The length of a rectangle is twice its width. The perimeter is 60 ft. Find its area.

The series ∑∞ n=1 an with terms [tex]a_n = (1 * 8 * 15 * ... * (7n-6)) / (7^n * n!)[/tex]diverges. Hence the correct option is 2.

Ratio Test:

For the series ∑∞ n=1 an with terms an, let:

lim n->∞ |an+1 / an| = L

If L < 1, the series converges.

If L > 1, the series diverges.

If L = 1 or the limit diverges, the test is inconclusive.

Applying the Ratio Test:

Here, [tex]a_n = (1 * 8 * 15 * ... * (7n-6)) / (7^n * n!)[/tex]

Let's analyze the limit as n approaches infinity for the ratio of successive terms:

Simplifying the numerator and denominator, we get:

[tex]lim n- > ∞ | 7^(^n^+^1^) * (n+1)! / (7^n * n!) | = lim n- > ∞ | 7 * (n+1) |[/tex]

As n approaches infinity, the constant term 7 becomes insignificant. Therefore:

lim n->∞ |an+1 / an| = lim n->∞ |n+1|

Since the limit approaches positive infinity as n approaches infinity, L > 1.

Conclusion:

Based on the ratio test, the series ∑∞ n=1 an with terms [tex]a_n = (1 * 8 * 15 * ... * (7n-6)) / (7^n * n!)[/tex]diverges. Hence the correct option is 2.

Complete question:

Use either the ratio test or the root test as appropriate to determine whether the series ∑∞, n=1 an with given terms an converges, or state if the test is inconclusive. an= 1⋅8⋅15⋯(7n−6)/7^n n!

The series converges.

The series diverges.

The test is inconclusive.

Answer:

D) [tex]8.7 * 10^{10}[/tex]

Step-by-step explanation:

The question is correctly written as below:

Which number is one million times larger than [tex]8.7 * 10^{4}[/tex]?

A) [tex]8.7 * 10^{7}[/tex]

B) [tex]8.7 * 10^{8}[/tex]

C) [tex]8.7 * 10^{9}[/tex]

D) [tex]8.7 * 10^{10}[/tex]

Consider [tex]8.7 x 10^{4}[/tex] to be number A and number B is one million times ([tex]10^{6}[/tex]) greater than number A

[tex]B = A * 10^{6}[/tex]

[tex]B = 8.7 * 10^{4} * 10^{6}[/tex]

[tex]B = 8.7 * 10^{4+6}[/tex]

[tex]B = 8.7 * 10^{10}[/tex]

D) [tex]8.7 * 10^{10}[/tex]

Answer:

The answer is option C on plato :)

Step-by-step explanation:

Answer: For those in the future!

The answer to this is D: (4g+2)(16g^2minus8g+4)

Step-by-step explanation:

The inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]

The given function is:

f(x)  =  7x  -  1

Make x the subject of the formula

[tex]f(x) = 7x - 1\\\\7x = f(x) + 1\\\\[/tex]

Divide through by 7

[tex]\frac{7x}{7}= \frac{f(x)}{7} + \frac{1}{7}\\\\x = \frac{f(x)}{7} + \frac{1}{7}[/tex]

Replace x by [tex]f^{-1}(x)[/tex] and replace f(x) by x:

[tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]

Therefore the inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]

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Final answer:

To express 2.6x10^-6 in standard decimal form, the decimal point is moved 6 places to the left, giving us 0.0000026.

Explanation:

To write 2.6x10^-6 in standard decimal form, start by understanding the exponent. The notation 10^-6 means that we are moving the decimal point 6 places to the left because it is a negative exponent. Therefore, we start with 2.6 and move the decimal point to the left 6 places, which means we have to add zeros to fill in the gaps.

The final expression in standard form will be 0.0000026.

Answer:

D

Step-by-step explanation:

edge

There are 60 people enrolled in the program, then 24 people will be sent to the new plant.

The percentage is defined as a ratio expressed as a fraction of 100.

To find the number of people sent to the new plant, we can multiply the percentage of people sent to the new plant by the total number of people enrolled in the training program. The percentage is given as a decimal by dividing the percentage by 100, so 40% is equal to 0.40.

The result is then multiplied by the number of people enrolled in the training program, which is 60.

40% of those enrolled in the training program will be sent to the new plant, which is 40/100 x 60 people = 24 people.

The final result is 24 people.

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To order the numbers √7, 2, √8/2 from least to greatest, simplify √8/2 to √2. Then compare √2, 2, and √7 to find the order.

To order the numbers √7, 2, √8/2 from least to greatest, first simplify √8/2. We know that √8 = √(4*2) = 2√2, so √8/2 = (2√2)/2 = √2. Now we have √7, 2, and √2. Comparing these numbers, √2 < 2 < √7.

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The total length of the curve with parametric equations give is 23.5 units.

A parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

Given that, a parametric equation, x = sin(t), y = sin(2t), z = sin(3t),

Finding the first derivative,

x' = cost

y' = 2cos2t

z' = 3cos3t

The parametric integral for length =

L = [tex]\int\limits^{t_2}_{t_1} \sqrt{ {x'^2+y'^2+z'^2} \, dx[/tex]

t₁ = 0, t₂ = 2π

T = [tex]\int\limits^{2\pi}_{0} \sqrt{ {(cost)^2+(2cos2t)^2+(3cos3t)^2} \, dt[/tex]

We will solve the integral by trapezoidal rule,

[tex]\int\limits^a_bf ({x}) \, dx = \frac{f(a)+f(b)}{2} (b-a)[/tex]

Therefore,

[tex]\int\limits^{2\pi}_{0} \sqrt{ {(cost)^2+(2cos2t)^2+(3cos3t)^2} \, dt[/tex]

= [tex]\frac{\sqrt{(cos2\pi)^2+(2cos2\pi)^2+(3+cos3\pi)^2} +\sqrt{(cos0)^2+(2cos0)^2+(3+cos0)^2}}2} (2\pi)[/tex]

= 23.5

Hence, the total length of the curve with parametric equations give is 23.5 units.

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An investment that grows by 5% per year for 20 years will increase by approximately 165.33% over the 20-year period. This calculation is based on the principle of compound interest.

In the given scenario, the growth of the investment is calculated using the principle of

compound interest

- a concept in Mathematics. Compound interest takes into account the phenomenon that, over time, your investment will grow not only from the initial amount invested but also from any interest or earnings that have been accumulated. Therefore, the 5% growth rate per year is being applied to an increasingly larger amount because the interest is being compounded, i.e., you're earning 'interest on interest'.

To calculate the overall percent increase after 20 years, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:

In this case, we can assume that P = 1 (representing 100% of the initial investment), r = 0.05 (5% growth per year), n = 1 (interest is compounded once per year), and t = 20 years. Substituting these values in, we get A = 1(1 + 0.05/1)^(1*20) = 2.6533 approximately. Therefore, the investment increased by about 165.33% over the 20-year period.

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the correct number label for point A on the number line is [tex]\( \frac{1}{20} \).[/tex]

Let's break this down step by step:

1. Determine the time available for each chore: Amy has 1/4 hour to do 5 chores. To find out how much time she can spend on each chore, divide the total time available (1/4 hour) by the number of chores (5).

[tex]\( \frac{1}{4} \div 5 = \frac{1}{4} \times \frac{1}{5} = \frac{1}{20} \)[/tex]  hour per chore.

2. Representing the fraction of an hour on a number line:The number line represents the whole hour. Since Amy has 1/20 hour per chore, each point on the number line represents 1/20 hour.

  - Let's label point A as [tex]\( \frac{1}{20} \).[/tex]

So, the correct number label for point A on the number line is [tex]\( \frac{1}{20} \).[/tex]

Amy has 1/4 hour to complete 5 chores. To find out how much time she can spend on each chore, we divide 1/4 by 5, which gives us 1/20 hour per chore. On the number line representing an hour, each point represents 1/20 hour, so point A is labeled as 1/20. This means that Amy can spend 1/20 hour on each chore to complete all five chores within the 1/4 hour time frame she has.

complete question

Amy has 1/4 hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore. What is the correct number label for point A?

4.5% = 0.045

 multiply 18.50 by 0.045 foe the amount of sales tax

18.50 * 0.045 = 0.83

 they pay 0.83, which is 83 cents in sales tax

The price per ticket (before any additional charges) is approximately $90.79. Let's assume the price of each ticket before any additional charges (handling charge and GST) is "x" dollars.

Given that a handling charge of $5 is charged per ticket, the total handling charge for 2 tickets will be $5 * 2 = $10.

Now, let's calculate the total cost of the tickets after adding the handling charge:

Total cost of tickets (before GST) = 2x + 10

Now, the GST of 5% is charged on the ticket price and handling charges. The GST amount can be calculated as:

GST amount = 5% of (2x + 10) = 0.05 * (2x + 10) = 0.1x + 0.5

The total charge for 2 tickets, including the handling charge and GST, is given as $201.16. So, we can set up the equation:

Total cost of tickets (including GST) = Total cost of tickets (before GST) + GST amount

$201.16 = (2x + 10) + (0.1x + 0.5)

Now, solve for "x":

2x + 10 + 0.1x + 0.5 = 201.16

2.1x + 10.5 = 201.16

2.1x = 201.16 - 10.5

2.1x = 190.66

x = 190.66 / 2.1

x ≈ 90.79

So, the price per ticket (before any additional charges) is approximately $90.79.

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Answer:

X+2y=12

Step-by-step explanation:

The mouse ran a distance of 11 feets before being caught by the cat

Using the information on the graph ;

Y - axis = Distance covered by the mouse and cat

X - axis = Time taken to cover Distance

The intersection point of the two lines is the point at which the mouse was caught .

Tracing the point to the y-axis , we get the required Distance value

Hence, from the graph, the distance is 11 feets

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Before being caught by the cat, the mouse sprinted 11 feet.

How can we apply the graph to our solution?

Using the data from the graph;

The distance traveled by the mouse and cat is represented by the Y axis.

X axis = Distance traveled in time

The spot where the two lines connect is where the mouse was trapped.

We get the requisite Distance value by tracing the point to the y-axis.

As a result of the graph, the distance is 11 feet.

The volume of a pyramid with a rectangular base and height of 2h is given by the formula V = (1/3) * Base area * Height. The base area for this pyramid is 32b² (derived from 4b * 8b), and the height is 2h. Hence, the volume equates to 64/3 b²h.

The volume of a pyramid is calculated with the formula V = (1/3) * Base area * Height. For the pyramid in question, the base is a rectangle with a length of 4b and a width of 8b, so the area of the base (A) is 4b * 8b = 32b². The height of the pyramid is given as 2h. So, by plugging these values into the formula, we obtain the volume of the pyramid as V = (1/3) * 32b² * 2h = 64/3 b²h.

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If the given function is F(x) = 10z. When z = 0.8, the value of the function is 8.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the given function is F(x) = 10z.

In the given function z is the independent variable while the value of the function is a dependent variable because its value depends upon the value of z.

The variable is reliant on other measurable factors. As a result of manipulating the independent variable(s) in an experiment, these variables are anticipated to change.

The value of the function is obtained by putting the value of z in the given function,

F(x) = 10z

F(x) = 10×0.8

F(x) = 8

Thus, if the given function is F(x) = 10z. When z = 0.8, the value of the function is 8.

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