What is the equation for an arithmetic sequence with a first term of 5 and a second term of 2? (5 points) an = 5 − 2(n − 1) an = 5 + 2(n − 1) an = 5 − 3(n − 1) an = 5 + 3(n − 1)

The line integral of F around the perimeter of the given rectangle is equal to 20.

To find the line integral, we need to parameterize the path along the perimeter of the rectangle and calculate the line integral of F along that path.

The perimeter of the rectangle consists of four line segments: (5,0) to (5,2), (5,2) to (2,2), (2,2) to (-2,2), and (-2,2) to (-2,0).

Let's go through each segment one by one:

(5,0) to (5,2):

Parameterize this segment as r(t) = (5, t), where 0 ≤ t ≤ 2. The differential vector dr = (0, dt).

Substitute the parameterization into F: F(r(t)) = 5(5 + t)i + 4sin(t).

Calculate the dot product: F(r(t)) · dr = [5(5 + t)i + 4sin(t)] · (0, dt) = 0 + 4sin(t)dt = 4dt.

Integrate over the interval: ∫[0,2] 4dt = [4t] from 0 to 2 = 4(2 - 0) = 8.

Parameterize this segment as r(t) = (5 - t, 2), where 0 ≤ t ≤ 3. The differential vector dr = (-dt, 0).

Substitute the parameterization into F: F(r(t)) = 5(5 - t)i + 4sin(2) = (25 - 5t)i + 4sin(2).

Calculate the dot product: F(r(t)) · dr = [(25 - 5t)i + 4sin(2)] · (-dt, 0) = -(25 - 5t)dt.

Integrate over the interval: ∫[0,3] -(25 - 5t)dt = [-25t + (5t^2)/2] from 0 to 3 = -75 + 45/2 = -60/2 + 45/2 = -15/2.

(2,2) to (-2,2):

Parameterize this segment as r(t) = (t, 2), where 2 ≥ t ≥ -2. The differential vector dr = (dt, 0).

Substitute the parameterization into F: F(r(t)) = 5(t + 2)i + 4sin(2) = (5t + 10)i + 4sin(2).

Calculate the dot product: F(r(t)) · dr = [(5t + 10)i + 4sin(2)] · (dt, 0) = (5t + 10)dt.

Integrate over the interval: ∫[-2,2] (5t + 10)dt = [(5t^2)/2 + 10t] from -2 to 2 = (20 + 40)/2 = 60/2 = 30.

(-2,2) to (-2,0):

Parameterize this segment as r(t) = (-2, 2 - t), where 2 ≥ t ≥ 0. The differential vector dr = (0, -dt).

Substitute the parameterization into F: F(r(t)) = 5(-2 + 2 - t)i + 4sin(2 - t) = -ti + 4sin(2 - t).

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Answer:

3a. (i). Sequence \(V_{n}\) is in Arithematic

(ii). Sequence \(W_{n}\) is in Geometric

3b. 2520 Sum of First 20 Arithmetic Sequence

3c. 98292 Sum of First 13 Geometric Sequence

Step-by-step explanation:

According to the Question,

3a. (i) Arithmetic Sequence (\(V_{n}\)) = 12 , 24 , 36 , 48 .....

it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12

(ii) Geometric Sequence (\(W_{n}\)) = 12 , 24 , 48 , 96 .....

A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2

3b. Sum of first 20 terms of Arithematic sequence, \(S_{n}=\frac{n}{2}[2a + (n-1) d]\)

(Where, a=first term of sequence , n= number of term & d=common difference)

\(S_{n}\)=10[2×12 + 19×12]

\(S_{n}\) =10×252  ⇔  2520

3c. Sum Of First 13 term of a geometric sequence, \(S_{n}= \frac{a(r^{n}-1) }{r-1}\)

(Where, a=first term of sequence , n= number of term & r= common ratio)

\(S_{n}\)=12(\(2^{13}\)-1) / 2-1

\(S_{n}\)=12×8191  ⇔  98292

Answer:

4/6 chance

Step-by-step explanation:

there is a 4/6 probability this will happen

Answer:

6x = 84 - 2y

14x = 72 - 2y

Step-by-step explanation:

x = 2 is the solution to the equation 5x - 2 = 8.

What is the logarithm?

A logarithm is a power to which a number must be raised in order to get some other number. For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.

The change of base formula for logarithms allows us to change the base of a logarithm without changing the value of the logarithm.

The formula is: logb(x) = (logc(x)) / (logc(b))

To solve 5x - 2 = 8 using the change of base formula, we will first bring the equation to one side and get 2 = 5x - 8.

Then we will add 8 to both sides of the equation to get 2 + 8 = 5x, which gives us 10 = 5x.

Finally, we will divide both sides of the equation by 5 to get x = 2.

x = 2

Therefore, x = 2 is the solution to the equation 5x - 2 = 8.

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The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer: 15.625 ft^3

Step-by-step explanation:

The volume of a cube is the side length cubed.

Therefore, the volume of this cube would be equal to 2.5^3

2.5^3 = 15.625 ft^3

Answer:

with what?

Step-by-step explanation:

Answer:

what's the question??

Step-by-step explanation:

Answer:

2(7) - 1/4 = 4 + 1/3x

x = 117/4

Step-by-step explanation:

solving an equation with one missing variable

step 1: multiply 2 * 7

ex: 14 - 1/4 = 4 + 1/3x

step 2: subtract 14 from 1/4

ex: 55/4 = 4 + 1/3x

step 3: subtract 4 from both sides of the equation

55/4 - 4 = 4 + 1/3x - 4   (39/4 = 1/3x)

step 4: divide both sides of the equation by 1/3

ex: 39/4 / 1/3 = 1/3x / 1/3   (x = 117/4 or x = 29 1/4)

step 5: to check your answer add the answer you got from the last equation which was 117/4 or 29 1/4 and input it into the original equation and get your final answer

ex: 2(7) - 1/4 = 4 + 1/3(117/4)

14 - 1/4 = 4 + 39/4

55/4 = 55/4 (if both sides of the equation are the same numbers like 55/4 = 55/4 then your answer is true)

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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A pressure of 14 pounds per square inch is needed to produce a volume of 30 cubic feet, assuming that the volume of the gas is inversely proportional to the pressure.

If the volume of a gas is inversely proportional to the pressure, we can use the formula:

P1 x V1 = P2 x V2

P1 and V1 are the initial pressure and volume, and P2 and V2 are the new pressure and volume.

P1 = 21 pounds per square inch and V1 = 20 cubic feet.

To find P2 when V2 = 30 cubic feet.

Plugging in the values we have:

21 x 20 = P2 x 30

Simplifying:

420 = 30P2

Dividing both sides by 30:

P2 = 14 pounds per square inch

We may apply the formula: if the volume of a gas is inversely proportional to the pressure.

P1 x V1 equals P2 x V2

The original pressure and volume are P1 and V1, whereas the new pressure and volume are P2 and V2.

V1 is 20 cubic feet, and P1 is 21 pounds per square inch.

when V2 = 30 cubic feet, to determine P2.

When we enter the values we have:

21 x 20 = P2 x 30

Condensing: 420 = 30P2

30 divided by both sides:

14 pounds per square inch is P2.

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Answer:

KJ = 6

Step-by-step explanation:

KJ = 1/2 * EG

=1/2 * 12

=6

Answer:

1  2/3

Step-by-step explanation:

The denominators are the same, so we have to borrow from the 4

Borrow  1 in the form 6/6

3 + 6/6+3/6  - 2 5/6

3 9/6   - 2 5/6

1 4/6

Simplify the fraction by dividing the top and bottom by 2

1  2/3

Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.

Notice here however that we have 3/6 - 5/6

which will give us a negative fraction.

Since this will cause us a lot of trouble, instead,

let's rewrite the first mixed number.

We can do this by thinking of 4 and 3/6 as 3 + 1 and 3/6

or 3 + 9/6 by changing 1 and 3/6 to an improper fraction.

So 4 and 3/6 can be written as 3 and 9/6.

So we have 3 and 9/6 - 2 and 5/6.

Now subtract the fractions.

9/6 - 5/6 is 4/6.

So we have 1 and 4/6 or 1 and 2/3.

As an improper fraction, the answer is 5/3.

The third one (left bottom corner)

A function cannot have 2 possible y values for 1 x value, but it can have 2 possible x values for one y value.

We are going to use the formula for the slope of the line with points A(2,5) and B(-8,-4). x1= 2, x2=-8, y1=5 and y2=-4

The slope of the line is 9/10

Answer: 1.001

Step-by-step explanation:

The probability of an event is always within 0 or 1.

     ✓ 0 > 0.001 > 1

     ✓ 0 > 1.0 > 1

     ✗ 0 > 1.001 > 1

     ✓ 0 > 0.999 > 1

     ✓ 0 > 0.0 > 1

1.001 is not within 0 or 1, so it's not a legitimate probability of an event.

Answer:

Step-by-step explanation:

Not legitimate:  1.001

Probability must be between 0 (impossible event) and 1 (guaranteed to happen).

To find the product of 4√18 and √12, we can simplify each square root separately and then multiply the resulting values.

First, let's simplify the square roots: √18 can be broken down as √(9 × 2), which simplifies to 3√2. √12 can be broken down as √(4 × 3), which simplifies to 2√3. Now we can multiply the simplified values: 4√18 multiplied by √12 is equal to (4 × 3√2) multiplied by (2√3). This gives us 12√2 × 2√3.

To multiply the terms with square roots, we can multiply the coefficients (12 × 2) and multiply the square root terms (√2 × √3). The product is 24√(2 × 3), which simplifies to 24√6. Therefore, the product of 4√18 and √12 is 24√6. The product of 4√18 and √12 is 24√6, where the coefficient is 24 and the square root term is √6.

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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The profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

Given the volume of timber in a forest at a certain time (t) as: V(t) = 10t - 0.2t^2

Let's differentiate the given volume function w.r.t 't' to find the maximum value of timber as follows:

           dV(t)/dt = 10 - 0.4t

Now, equate dV(t)/dt = 0 to find the value of 't' for which V(t) is maximum.0

                                   = 10 - 0.4t0.4t = 10t

                                   = 10/0.4t = 25years

Therefore, the number of years that would be associated with the maximum volume of timber is 25 years.

Let's suppose the volume of timber in a forest is given by the function: V(t) = 20t

We need to find the profit-maximizing number of years (t) that a forester would wait before harvesting the timber when the interest rate is 20%.

It is given that, the interest rate (i) = 20%

                                                        =0.2

The cost of harvesting the timber is given by the formula:

                                           C = K +r*W where K is the fixed cost,

r is the interest rate,

and W is the amount of timber harvested.

Let's suppose the fixed cost (K) = $50 and the price of timber (p)

                                                    = $10 per unit.

Therefore, the profit function can be written as:

P(t) = p*V(t) - C

     = $10*20t - (50 + 0.2*10t)

     = $200t - 50 - 2t= 198t - 50

Now, differentiate P(t) w.r.t t to find the value of t for which P(t) is maximum.

dP(t)/dt = 198Equating dP(t)/dt  

= 0, we get,0

= 198t

= 198/20t

= 9.9

Therefore, the profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

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If sales tax in Kensington is 15%,  the total cost of a pair of headphones is $23.00

On the basis of a 60% discount, what is the after-discount price?

The fact that 60% is given off the original price of $50 means that the price after the discount is 40% of the original price, which implies that the discount is the original price multiplied by 40% of the original price multiplied by 1 minus 40% as shown below:

after-discount price=$50*(1-60%)

after-discount price=$20

after-discount price +sales tax=$20+($20*15%)

after-discount price +sales tax=$23.00

Remember the sales tax is an additional cost to the buyer, hence, it is added to the discounted price to ascertain the total cost

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Answer:

180 degrees

Step-by-step explanation:

Since the angles of a triangle will always be 180 you just have to find the other angles. You already know that one is 34 degrees, but the angle that is 140 degrees is a supplementary angle becuase if you see the bottom line it is straight and that means that you can make 140+x=180 and if you subtract 140 from both sides you know that the inside angle equals 40 degrees. If you add 34 and 40 together you get 74 and when you subtract that from 180 you get 106 so that means the measure of angle 1 is 180 degrees

Using the binomial distribution, you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 12/52 = 420/52 = 8.

Thus, you would expected to draw a face card 8 times.

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Answer:

121ft

Step-by-step explanation:

Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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The probability that both Bonnie and Kelly will sit court-side is 1/55, or approximately 0.018. To express this as a percentage, we multiply by 100: the answer is 1.8%

The probability of Bonnie and Kelly both choosing court-side seats can be calculated as the number of favorable outcomes divided by the total number of possible outcomes. There are two court-side seats and two people choosing, so there is only one favorable outcome: both Bonnie and Kelly choose court-side seats. The total number of possible outcomes is the number of ways to choose two seats from the available two court-side seats, five upper-level seats, and four general admission seats. This can be calculated as the number of combinations of two seats from the total of eleven available seats, which is 11 choose 2 or 11C2 = 55.

The probability that both Bonnie and Kelly will sit court-side is 1/55, or approximately 0.018. To express this as a percentage, we multiply by 100:

0.018 * 100 = 1.8%

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In throwing a dice, there are 6 possible outcomes, namely 1, 2, 3, 4, 5 and 6.

P=(no. of favourable outcomes)/(no. of possible outcomes)

When we multiply the probability of an event with no. of trials, the we get the expected frequency of that event.

1) P(getting 1)=1/6

expected frequency of getting 1

=P(getting)1)×no. of trials

=1/6×600=100

But it is given that one is scored 200 times, so it makes a large difference from expected frequency, which is 100.

Therefore, the dice is not fair.

2) P(getting a tail)=0.3

estimate for the number of times the coin will land on a tail

=expected frequency of getting a tail

=P(getting a tail)×no. of trials

=0.3×150=45

3)P(getting a six)=2/3

expected frequency of getting a six

=P(getting a six)×no. of trials

=2/3×300=200

4)P(getting a three)=0.5

expected frequency of getting a three

=P(getting a three)×350

=0.5×350=175

The total distance of the trip is 50 miles

From the question, we have the following parameters

Distance completed = 40%

Distance travelled = 20 miles

Represent the total distance with x

So, we have the following equation

Distance travelled = Distance completed  *Total distance

This gives

Distance travelled = Distance completed  * x

So, we have

20 miles = 40% * x

Divide both sides by 40%

x = 50 miles

Hence. the length of the trip is 50 miles

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