A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.

Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot

Answer:

The area of the regular hexagon is 166.3 square units (to the nearest tenth).

Step-by-step explanation:

The formula for the area of a regular polygon is:

[tex]\boxed{\textsf{Area}=\dfrac{r^2n\sin\left(\frac{360^{\circ}}{n}\right)}{2}}[/tex]

where:

From inspection of the given regular polygon:

Substitute the values into the formula and solve for area:

[tex]\begin{aligned}\textsf{Area}&=\dfrac{8^2\cdot 6 \cdot \sin\left(\frac{360^{\circ}}{6}\right)}{2}\\\\&=\dfrac{64\cdot 6 \cdot \sin\left(60^{\circ}\right)}{2}\\\\&=\dfrac{384 \cdot \frac{\sqrt{3}}{2}}{2}\\\\&=\dfrac{192\sqrt{3}}{2}\\\\&=96\sqrt{3}\\\\&=166.3\; \sf square\;units\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the area of the regular hexagon is 166.3 square units (to the nearest tenth).

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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The estimated area is about 22.5 square units

To estimate the perimeter of a patio, you need to measure the length of each side and then add those lengths together.

Here's a step-by-step guide to help you:

Determine the shape of your patio: Before you can estimate the perimeter, identify whether your patio is a rectangle, square, circle, or any other shape. The method for calculating the perimeter will vary depending on the shape.

Measure the sides:

a. For rectangular or square patios: Measure the length (L) and width (W) of the patio using a measuring tape. Ensure that the measurements are taken in the same unit (e.g., feet, meters, etc.).

b. For circular patios: Measure the diameter (D) or radius (R) of the patio. The radius is the distance from the center of the circle to any point on its edge.

c. For irregularly-shaped patios: Break the patio down into smaller, regular shapes (like rectangles, squares, or triangles), and measure each side of these smaller shapes.

Calculate the perimeter:

a. For rectangular or square patios: Use the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

b. For circular patios: Use the formula P = 2πR or P = πD, where P is the perimeter, R is the radius, and D is the diameter. π (pi) is approximately 3.14159.

c. For irregularly-shaped patios: Add up the side lengths of each smaller shape that you've broken the patio into. The sum of these lengths will give you the total perimeter.

(look at the image)

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The approximate volume of the solid is 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is 8.17 × 10^20 π cubic inches.

We have,

1.

The volume V of a cylinder is given by V = πr²h,

where r is the radius and h is the height.

Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.

V = π (2.0 × 10^7)² (4.0 × 10^5)

Simplifying,

V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)

2.

The volume of a cone is given by V = 1/3πr²h,

where r is the radius, h is the height, and we are given the diameter (d = 2r).

Substituting,

d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and

h = 5.0 × 10^5 inches, we get:

V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)

Simplifying,

V = 2.6 × 10^20 π cubic inches

(using scientific notation and leaving the answer in terms of π)

Rounding to the nearest hundredth,  

V = 8.17 × 10^20 π cubic inches.

Thus,

The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.

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The area of the replaceable is [tex]15[/tex] square inches.

The area of a regular hexagon, we can use the formula:

[tex]A = (3\sqrt3 / 2) \times s^2[/tex]

Where A is the area of the hexagon and s is the length of one of its sides.

To find the area of the replaceable head, we can split it into two shapes: a rectangle and a triangle.

The rectangle has a length of 10 mm and a width of 12 mm, so its area is:

Area of Rectangle [tex]= length \times width = 10 mm \times 12 mm = 120 mm^2[/tex]

The triangle has a base of  [tex]12 mm[/tex] and a height of [tex]6 mm[/tex], so its area is:

Area of Triangle [tex]= 1/2 \times base \times height = 1/2 \times 12 mm \times 6 mm = 36 mm^2[/tex]

To find the total area of the replaceable head, we add the area of the rectangle and the area of the triangle:

Total Area =Area of Rectangle  +  Area of Triangle [tex]= 120 mm^2 + 36 mm^2 = 156 mm^2[/tex]

Therefore, the area of the replaceable head is   [tex]156[/tex]mm².

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The probability of a simple event is the likelihood or chance of that event occurring. The formula is P(A) = Number of favorable outcomes / Total number of possible outcomes.

It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The formula for the probability of a simple event is:

P(A) = Number of favorable outcomes / Total number of possible outcomes

For example, if we toss a fair coin, the probability of getting heads is:

P(Heads) = 1 (number of favorable outcomes) / 2 (total number of possible outcomes)

So, the probability of getting heads is 0.5 or 50%.

A simple event is an event that has only one possible outcome. For instance, rolling a specific number on a dice, drawing a specific card from a deck of cards, or picking a specific colored ball from a bag of balls are all examples of simple events.

In summary, the probability of a simple event is the ratio of the number of ways the event can happen to the total number of possible outcomes.

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The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.

We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter

V = (4/3)πr^3 = (1/6)πd^3,

where V is the volume, r is the radius, and d is the diameter.

Taking the derivative with respect to time t, we get

dV/dt = (1/2)πd^2 (dd/dt),

where dd/dt is the rate of change of diameter.

We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt

dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.

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Answer:

k = 30

Step-by-step explanation:

an equation of proportionality has the form

y = kx ← k is the constant of proportionality

y = 30x ← is in this form

with k = 30

The coordinates of triangle A'B'C' after a dilation centered at the origin with a scale factor of 2 are:

A' (-10, -14).

B' (12, -6).

C' (4, 14).

In Geometry, a dilation is a transformation that is typically used for changing the dimension (size) of a geometric figure, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 2 that is centered at the origin as follows:

Ordered pair A (-5, -7) → Ordered pair A' (-5 × 2, -7 × 2) = Ordered pair A' (-10, -14).

Ordered pair B (6, -3) → Ordered pair B' (6 × 2, -3 × 2) = Ordered pair B' (12, -6).

Ordered pair C (2, 7) → Ordered pair C' (2 × 2, 7 × 2) = Ordered pair C' (4, 14).

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An equation of the line that passes through the point (6,2) and has a slope of -1/2 is y = -1/2(x) + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (6, 2) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/2(x - 6)  

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

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

y = -1/2(x) + 5

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If for an arithmetic-sequence, the terms are t₅ = -154 and t₉ = -274, then the first-three terms are t₁ = -274, t₂ = -244 and t₃ = -214.

An "Arithmetic-Sequence" is defined as a sequence of numbers in which the difference between any two consecutive terms is always the same, which is called the "common-difference".

To find first 3 terms of an "arithmetic-sequence" given the values of t₅ and t₉, we use formulas for "nth-term" of an arithmetic sequence, which is

⇒ tₙ = t₁ + (n - 1)d,

where tₙ = nth term, t₁ = first term, n = position of term in sequence, and d = common-difference,

Given that t₅ = -154 and t₉ = -274,

So,

⇒ t₅ = t₁ + (5 - 1)d = -154,

⇒ t₉ = t₁ + (9 - 1)d = -274,

We first find the "common-difference" by subtracting "t₁" from both sides of first equation and "t₉" from both sides of second-equation,

We get,

⇒ 4d = -154 - t₁,

⇒ 8d = -274 - t₁,

Simplifying further,

We get,

⇒ 4d = 120,

⇒ d = 30,

Now, we substitute it in "4d = -154 - t₁",

We get,

⇒ 4(30) = -154 - t₁,

⇒ 120 = -154 - t₁,

⇒ t₁ = -154 - 120,

⇒ t₁ = -274

So, the first term is = -274;

Now we use "d = 30" to find second and third terms of sequence,

We get,

⇒ t₂ = t₁ + (2 - 1)d = -274 + 30 = -244,

⇒ t₃ = t₁ + (3 - 1)d = -274 + 60 = -214,

Therefore, first three-terms of arithmetic sequence are -274, -244, and -214.

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The given question is incomplete, the complete question is

Find the first 3 terms of arithmetic sequence if t₅ = -154 and t₉ = -274. Find t₁, t₂, t₃.

We can rewrite the following logarithms to common logarithms as follows:

1. 2.3768

2. 3.8173

To rewrite the logarithms in the common format we can use the following formula.

loga b = log10 b / log10 a

So, we have:

log5 46 = log10 46 / log10 5

Using a calculator, we find that log10 46 ≈ 1.66276 and log10 5 ≈ 0.69897, so:

log5 46 ≈ 1.66276 / 0.69897 ≈ 2.3768

For the second one, we can approach the problem this way:

loga b = log10 b / log10 a

So, we have:

log3 66 = log10 66 / log10 3

Using a calculator, we find that log10 66 ≈ 1.81954 and log10 3 ≈ 0.47712, so:

log3 66 ≈ 1.81954 / 0.47712 ≈ 3.8173

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None of the provided circle graphs correctly represents the data in the table.

The total number of visitors in the table is 300, but the percentages in all the circle graphs add up to more than 100%, indicating that the data has been incorrectly represented.

To create a correct circle graph, we need to calculate the percentage of visitors for each type of transportation, which can be done by dividing the number of visitors for each type by the total number of visitors (300) and multiplying by 100.

Walk: (120/300) x 100 = 40%

Bicycle: (24/300) x 100 = 8%

Car Service: (45/300) x 100 = 15%

Bus: (30/300) x 100 = 10%

Subway: (81/300) x 100 = 27%

Thus, a correct circle graph representing the data in the table would have five sections labeled "Walk 40%", "Bicycle 8%", "Car Service 15%", "Bus 10%", and "Subway 27%".

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Answer:

They are length, thickness and temperature

Answer:

-18.67.

Step-by-step explanation:

If you think math is boring, think again. Here is a fun way to learn how to find the rational number that we need to divide -15/56 by to get -5/7. It's like a puzzle, but with fractions!

First, we need to make -15/56 look nicer. How do we do that? By dividing both the top and the bottom by -1. That's like flipping the sign. So we get 15/56. Much better!

Next, we need to find a mystery number that makes -5/7 and 15/56 equal when we multiply them. That's like finding a missing piece of a jigsaw puzzle. How do we do that? By cross-multiplying! That's when we multiply the top of one fraction by the bottom of the other and set them equal. So we get:

-5 times 56 equals 15 times mystery number

Now we just need to solve for the mystery number. How do we do that? By dividing both sides by 15. That's like cutting a cake into equal slices. So we get:

Mystery number equals (-5 times 56) divided by 15

Now we just need to simplify. How do we do that? By using a calculator or our brains. Either way, we get:

Mystery number equals -18.67

And that's it! We found the rational number that we need to divide -15/56 by to get -5/7. It's -18.67. Isn't math fun?

The 6 steps for inferential statistics to test researchers question can be:

It is the branch of statistics that is concerned with obtaining information about a population from a sample of that population. It is used to make inferences, that is, draw conclusions and make predictions about the population based on the information obtained from the sample.

These assertions are based on hypothesis tests, confidence intervals and statistical models.

Therefore, the goal of inferential statistics is to make accurate and reliable statements about the population using limited sample information.

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The statement " A(n) method is like a blueprint, or template, for all the objects within a class" is true because methods define the behavior or operations that an object can perform and are defined within a class, acting as a blueprint or template for creating objects in object-oriented programming.

A method in object-oriented programming is a set of instructions that defines the behavior or operations that an object can perform. It is a part of a class, which acts as a blueprint or template for creating objects. When an object is created from a class, it can access and use the methods defined within that class.

Methods can be used to perform tasks, manipulate data, or interact with other objects. They are an essential aspect of encapsulation in object-oriented programming, as they allow for data to be accessed and manipulated in a controlled manner. Overall, methods are a crucial tool for developers to create robust and scalable applications.

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The length of the hypotenuse in the given right-angle triangle is 7.5 feet.

According to Pythagoras' theorem, "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides." Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

It is a right-angle triangle.

[tex]c = \sqrt{6^{2} +4^{2} } \\c = \sqrt{36 + 16}\\ c = \sqrt{56}\\ c = 7.48[/tex]which is nearly equal to 7.5

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Complete question:

The length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

The lengths of the trim pieces that make an X on the door form the legs of a right triangle, and the diagonal of the door forms the hypotenuse of the right triangle. Using the Pythagorean theorem, we can find the length of the hypotenuse:

a^2 + b^2 = c^2

where a and b are the lengths of the trim pieces and c is the length of the hypotenuse.

Each trim piece forms a right triangle with the height of the door (7 feet) and one half of the width of the door (1.5 feet). Using the Pythagorean theorem, we can find the length of each trim piece:

a^2 + b^2 = c^2

where a = 7 feet and b = 1.5 feet

c = sqrt(a^2 + b^2) = sqrt((7 feet)^2 + (1.5 feet)^2) = sqrt(49 + 2.25) = sqrt(51.25) ≈ 7.154 feet

The length of each trim piece is approximately 7.154 feet. Since there are two trim pieces that intersect at the center of the door, the length of the hypotenuse is twice this length:

2 * 7.154 feet ≈ 14.308 feet

Therefore, the length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.

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Pi/(180 degrees) equals 1 degree in radians.

Radians are a unit of measurement for angles, just like degrees. The radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

To visualize this, imagine taking a circle with a radius of r and drawing an arc on the circle that is the same length as the radius. The angle subtended by this arc at the center of the circle is one radian. Since the circumference of a circle is 2pir, there are always 2*pi b in a full circle.

(180 degrees)/pi is equivalent to the value of 180 degrees in radians. To convert from degrees to radians, we multiply the degree value by (pi/180). So:

(180 degrees)/pi = (180 degrees) * (pi/180) = pi radians

Therefore, (180 degrees)/pi equals pi in radians.

On the other hand, pi/(180 degrees) is equivalent to the value of 1 degree in radians. To convert from radians to degrees, we multiply the radian value by (180/pi). So:

pi/(180 degrees) = pi * (180/pi) = 180 degrees

Therefore, pi/(180 degrees) equals 1 degree in radians.

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Answer:

4/5 ×400

0.8 × 400

=320 freshmen study algebra.

I had used fraction method.

The coordinates of P that partitions AB in the ratio 1 to 3 include the following: [4, -4].

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 3.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical equation:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(1(6) + 3(2))/(1 + 3)],  [(1(6) + 3(-6))/(1 + 3)]

P(x, y) = [(6 + 6)/(3)],  [(6 - 18)/3]

P(x, y) = [12/3],  [(-12)/(3)]

P(x, y) = [4, -4]

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Missing information:

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

Answer:

We can use the double angle formulas to find sin(2θ) and cos(2θ):

sin(2θ) = 2sin(θ)cos(θ)

cos(2θ) = cos^2(θ) - sin^2(θ)

Since sin(θ) = -4/5 and θ is in the third quadrant (π < θ < 3π/2), we can use the Pythagorean identity to find cos(θ):

sin^2(θ) + cos^2(θ) = 1

cos^2(θ) = 1 - sin^2(θ)

cos(θ) = -√(1 - sin^2(θ))

cos(θ) = -√(1 - (-4/5)^2) = -√(1 - 16/25) = -√(9/25) = -3/5

Now we can substitute these values into the double angle formulas:

sin(2θ) = 2sin(θ)cos(θ) = 2(-4/5)(-3/5) = 24/25

cos(2θ) = cos^2(θ) - sin^2(θ) = (-3/5)^2 - (-4/5)^2 = 9/25 - 16/25 = -7/25

Therefore, the exact values of sin(2θ) and cos(2θ) are sin(2θ) = 24/25 and cos(2θ) = -7/25, respectively.

Finally, we can find the value of sin^2(2θ)cos^2(2θ):

sin^2(2θ)cos^2(2θ) = (sin(2θ))^2(cos(2θ))^2

sin^2(2θ)cos^2(2θ) = (24/25)^2(-7/25)^2

sin^2(2θ)cos^2(2θ) = 24^2/25^2 * 7^2/25^2

sin^2(2θ)cos^2(2θ) = (24*7)^2/25^4

Therefore, the exact value of sin^2(2θ)cos^2(2θ) is (24*7)^2/25^4.

Answer:

a) m || n

b) p || q, and m must be perpendicular to both p and q.

c) p || q

d) p || q

e) m || n and p || q

Therefore, C) The median for Felicia's data is bigger than the median for Gabriella's data is the claim best supported by the data in the box plots.

Basketball is a team sport played by two teams of five players each on a rectangular court. The objective of the game is to score points by shooting a ball through a hoop, which is located 10 feet high on a backboard at each end of the court.

In statistics, quartiles are values that divide a dataset into four equal parts, with each part comprising 25% of the data. The three quartiles that divide the data into four equal parts are the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The second quartile (Q2) is the same as the median of the dataset.

From the given box plots, we can see that Felicia's maximum number of points scored in one game is 28 and Gabriella's maximum is 24. Therefore, statement A is false.

The range of the data for Felicia is from 6 to 28, which is 22. The range of the data for Gabriella is from 10 to 24, which is 14. Therefore, statement B is false.

The median for Felicia's data is approximately 19 and the median for Gabriella's data is approximately 16. Therefore, statement C is true.

The first quartile for Felicia's data is approximately 12 and the first quartile for Gabriella's data is approximately 11. Therefore, statement D is false.

Thus, the statement best supported by the information in the box plots is C) The median for Felicia’s data is greater than the median for Gabriella’s data.

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The probability of passing the true/false test of 60 questions if the minimum passing grade is 60% and all responses are random guesses is approximately 0.9802 or 98.02%.

Assuming that all responses are random guesses, we may describe this issue using a binomial distribution, where the number of right responses follows a binomial distribution with [tex]n = 60[/tex] and [tex]p = 0.5.[/tex]

If X represents the total number of accurate responses, it will follow a binomial distribution with[tex]n = 60[/tex] and [tex]p = 0.5[/tex] as its parameters.

If the passing grade is [tex]60%[/tex], then there must be a minimum of [tex]36[/tex]accurate responses [tex](0.6 * 60 = 36).[/tex]

The normal-approximation can be used to calculate the likelihood of receiving at least [tex]36[/tex] correct responses. We must determine the mean and variance of the binomial distribution in order to utilise the normal approximation.

The variance of a binomial distribution is

[tex]2 = np(1-p)[/tex]

[tex]= 60 * 0.5 * 0.5[/tex]

[tex]= 15[/tex]

and the mean is

[tex]= np[/tex]

[tex]= 60 * 0.5[/tex]

[tex]= 30.[/tex]

To calculate the probability of passing, we can use the normal distribution with mean 30 and variance 15 to approximate the binomial distribution with continuity correction.

[tex]P(X \geq 36) = P(Z \geq (36 + 0.5 - 30) / \sqrt{15})[/tex]

where Z is a standard normal random variable.

[tex]P(Z \geq 2.08) = 1 - P(Z \leq 2.08)[/tex]

[tex]= 1 - 0.0198[/tex]

[tex]= 0.9802[/tex]

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Answer: $34,828.59

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r)^t

where:

P = the principal (in this case, $14,275)

r = the annual interest rate (6%, or 0.06 as a decimal)

t = the number of years (18)

Plugging in the values we know, we get:

A = $14,275(1 + 0.06)^18

A = $14,275(1.06)^18

A = $34,828.59 (rounded to the nearest penny)

Therefore, the value of the investment after 18 years, rounded to the nearest penny, is $34,828.59

1) n²+n is always an even integer

2. n² +n is always an even integer when n is even

3. n² +n is always an even integer when n is odd

Since, if n is an integer,

Then n = even or odd,

If n = even ⇒  = even

⇒ = even+ even = even  

Now, If n = odd ⇒  = odd   ( square of a odd number is always odd )

⇒  = odd + odd = even

Hence, however, n is odd or even,

is always an even number.

⇒ Options 1), 2) and 3) are correct.

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The 30th partial sum of the sequence 5x-12 = 1965

To derive the 30th partial sum of the sequence 5x -12, we need to add up to the first 30 terms of the sequence.

Th e nth term of the sequence will be:

5 -12

the first 30th terms are:

5(1) -12 = -7

5(2) -12 = -2

5(3) -12 = -3

5(4)  -12 = -8

and so on

So to get the 30th partial sum, we write:
-7 + (-2) = 3+ 8 ...... + (5(30)-12

If simplified, this expression will given us:

S = (n/2) (a+l)

In this case,

s is the sum of the n terms
A is the first term and
L is the last term.

In this ase, a = -7 (the first term) and L= 5(30) -12 = 138 (the 30th term) So  for the partial sum we say:

S30 = (30/2) (-7 + 138) = 30(131)/2
S30 = 1965

Thus, the partial sum of the sequence 5x-12) is 1965

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