a lattice point is a point in the plane with integer coordinates. how many lattice points are on the line segment whose endpoints are $(3,17)$ and $(48,281)$? (include both endpoints of the segment in your count.)

The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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There are two integer coordinates on the line segment AB: (81, 36) and (349, 230).

We can use the two-point form of the equation of a line to find the equation of the line passing through points A and B:

(y - 35)/(x - 73) = (230 - 35)/(178 - 73)

y - 35 = (195/105)(x - 73)

y - 35 = (39/21)(x - 73)

y = (39/21)x - (39/21)(73) + 35

y = (39/21)x - 2/3

To find the integer coordinates on the line segment AB, we need to determine the x-values that correspond to integer y-values between 35 and 230 (inclusive), and then check if the resulting points lie on the line segment AB.

First, we can find the x-values that correspond to the endpoints of the line segment AB:

x_a = 73

x_b = 178

Next, we can find the x-values that correspond to integer y-values between 35 and 230 (inclusive):

y = 36 -> x = 81

y = 37 -> x = 84

y = 38 -> x = 86

...

y = 228 -> x = 343

y = 229 -> x = 346

y = 230 -> x = 349

Finally, we can check which of these points lie on the line segment AB:

Point (81, 36) lies on the line segment AB.

Point (84, 37) does not lie on the line segment AB.

Point (86, 38) does not lie on the line segment AB....

Point (346, 229) does not lie on the line segment AB.

Point (349, 230) lies on the line segment AB.

Therefore, there are two integer coordinates on the line segment AB: (81, 36) and (349, 230).

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Answer:

x=3

Step-by-step explanation:

13-1=12

12÷4=3

Answer:

The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Step-by-step explanation:

Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.

Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.

Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm

So the perimeter of the triangle is P = a + b + c

substituting the values of a, b and c, we have

P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm

opening the brackets and collecting like terms, we have

P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm

P = (9.1p + 2.4q - 4.1) centimetres

So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Answer:

Shelly can be a CrossFit member is 8 Months

($60-900) / $120 = Months

Step-by-step explanation:

Joining the gym costs 60$ so that would be your first month, it then costs $120 every month after. So we would start by subtracting $60 from the total $900

$60 - $900 = $840

Next you would divide your remaning money ($840) by the amount of money it cost per month ($120).

$840 / $120 = 7 Months

7 months plus the Enitial Month

The total number of months that Shelly can be a CrossFit member is 8 Months.

Answer:

130°

Step-by-step explanation:

All the interior angles should add up to 540 degrees because it's a pentagon

∠T ≅∠S, so ∠T is also 115°

∠P and ∠R are both 90°

Add everything up and solve for ∠Q:

115 + 115 + 90 + 90 + m∠Q = 540

410 + m∠Q = 540

m∠Q = 130°

If the land area of Alabama is about 2¹⁷ square kilometers, then the "average-number" of people per-square-kilometer in 2030 is 36.

In order to find the average number of people per square kilometer in Alabama in 2030, we divide the projected population by the land area,

⇒ Average number of people per square kilometer = (Projected population)/(Land area);

Substituting the given values:

We get,

⇒ Average number of people per square kilometer = (2.25×2²¹)/(2¹⁷),

Now, we simplify this expression using exponent rules,

⇒ Average number of people per square kilometer = 2.25×2²¹⁻¹⁷,

⇒ Average number of people per square kilometer = 2.25×2⁴,

⇒ Average number of people per square kilometer = 2.25×16,

⇒ Average number of people per square kilometer = 36.

Therefore, the predicted average number of people in Alabama in 2030 is 36 square kilometer.

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The given question is incomplete, the complete question is

The projected population of Alabama in 2030 is about 2.25×2²¹. The land area of Alabama is about 2¹⁷ square kilometers. Predict the average number of people per square kilometer in 2030.

In a ternary communication system transmitting one of three equiprobable signals s(t), 0, or -s(t) every T seconds, the optimum receiver calculates the correlation metric U and compares it to thresholds A and -A for decision-making.

The received signal r_l(t) can be one of three forms: s(t) + z(t), z(t), or -s(t) + z(t), where z(t) is white Gaussian noise. The optimum receiver computes the correlation metric U = Re[∫_0^T r_l(t)s*(t)dt] and compares it to the thresholds A and -A.

If U > A, the decision is made that s(t) was sent. If U < -A, the decision is made in favor of -s(t). If -A ≤ U ≤ A, the decision is made in favor of 0. The receiver uses these thresholds to determine the most likely transmitted signal in the presence of noise.

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Answer:c

Step-by-step explanation:

Answer:

(3x-16)(2x+15)=0

Answer:

AC and BD are vertically oposite

and both sides are equal (equilateral) so AC = BD

As i think

Answer:

x<−2

Step-by-step explanation:

−3(−7x−6)−7<x−29

Step 1: Simplify both sides of the inequality.

21x+11<x−29

Step 2: Subtract x from both sides.

21x+11−x<x−29−x

20x+11<−29

Step 3: Subtract 11 from both sides.

20x+11−11<−29−11

20x<−40

Step 4: Divide both sides by 20.

20x

20

<

−40

20

x<−2

Answer:

answer is x<−2

Step-by-step explanation:

The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.

To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.

Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:

s'(x) = -6 + 16x + 5

s''(x) = 16

The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.

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Parameters are the values that are computed from a complete census, which are considered to be precise and valid measures of the population. So, option(b) is right one.

In statistics, a population parameter is a number that identifies an entire group of people or population. This should not be confused with arguments in other forms of mathematics that refer to values that remain constant for a mathematical function. Note that the population parameter is not a statistic, it refers to data for a sample or group of the population. With good research, we can get statistics that accurately estimate the population. Statistics is a numerical measure described with sample data. Therefore, the parameter is a numerical description of the characteristic of population.

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Complete question:

Values that are computed from a complete census, which are considered to be precise and valid measures of the population, are referred to as:

a) statistic

b) parameters

The solution of the given initial value problem is: \(y = y0e6t\) where y0 is the initial condition that is

y(0) = 6. Placing this value in the equation above, we get:

\(y = 6e6t\)

Given that the initial condition is y0 = 6,

the differential equation is\(dy/dt = 6y.\)

As we know that the solution of this differential equation is:\(y = y0e^(6t)\)

where y0 is the initial condition that is y(0) = 6.

Placing this value in the equation above, we get :\(y = 6e^(6t)\)

Hence, the solution of the given initial value problem is\(y = 6e^(6t).\)

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- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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The ticket price that will maximize the airline's revenue is $300, and the number of tickets sold at that price is 600.

To find the ticket price and the number of tickets sold that will maximize the airline's revenue, we will follow these steps:
Set up the given information as functions:
- The base ticket price (P) is $400.
- The base number of tickets sold (Q) is 100.
- For each $10 price reduction (x), 50 more tickets are sold.
Write the functions for price and quantity:
- Price: P(x) = 400 - 10x
- Quantity: Q(x) = 100 + 50x
Calculate the revenue function:
Revenue (R) = Price × Quantity
R(x) = P(x) × Q(x)
R(x) = (400 - 10x)(100 + 50x)
Expand the revenue function:
R(x) = 40000 + 20000x - 1000x^2
Find the critical points by taking the derivative of the revenue function and setting it equal to 0:
R'(x) = 20000 - 2000x
0 = 20000 - 2000x
Solve for x:
2000x = 20000
x = 10
Substitute the critical point (x=10) back into the price and quantity functions to find the optimal price and quantity:
- Price: P(10) = 400 - 10(10) = 400 - 100 = $300
- Quantity: Q(10) = 100 + 50(10) = 100 + 500 = 600

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Positive value of z, the probability that a standard normal variable is between 0 and Z, the value of Z is 1.16

Given that:

P(0<Z<z)= 0.3770

P(Z<z)- P(Z<z)= 0.3770

P(Z<z)=0.3770- P(Z<z)

P(Z<z)=0.3770+ 0.5000        

{ we know that : P(Z<z)= P(Z<z)= 0.5}

P(Z<z)= 0.8770

so far calculating the value of Z, we look at the standard normal distribution table, we move to left until we reached first column we observe the value was 1.1 and then in the top value was observed we get the value that is 0.06. Then, we intersect the row and column we get the value of Z,

i.e, [1.1+ 0.06= 1.16]

Therefore P(Z≤1.16) = 0.8770

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Answer:

All of the above

Step-by-step explanation:

A whole number and integers are numbers that don't have decimals.

A rational number is a number that can be written as a fraction

A real number is any number that is not complex, which means that it has an imaginary solution or imaginary number part of it.

Answer: the answer is B

Step-by-step explanation:

Answer:b

Step-by-step explanation:

A(n) MODEL is a mathematical representation of an object created by a special software.

In computer science, a model is a mathematical abstraction of a system, process, or phenomenon that is intended to be simulated or executed on a computer system. A model is used to represent a system or process as a set of mathematical equations or logical rules in order to simulate or analyze it with a computer program.

                                                  It can be a physical object, such as a car or building, or an abstract concept, such as an economic system or a social network. In general, a model can be a simple or complex representation of a real-world object or process, and it can be used for a variety of purposes, such as predicting future outcomes, testing hypotheses, or designing new systems.

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The graph of f(x) = x will shift to the left 11 units because negative 11 is being subtracted from x which will be the required transformation.

Taking into account that f(x) = x becomes f(x) = x+11

This shows a horizontal displacement of x of 11 units to the left.

This is true since the original graph's origin is the x intercept. for a new purpose

x's intercept is -11.

The option it contains is the right one.

11 units to the left, I shifted.

x is taken away from by a negative -11.

Transform the coordinate plane's shapes by translating, rotating, or reflecting them. In the 19th century, Felix Klein introduced transformational geometry, a novel perspective on geometry. The majority of proofs in geometry are built upon object transformations. Any image in a coordinate plane can be altered using transformations.

Disclaimer : the complete question is :

How will the input of f(x + 11) affect the graph of f(x) = x? Explain.

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The curves in the diagram should be correctly identified as follows: C. E = marginal cost curve; F = average total cost curve; G = average variable cost curve; H = average fixed cost curve.

In Financial accounting, costing can be defined as a strategic process that is typically used for the measurement of the cost of production of goods and services, especially by assessing the fixed costs and variable costs that are associated with each step of production.

Generally speaking, a fixed cost is a predetermined expense in a business that remains constant for a specific period of time, regardless of the quantity of production or level of outputs in a plant.

Conversely, a variable cost is the cost that changes with respect to the level of production or the amount of output.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

According to the question 1.) False - 3 × 5 matrix columns can be linearly independent. 2.) True , 3.) True , 4.) True , 5.) True , 6.) True - 3 × 2 matrix transformation not one-to-one.

1.) True. If the set of columns of a 3 × 5 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

2.) False. The effect of a linear transformation on the columns of the n × n identity matrix only determines the image of the standard basis vectors. It does not completely determine the entire transformation.

3.) False. If each row of matrix A has a pivot, it means that the rows of A are linearly independent, not linearly dependent.

4.) True. If A has a pivot in each row, it means that the rows of A are linearly independent, and the linear transformation T : Rn → Rm represented by A is one-to-one.

5.) True. Similar to statement 1, if the set of columns of a 5 × 3 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

6.) True. If A is a 3 × 2 matrix, it means that the transformation x → Ax maps from R2 to R3. Since the dimensions of the domain and codomain are different, the transformation cannot be one-to-one.

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Answer:

We have, sinx+sin3x+sin5x=0

∴(sinx+sin5x)+sin3x=0

∴2sin(

2

x+5x

)cos(

2

5x−x

)+sin3x=0

∴2sin3xcos2x+sin3x=0

∴sin3x(2cos2x+1)=0

Either sin3x=0 or 2cos2x+1=0

i.e. sin3x=0 or cos2x=−

2

1

Now, cos2x=−cos

3

π

∴cos2x=cos(π−

3

π

)

∴cos2x=cos

3

2π

∴sin3x=0 or cos2x=cos

3

2π

3x=nπ,n∈Z or 2x=2mπ±

3

2π

where m∈Z

Hence, x=

3

nπ

or x=mπ±

3

π

, where n,m∈Z.

Step-by-step explanation:

a. 6 £/hr

b. 6.8 £/hr.....is this right?

Answer:

B) 1 hour = £10

Step-by-step explanation:

the higher rate starts from 20 hours and the pay is £120 if you go to 30 hours, the pay rate is £220. A raise of £100. This means the new pay rate is for every 1 hour worked, you get £10

In order to identify the transversal connecting angles ∠3 and ∠5 and classify their relationship, I would need to analyze a visual representation or diagram that shows the angles in question.

Without access to a specific photo or diagram, it is not possible to determine the transversal or the relationship between ∠3 and ∠5. However, in general, if angles ∠3 and ∠5 are part of a pair of intersecting lines or line segments, then the transversal would be the line or line segment that intersects both lines or line segments. The relationship between ∠3 and ∠5 would depend on the specific angles formed by the transversal and the intersecting lines or line segments.

This relationship could be classified as corresponding angles, alternate interior angles, alternate exterior angles, vertical angles, or any other relevant geometric relationship. Without the visual context, it is not possible to provide a specific classification of the relationship between ∠3 and ∠5 or to determine the transversal connecting them.

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35, ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

What is alternate interior angles?

Given

           m∠4=35

From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines.

Therefore, ∠2 and ∠4  are alternate interior angles.

Thus,

m ∠2 = m∠4 (alternate interior angles theorem)

since m∠4 = 35°

therefore m∠2 = 35°

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