Let a1 = 2, a2 = 4, and an+2 =5an+1- 6an for all n>=1.Prove that an = 2n for allnatural numbers n.

The approximate total cost of manufacturing 900 yards of ribbon using left endpoints of 5 subintervals is $485.88.

To approximate the total cost, we'll use the left endpoint Riemann sum. First, we divide the interval [0,900] into 5 equal subintervals of width Δx = 900/5 = 180. Next, we evaluate the marginal cost function C'(x) at the left endpoints of each subinterval.

Using the left endpoint of the first subinterval (x = 0), C'(0) = -0.00002(0)^2 - 0.04(0) + 55 = 55 cents. Similarly, we compute C'(180) = 51.80, C'(360) = 48.20, C'(540) = 44.40, and C'(720) = 40.40 cents.

Now we can calculate the approximate total cost using the left Riemann sum formula: Δx * [C'(0) + C'(180) + C'(360) + C'(540) + C'(720)]. Plugging in the values, we get 180 * (55 + 51.80 + 48.20 + 44.40 + 40.40) = 180 * 240.80 = 43,344 cents.

Finally, we convert the total cost to dollars by dividing by 100: 43,344 / 100 = $433.44. Rounded to the nearest cent, the approximate total cost of manufacturing 900 yards of ribbon is $485.88.

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In Luther v. Borden, 1849, it is true that the Supreme Court abdicated its role in clarifying whether the people had the right to abolish their state governments. The great statesman Daniel Webster argued that people do indeed possess the right to overthrow their government.

Luther v. Borden, 1849 was a United States Supreme Court case that decided whether the court should intervene in a political question, specifically the Rhode Island Dorr Rebellion of 1841 to 1842. In this case, the court declined to do so and ruled that the authority to decide whether a rebellion against a state government exists or not, rests solely with the United States government. The Court refused to support either side in the rebellion and thus upheld the lower court's decision.

The decision is well-known for declaring that the federal government must guarantee a "republican form of government" in the states. In this context, Webster argued that people possess the right to overthrow their government as they possess the ultimate sovereignty. True.

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To answer this question, we have to find 75% of 40.

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:

B

Step-by-step explanation:

Expand (x+5)^2 through binomial expansion and you get x^2+10x+25.

Break up the problem into little pieces like (x-5)(x+5) and 10(x+5)

Solve the first piece (x-5)(x+5) by doing something like FOIL.

x^2-25

Do the second piece

10x+50

When you add them together, it becomes x^2+10x+25, and (x+5)^2=(x-5)(x+5)+10(x+5).

Assume that at least one of each aquatic pets must be bought

The probability of an event is a number that indicates how likely the event is to occur.

Scenario 1 (Greatest number of legs)

Assume he bought 5octopus and 1 sea star

(5 x 8) + (1 x 5)legs = 45 legs in all

Scenario 2 (Least number of legs)

Assume he bought 1 octopus and 5 sea star

(1 x 8) + (5 x 5)legs = 33 legs in all

Scenario 3 (an odd number of legs)

To get an odd number, the number of star fish should be odd.

therefore It is possible to get an odd number of legs.

Scenario 4 (An even number of legs)

To get an even number of legs, the number of octopus should be even.

therefore It is possible to get an even number of legs.

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Answer:
3(n+7) =
(3)(n) + (3)(7) =
3n + 21

Step-by-step explanation:

I hope this helps you :D

Answer:

37/6x=37

x=6

11/2x+2/3x=37

Step-by-step explanation:

The amount before she took out any money is $785

The given parameters are:

Amount taken out = $135

Balance = $650

Let the amount before she took out any money be x

So, we have

x = $135 + $650

Evaluate

x = $785

Hence, the amount before she took out any money is $785

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

0.36

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

Answer:

Yes, you are correct! 0.36363636... is the answer. 0.364 would be closest.

Happy learning!

--Applepi101

Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

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Based on the information in the graph, we can infer that the star with the highest initial mass is likely to be at position A.

To find the position of the star with the greatest initial mass we must analyze the graph. In this case, the graph shows us the temperature on the x axis and the luminosity on the y axis. According to these data, we can assume that the star with the greatest mass has the greatest luminosity, so we could establish that the position of this star is the one that corresponds to the greatest luminosity. In this case, the place with the greatest luminosity would be position A.

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Answer:

The inside angles have to equal 180 degrees so

So Hazel is correct

Answer:

Domain and Range are both all real numbers.

Step-by-step explanation:

The housing supply function is given by h(I,R) = a log1 + bR + cR log1. The housing supply responds to changes in I with a rate of a, and to changes in R with a rate of b + c log1.

Based on the given equation, the housing supply (h) is determined by two variables: I and R. The equation shows that h is a function of R, with a log-linear relationship. The variable I only appears as a constant (a) in the equation, so changes in I do not directly affect the supply of houses.
On the other hand, changes in R (or OR, which is the same variable) do affect the supply of houses. Specifically, an increase in R leads to an increase in the supply of houses. The magnitude of this increase depends on the values of b and c in the equation.
To see this, we can take the partial derivative of h with respect to R:
dh/dR = b + cR/(ln(10))
This equation tells us how much the housing supply changes in response to a change in R. The derivative is positive (i.e. the supply increases) as long as c is positive. The larger c is, the greater the increase in supply for a given increase in R.
Therefore, the correct answer is:
b + cR/(ln(10))

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Answer:

Use multiplication and dividing.

Step-by-step explanation:

If you want to convert to a smaller unit, you must multiply.

For example...

4 Feet to Inches:

\(4 * 12 =48\) inches

2 Yards to Inches:

\(2 * 3 = 6\) feet

\(6 * 12 = 72\) inches

If you want to convert to a larger unit, you must divide.

336 Inches to Feet:

\(336/12=28\) feet

756 Inches to Yards:

\(756/12=63\) feet

\(63/3=21\) yards

Answer:

It's D

Step-by-step explanation:

Stay frosty

Answer:

D

NO STEP BY STEP!

Hello Human <3

Here is the answer:

X ∈  { 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 206, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414 }

Step-by-step explanation:

Answer:

The answer is "\(\overarc{ADC} = m\angle CPD + m\angle DPA = 186\)"

Step-by-step explanation:

Please find the image of the question:

In the circle p:

\(\to m\angle APB + m\angle BPC + m\angle CPD + m\angle DPA = 360^{\circ} \\\\\to 70 + 104 + m\angle CPD + m\angle DPA = 360\\\\\to m\angle CPD + m\angle DPA = 360 - 70 - 104 = 186\)

Let P is in the center

\(\to\) arc AD= \(m\angle APD\)

\(\to\) arc DC = \(m\angle CPD\)  

\(\to\) arc BC = \(m\angle BPC\)  

arc AB =

When D is on arc AC:

\(\to\)arc ADC =  arc AD  + arc DC  

\(\to\)arc ADC = \(m \angle CPD + m\angle DPA = 186\)

In an isosceles triangle the measure of the each of the base angle is equal to 55 degrees.

Let us consider measure of each of the base angle in an isosceles triangle is equal to y degrees.

Vertex angle of the isosceles triangle = 70 degrees

Sum of the measure of all the interior angles in a triangle = 180°

⇒ y° + y° + 70° = 180°

⇒ 2y° + 70° = 180°

Subtract 70° from both the sides we get,

⇒ 2y° = 180° - 70°

⇒ 2y° = 110°

⇒ y° = 110° / 2

⇒ y° = 55°

Therefore, the measure of the each base angle in an isosceles triangle is equal to 55 degrees.

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Answer:

0.6 = \(\frac{6}{10}\)

Answer:

a) 30cm²

b) 8.75cm²

c) 30cm²

Step-by-step explanation:

a) Area of a triangle = 1/2 × base × perpendicular height

= 1/2 × 12 × 5

= 30cm²

b) Area of a triangle = 1/2 × base × perpendicular height

= 1/2 × 3.5 × 5

= 8.75cm²

c) Area of a triangle = 1/2 × base × perpendicular height

= 1/2 × 5 × 12

= 30cm²

Answer:

4m-15 is the answer

Step-by-step explanation:

Hope this helps!!

Answer:

I think its $172800  bc I = PRT so I multiplied 36x 800 x 6 which is 172800

If my answer is wrong pls let me know and that I am very very very sorry :(

Step-by-step explanation:

Answer:

730864

Step-by-step explanation:

654321 +76543=730864

In the question given that :he​ reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11

From the question, we have the information available is:

Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11, 12.

and, there are 11​ outcomes, he​ reasoned, the probability of rolling a nine must be one eleventh.

To write the what is wrong with  Bob's reasoning.

Now, According to the question:

In the probability:

He rolled 11 times:

So, we can represent the \(w_2\) is the outcome with the sum of pints in two die are 2.

Then the probability is:

\(P(w_2 = 2) = (\frac{1}{6} ).(\frac{1}{6} )=\frac{1}{36}\neq \frac{1}{11}\)

So, in the question given that :he​ reasoned, the probability of rolling a nine must be one eleventh but bob is wrong because the probability is 1/36 which is not equal to 1/11.

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