Please use the information below for an arithmetic sequence to do the following:

a. sub 1 equals 3 d equals 4

A) List the first 6 terms of the sequence

B) Write the terms of this sequence as a series.

C) Provide a graph of the aritmetic sequence.

D) List the first 6 partial sums of the series.

SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!

Answer:

x=4, -4/3

Step-by-step explanation:

(x-4)(3x+4)=0

Using the zero product property, we can set each factor to zero and solve.

x-4 =0     3x+4 =0

x=4            3x =-4

x=4                x = -4/3

The solutions for x are:

x=4, -4/3

Answer:

4, -4/3

Step-by-step explanation:

The mistake in the solution of the expression is in step 3, where the product should be solved first.

Here we have the expression:

0.5*(3*5 + 1) - 2

And we also have the solution in steps, and we want to find in which step we have a mistake.

The first step gives:

0.5*(15 + 1) - 2

Where the first product is solved.

The second step is

0.5*16 - 2

Where we solved the parentheses.

The third step gives:

0.5*14

Here they subtracted the 2 from the 16, but this is incorrect, the first thing that needs to be solved here is the product between 0.5 and 16, we should get:

0.5*16 - 2

8 - 2

6

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The width of the blackboard is 4 feet and the length is 11 feet.

To solve the equation[tex](w - 2) (w + 2) = 12[/tex]for the width of the blackboard, we can use the distributive property to simplify the left-hand side:

[tex]w^2 - 4 = 12[/tex]

Then we can add four to both sides:

[tex]w^2 = 16[/tex]

When we take the square root of both sides, we get:

w = ±4

We choose the positive solution because the width of the blackboard cannot be negative:

w = 4

We can calculate the length of the blackboard by dividing the area by the width:

l = 44 square feet / 4 feet = 11 feet

As a result, the blackboard's width is 4 feet and its length is 11 feet.

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The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.

We can use the formula for the volume of a cone, which is:

Volume = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:

13.4 = (1/3)π(3.2)²h

Multiplying both sides by 3 and dividing by π(3.2)², we get:

h = 3 × 13.4 / π(3.2)²

h ≈ 2.5 m

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Answer:

5a² + 4ab = a(5a+4b)

6p - pq - 5pr = p(6-q-5r)

8st +9su + 7sv = s(8t+9u+7v)

8pq² +9qr+ 7pqr = q(8p²+7pr+9r)

2a²b + ab² - 6ab = ab(2a+b-6)

6t²u +8tu²y + 5tuw = tu(6t+8uy+5w)

18abc²-42a²bc + 18ab²c = 6abc(3c-7a+3b)

24pqrs +56q²rs - 40qrs = 8qrs(3p+7q-5)

The angle that satisfies the necessary requirements is  1041° - 2(360°) = 321°. Coterminal angles are those with the same terminal point in the standard position.

To understand, follow the 2 basic steps:

Step 1: Find the specified angle.

Step 2: Finding a coterminal angle.

Tally up or tally down a multiple of 360.

θ = 1041°

Every multiple of 360 degrees added or subtracted results in an angle that is coterminal with the provided angle.

Hence, 1041° - 2(360°) = 321° is an angle that satisfies the necessary requirements.

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The nature of formula (Permutations or Combinations) for each scenario is the following:

1) Permutations ; 2) Combination

3) Combination ; 4) Permutations

5)Permutations ; 6)Combination

7) Combination ; 8)Combination 9)Combination ; 10)Combination.

Permutations formula: Permutation is considered an ordered combination. The general formula for this is,

P(n, r) = n! /(n-r)!

Combination formula: It is considered arrangement ways but without ordered combination. The general formula for this is C(n, r) = n!/ (n-r)! r!

Now, we have provide some situations and we have to resolve them.

1) Determining the top three winners ing Science Quiz have to Bee is an example of Permutation as here we just arrange the position for top winners.

2) Forming lines from six given points with no three of which are collinear, is an example of combination because only pair of points is needed.

3) It will be a combination as here we select 3 points to make a triangle user.

4) Four people posing for pictures is an example of Permutation as oder does not matter.

5) Assembling a jigsaw puzzle is an example of Permutations.

6) As here we choose 2 household chores so it is a combination.

7) Selecting 5 basketball players out of 10 team members for the different positions members it is a combination.

8) Choosing three friend for birthday party is combination formula.

9) Picking 6 balls from a basket by 12 balls is combination formula.

10) Forming a committe of 5 members from do people 20 combinations people.

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Complete question:

P- Permutations or C- Combinations.

1. Determining the top three winners in a Science Quiz Bee

2. Forming lines from six given points with no three of which are collinear

3. Forming triangles from 7 given points with no three of which are collinear

4. Four people posing for pictures

5. Assembling a jigsaw puzzle

6. Choosing 2 household chores to do before dinner

7. Selecting 5 basketball players out of 10 team members for the different positions

8. Choosing three of your classmates to attend your party

9. Picking 6 balls from a basket of 12 balls

10. Forming a committee of 5 members from 20 people

The value of x is 61° ( nearest degree)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. If side opposite the acute angle is the opposite side and the longest side is hypotenuse.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan( tetha) = opp/ adj

In this case,

the hypotenuse = 8

opposite = 7

therefore sin x = 7/8

sin x = 0.875

x = sin^-1 ( 0.875)

x = 61° ( nearest degree)

therefore the value of x is 61°

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The ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

Given data:

Claire's score = 7 * Ali's score

Ben's score = 0.5 * Claire's score

How to solve for the ratio of Ali's score to Ben's score to Clare's score

let Ali's score = x

let Ben's score = y

let Claire's score = z

z = 7 * x = 7x

z = 7x

y = 0.5 * z = 1/2 * z = z / 2

plugging the value of z gives

y = 7x / 2

writing the ratios in terms of x gives

Ali : Ben : Claire

x : y : z

x : 7x/2 : 7x

Reducing the terms by dividing through by x

1 : 7/2 : 7

OR

1 : 3.5 : 7

clearing the fraction gives

2 : 7 : 14

Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

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There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.

To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.

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Answer:

9/8

Step-by-step explanation:

1 1/3 + 2 1/4 = (4/3 + 9/4) = (16/12 + 27/12) = 43/12

8 5/8 - 7 1/2 = (69/8 - 15/2) = (69/8 - 60/8) = 9/8

Therefore, 1 1/3 + 2 1/4 = 43/12 and 8 5/8 - 7 1/2 = 9/8.

a) There are 1,000 small cubes in the large one.

b) if each side has 3 times more cubes, then the total number of cubes will be 27 times larger.

So we know that the large cube has 10 small cubes in each side.

Then each one of the faces of the cube will have:

10*10 = 100 small cubes on it.

Now, if we look at one of the faces, you can see 10 of these 100 square arrays on it, then the total number of small cubes is:

10*100 = 1000 small cubes.

b) If there are 3 times as many cubes per side, then each side has 30 cubes now, and the total number of cubes needed will be:

30*30*30 = 27,000

This is 27 times the amount of small cubes that we had before,  then here the answer is no.

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A pavement 4m wide is constructed along the outer side of the boundary of a square shaped ground having it's side of 13m length. The cost of levelling the pavement at the rate of Rs 1.25 per square meter is Rs 340.

As per given  information,

Side of a square shaped ground = 13 m

Width of pavement constructed = 4 m

We need to find the cost of levelling the pavement at the rate of Rs 1.25 per square meter.

Area of the square shaped ground = Side × Side= 13 × 13= 169 sq.m

Area of the square shaped ground along with pavement constructed

= (13 + 8) × (13 + 8)

= 21 × 21

= 441 sq.m

Area of the pavement constructed

= Area of the square-shaped ground along with pavement constructed - Area of the square shaped ground

= 441 - 169

= 272 sq.m

Cost of levelling 1 sq.m of pavement = Rs 1.25

Cost of levelling 272 sq.m of pavement = 272 × Rs 1.25 = Rs 340

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Answer:

a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.

b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:

Additional amount owed = Taxes owed - Amount withheld

= $4,576 - $4,323

= $253

Therefore, the person would owe an additional $253.

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The container can hold the feed equal to volume = 181.5 cube

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section. The study of shapes and the arrangement of objects is known as Geometry. The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms. The prism's net area is equal to its surface area.

To find how much feed the rectangular prism can hold you have to find its volume.

The formula to find the volume form a rectangular prism is:

Volume= Length x Width x Height

Now we must insert the values you have given:

Volume= 2.75 x 16.50 x 4

When you multiply that out it comes to:

Volume= 181.5

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One possible set of values could be:

29, 30, 31, 52, 53, 54

Given:

Range = 22

Median = 40

Mode = 52

Number of values in the data set = 6

Since the median is 40, it indicates that two values in the data set are below 40, and three values are above 40.

The mode is given as 52, which means that at least one value in the data set is equal to 52.

There are six values in the data set, we can construct a possible set of values:

Min Value + 2 values below median + Mode + 3 values above median + Max Value = 6 values

Let's try one possible combination:

Min Value = 40 - 11 = 29

Max Value = Min Value + Range = 29 + 22 = 51

One possible set of values could be:

29, 30, 31, 52, 53, 54

Here, the range is 51 - 29 = 22, the median is 52, and the mode is also 52.

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Answer: 71  1/2$

Step-by-step explanation:

The chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.

When we choose two balls at random without replacement, there are 50C2 = (50*49)/(2*1) = 1225 ways to choose two balls from 50 balls. Using the conditional probability formula, P(A and B) = P(A) * P(B|A), where A is the event of choosing a red ball and B is the event of choosing a blue ball.

P(A) = (20/50) = 0.4 (Probability of choosing a red ball at random from the bag)

P(B|A) = (15/49) = 0.306 (Probability of choosing a blue ball at random from the bag after choosing a red ball in the first trial)

Similarly, P(B) = (15/50) = 0.3 (Probability of choosing a blue ball at random from the bag)

P(A|B) = (20/49) = 0.408 (Probability of choosing a red ball at random from the bag after choosing a blue ball in the first trial)

Therefore, P(choosing one red and one blue) = P(A and B) + P(B and A) = P(A) * P(B|A) + P(B) * P(A|B)

= 0.4 * 0.306 + 0.3 * 0.408

= 0.1224 + 0.1224

= 0.2448 or 24.48%

Therefore, the chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.

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10 v^5 w^10

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The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.

In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.

To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:

Area = base x height

Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:

72 = 12 x h

h = 72/12

h = 6

Therefore, the value of h in the parallelogram is 6 units.

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Therefore, the value of x, to the nearest foot, is A. 11 in the right triangle in the diagram below.

A triangle is a two-dimensional geometrical shape with three sides and three angles. It is a polygon with the least number of sides. Triangles are classified based on the length of their sides and the measure of their angles. The three sides of a triangle can be classified as equal, two equal sides, or three unequal sides. Triangles can also be classified based on their angles as acute (all angles less than 90 degrees), right (one angle is equal to 90 degrees), obtuse (one angle greater than 90 degrees), or equiangular (all angles are equal). The interior angles of a triangle always add up to 180 degrees. The longest side of a right triangle is called the hypotenuse, and it is opposite to the right angle. The Pythagorean theorem is used to find the missing side of a right triangle. Triangles are widely used in mathematics, physics, engineering, and other fields. They form the basic building block of more complex geometrical shapes and structures.

Here,

Using trigonometry, we can find that:

tan(40°) = x/14

Multiplying both sides by 14, we get:

x = 14 * tan(40°)

Using a calculator, we get:

x ≈ 11.0

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Complete question:

Given the right triangle in the diagram below. what is the value of x, to the nearest foot?

A. 11

B. 17

c. 18

D. 22

The median of the numbers 8.5, 1.2, 7.6, 3.8, 8.1, 9.4, 8.9, 0.7, 2.7  is 7.6.

The median of numbers is the value that's exactly in the middle of a dataset when it is ordered.

Therefore, before we find the middle value of the dataset, we have to arrange the numbers in ascending or descending order.

Hence, let's find the median of 8.5, 1.2, 7.6, 3.8, 8.1, 9.4, 8.9, 0.7, 2.7

Firstly, let arrange the numbers in ascending order.

Hence,

0.7, 1.2, 2.7, 3.8, 7.6, 8.1, 8.5, 8.9, 9.4

Therefore,

median = 7.6

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Step-by-step explanation:

[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]

Substitute for x as -2;

[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:-9

Step-by-step explanation:

h(-2)=h(x)

it symbolize that x=-2;

so, we'll replace every x with -2:

-2^2+3*(-2)-7=4-6-7=-9

Using the distance formula of coordinate geometry the expression represents the distance between point J and point K where J= (6, -2) and K= (6, -9) is  7 units.

To find the distance between point J and point K, we use the distance formula, which involves the coordinates of the two points in a coordinate plane.

Identify the coordinates of point J and point K. In this case, we are given that J has coordinates (6, -2) and K has coordinates (6, -9).

Substitute the values of the coordinates into the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²].

For x1 and y1, use the coordinates of point J, which are x1 = 6 and y1 = -2.

For x2 and y2, use the coordinates of point K, which are x2 = 6 and y2 = -9.

Simplify the formula by substituting the values and solving:

d = √[(6 - 6)² + (-9 - (-2))²]

d = √[0² + (-7)²]

d = √[49]

d = 7

Therefore, the distance between point J and point K is 7 units.

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The percentage of 65 out of 140 will be 46.428%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

[tex]\text{Percentage (P) = [Final value - Initial value] / Initial value x 100}[/tex]

The whole numbers are 65 and 140.

Then the percentage is written as,

[tex]P = (65 \div 140) \times 100[/tex]

[tex]P=0.46428 \times 100[/tex]

[tex]P=46.428\%[/tex]

The percentage of 65 out of 140 will be 46.428%.

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Class imbalance is a common problem in logistic regression analysis, where one class of data significantly outnumbers the other.

Class imbalance can be problematic because it leads to an over-representation of one class and an under-representation of the other, which can bias the model’s prediction towards the more frequently occurring class.

Class imbalance can cause the model to focus on optimizing accuracy by predicting the majority class more often than the minority class, leading to an underestimation of the minority class. It can also reduce the model’s ability to capture the nuances of the data that can be associated with the minority class. To address this, techniques such as oversampling, undersampling, and cost-sensitive learning can be employed to balance the data and improve model performance.

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Answer:

Choice B:  distance from home to library is length of HL

HL = 75      see calculations below

Step-by-step explanation:

use points (0,0) and (2.1, 7.2) to find HL:

HL = √(2.1 - 0)² + (7.2 - 0)² = √4.4 + 51.8 = √56.25 = 7.5

Step-by-step explanation:

Well, since this is a 45, 45, 90 triangle, it means that the given side and y have the same length.

Y = 1.5sqrt(2)

this means that X, the hypotenuse is equal to 1.5sqrt(2)^2 + 1.5sqrt(2)^2 = X^2

X is equal to 2.44948974278

The probability that a randomly selected firm will earn less than 73 million dollars is 0.9842.

The mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars, we need to find the probability that a randomly selected firm will earn less than 73 million dollars.

We can assume that the income distribution of firms is normal. Therefore, we can use the z-score formula to find the required probability.

We have, z = (X - μ) / σ, where X is the income of the firm, μ is the mean income, and σ is the standard deviation.

z = (73 - 45) / 13

z = 2.15

Using the z-table, we can find the area under the standard normal curve to the left of z = 2.15.

The area to the left of Z-score of 2.15 is 0.984, the probability that a randomly selected firm will earn less than 73 million dollars is 0.9842

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The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]

To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula

CI = X ± Zα/2 (σ/√n)

where

X = sample mean = 35.8

Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.

σ = sample standard deviation = 2.5

n = sample size = 40

Substituting these values into the formula, we get

CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].

Therefore, the correct option is (a) [34.7296, 36.8704]

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