The table below represents the value, y, of an antique table x years after purchase.



The data was modeled with a linear best-fit function. What was the initial purchase price?

$5,625

$5,000

$625

$2,500

Answer54: A, 55: G, 56: D

Step-by-step explanation:

Answer:

54. 2cm

55. between 6 and 7

56. two irrational numbers

Step-by-step explanation:

The series n=0 to infinity \(2^{n}\) \(3^{n}\) /n! is (e) convergent by ratio test and its sum is e⁶.

The given series can be written as:

S = Σ(n=0 to ∞) (2ⁿ * 3ⁿ) / n!

In order to determine if the series is convergent, let's apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, this can be expressed as:

lim(n→∞) |(a(n+1) / an)| < 1

Taking the ratio of a(n+1) to an is 6 / (n+1)

Now, let's take the limit as n approaches infinity:

lim(n→∞) |(6 / (n+1))| = 0

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Answer:

"the product of n and 4 plus 7" would be the middle box

"the sum of 4 and the product of 7 and n" would be the third box

"the product of 7 and the sum of n and 4" would be the first box

Step-by-step explanation:

Answer:

2, 3, 4, 5, 6

Step-by-step explanation:

Let's break this inequality into two parts:

Solve Inequality I.

Add 1 to both sides.

Divide both sides by 3.

Solve Inequality II.

Subtract 2x from both sides.

Add 1 to both sides.

Combine these two inequality solutions.

Integer solutions to this inequality would be any integer between 1 (4/3 = 1.3...) and 7, exclusive.

These five numbers are 2, 3, 4, 5, 6.

Answer:

P = 12m

A = 6m^2

Step-by-step explanation:

Perimeter is the sum of all the lengths of a shape. The lengths of the triangle are given as 3m, 4m, and 5m, so to find the perimeter we just need to add them all together. 3+4+5=12, so the perimeter of the triangle is 12m.

The area of a triangle is found by multiplying its height by its base and then dividing the result by 2. The height of the triangle is not given, but the side lengths (3,4 and 5) indicate that the triangle is a right triangle. This means we can use the middle length as the height and the shortest length as the base.

So, the height of the triangle is 4m, and the base is 3m, so to calculate the area:

(3x4)/2=12/2=6m^2.

The area of the triangle is 6m^2.

Hope this helped!

30° is the angle of elevation from the base to the top of the mountain.

Trigonometric ratios are the ratios of the length of sides of a triangle.

These ratios in trigonometry state the relation between the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

Sin θ = Perpendicular / Hypotenuse

According to the question,

Perpendicular = Vertical height of Mountain. = 1290 m

Hypotenuse    = The distance from the top of the mountain to the base                               of the Mountain. = 2580 m

⇒ Sin θ = 1290/ 2580

⇒ Sin θ = 1/2⇒ θ = Sin⁻¹(1/2)

⇒ θ = 30°

Hence, 30° is the angle of elevation from the base to the top of the mountain.

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The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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Answer:

Step-by-step explanation:

  0

r

= 1

Answer:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

-2x+2y=6,4x+2y=-5

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

-2x+2y=6

-2x=-2y+6

x=-\frac{1}{2}\left(-2y+6\right)

x=y-3

4\left(y-3\right)+2y=-5

4y-12+2y=-5

6y-12=-5

6y=7

y=\frac{7}{6}

Step-by-step explanation:

x=\frac{7}{6}-3

x=-\frac{11}{6}

x=-\frac{11}{6},y=\frac{7}{6} the answer

Answer: 28282

Step-by-step explanation:

I think

Answer:

im pretty sure 140 because if you take away the seperating line between the given angle and 3 its 180 which if you would do the same to the other side it would be identical. So Try 140

Step-by-step explanation:

It is Option A 140° as the opposite angles are of equal measures in intersecting lines.

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:

–500 N

Step-by-step explanation:

Action and reaction forces are equal in magnitude but opposite in direction. The negative sign indicates opposite direction (Refer to Newton's 3rd Law of motion).

Answer:

  (23/3)π ≈ 24.09 in

Step-by-step explanation:

You want the perimeter of the figure bounded by two arcs, one that is a semicircle of radius 3 in, the other being an arc of 210° of radius 4 in.

The length of an arc is given by the formula ...

  s = rθ . . . . . where r is the radius and θ is the central angle in radians

The central angle of a semicircle is 180°, or π radians.

The central angle of an arc of 210° is 210°, or (210/180)π = 7π/6 radians.

The perimeter of the figure is the sum of the two arc lengths that make it up:

  (4 in)(7π/6) +(3 in)(π) = 23π/3 in ≈ 24.09 in

The perimeter of the figure is about 24.09 inches.

__

Additional comment

Arcs with those dimensions do not meet at their ends. The larger arc would need to have a measure of about 262.8° to meet the ends of a 6" semicircle.

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I already answered on your previous post, but here's the answer again. By the way, it's still flipped the wrong way

Mark and Lisa both started with 5/4 litres (l),

Mark drank 1/3 l => 5/4 - 1/3 = 11/12 left

Lisa spilled and had 2/5 l left => 5/4 - 2/5 = 17/20 spilled

0.57 mi²  = 15,890,688 ft² after converting square miles in square foot.

The given conversion in question is-

0.57 mi²  = __ ft²

We know that

1 mi²  = 27,878,400 ft²

Then, multiply both sides by 0.57

1 x 0.57 mi²  = 27,878,400 x 0.57 ft²

0.57 mi²  = 15,890,688 ft²

Thus, the conversion of 0.57 mi²  = 15,890,688 ft².

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A probability distribution lists all possible outcomes for an experiment and the corresponding probability for each of those outcomes.

The probabilities cannot be negative; each probability must be between 0 and 1, and the sum of the probabilities for all of the outcomes must be equal to 1. In probability theory, a probability distribution is a mathematical function that links every result of an experiment with the likelihood of it occurring. It describes the chance of occurrence of different possible outcomes in an experiment.

The following are the rules that must be followed for a probability distribution:Each probability value cannot be negative.The range of probabilities for each event must be between 0 and 1.The total probability of all the possible outcomes must be 1. when summed up, all the probabilities of a random variable must add up to 1. A probability distribution lists all possible outcomes for an experiment and the corresponding probability for each of those outcomes.

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To provide a baseline against which they can evaluate the effects of a specific treatment, experimenters make use of a(n) Control condition (Option D).

Now,

Hence, to provide a baseline against which they can evaluate the effects of a specific treatment, experimenters make use of a(n) Control condition (Option D).

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The measure of the length of arc with a cental angle of 50 degree and radius 7cm is approximately 35π/18 cm.

An arc length is simply the distance between two points along a section of a curve in a circle.

It can be expressed as:

Length of arc = θ/360 × 2πr

Where θ is the central angle in degree and r is the radius.

From the diagram:

Central angle θ = 50 degree

Radius r = 7 cm

Arc length = ?

Plug the given values into the above formula and solve for the arc length:

Length of arc = θ/360 × 2πr

Length of arc = 50/360 × 2 × π × 7cm

Length of arc = 35π/18 cm

Therefore, the arc length measures 35π/18 cm.

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For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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Answer:

2\(n\) = \(\alpha n\) and \(n + n\) = \(\alpha n\)

Step-by-step explanation:

The expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Therefore, the expected time for these activities is 2.8 hours.

To calculate the expected time for activities, we can use the formula for expected value.

The expected value is calculated by multiplying the time for each activity by its probability of occurrence, and then summing up these values. The formula for expected value is: Expected Value = (Time1 * Probability1) + (Time2 * Probability2) + ... + (TimeN * ProbabilityN) Here's a step-by-step example:

1. List all the activities and their corresponding times and probabilities.

2. Multiply the time for each activity by its probability.

3. Sum up the values obtained in step 2.

For example, let's say we have two activities: Activity 1: Time = 2 hours, Probability = 0.6 Activity 2: Time = 4 hours, Probability = 0.4 Using the formula, we calculate the expected time as follows: Expected Time = (2 hours * 0.6) + (4 hours * 0.4) = 1.2 hours + 1.6 hours = 2.8 hours

Therefore, the expected time for these activities is 2.8 hours.

Here full question is not provided  but the full answer given above.

Remember, this is just one example, and you can use the same formula for any number of activities with their respective times and probabilities. In summary, to calculate the expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Then, sum up these values to get the expected time.

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The linear regression equation is y ≈ -2.02x + 670.38, and the projected number of new cases for 2008 is approximately 650.

To find the linear regression equation that represents the given set of data, we can use the least squares method to determine the best-fit line. The equation will have the form y = mx + b, where m is the slope and b is the y-intercept.

First, let's calculate the mean values of x and y:

mean(x) = (0 + 1 + 2 + 3 + 4 + 5) / 6 = 15 / 6 ≈ 2.5

mean(y) = (703 + 675 + 706 + 643 + 660 + 605) / 6 = 3992 / 6 ≈ 665.33

Next, we'll calculate the values needed to determine the slope:

Σ(x - mean(x)) = (0 - 2.5) + (1 - 2.5) + (2 - 2.5) + (3 - 2.5) + (4 - 2.5) + (5 - 2.5) = 0 - 1 - 0.5 + 0.5 + 1 + 2 = 2.5

Σ(y - mean(y)) = (703 - 665.33) + (675 - 665.33) + (706 - 665.33) + (643 - 665.33) + (660 - 665.33) + (605 - 665.33) ≈ -35.33

Σ(x - \(mean(x))^2 = (0 - 2.5)^2 + (1 - 2.5)^2 + (2 - 2.5)^2 + (3 - 2.5)^2 + (4 - 2.5)^2 + (5 - 2.5)^2\)= 6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25 = 17.5

Now, we can calculate the slope:

m = Σ[(x - mean(x)) * (y - mean(y))] / Σ[(x - \(mean(x))^2\)] ≈ (-35.33) / 17.5 ≈ -2.02

Next, we can determine the y-intercept:

b = mean(y) - m * mean(x) ≈ 665.33 - (-2.02) * 2.5 ≈ 665.33 + 5.05 ≈ 670.38

Therefore, the linear regression equation for the given data is y ≈ -2.02x + 670.38.

To find the projected number of new cases for 2008 (10 years since 1998), we substitute x = 10 into the equation:

y ≈ -2.02(10) + 670.38 ≈ -20.2 + 670.38 ≈ 650.18

Rounding to the nearest whole number, the projected number of new cases for 2008 is approximately 650.

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Answer:

Step-by-step explanation:

Answer:

8,5,2

Step-by-step explanation:

8 , 5, 2 Just use rigorous trial and error

Answer:

The name of the solid with 20 faces that are congruent equilateral triangles is icosahedron.

The solid you are referring to is called an icosahedron. An icosahedron is a specific type of convex polyhedron that has 20 faces. In this case, all 20 faces are congruent equilateral triangles. Option d is correct answer.

To understand why this solid is called an icosahedron, let's break down the term. "Icosa-" comes from the Greek word for twenty, while "-hedron" means face. Therefore, an icosahedron is a polyhedron with twenty faces.

Each face of an icosahedron is an equilateral triangle, meaning that all three sides of the triangle are equal in length, and all three angles are equal to 60 degrees. Since all 20 faces are congruent, they have the same side lengths and angles.

The icosahedron has a total of 12 vertices and 30 edges. The vertices are the points where three edges meet, and the edges are the line segments connecting the vertices. The icosahedron has a symmetrical and regular structure, making it one of the five Platonic solids.

An icosahedron is a convex polyhedron with 20 congruent equilateral triangle faces, 12 vertices, and 30 edges.

Option d is correct answer.

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Answer: 400 cm²

Step-by-step explanation:

the area of a trapezoid is: A = (b1+b2)/2 x h

using this formula:

A = (30+10)/2 x 20

A = 40/2 x 20

A = 20 x 20

.: A = 400cm²

Hope this helped :)