such as geometry, trigonometry, and calculus, depend on angles.

given

We must apply the following algorithm to determine the size of the bolded arc:

arc length is equal to (angle / 360) times 2r.

where r is the radius, angle is the central angle in degrees, and is a mathematical constant roughly equivalent to 3.14.

Inputting the numbers provided yields:

(118/360) * 2 = arc length (4)

8.24 cm arc length is equal to (0.3278) × (25.12) arc length.

As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.

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The first term is 9, the second term is 17, and the third term is 25.

The 100th term of an arithmetic sequence is given by the formula:

Tn = a + (n-1)d

Where Tn is the nth term, a is the first term, n is the number of terms, and d is the common difference.

In this case, the 100th term is 783, the common difference is 8, and the first term is 9.

Plugging in the values into the formula, we get:

783 = 9 + (100-1)8

Solving for the first term, we get:

783 = 9 + 792

783 = 801

a = 9

The second term, Q2, can be found by adding the common difference to the first term:

Q2 = a + d

Q2 = 9 + 8

Q2 = 17

The third term, az, can be found by adding the common difference to the second term:

az = Q2 + d

az = 17 + 8

az = 25

the first term is 9, the second term is 17, and the third term is 25.

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If Bici expects to produce more than 500 bikes, then they should follow the second plan, and if they expect to produce fewer than 500 bikes, then they should follow the first plan.

Under the first plan, the total cost to design and build a prototype bicycle is $125,000, and the combined materials and labor costs for each bike made under this plan will be $225. This means that for each bike produced, the total cost will be $125,000 + $225 = $125,225.

Under the second plan, the total cost to design and build a prototype bicycle is $100,000, and the combined materials and labor costs for each bike made under this plan will be $275. This means that for each bike produced, the total cost will be $100,000 + $275 = $100,275.

To determine which plan is more cost-effective, we need to consider the breakeven point where the costs of both plans intersect:

125, 000 + 225x = 100, 000 + 275x

50x = 25, 000

x = 500 bicylces

If Bici Bicycle Company plans to produce more than 500 bikes, then the second plan would be more cost-effective. However, if Bici plans to produce fewer than 500 bikes, then the first plan would be more cost-effective.

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The set W of points described in Exercises 22-26 can be written as a subset of R2 as follows: 22. The points on the line x – 2y = 1: W = {(x, y) | x - 2y = 1}, 23. The points on the x-axis: W = {(x, y) | y = 0}, 24. The points in the upper half-plane: W = {(x, y) | y > 0}, 25. The points on the line y = 2: W = {(x, y) | y = 2} and 26. The points on the parabola y = x2: W = {(x, y) | y = x2}

In other words, the set W contains all points (x, y) that satisfy the equations given in Exercises 22-26. As such, it is a subset of the two-dimensional Euclidean space R2. In Exercises 22–26, give a set-theoretic description of the given points as a subset W of R² is a problem where we need to find a set-theoretic description of the given points in each exercise.

Therefore, we can write the set W asW = { (x, y) ∈ R² | y ≥ 0 } The points on the line y = 2The equation of the line is y = 2Therefore, we can write the set W asW = { (x, y) ∈ R² | y = 2 }  The points on the parabola y = x²The equation of the parabola is y = x²Therefore, we can describe the set W asW = { (x, y) ∈ R² | y = x² }

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In the parallel line measure of angle [tex]m\angle 7[/tex] is 32°.

In a plane, two lines are said to be parallel if they never cross at any point. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".

Here we know that If two lines which are parallel are intersected by a transversal then the pair of corresponding angles are equal.

Then,

=> [tex]m\angle3= m\angle10[/tex]

Here the given [tex]m\angle3=58\textdegree[/tex] the [tex]m\angle10=58\textdegree[/tex].

Now we know that sum of all angles in straight line is 180°.Then,

=> [tex]m\angle6+m\angle7+m\angle10=180\textdegree[/tex]

=> [tex]90\textdegree+m\angle7+58\textdegree=180\textdegree[/tex]

=> [tex]m\angle7=180\textdegree-90\textdegree-58\textdegree=32\textdegree[/tex]

Hence the measure of [tex]m\angle 7[/tex] is 32°.

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The gradient of line A is 4 and the gradient of line B is -2.

Graph is a data structure that consists of nodes (or vertices) connected by edges. It is a way of representing data in a structured form and can be used to represent any type of real-world relationship. It can be used to represent geographical relationships between cities, social networks, and even computer networks. Graphs are often used in computer science, mathematics, and engineering to represent relationships between data points.

To calculate the gradient of a line, the formula is rise/run. Thus, the gradient of line A can be calculated as rise/run = 72/4 = 18. On the other hand, the gradient of line B can be calculated as rise/run = 6/-2 = -3

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The value of x, considering the angle addition postulate, is given as follows:

x = -5.

The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.

The larger angle in this problem is QRS, hence the equation to obtain the value of x is given as follows:

3x + 93 + 66 + x = -x + 134

4x + 159 = -x + 134

5x = -25

x = -25/5

x = -5.

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Answer:

9

Step-by-step explanation:

Answer:

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

Vertical compression of a function by a factor of a is:

Vertical compression of a function by a factor of 5 is:

Shifting up by b units is:

If we apply both transformations we get:

Option C is correct.

Answer:

  75 cm

Step-by-step explanation:

You want to know the length of the struts between the edge of a parabolic dish 120 cm in diameter and 15 cm deep, and the collector at the focus of the dish.

The equation of a parabola with its vertex at the origin and passing through points (±60, 15) can be written as ...

  y/15 = (x/60)² . . . . parabola scaled vertically by 15, horizontally by 60

  240y = x² . . . . . .  multiply by 3600

  4(60)y = x² . . . . . factor out 4 from the coefficient of y

This equation is of the form ...

  4py = x²

where p = 60 is the distance from the vertex to the focus. Since the dish is 15 cm deep, the focus lies 60-15 = 45 cm above the edge of the dish.

The length of each strut from the edge of the dish to the focus will be the hypotenuse of a right triangle with legs 45 and 60. The Pythagorean theorem tells us that length is ...

  c² = a² +b²

  c = √(a² +b²) = √(45² +60²) = 15√(9+16) = 75

The length x of each strut is 75 cm.

Step-by-step explanation:

Refer to pic............

Answer: $29.4

Step-by-step explanation: one taco cost 4.20 so multiply the price of the tacos times the amount of tacos gina buys and you should get your answer which is 29.4

To solve for v in the equation 3(v-4)-6=-7(-4v+4)-7v, we need to simplify the equation and isolate the variable v on one side of the equation. Here are the steps:

Step 1: Distribute the 3 and -7 on the left and right sides of the equation respectively:

3v - 12 - 6 = 28v - 28 - 7v

Step 2: Combine like terms on both sides of the equation: 3v - 18 = 21v - 28

Step 3: Move the variable terms to one side of the equation and the constant terms to the other side: 3v - 21v = -28 + 18

Step 4: Simplify both sides of the equation:

-18v = -10

Step 5: Divide both sides of the equation by -18 to solve for v: v = -10/-18

Step 6: Simplify the fraction: v = 5/9

Therefore, the solution for v is 5/9.

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The Vdp for the plug permeability is given as 0.46, which indicates that the variability of permeability in the plug is lower than that of the porosity and permeability in the core samples.

From the plots of porosity and permeability vs depth given in Question 2, we can say that both porosity and permeability have a certain degree of variability as they change with depth. However, the variability of permeability appears to be greater than that of porosity as the values of permeability change more drastically with depth compared to the values of porosity.

To calculate the coefficient of variation for both porosity and permeability, we can use the formula:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100

For porosity:

Mean = (10 + 15 + 25 + 30 + 20) / 5 = 20

Standard Deviation = √[(10 - 20)² + (15 - 20)² + (25 - 20)² + (30 - 20)² + (20 - 20)²] / 5 = 7.07

CV = (7.07 / 20) * 100 = 35.35%

For permeability

Mean = (0 + 600 + 100 + 200 + 300 + 400 + 500) / 7 = 300

Standard Deviation = √[(0 - 300)² + (600 - 300)² + (100 - 300)² + (200 - 300)² + (300 - 300)² + (400 - 300)² + (500 - 300)²] / 7 = 200

CV = (200 / 300) * 100 = 66.67%
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The practical range is: $76.50 ≤ f(t) ≤ $153

The minimum number of hours is 5 hours, so the minimum money earned is:

minimum money = 15.30 * 5 = $76.50

The maximum number of hours is 10 hours, so the maximum money earned is:

maximum money = 15.30 * 10 = $153

2. Since the words “at least” and “not more than” are used, hence this is inclusive.

3. The practical range is: $76.50 ≤ f(t) ≤ $153

The domain is the number of hours he worked. It says that he works at least 16 hours, but not more than 24.

This means that the number of hours he worked can be any number between 16 and 24, including 16 and 24 as a possible number of hours.

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