Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 5 and 625, respectively.

multiply 4 by the cos(45)

4 x cos(45) = 2sqrt(2) approximately 2.828cm

so depending how you are supposed to answer, either 2 sqrt(2) or approximately 2.83 cm

The dimensions of the rectangle are a length of 16 yds and a width of 18 yds.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

Given that the perimeter is 68 yd

We know that the perimeter of a rectangle is:

P = 2(L + W)

∴ P = 68

68 = 2(L + W)

68/2 = L + W

34 = L + W

34 - L = W ....(i)

The area of a rectangle is:

A = L × W ....(ii)

∴ A = 288

Substitute the value W = 34 - L in equation (ii), and solve for L

288 = L(34 - L)

288 = 34L - L²

L² - 34L + 288 = 0

(L - 16)(L - 18)

L - 16 = 0 and L - 18 = 0

L = 16 and L = 18

Take L = 16 and substitute the value in the equation (i)

So, W = 34 - 16 = 18

Therefore, the rectangle's length is 16 yds and its width is 18 yds.

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see the formula in the picture

R is larger diameter, r is smaller diameter

Answer:

population in 2003 is 234 million.

Step-by-step explanation:

A country's population in 1991 was 231 million

In 1999 it was 233 million.

We have to calculate the population in 2003.

Since population growth is always represented by exponential function.

It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]

Here t is time in years, k is the growth constant, and  is initial population.

For year 1991 ⇒

233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]

[tex]\frac{231}{233}= e^{8k}[/tex]

Taking ln on both the sides ⇒

[tex]ln(\frac{233}{231})=lne^{8k}[/tex]

ln 233 - ln 231 = 8k  [since ln e = 1 ]

5.451 - 5.4424 = 8k

k = [tex]\frac{0.0086}{8}=0.001075[/tex]

For year 2003 ⇒

[tex]P(t)=P_{0}e^{kt}[/tex]

P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]

     = 231 × [tex]e^{0.0129}[/tex]

     = 231 × 1.0129

     = 233.9 ≈ 234 million

Therefore, population in 2003 is 234 million.

The dimensions of the rectangle that maximize the enclosed area are L = 80 yards and W = 80 yards. The maximum area is A = 80 * 80 = 6400 square yards.

To find the dimensions of the rectangle that maximize the enclosed area using 320 yards of fencing, we'll use the concept of optimization. Let's solve it step by step:

Let's assume the length of the rectangle is L and the width is W.

Perimeter constraint:

The perimeter of the rectangle is given as 2L + 2W, which must equal 320 yards:

2L + 2W = 320

Simplify the perimeter equation:

Divide both sides by 2 to get:

L + W = 160

Express one variable in terms of the other:

Solve the equation for L:

L = 160 - W

Area equation:

The area of the rectangle is given by A = L * W.

Substitute the value of L from the previous step into the area equation:

A = (160 - W) * W

A = 160W - W^2

Maximize the area:

To find the maximum area, we need to maximize the function A = 160W - W^2. This is achieved when the derivative is zero.

Take the derivative of A with respect to W:

dA/dW = 160 - 2W

Set dA/dW = 0 and solve for W:

160 - 2W = 0

2W = 160

W = 80

Substitute the value of W back into the perimeter equation to find the corresponding value of L:

L = 160 - W = 160 - 80 = 80

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The optimization problem involves finding the dimensions of a rectangle to maximize its area using a fixed amount of fencing. The dimensions that maximize the area are both 80 yards, making the maximum area 6400 square yards.

The subject of this question is Mathematics, specifically a problem about optimization in the field of Calculus. In the given problem, we wish to find a rectangular area that can be enclosed by 320 yards of fencing that maximizes the area.

Let's designate the rectangular area's width and length as x and y respectively. The problem can now be rephrased. With the total length of fencing equal to 320 yards, you can express this as 2x + 2y = 320. Simplifying this equation, we get x + y = 160, or y = 160 - x.

The area of a rectangle is computed as width times length, or in this case, x(160 - x). This is a quadratic function, and its maximum value happens at the vertex of the parabola defined by this function. For a quadratic in standard form like y = ax^2 + bx + c, the x-coordinate of the vertex is at -b/2a. In this case, the maximum area happens when x = 160/2 = 80.

Substituting this value back into the equation for the rectangle's dimensions gives y = 160 - 80 = 80. So, the dimensions that maximize the area for a rectangle with a parameter of 320 yards are both 80 yards. Therefore, the maximum area possible is 80*80 = 6400 square yards.

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Final answer:

The function t(x) with ordered pairs (0, 1), (1, 3), and (3, 27) most likely represents the exponential function because it shows rapidly increasing growth rates, which is a defining feature of exponential behavior.

Explanation:

The function that most likely represents the exponential function is the one whose growth rate increases significantly for larger values of x. Examining the ordered pairs, the function t(x), which passes through the points (0, 1), (1, 3), and (3, 27), clearly demonstrates this behavior as the increase between the y-values gets dramatically larger as x increases.

This is a classic characteristic of exponential growth. In contrast, the function p(x) that passes through (0, 2), (1, 3), (3, 11), (5, 27), and (6, 38) shows a more consistent increase in y-values as x increases, indicative of a quadratic function.

As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of China is 1,388,979,446.

China’s population is equivalent to 18.47% of the total world population.

18.47% of the total world population is composed by China’s population.

China is ranked number 1 in the list of countries by population.

Rounding that number off to the nearest 100,000, it would be 1,388,980,000.

As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of India is 1,344,431,890.

17.86% of the total world population is composed by India’s population.

India is ranked number 2 in the list of countries by population.

Rounding that number off to the nearest 100,000, it would be 1,344,400,000.

The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .

First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.

Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.

Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."

P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)

P(A|B) = 8 / 15

To express this as a percentage, multiply by 100:

P(A|B) * 100 ≈ 0.5333

Rounded to the nearest hundredth, the probability is 0.53 or 53%.

The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .

First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.

Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.

Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."

P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)

P(A|B) = 8 / 15

To express this as a percentage, multiply by 100:

P(A|B) * 100 ≈ 0.5333

Rounded to the nearest hundredth, the probability is 0.53 or 53%.

For two successes in seven binomial trials with a success probability of 0.06, use the binomial probability formula. Calculate (7 choose 2) * (0.06^2) * (0.94^5) to get the probability of 0.0554.

To calculate the probability of two successes in seven trials with a success probability of 0.06, you can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * q^(n-k), where 'n' is the number of trials (7), 'k' is the number of successes (2), 'p' is the probability of success (0.06), and 'q' is the probability of failure (q = 1 - p = 0.94).

First, calculate the binomial coefficient using 'n choose k', which is (7 choose 2). Then, raise the probability of success to the power of the number of successes (0.06^2) and the probability of failure to the power of the number of failures (0.94^5). Lastly, multiply these values together to get the probability.

The calculation is as follows:

(7 choose 2) * (0.06^2) * (0.94^5) = 21 * 0.0036 * 0.7339 = 0.0554

Answer:

the answer is true

Step-by-step explanation:

it's what I got

Answer:  

-3

Step-by-step explanation:

use AE and CE to find the angle

AE = 20, CE = 6

 so the angle FOR CAE = tan^-1(6/20) = 16.7 degrees

 to Find DF

a^2 = b^2 +c^2-2abcos(A)

a^2 = 10^2 + 14^2 -2(14)(10)cos(16.7)

a^2 = 30

sqrt((30)=5.47 rounded to 5.5

EF =

a^2 = b^2 +c^2-2abcos(A)

a^2 = 20^2 + 14^2 -2(14)(20)cos(16.7)

a^2 = 64

sqrt(64)=8

C = 2* pi *r = 36 pi

 r = 36pi/2pi = 18

We know that A= r^2 * pi

A = 18^2 * pi = 324 pi

the area would be 324PI square units