Isaiah is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
What is the surface area of the box, in square meters, that
Isaiah decorates

The resultant of the recurrence relation bn = 4bn-1-4bn-2 with initial values bo = 1 and b₁ = 2 is bn = (1 + (n/2)) 2ⁿ.

The given recurrence relation is

bn = 4bn-1 - 4bn-2 with initial values bo = 1 and b₁ = 2. Now, we have to find the solution to the recurrence relation. It can be observed that the given recurrence relation is a second-order recurrence relation. The characteristic equation of the recurrence relation is given by:

r² = 4r - 4, which can be simplified as r² - 4r + 4 = 0. We need to solve this equation. It can be solved as r = 2

The characteristic equation of the given recurrence relation has two equal roots r1 = r2 = 2. Therefore, the general result of the recurrence relation is given by:

bn = (A + Bn) 2ⁿ

For the given initial values b₀ = 1, and b₁ = 2 we can write:

b₀ = (A + B(0)) 2⁰ => A = 1b₁ = (A + B(1)) 2¹ => A + 2B = 2

On solving these equations, we get A = 1 and B = 1/2

The resultant to the recurrence relation is:

bn = (1 + (n/2)) 2ⁿ

You can learn more about recurrence at: brainly.com/question/30479680

#SPJ11

1. The value of your account upon withdrawal on June 30, 2023, was $1,031.49.

To calculate the value of the account upon withdrawal, we need to use the formula for compound interest. The future value (FV) of the account is given by:

FV = P * (1 + r_1/n)^(n*t)

Where P is the principal amount ($1000), r_1 is the monthly interest rate, n is the number of compounding periods per year (12 for monthly), and t is the time in years (6 months = 0.5 years).

Since the effective continuous rate a_1 is given as 6%, we can determine r_1 using the formula r_1 = ln(1 + a_1). Substituting the value of a_1 = 6% into the equation, we find r_1 = ln(1 + 0.06).

Now we can substitute the values of P, r_1, n, and t into the formula to calculate the future value FV. Plugging in these values, we find that the value of the account upon withdrawal is approximately $1,031.49.

2. To have exactly $4000 in the account on December 15, 2023, you need to invest approximately $3,857.02 on July 1, 2023.

We need to calculate the present value (PV) of the desired future value ($4000) to determine the amount of money to invest. The present value formula is:

PV = FV / (1 + r_2)^n

Where FV is the desired future value, r_2 is the daily interest rate, and n is the number of compounding periods.

Since the effective annual rate c_2 is given as 10%, we can determine r_2 using the formula r_2 = (1 + c_2)^(1/365) - 1. Substituting the value of c_2 = 10% into the equation, we find r_2 = (1 + 0.1)^(1/365) - 1.

Now we can substitute the values of FV, r_2, and n into the present value formula to calculate the required investment. Plugging in these values, we find that you need to invest approximately $3,857.02 on July 1, 2023.

To know more about withdrawal refer here:

https://brainly.com/question/30481846

#SPJ11

Answer:

c = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

c² = 7² + 3² = 49 + 9 = 58 ( take the square root of both sides )

c = [tex]\sqrt{58}[/tex]

Answer:

Step-by-step explanation:

According to Pythagoras Theorem:

[tex] {7}^{2} + {3}^{2} = {c}^{2} [/tex]

Hence,

[tex] = > {c}^{2} = {7}^{2} + {3}^{2} [/tex]

[tex] = > {c}^{2} = 49 + 9[/tex]

[tex] = > {c}^{2} = 58[/tex]

[tex] = > c = \sqrt{58} [/tex]

So,

[tex]c = \sqrt{58} [/tex]

Is the answer.

The continuity property of H is that it is:

c. right-continuous

Continuity property: A function is continuous if it has no jumps, i.e., the graph can be drawn without lifting the pencil from the paper. For any random variable X, the function H is right-continuous.

This is due to the fact that the limit of H(x) as x approaches any value from the right side is equivalent to H(x) as x approaches that value from the right side, so H is continuous from the right side.

To know more about continuity property, visit the link : https://brainly.com/question/30328478

#SPJ11

The integral that represents the length of the curve from the point (-3,6) to the point (2,36) is L = ∫[-3 to 2] √101 dx.

To find the length of the curve defined by the equation y = 47° + 10x from the point (-3,6) to the point (2,36), we can use the arc length formula for a curve:

L = ∫[a to b] √(1 + (dy/dx)^2) dx

First, let's find dy/dx by taking the derivative of the given equation:

dy/dx = d/dx(47° + 10x) = 10

Now we can substitute this value into the arc length formula:

L = ∫[-3 to 2] √(1 + (10)^2) dx

Simplifying:

L = ∫[-3 to 2] √(1 + 100) dx

L = ∫[-3 to 2] √101 dx

Thus, the integral that represents the length of the curve from the point (-3,6) to the point (2,36) is:

L = ∫[-3 to 2] √101 dx

Know more about the arc length formula click here:

https://brainly.com/question/30764783

#SPJ11

Answer:  261,608in²

Step-by-step explanation:

A = bh

A = (1,234)(212)

A= 261,608in²

Answer:

29 minutes

Step-by-step explanation:

Let

x = number of minutes

y = the height of the airplane above sea level in feet

y = 32,000 - 1000x

y = 3,000

Therefore,

y = 32,000 - 1000x

3,000 = 32,000 - 1000x

3,000 - 32,000 = -1000x

-29,000 = -1,000x

x = -29,000 / -1,000

x = 29 minutes

it will take 29 minutes for the airplane to land at an airport 3000 feet above sea level

Answer:

150.72

Step-by-step explanation:

C = 2*pi * r

C = 2* 3.14 * 6

C = 37.68

1 revolution = 37.68

4 revolutions = 4 * 37.68

4 revolutions = 150.72

Answer:

8 shirts

Step-by-step explanation:

Answer:

The average (mean) weight for each dinner is 13.33 oz.

Step-by-step explanation:

mean = sum of all data points / total number of items in the set

mean = 40 / 3

mean = 13.33 oz

Answer:

more info?

Step-by-step explanation:

It should be noted that Yes, there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.

The sample data shows that 54.6% of urban dwellers (325/598) agree with the statement, while only 40.1% of rural dwellers (54/137) agree. This difference is statistically significant at the p < 0.05 level (two-tailed).

The test statistic is 2.83. The p-value for this test statistic is 0.0047. Since this p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.

Learn more about hypothesis on

https://brainly.com/question/606806

#SPJ4

The first term of the arithmetic sequence is 16 and the 22nd term is 148.

To solve for the first term, we can use the following formula:

a_n = a_1 + d(n-1)

where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

d is the common difference of the sequence

We know that the 4th term is 16 and the 37th term is 115. We can use these values to solve for d.

d = a_{37} - a_4 = 115 - 16 = 99

Now that we know d, we can solve for a_1 using the value of the 4th term.

a_1 = a_4 - d = 16 - 99 = -83

Finally, we can solve for the 22nd term using the value of a_1 and d.

a_{22} = a_1 + d(22-1) = -83 + 99(21) = 148

Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.

Here is a more detailed explanation of the solution:

The first step is to identify the common difference of the sequence. This can be done by subtracting any two consecutive terms in the sequence. In this case, the 4th term is 16 and the 37th term is 115. Subtracting these two terms, we get 115 - 16 = 99. This is the common difference of the sequence.

Once we know the common difference, we can solve for the first term by using any of the terms in the sequence. In this case, we will use the 4th term. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1), where a_n is the nth term, a_1 is the first term, and d is the common difference. Substituting the 4th term, the common difference, and n = 4, we get a_4 = a_1 + d(4-1). Simplifying this equation, we get 16 = a_1 + 99. Solving for a_1, we get a_1 = -83.

Finally, we can solve for the 22nd term by using the first term and the common difference. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1). Substituting the first term, the common difference, and n = 22, we get a_{22} = -83 + 99(22-1). Simplifying this equation, we get a_{22} = 148.

Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.

Learn more about arithmetic sequence here:

brainly.com/question/28882428

#SPJ11

Answer:

42.33+49.8

Step-by-step explanation:

add sides man i think

Answer:

Step-by-step explanation:

Answer:

A box has 6 pencils. Each pencil weighs x grams. The 6 pencils weigh a combined total of 54 grams.

Step-by-step explanation:

Answer:

a) 1224 in³

b) 3060 in³

Step-by-step explanation:

a) 15x12x17=3060, 3060/2.5=1224 cubic inches

b) 3060; 15x12x17

extra note:

Volume of rectangular prism formula:

V = l·w·h (length times width times height)

I assumed the jewelry in 2.5 cubic inches in volume so i hope its right

hope this helps  :)

Answer:

Ellipse. It is irregular at some points.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

20,19,18

Step-by-step explanation:

because you have to go backwards

Answer:

36

Step-by-step explanation:

3*12=36

We need to prove that the sequence of functions fn(x) = (1/2)cos^2(√nx) converges uniformly to 0 on the real numbers.

To prove uniform convergence, we need to show that for any ε > 0, there exists a positive integer N such that |fn(x) - 0| < ε for all n > N and for all x in the real numbers.

Given fn(x) = (1/2)cos^2(√nx), we observe that as n increases, the argument √nx inside the cosine function becomes larger, causing the cosine to oscillate more rapidly between 0 and 1. Since we are multiplying the cosine by (1/2) and taking its square, fn(x) gradually approaches 0 as n increases.

To formally prove uniform convergence, we can start by fixing ε > 0 and then choose N such that √Nx > 1/ε. By selecting this N, we can show that for all n > N, |fn(x) - 0| < ε for any x in the real numbers. This demonstrates that the sequence of functions fn(x) converges uniformly to 0 on the real numbers.

To learn more about real numbers click here :

brainly.com/question/31715634

#SPJ11

Answer: 3/4. fraction to decimal calculator to find what's an equivalent decimal for the fractional number 3/4.

0.75 is a decimal and 75/100 or 75% is the percentage for 3/4.

Step-by-step explanation:fraction simplification calculator to find what's a reduced or simplest form for 75/100 at its lowest terms. 3/4 is a simplified fraction for 75/100

Answer:

There were 300 videos.

Step-by-step explanation:

Since there are 24 videos that got awards, and that's only 8% of the total videos, you put those together. We want the number of 100% of the videos. I would solve this by setting up a ratio and solving for [tex]x[/tex]. This is would look like:

[tex]\frac{24}{8} =\frac{x}{100}[/tex]  

In order to get to 100, you must multiply 8 by 12.5. Therefore, you can multiply 24 by 12.5 to complete the ratio. That would make the ratio look like:

[tex]\frac{24}{8} =\frac{300}{100}[/tex]

Therefore there are 100% of the videos in the contest is 300.

There are 28 relations on set A.

To determine the number of relations on set A, we need to understand the concept of a relation. A relation between two sets A and B is a set of ordered pairs (a, b) where a is from set A and b is from set B. In this case, both sets A and B are the same, so we are looking for relations within set A.

In a relation on set A, each element of A can be related to any other element of A, including itself. This means that for each pair of elements in set A, we have two possibilities: either they are related or they are not.

Since there are 8 distinct elements in set A, for each pair, we have two choices: either they are related or not related. Therefore, for each pair of elements, we have 2 possibilities.

Now, the total number of relations on set A can be calculated by multiplying the number of possibilities for each pair of elements. Since there are 8 distinct elements in set A, there are (8 choose 2) pairs of elements in total.

Using the binomial coefficient formula, (n choose k) = n! / (k!(n-k)!), we can calculate (8 choose 2):

(8 choose 2) = 8! / (2!(8-2)!)

            = (8 * 7) / (2 * 1)

            = 28

Therefore, there are 28 different relations on set A.

To know more about relations, refer here:

https://brainly.com/question/2253924

#SPJ4

Answer:

By substituting the values of A, C, and D the equation modelling the function is;

g(x) = 3·sin(x - π/2) - 4

Step-by-step explanation:

From the given information, we have;

The vertical stretch of the sine function = 3 × The parent function

∴ A = 3

Given that the horizontal shift left = π/2 units, (from an online source with similar question)

The vertical shift down = 4 units

The given function, g is g(x) = A·sin(x + C) + D

Where;

A = The amplitude = The maximum displacement from the rest or equilibrium position = 3

C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)

D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)

Therefore, the equation modelling the function is;

g(x) = 3·sin(x - π/2) - 4

Answer:

g(x) = 3·sin(x + π/2) - 4

Step-by-step explanation:

shifted left, it will be positive inside the parentheses