the slope of the line shown between the points (-8, 4) and (-4, 0) is equal to its slope between the points (-2, -2) and (5, -9).

The recursive rule for this sequence is given as follows;a(n) = -3a(n-1)

Recursive rule for the following sequence: 5, -15, 45, -135, . . . :This sequence is formed by multiplying each term by -3 to get to the next term. That is 5 x (-3) = -15 and -15 x (-3) = 45.The first term of the sequence is 5.

The recursive rule for this sequence is given as follows;a(n) = -3a(n-1)

where n is the position of the term, a(1) = 5 and -3 is the common ratio. Therefore, the next term in the sequence can be generated by multiplying the previous term by -3.In a recursive rule, we define a sequence of numbers such that the rule is applied to a term to produce the next term until we get the desired term of the sequence.

The recursive rule for a sequence is a formula that specifies the nth term in a sequence based on the previous term. This is a linear recursive rule because the sequence is multiplied by a constant in order to generate the next term.

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"Problem Solving/Data Analysis," "Heart of Algebra," and "Passport to Advanced Mathematics" are additional topics in math that are commonly found in standardized tests such as the SAT.

These topics are often included in math sections of standardized tests to assess students' problem-solving skills, data analysis abilities, algebraic reasoning, and advanced mathematical concepts.

Problem Solving/Data Analysis: This topic focuses on real-world scenarios where students are required to analyze data, interpret graphs and charts, apply mathematical concepts to solve problems, and make inferences based on given information.

Heart of Algebra: This topic emphasizes algebraic skills, including linear equations and inequalities, systems of linear equations, functions, and graphing. It involves solving equations, manipulating algebraic expressions, and understanding the fundamental concepts of algebra.

Passport to Advanced Mathematics: This topic builds upon the foundational algebraic skills and introduces more advanced mathematical concepts. It includes topics such as quadratic equations, exponential and logarithmic functions, polynomials, rational expressions, and complex numbers.

These topics are essential for developing strong mathematical problem-solving abilities and are often covered in high school math courses and tested in standardized exams.

"Problem Solving/Data Analysis," "Heart of Algebra," and "Passport to Advanced Mathematics" are additional topics in math that are frequently encountered in standardized tests, and mastering these topics is crucial for success in math assessments and beyond.

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Miami gets 6.12 more inches of rain.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The average rainfall in inches in Miami from January to May is 1.61, 2.24, 2.99, 3.15, 5.35, and 9.68

While it is 2.24, 2.8, 3.03, 2.05, 2.09, and 6.69 during the same period in Tampa.

Hence, For Miami;

= 1.61 + 2.24 + 2.99 + 3.15 + 5.35 +9.68

= 25.02

For Tampa;

= 2.24 + 2.8 + 3.03 + 2.05 + 2.09 + 6.69

= 18.90

Thus, Find difference as;

= 25.02 - 18.90

= 6.12

Therefore, Miami gets 6.12 more inches of rain.

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Your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

To show that your viewing angle α is determined by the length of the blackboard and its distance from the wall, we can use geometry and trigonometry.

Let's consider a right triangle formed by your line of sight, the distance from the wall to the blackboard, and the length of the blackboard.

The adjacent side of the triangle is the distance from the wall to the blackboard, which is 5 ft. The opposite side is half the length of the blackboard since you are looking at the midpoint of the blackboard. Therefore, the opposite side is (11 ft)/2 = 5.5 ft.

We can use the tangent function to calculate the viewing angle α:

tan(α) = opposite/adjacent

tan(α) = (5.5 ft)/(5 ft)

tan(α) = 1.1

To find α, take the arctan (inverse tangent) of both sides:

α = arctan(1.1)

Using a calculator, we find that α ≈ 46.34 degrees.

Therefore, your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

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Absorption costing net income is calculated by subtracting selling and administrative expenses from gross profit.

By subtracting the selling and administrative expenses from the gross profit, we arrive at the absorption costing net income. This net income figure reflects the overall profitability of the company, considering both the operational costs of production and the expenses associated with selling and administration.

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The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

Given,

In the question:

Your grandmother is 87 years old and she has remarked to you that nearly all of her friends are women. She told you that it is rare to see a man older than age 85. She is correct because, after age 85, for every 100 men, there are __________.

Now, According to the question:

Your grandmother is 87 years old and she told you that all of her friends are women. There is no single man in her circle of friends. She also told that it is rare to see a man over the age of 85. It is because of the fact that women are more in number than man above the age of 85 and this ratio is like 100 men per 200 women, which means the chances of getting a male friend is almost half after the age of 85. So women are more in number than men.

Hence, The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

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Answer:

27 and 597

Step-by-step explanation:

To evaluate A5 and A100, substitute n = 5, n = 100 into An , that is

A5 = 6(5) - 3 = 30 - 3 = 27

A100 = 6(100) - 3 = 600 - 3 = 597

Answer:

5n=6n-3

C.L.T

6n-5n=3

n=3

ii.100n=6n-3

C.L.T

100n-6n= -3

94n/94=-3/94

n=-0.032

For the given systems of equations, we have that:

17. The solution is: x = 3, y = 4.

18. The company can afford to promote 2 engineers to level II.

19. The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For item 17, the system is:

Adding the equations, we can eliminate y and solve for x, hence:

7x = 21

x = 3.

Then the solution for y is given as follows:

3x + 2y = 17

3(3) + 2y = 17

2y = 8

y = 4.

For item 18, the variables are given as follows:

The company has 8 engineers, hence:

x + y = 8 -> x = 8 - y.

The company can afford to pay a total of $472,000 to the engineers, hence, considering the salaries(in thousands of dollars) of each:

56x + 68y = 472.

We want to solve for y, hence, since x = 8 - y:

56x + 68y = 472.

56(8 - y) + 68y = 472.

12y = 24.

y = 2.

The company can afford to promote 2 engineers to level II.

The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

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Answer:

This is my other account. I just needed 1+ answers togive brainliest for the other person. dont mind this

Step-by-step explanation:

Answer:

hundredths

Step-by-step explanation:

As per questions,

\( \frac{1}{9} \times \frac{3}{4} \)

As 3 and 9 can be cancelled, we get,

\( \frac{1}{3} \times \frac{1}{4} \)

Now multiplying denominators and numerators,

\( \frac{1}{12} \)

Hence, the required answer is \( \frac{1}{12} \)

\( \frac{ \frac{5}{7} }{ \frac{2}{3} } \)

When the base denominator (2/3) is reciprocaled,

\( \frac{5}{7} \times \frac{3}{2} \)

As we can't directly divide, so we can multiply them,

\( \frac{5 \times 3}{7 \times 2} \)

\(→ \frac{15}{14} \)

Hence, the required answer is \( \frac{15}{14} \)

\(7.89 - 3.9\)

Direct subtraction, (Check solution in attached image)

\(→3.99\)

Answer:

I probably think the qns is no A

Answer:

A

Step-by-step explanation:

The value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.

The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.

The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.

Let b be the number of days a busy student puts off doing laundry.

The given information is tabulated as below:

Days(b)                      1              2

Probability, p(b)       2/3          1/3

The expected time is given as,

E(b)=∑i=1ᵇp(b)

=(1×(2/3))+(2×(1/3))

=4/3

=1.3333

Therefore, the value of ex(b):

1.3333 day ≈ 1 day

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Answer:

x≤−6 or x≥−4

Step-by-step explanation:

We need to graph the inequality \(x^2+10x\ge -24\)

We can find the solution of the graph as follows :

\(x^2+10x+24\ge 0\\\\x^2+6x+4x+24\ge 0\\\\x(x+6)+4(x+6)\ge 0\\\\(x+4)(x+6)\ge 0\\\\x\le -6\ \text{and}\ x\ge -4\)

The attached figure shows the graph for the given inequality.

Answer:

Step-by-step explanation:

Work:

Hence, an African Elephant is about 80000000 times larger than the bee.

Hoped this helped.

\(BrainiacUser1357\)

In a linear time-invariant system, the zero-state response (ZSR) is the output of the system when the input is zero, assuming all initial conditions (such as initial voltage or current) are also zero.

(a) For H1(s) = 1, the zero-state response Yzs(s) is simply the product of the transfer function H1(s) and the input Ei(s):

Yzs(s) = H1(s) * Ei(s) = (45+2)

To find the time-domain zero-state response yzs(t), we need to take the inverse Laplace transform of Yzs(s):

yzs(t) = L^-1{Yzs(s)} = L^-1{(45+2)} = 45δ(t) + 2δ(t)

where δ(t) is the Dirac delta function.

(b) For H2(s) = 45+1, the zero-state response Yzs(s) is again the product of the transfer function H2(s) and the input E2(s):

Yzs(s) = H2(s) * E2(s) = (45+1)E2(s)

To find the time-domain zero-state response yzs(t), we need to take the inverse Laplace transform of Yzs(s):

yzs(t) = L^-1{Yzs(s)} = L^-1{(45+1)E2(s)} = (45+1)e^(t/2)u(t)

where u(t) is the unit step function.

(c) For H3(s) = ns, the zero-state response Yzs(s) is given by:

Yzs(s) = H3(s) * E3(s) = ns * 542

To find the time-domain zero-state response yzs(t), we need to take the inverse Laplace transform of Yzs(s):

yzs(t) = L^-1{Yzs(s)} = L^-1{ns * 542} = 542L^-1{ns}

Using the inverse Laplace transform from problem 1, we have:

yzs(t) = 542 δ'(t) = -542 δ(t)

where δ'(t) is the derivative of the Dirac delta function.

(d) For H4(s) = 2e^(-4s) / (s+3)(4s+1), the zero-state response Yzs(s) is given by:

Yzs(s) = H4(s) * E4(s) = (2e^(-4s) / (s+3)(4s+1)) * (1/(s+3))

Simplifying the expression, we have:

Yzs(s) = (2e^(-4s) / (4s+1))

To find the time-domain zero-state response yzs(t), we need to take the inverse Laplace transform of Yzs(s):

yzs(t) = L^-1{Yzs(s)} = L^-1{(2e^(-4s) / (4s+1))}

Using partial fraction decomposition and the inverse Laplace transform from problem 1, we have:

yzs(t) = L^-1{(2e^(-4s) / (4s+1))} = 0.5e^(-t/4) - 0.5e^(-3t)

Therefore, the zero-state response for each of the four LTIC systems is:

(a) Yzs(s) = (45+2), yzs(t) = 45δ(t) + 2δ(t)

(b) Yzs(s) = (45+1)E2(s), yzs(t) = (45+1)e^(t/2)u(t)

(c) Yzs(s) = ns * 542, yzs(t) = -542 δ(t)

(d) Yzs(s) = (2e^(-4s) /

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A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

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The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

Answer:

4 chairs for every table.

Step-by-step explanation:

Write a ratio:

12 chairs : 3 tables = 4 chairs : 1 table

4 chairs for every table.

There are 4 chairs for every table is equivalent to the given sentence " 12 chairs for every 3 tables"

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The given statement is "12 chairs for every 3 tables"

According to the given question, translate the phrase into an algebraic form :

We can write a proportion as

12 chairs : 3 tables = 4 chairs : 1 table

12 / 3 = 4 / 1

This means 4 chairs for every table.

Therefore, there are 4 chairs for every table is equivalent to the given sentence " 12 chairs for every 3 tables"

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The polar coordinates of the point (6, 6) are approximately (8.49, 0.79) in radians.

To convert the point (6, 6) from Cartesian to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y/x)

Given that the point is (6, 6), we can substitute the values into the formulas to find the polar coordinates.

r = √(6² + 6²) = √(36 + 36) = √72 ≈ 8.49

θ = arctan(6/6) = arctan(1) = π/4 ≈ 0.79 (radians)

In polar coordinates, the value of r represents the distance from the origin (0, 0) to the point, and the value of θ represents the angle (measured in radians) between the positive x-axis and the line connecting the origin to the point. The angle θ is usually measured counterclockwise from the positive x-axis.

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Complete question is:

Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.

(6,6)

The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Answer:

x = 14

Step-by-step explanation:

Add 10 to both sides.

x− 10 + 10 = 4 + 10

x=14

The probability of having a 5-card hand that is a flush or royal flush is 0.00196

Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Flush, straight flush, and royal flush probabilities are calculated as follows: 5148/2598960≅0.00198

A flush's likelihood (while eliminating straight and royal flushes) is 5108/2598960, ≅0.00196.

Finding the fraction with the number of ways to have a flush as the numerator and the number of possible five-card hands as the denominator will allow us to determine the likelihood.

Combinations will be used to find each of these numbers (we don't care about the draw order; only about what shows up in our hand). Combinations' general formula is Cn,k=n!/(k)!(n-k)! with k=picks and n=population

Let's first determine the denominator by selecting 5 cards at random from a deck of 52 cards: C52,5=52!/(5)!(525)!

=52!/(5!)(47!)

Let's assess it!

52×51×50^10×49×48^2×47!/5×4×3×2×47!=52×51×10×49×2=2,598,960

Let's now determine the numerator.

In order to examine each hand with five cards of the same suit, we will compute all hands that feature a flush (including straight flushes, royal flushes, and flushes) (with a suit having 13 cards in total). We can say that we understand this by:

C13,5

Remember that there are 4 suites in which this might occur, but we only want 1, so multiply by C4,1. Putting it all together, we obtain:

C4,1×C13,5=4!/(1!)(4−1)!×13!/(5!)(13−5)!=4!13!/3!5!8!

Let's assess this.

4!×13×12×11×10×9^3×8!/3×2×5×4!×8!=13×12×11×3=5148

(Remember that we just calculated all hands, including straight flushes and royal flushes, that have a flush component to them!

The probability of getting a hand with a flush is:

5148/2598960≅.00198

We may exclude straight and royal flush possibilities from the 5148 flush hands by excluding those hands (which are hands with 5 consecutive value cards in the same suit, such as 3, 4, 5, 6, and 7 of hearts). Since there are four suits and 10 potential ways to get a straight (A-5, 2-6, 3-7,..., 10-A), we can subtract 4 from 5148 to get 5108 hands, which gives us the result 5108/2598960=0.00196.

The probability of having a 5-card hand that is a flush or royal flush is 0.00196

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So, x must be an odd multiple of 1/2 in a triangle. The largest odd possible value of x in multiple of 1/2 and less than 50 is 4x + 2 .

Therefore, the largest possible value of x is 49/2. we know that 4x + 2 is even since 2 is even and 4x is even for any integer x. Therefore, x must be a multiple of 1/2 for 4x + 2 to be an integer.

Here we can set up the following equations:

PR = 2PQ + 12

QR = 4PQ + 2

Substituting PQ = x into these equations, we get:

PR = 2x + 12

QR = 4x + 2

For the triangle to have integer side lengths, PR, PQ, and QR must all be integers.

We know that 2x + 12 is even since 12 is even and 2x is even for any integer x.

Therefore, x must be odd for 2x + 12 to be an integer.

Similarly, we know that 4x + 2 is even since 2 is even and 4x is even for any integer x.

Therefore, x must be a multiple of 1/2 for 4x + 2 to be an integer.( from figure we get 4x+2).

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Correct Question:

In the given figure, PR is 12 more than twice PQ, and QR is two more than four times PQ. If all three sides of the triangle have integer lengths, what is the largest possible value of x?

Answer: -x^2 +4x -2

Step-by-step explanation:

5x+2(3x-1)

Use that

x(x+7)

minus the use that equation by this one and get the answer

Answer:

6/7

Step-by-step explanation:

\( \sf3 \times \frac{2}{7} = \)

\( \sf = \frac{(3 \times 2)}{7} \)

\( \sf = \frac{6}{7} \)

Moga membantu..

The x-coordinate of the vertex is 0.  the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

To find the dimensions that will create the maximum area of the prop section, we need to analyze the given equation A = -x^2 + 40. The equation represents a quadratic function in the form of A = -x^2 + 40., where A represents the area of the prop section and x represents the dimension.

The quadratic function is in the form of a downward-opening parabola since the coefficient of is negative (-1 in this case). The vertex of the parabola represents the maximum point on the graph, which corresponds to the maximum area of the prop section.

To determine the x-coordinate of the vertex, we can use the formula x = -b / (2a), where the quadratic equation is in the form Ax^2 + Bx + C and a, b, and c are the coefficients. In this case, the equation is -x^2 + 40, so a = -1 and b = 0. Plugging these values into the formula, we get x = 0 / (-2 * -1) = 0.

Therefore, the x-coordinate of the vertex is 0. To find the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation  A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

Hence, the equation that reveals the dimensions that will create the maximum area of the prop section is A = 40. This means that regardless of the dimension x, the area of the prop section will be maximized at 40 units.

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Answer:

124.8

Step-by-step explanation:

Answer: $130

Step-by-step explanation:

60% = 78

1% = 78/ 60

100% = 78/60 ×100

Discount is 40% = $52

A general formula to describe is F = 1.6×d² will be correct answer.

A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.

Finding the general formula we obtain:

F=kd²

40=k×5²

k=1.6

so, F =1.6×d².

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Given:

Susie's dog is 2 feet tall. When she measures her dog in inches he was 24 inches.

To find:

Why is there an increase in inches.

Solution:

It is given that Susie's dog is 2 feet tall.

We know that,

1 feet = 12 inches

Using this conversion, we get

2 feet = 2×12 inches

2 feet = 24 inches

So, the measures 2 feet and 24 inches are equal.

Therefore, if Susie's dog is 2 feet tall then he is 24 inches tall because both of these measure are equal.