Solve each system of equations algebraically. y=x + 15, y= 2x

The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

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(a) The probability that the series will last exactly m games is:(1 - (pA + pB))^m(pA (1 - pB) + pB (1 - pA))where pA and pB are the probabilities of teams A and B, respectively. Therefore, the probability that the series will last less than 5 games is the probability that the series will last exactly 3 games or exactly 4 games:1 - (1 - 0.6 * 0.4)^3 - (1 - 0.6 * 0.4)^4 ≈ 0.684.

The probability that the series will last 5 games is the probability that the first four games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 4 ≈ 0.055.The probability that the series will last 6 games is the probability that the first five games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 5 ≈ 0.077The probability that the series will last 7 games is the probability that the first six games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 6 ≈ 0.091.

The expected number of games played is thus approximately:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + ∑m=8^∞ (1 - (pA + pB))^m(m + 1)(pA (1 - pB) + pB (1 - pA))The sum above can be computed by expressing it as the product of three factors:1 - (pA + pB) is a common factor for all terms, (pA (1 - pB) + pB (1 - pA)) is a sum of two terms that can be replaced by 1 - (1 - pA)(1 - pB), and m + 1 is a sum of m and 1. After replacing the sum of two terms, we obtain:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + (1 - (0.6 + 0.4))^8(8 + 1)(1 - (1 - 0.6 * 0.4)^2) / (0.6 + 0.4 - 0.6 * 0.4) ≈ 0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + 0.02525 / 0.34 ≈ 5.43.

Therefore, the expected number of games played is approximately 5.43.(b) Given that Team B wins the first game, the series can last 7 or 8 games. The probability that the series will last 8 games is the probability that the first seven games have three wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 ≈ 0.013824.The probability that the series will last at least 8 games is therefore approximately 0.091 + 0.013824 = 0.104824, or 10.48%.Answer: (a) The expected number of games played is approximately 5.43. (b) The probability that the series will last at least 8 games is approximately 0.104824 or 10.48%.

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The company made a profit of $770

Profit is the difference between revenue and costs. In this scenario, the revenue from selling 110 selfie sticks is $10 × 110 = $1100.

Therefore, the costs of producing the same number of selfie sticks are

110 × $3 = $330

So, the profit that Gamboa, Inc. made is

$1100 - $330 = $770.

As we can see, based on the number of selfie sticks together with their production, we managed to obtain a profit of $770.

Hence, the company made a profit of $770.

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Answer:

The amount of money in the account increases by 3% every six months, or biannually.

To see why, we can break down the function f(t) = 2000(1.03)^(2t):

Since the interest is compounded biannually, the exponent of 2t indicates the number of six-month periods that have elapsed. For example, if t = 1, then 2t = 2, which means two six-month periods have elapsed (i.e., one year).

Each time 2t increases by 2, the base amount is multiplied by (1.03)^2, which represents the interest accrued over the two six-month periods.

Thus, the amount of money in the account increases by 3% every six months, or biannually.

As for the second part of the question, the amount of increase is not 2%, 3%, or 103%.

hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that

[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]

(a) False; A subspace is formed by the set of vectors that do not belong to the column space.

(b) True; If the matrix contains solely the zero vector, then it is the zero matrix.

(c) True; The column space of a particular matrix is equivalent to the column space of another specified matrix.

(d) False; The column space of one matrix is identical to the column space of another matrix.

(a) False; if A = [1 0; 0 0], then the column space of A is { e1 }, where e1 is the standard unit vector in the plane. If v is not in the column space of A, but w is not in the column space of A, then v + w is not in the column space of A.

Therefore, the set of vectors that are not in the column space of A does not form a subspace.

(b) True; if every vector in Rn is in the null space of A, then in particular, every standard unit vector is in the null space of A. Thus, the ith column of A is zero for i = 1, . . . , n, so A is the zero matrix.

(c) True; the column space of A is generated by the columns of A, while the column space of AB is generated by linear combinations of the columns of AB. By definition of matrix multiplication, the columns of AB are linear combinations of the columns of A, so the column space of AB is a subspace of the column space of A. Conversely, let b be in the column space of A. Then there is an x in Rm such that Ax = b. Thus, ABx = A(Bx), so b is in the column space of AB. Therefore, the column space of A is a subspace of the column space of AB. Hence the two column spaces are equal.

(d) False; if A = [1 0; 0 0] and B = [0 0; 0 1], then the column space of A is { e1 }, while the column space of B is { e2 }. The column space of AB is { 0 }, so it is not equal to either column space.

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Using the unitary method we calculate that the friend would be 20 miles closer in an hour.

If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:

5 miles / hour - (- 15 miles / hour) = 20 miles / hour

Also, we know that

speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,

20 miles/hour × 1 hour = 20 miles

Therefore, you would be 20 miles closer to each other after 1 hour.

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By answering the presented question, we may conclude that Sanderson amount Equipment Company owes $42,000 Galaxy Furniture Supply owes $13,360. $55,360 in total liabilities

aggregate attempting to determine the time required, total number or amount. The quantity at sight or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, or a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity signifies how much there still is, how often you have, the amount you require, or the amount that you get. He needs that quantity of cash to get by.

The following figures would appear on Dr. Ortiz's balance sheet:

Assets:

Cash: $31,000

$11,300 for dental supplies

$57,100 for dental equipment

$20,000 for office furnishings

The total value of the assets is $119,400.

Liabilities:

Sanderson Equipment Company owes $42,000

Galaxy Furniture Supply owes $13,360.

$55,360 in total liabilities

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The distribution of C) X+Y is a Poisson RV with parameter 9.

This is because the sum of two independent Poisson distributions with parameters λ1 and λ2 is also a Poisson distribution with parameter λ1 + λ2. Therefore, X+Y follows a Poisson distribution with parameter 4+5 = 9.

Option A is incorrect because an exponential distribution cannot arise from the sum of two Poisson distributions. Option B is also incorrect because the parameter of X+Y is not the average of the parameters of X and Y. Option C is the correct answer as explained above.

In summary, the distribution of X+Y is Poisson with parameter 9.

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Answer:

Another order pair could be (30,10).

Every y value is "one-third of" every x value.

The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.

We have, The sides of a triangle have lengths of 15, 20, and 25.

To find, The length of the shortest altitude of the triangle.

Steps to solve the problem:

Area = 1/2 * base * height

Area of the triangle = 1/2 * 20 * h ⇒ 10h

A = √(s(s-a)(s-b)(s-c))

Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.

According to the given problem, the sides of the triangle are 15, 20, and 25.

s = (a + b + c)/2

= (15 + 20 + 25)/2

= 30

Therefore, the area of the triangle can be calculated as:

A = √(30(30-15)(30-20)(30-25))

= √(30*15*10*5)

= 150 sq. units

Therefore, we can write the formula for the area of the triangle as:

150 = 10 h

h = 15 units

Therefore, the length of the shortest altitude of the triangle is 15 units.

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Answer:

34

Step-by-step explanation:

1/2 multiplied by 68=34

34 is 1 half of 68 .

Here, we have,

given that,

what is 1 half of 68

we know that,

Half of a number can be found by dividing the number by 2.

i.e. we have to find half of 68,

for that, we need to divide 68 by 2

so, we get,

To find half of 68:

68 / 2 = 34

Therefore, half of 68 is 34.

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The derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

Using the product rule of differentiation, we can find the derivative of the function f(x) = x⋅5x as follows:

f'(x) = (x)'(5x) + x(5x)'

where (x)' and (5x)' are the derivatives of x and 5x with respect to x, respectively.

(x)' = 1 (the derivative of x with respect to x is 1)

(5x)' = 5 (the derivative of 5x with respect to x is 5)

Substituting these values, we get:

f'(x) = 1⋅5x + x⋅5

Simplifying further, we get:

f'(x) = 5x + 5x

Therefore, f'(x) = 10x.

In conclusion, the derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

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If the null hypothesis is actually true, then there is a 5% chance that the researcher will end up accepting the alternative hypothesis in error, the statement is true.

If a hypothesis test is performed with a level of significance of 0.05 and the null hypothesis is actually true, then there is a 5% chance (or 0.05 probability) that the researcher will reject the null hypothesis and accept the alternative hypothesis in error.

This is known as a Type I error. The Type I error rate is determined by the level of significance of the test.

In other words, if the null hypothesis is true, but the researcher concludes that it is false (i.e., accepts the alternative hypothesis), this is an incorrect decision that is made with a probability of 0.05 or 5%, assuming a significance level of 0.05.

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In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.

The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.

Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.

Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.

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Regression lines can be used to visually represent the relationship between the independent( x) and dependent( y) variables on a chart. This is point C

Point C represents the residual of the circled point in Graph 1.

The regression line is occasionally called the" best-fit line" because it's the line that stylish fits through the points. This is the line that minimizes the gap between factual results and anticipated results.

There are two charts:

In graph 1, one point is circled.

The five points labeled A, B, C, D and E can be set up in Graph 2.

Find which point on path 2 represents the remainder of the circled point on path 1

Point C represents the remainder of the circled point in Graph 1

Question

fiber diameter and fleece weight data were collected from a sample of 20 lamb. The data is presented in the graphs below. The plot is a scatterplot of pile weight versus fiber periphery, with the corresponding least places regression line indicated. Map 2 is a identified plot of residuals versus prognosticated values. Map 1 chief Weight 35 40 30 Fiber Periphery Map 2 Fiber Periphery Map 2 Remaining chief Weight 1. D 7 8 9 10 11 12 Anticipated chief Weight 13 14 15 A point is filled in the map and the points marked with ABC are displayed in the map 2 which represents the graph the rest of the circled point on the graph? Peille coat weight In Diagram 1, one point is circled. Five points, labeled A, B, C, D, and E, are linked in map

2 Which point on Chart 2 is the residual for the circled point on Chart 1?

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The length of BC is approximately 3.5 cm

A triangle is described as a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

We construct triangle ABC, through the following steps:

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Mathematically shown as:

a/sin(A) = b/sin(B) = c/sin(C)

5/sin(95) = BC/sin(34)

BC = (5*sin(34))/sin(95)

BC ≈ 3.5cm

In conclusion, the length of BC is approximately 3.5 cm.

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On the first day of ticket sales for the school’s spring musical, 46 senior citizen tickets and 44 child tickets were sold, bringing the total number of tickets sold to 362.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

The second day saw a slightly lower number of tickets sold, with two senior citizen tickets and 25 child tickets purchased, for a total of 85. The price of a senior citizen ticket and a child ticket was likely the same on both days, and likely the same price as it is for the rest of the ticket sales.

The school likely has a set price for tickets, which would not change as the number goes up or down. It is common for schools to give discounts for senior citizens, so the price of their tickets is usually lower than the price of a child ticket. The school set the prices of the tickets in a way that would bring in the most money, while still being affordable for the community to attend.

The school likely had a plan in place for how many tickets they wanted to sell and what prices they wanted to set. They also likely had a goal of how much money they wanted to bring in from the ticket sales. After the two days of ticket sales, the school was able to see how many tickets were sold and how much money was collected. This can help the school to adjust their plan, if necessary, to reach their goal.

The money brought in from the ticket sales will likely help the school to cover the costs of putting on the musical. It may also help to pay for any other expenses associated with the production of the show. The school may also use the money to purchase new materials or supplies for the performing arts department.

Overall, the school was able to bring in a total of 447 from the two days of ticket sales. This money will help to ensure that the school’s spring musical is a success. The school was also able to offer discounted tickets to senior citizens, which allowed more people to attend the show.

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The price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

Jack's school is selling tickets to a spring Musical. On the first day of ticket sales, the school sold a total of 362 tickets, 46 of which were senior citizen tickets and 44 of which were child tickets. On the second day of ticket sales, the school sold two senior citizen tickets and 25 child tickets, for a total of 85 tickets.

To calculate the price of each ticket, we can divide the total amount taken in by the number of tickets sold. For senior citizen tickets, the total amount taken in was 85, and two were sold, so the price of a senior citizen ticket is 85/2 = 42.50. For child tickets, the total amount taken in was 85, and 25 were sold, so the price of a child ticket is 85/25 = 3.40.

In conclusion, the price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

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Answer: 2 solutions

Step-by-step explanation:

To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)

Setting them equal, we get (180n-360)/n = 1680.

Multiplying by n on both sides, we get 180n-360 = 1680n.

Solving, we get 1500n = 360.

n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.

The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.

Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.

Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.

The probability that both tests yield the same result is 7.7%.

Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-

0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-

[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]

hence, the probability of the two tests yield the same result is 7.7%.

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Answer:

Zeros: x = -10 and x = -3

Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Step-by-step explanation:

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

0 = -(x+3)(x+10)

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3

x+10=0

x = -10

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]

So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Answer:

aeqtq34t

Step-by-step explanation:

q34t35t134

The evaluation of the expression -0.25 + 0.3 - ( - 3/10 ) + 1/4 is 3 / 5.

An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Therefore, let's solve the expression as follows:

-0.25 + 0.3 - ( - 3/10 ) + 1/4

let's convert it to fraction

- 1 / 4 + 3 / 10 + 3 / 10 + 1 / 4

Hence,

3 / 10 + 3 / 10 +  1 / 4  - 1 / 4

3 + 3 / 10

6 / 10 = 3 / 5

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Answer:

2

Step-by-step explanation:

3(2)-1<8

6-1<8

5<8

if you go up to 3 as the whole number then the equation ends up 8<8, and the sign is less than (<) not less than or equal to.

So 2 would be the answer.

Answer: Gavin drank 2.25 quarts today.

Step-by-step explanation: First you need to find out how many quarts are in 8 ounces -the answer to that is 0.25. Then you will need to times that by 9.

The expected value of cases in which juries got the right decision is 150, and the variance is 375.

1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.

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Answer:

5:3 = 5/3

Step-by-step explanation:

Given Sin∅ = 3/5

We know sin∅ = Perpendicular/Hypotenuse

And, By inverse relationship, we get

cosec∅ = Hypotenuse/Perpendicular = 1/sin∅

So, csc∅ = 5/3, 5:3

The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

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