5. Write the following Arithmetic Sequence using an Explicit Formula: a₁ = 8, an = an-1-2
an = 8+2(n-1)
an=8-2(n-1)
an=2-8(n-1)
an=2+8(n-1)

Using the FOIL method, the products are:

1.  x² + 6x - 16

2. x² - 6x - 72

3. x² + 13x + 36

4. x² + 8x + 12

5. x² + 15x + 54

6. x² + x - 20

7. x² - 9

8. x² + 20x + 100

9. x² + 9x - 36

10. x² + x - 12

11. x² + 7x + 10

12. x² - 7x + 12

The FOIL method is an acronym that stands for "First, Outside, Inside, and Last". This method simply describes the order you use in multiplying the terms of a given expression, that is, you have to multiply first terms, then outside terms, then inside terms, then last terms. The final step is to combine like terms together to arrive at your final answer.

Therefore, using the FOIL method, we have the following products:

1.  (x - 2)(x + 8)

x² + 8x -2x - 16

Combine like terms

x² + 6x - 16

2. (x + 6)(x - 12)

x² - 12x + 6x - 72

Combine like terms

x² - 6x - 72

3. (x + 9)(x + 4)

x² + 4x + 9x + 36

x² + 13x + 36

4. (x + 6)(x + 2)

x² + 2x + 6x + 12

Combine like terms

x² + 8x + 12

5. (x + 6)(x + 9)

x² + 9x + 6x + 54

Combine like terms

x² + 15x + 54

6. (x - 4)(x + 5)

x² + 5x - 4x - 20

x² + x - 20

7. (x + 3)(x - 3)

x² - 3x + 3x - 9

x² - 9

8. (x + 10)(x + 10)

x² + 10x + 10x + 100

x² + 20x + 100

9. (x - 3)(x + 12)

x² + 12x - 3x - 36

x² + 9x - 36

10. (x + 4)(x - 3)

x² - 3x + 4x - 12

x² + x - 12

11. (x + 5)(x + 2)

x² + 2x + 5x + 10

x² + 7x + 10

12. (x - 3)(x - 4)

x² - 4x - 3x + 12

x² - 7x + 12

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The solutions to the quadratic equation 8x² - 3x = 5 are x = 1 and x = -5/8

From the question, we have the following parameters that can be used in our computation:

8 x squared - 3 x = 5

Express properly

So, we have

8x² - 3x = 5

This gives

8x² - 3x - 5 = 0

The quadratic formula is represented as

x = (-b ± √[b² - 4ac])/2a

Substitute the known values in the above equation, so, we have the following representation

x = (3 ± √[(-3)² - 4 * 8 * -5])/(2 * 8)

Evaluate

x = (3 ± √169)/16

So, we have

x = (3 ± 13)/16

Expand

x = (3 + 13)/16 and x = (3- 13)/16

Evaluate

x = 1 and x = -5/8

Hence, the solution is x = 1 and x = -5/8

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On the 19th day, the lily pad covered half the pond.

The reason behind this is, If the lily pad doubles in size every day, then on the 20th day it will be twice as large as it was on the 19th day. That means it was already covering half the pond on the 19th day.

In this puzzle, the water lily is described as doubling in size every day. This means that on the first day, the lily pad is small, but by the second day, it has doubled in size. On the third day, it doubled in size again, and so on. By the 20th day, the lily pad has grown so large that it covers the entire pond.

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By solving the system of equation, length of flag = 1290ft and width = 1030 ft.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.

The substitution method is a technique for solving a system of equations, which is a set of two or more equations that contain multiple variables. The goal of the substitution method is to find the values of the variables that make all of the equations in the system true simultaneously.

To solve a system of equations using the substitution method, you follow these steps:

Identify one of the equations that contains only one variable.

Solve that equation for that variable.

Substitute the expression you found for the variable into the other equation(s) in the system.

Solve the resulting equation(s) for the remaining variable(s).

Substitute the values you found for the variables back into one of the original equations to check your solutions.

To find the width and length of the flag, we can set up the following system of equations:

width + length = 2,320

length = width + 260

We can solve this system of equations by substitution. First, we can solve for width in the second equation by subtracting 260 from both sides:

length - 260 = width

Then, we can substitute this expression for width into the first equation:

(length - 260) + length = 2,320

2 * length - 260 = 2,320

2 * length = 2,580

length = 1,290

Now that we know the value of length, we can substitute it back into the second equation to find the value of width:

length = width + 260

1,290 = width + 260

width = 1,030

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This ratio is used to compare the variances of the two samples and determine if they are statistically equal.

The test for the equality of two population variances is a statistical test used to determine whether or not the variances of two populations are equal. This test is based on the ratio of the two sample variances, which is calculated by dividing the difference between the two sample variances by the difference between the two sample means. This ratio is then compared to the value of a critical statistic to determine whether or not the two population variances are statistically equal. If the ratio is greater than or equal to the critical statistic, then the two population variances are considered equal. If the ratio is less than the critical statistic, then the two population variances are considered unequal. This test is useful for determining if the two populations have similar amounts of variation or if one population has more variation than the other.

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By applying the concept of algebra, it can be concluded that the two cost plans will be the same after 125 minutes.

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve a mathematical problem. In everyday life, algebra is often used for financial planning, plan or scheme comparison, and so on.

In the given problem, we are asked to compare the two calling plans.

Let's say the total cost for the first plan is P1, then:

P1 = monthly fee + total cost per minute

   = 20 + (0.08 x number of minutes)

The total cost for the second plan is P2, then:

P2 = monthly fee + total cost per minute

    = 25 + (0.04 x number of minutes)

Let's say the two total costs become equal after x minutes, then we can equate the two expressions given above as follows:

   20 + 0.08x = 25 + 0.04x

0.08x - 0.04x = 25 - 20

            0.04x = 5

                    x = 5 : 0.04

                       = 125 minutes

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The relation that is displayed by the given table is: B. {(1,2), (3,4), (5,6), (8,7)}

A relation can be described as a set of ordered pairs which contain one object from each sets, of which one pair is represented as (x, y). So, in a table, a relation can be represented by having all the set of x-values one column, and their corresponding y-values on another column.

Given the table below:

x   |  y

1      2

8     7

5     6

3     4

We can list out the set of ordered pairs as follows:

(1, 2), (8, 7), (5, 6), and (3, 4).

Ordering the pairs of values, we would have the following relation of the table, which is expressed as: B. {(1,2), (3,4), (5,6), (8,7)}

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Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.

Scalene-Triangle-1

In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.

One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°

the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on

Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.

Examples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.

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Answer:

D. [tex]y=\dfrac{-2}{3}x + 2[/tex]

Step-by-step explanation:

All of these answer choices are in slope intercept form:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the line's slope and [tex]b[/tex] is its y-intercept.

First, we'll find the line's slope using the points [tex](-3,4)[/tex] and [tex](0, 2)[/tex].

[tex]m=\dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{2-4}{0-(-3)} = \dfrac{-2}{3}[/tex]

Then, plug that [tex]m[/tex]-value into the slope intercept form equation:

[tex]y = \dfrac{-3}{2} + b[/tex]

Next, find the y-value at which the line crosses the y-axis:

[tex]b=2[/tex]

Finally, plug that [tex]b[/tex]-value into the slope intercept form equation and look at which answer choice the equation we solved for matches.

D. [tex]y=\dfrac{-2}{3}x + 2[/tex]

Answer:

angle 3 = 44 degrees

angle 2 = 136 degrees

angle 4 = 136 degrees

Step-by-step explanation:

angle 2 = angle 4

angle 1 = angle 3

angle 1 + angle 2 = 180 degrees

angle 3 +  angle 4 = 180 degrees

Answer: B. 6

Step-by-step explanation:

I think 6 because it says seven liked football and 10 liked basketball, so 1 didn't pick.

We also know that 5 like both and 1 didn't pick, so 1 + 5 = 6 students

The value of u.v is 32.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.

Given are two vectors, u = ⟨2, –8⟩ and v = ⟨8, –2⟩,

We know, x.y = x₁.x₂+y₁+y₂

Therefore, u.v = 2×8+(-2)(-8)

= 16+16

= 32

Hence, The value of u.v is 32.

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In a lottery game, if a player picks 6 numbers then the total 9366819 different choices player have if order doesn't matter.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, regardless of the order of selection. Formula is

ⁿCᵣ = n! /r!(n-r)!

where n is total number of objects

r is total number of choosing objects

We have given that,

In a lottery game total number = 46 = { 1,2,...., 46}

A player can pick total number = 6 numbers

We have to calculate different choices does the player have if order doesn't matter.

Using Combination formula,

we have , n = 46 , r = 6

⁴⁶C₆ = 46!/6!(40!)

=> ⁴⁶C₆ = 46×45×44×43×42×41×40!/40!(6!)

= 46×45×44×43×42×41 /(6×5×4×3×2×1)

= 23×3×7×11×43×41

= 9366819

Hence, the required ways are 9366819..

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The total number of possibilities for matching up players, assuming that in each game it does matter who has the white pieces, is 670442572800.

A permutation is a mathematical way of an arrangement of objects in a particular way or order. We have, there is total 20 people at chess club on a particular day. Now, these 20 people divided into two groups each find opponents and start playing. There are 10 games in total. Let's say the first player in line plays with the white pieces in the first game. The second person in line plays with the black pieces in the first game. The third person plays with the white pieces in game two. The fourth person plays with the black pieces in game two, and so on. There are 20 of them! ways to do it. But we have to remember that the order of the games doesn't matter, so we have to divide this number by 10! , i.e, number of game permutations . Therefore, the total number of possible arrangement is,

20!/10! = 20×19×---×10!/10! = 20× 19×--× 11

= 670442572800.

Hence, required possibilities is 670442572800.

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Complete question:

There are 20 people at a chess club on a certain day. They each find opponents and start playing. How many possibilities are there for how they are matched up, assuming that in each game it does matter who has the white pieces (in a chess game, one player has the white pieces and the other player has the black pieces)?

Answer:

There are several equations or inequalities that could describe this situation. Here are a few examples:

- The total number of plants cannot exceed 60: c + t ≤ 60

- The total number of plants must be at least 60: c + t ≥ 60

- The total amount of growing space must not exceed 300 square feet: 6c + 4t ≤ 300

- The total amount of growing space must be at least 300 square feet: 6c + 4t ≥ 300

Step-by-step explanation:

Any equation or inequality that accurately represents the given constraints on the number and types of plants, and the amount of growing space available, could be used to describe this situation.

Answer:

L = 12ft

W = 13ft

Step-by-step explanation:

Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).

The length and width are consecutive integers

L+1=W

The area of the rectangle is 156 square feet.

L*W=156

We know that W=L+1 from our first equation, so substituting that information into our second equation we get

L*(L+1)=156

Let's distribute that L

L^2 + L = 156

and subtract 156 from both sides

L^2 + L - 156 = 0

Now we can use the quadratic formula to find L. L cannot be negative, so

L = 12

using our very first equation we know L, so we can solve for W.

L+1=W

12+1=W

W = 13

We will discover that the probability that you will at random wind up with an orange hat is as follows: P = 1/12

Observe how we arrived at that now:

4 pieces of clothing (shirt, pants, socks, or hat)

three hues (purple, blue, or orange)

The color of only one item of clothing will change. The likelihood that you will receive an orange hat is what we are looking for.

We must first determine the likelihood that you will choose a hat at random. The likelihood of picking your hat at random is if all the apparel has the same probability of being chosen, just one more than the number of options (4). p = 1/4

The color is now chosen at random using the same methodology as before, with the likelihood that orange will be chosen at random being: q = 1/3.

When we multiply the individual probabilities by the joint probability, we obtain:

P = q*p = (1/4)*(1/3) = 1/12

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The price of the winter coats is going to be $17.325.

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price.

given,

Marked Price of winter coats = $57.75 and  discount = 70%

Discount = 70%

57.75 × 70/100

5.775 × 7

40.425

Selling Price = M.P - Discount

57.750 - 40.425

17.325

therefore ,

The price of the winter coats is going to be $17.325.

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27  is the percentile score of 71 on this test score and 71 is the score of victor.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula.

[tex]R_{100} =\frac{100(N < )+\frac{1}{2}N }{N}[/tex]

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60 th percentile.

[tex]R_{100} =\frac{100(N < )+\frac{1}{2}N }{N}[/tex]

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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Answer:  The correct answer is x = 19 / 5

Step-by-step explanation:

Solve the equation

5x + 3 = 22

Subtract 3 from both sides

5x + 3 − 3 = 22 − 3

5x = 19

Divide both sides by 5

5x/5 = 19/5

x = 19 / 5

In one well-developed paragraph with a topic sentence and supporting details, compare and contrast the experience of reading "The Highwayman" with listening to it. Explain, using examples from the text, how hearing the poem read aloud changes or increases your understanding of a poem.

The value of the account to the nearest dollar in 2007 is $6,929.76

We should know that value is the amount left in an account at a particular time

The  given parameters are

In 1990 the value is = $4,800.

In 1998,  the value is =$6,300

From 1990 to 1998 there are 8 years

Increase in the investment

Using simple interest,

SI= (P*T*R)÷100

Applying the figures in the formula

1500=(4800*8*R)÷100

⇒ 15000=30400R

Making R the subject we have

R= 4.93%

⇒ 4.93% of 4800 *9 = $2129.76

Add initial cost of investment and the interest for 9 years

=$(4800+2129.76)

=$6929.73

In conclusion,  the value of the account would on the $6929.76

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Answer: 114 red marbles

Step-by-step explanation:

We know that for every 20 marbles, there are 19 red and 1 black marble.

So to get from 20 to 120, we multiply by 6. So we take 19 times 6 = 114 red marbles and 6 black marbles,

Answer:

y-int. is (0,7) and slope is 2/3

just repeat the points 3 times

If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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To the nearest of tenth hour kwan has driven total 234 miles.

Speed is the pace at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Speed= distance/time

Based on his speed and the distance driven within that time, Kwan will have driven 234 miles

First find out Kwan's speed per hour:

Speed = Distance / Time

Convert the time to decimals:

= 1 + 1/10 hours

= 1 + 0.1

= 1.1 hours

Speed:

= 234 / 1.1

= 212 miles per hour

In tenth of an hours therefore, Kwan would have gone:

= 212*1.1 hours

= 234 miles

Therefore,Kwan would have driven 234 miles.

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Answer:he drives 234 in 1.1 miles

Step-by-step explanation:

i jus know

324 miles can Mario drive with 9 gallons of gas.

The term "proportional" refers to any connection where the ratio and amount fluctuate directly with one another.

As per the details share in the above question we get,

The data are as follow,

Mario has a driving range of 18 miles  ½ gallon of gas.

Here we have to find how many miles can mario drive with 9 gallons of gas.

Thus we know that,

He can travel 18 miles on just half a gallon of fuel.

Let x be the amount of miles that 9 gallons of gas will cover.

Thus, if we use the notion of proportion, we obtain

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Mario can travel 324 miles on 9 gallons of gas.

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The division represented by the model is:

B:1/6÷2

First, we can see a square that is divided into 6 strips, and one of these strips (actually half of it) is shaded, so we can start by writing:

1/6

Now, notice that only half of the strip is shaded, so we need to divide again by 2, then we will get the division:

(1/6)/2

That is the division represented by the model. So the correct option is B

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Answer:

22

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −22 and 0 is 22 .