Construct each segment as directed.

a segment separated into five congruent segments

The amount of money you will get if you invest $1000 in an account with 4.5% annual interest, compounded annually, in 5 years is: $1221.

If we assume that the interest is compounded annually, the formula we would apply to calculate the future value of an investment is given as:

\(FV = PV x (1 + r)^n\) where we have:

PV = present value (the initial investment)

r = annual interest rate (as a decimal)

n = number of compounding periods

In this case, we are given the following:

PV = $1000

r = 0.045 (4.5% expressed as a decimal)

n = 5 (5 years)

Substituting these values into the formula, we would get the following:

FV = $1000 x (1 + 0.045)^5

FV = $1000 x 1.221

FV = $1221

Learn more about compound interest on:

https://brainly.com/question/24274034

#SPJ1

Answer:

8.5%

Step-by-step explanation:

8.50% of 52= 4.42

Answer:

angle 2 and 3 are vertical angles

Step-by-step explanation:

because they are opposite angles made from two intersecting lines.

Answer:

a) \(x(x+3)\)

b) \(2x(x-8)\)

c) \(3x(2+3x^{2})\)

d) \(4x^{2} (3x-1)\)

Step-by-step explanation:

a) \(x^{2} +3x=x(x+3)\)

b) \(2x^{2} -8x=2x(x-8)\)

c) \(6x+9x^{3} =3x(2+3x^{2})\)

d) \(12x^{3} -4x^{2} =4x^{2} (3x-1)\)

Factors of the following algebraic expression are

a. Factors of x² + 3x   are x and x+3

b. Factors of 2x² -8x  are 2, x and ( x-4)

c. Factors of 6x +9x³ are 3, x  and (2 + 3x²)

d. Factors of 12x³ - 4x² are 4, x, x and (3x -41)

The factor of an given algebraic expressions are one or more numbers or linear or other expressions that multiply to form the given algebraic expression and cannot be broken down further into simpler expressions.

For finding factors of an algebraic expression we can simply take out common expressions from all the terms of the expression and try to simplify it.

a. x² + 3x = x( x+3), (taking x common from both terms)

b. 2x² -8x = 2x ( x-4) (taking 2x common from both terms)

c.  6x +9x³ = 3x (2 + 3x²)   ( taking 3x common from both terms)

d.12x³ - 4x² = 4x× x × (3x -41) ( taking 4x²  common from both terms)

Also, Learn more about the factors of the algebraic expression from the link below:

brainly.com/question/1245504

#SPJ1

Answer:

99 degrees.

Step-by-step explanation:

degree of arc is half the degree of the angle.

Answer:

The Answer is 47

Step-by-step explanation:

Because you do A squared plus B squared equals C squared and Squared is just multiplying both by two.

Answer:

Step-by-step explanation:

1. make common denominators

13/16-12/16

1/16

Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

To know more about standard deviation, visit:

https://brainly.com/question/475676

#SPJ1

Answer:

Number 6 is x=65 number 7 is x=-1

Step-by-step explanation:

I just did number 6 on another persons page but ill repeat it as best i can

You're going to set to X plus 2 = 3X -63 then you are going to subtract 2X from both sides which will leave you 2 equals X -63 and then you add 63 to both sides which will leave you x equals 65

Number 7

2X plus 20=6X plus 24

1st Subtract 2X from both sides which will leave you with 20 = 4X plus 24

2nd you're going to subtract 24 from both sides Which will leave you with negative 4 = 4X

Then you're going to divide both sides by 4 which will leave you with X equals negative one

Answer:

yes she is correct

Step-by-step explanation:

(4^3)^3=262144 and 2^18=262144

(4^3)^3=2^18

hope this helps! :)

(4^3)^3 can be rewritten as 2^18 .

The result of multiplying an integer (not a fraction) by itself is called square of a number. Example: 4 × 4 = 16, so 16 is a square number.

Now the given number is,

(4^3)^3

Since we know tha 4 is the square of 2

i.e 2x2 = 4

or, 2^2 = 2x2 =  4

Therefore we can write,

{(2^2)^3}^3

Using the exponential property,

(a^b)^c = a^bc

So,

(2^2)^3 = 2^6

and,

{(2^2)^3}^3 = (2^6)^3 = 2^18

Hence,(4^3)^3 can be rewritten as 2^18

To learn more about square:

https://brainly.com/question/14198272

#SPJ2

Answer:

4x² (3x - 1)

Step-by-step explanation:

→ Find the LCM of 12 and 4

LCM = 4

→ Find the LCM of x³ and x²

LCM = x²

→ Combine both LCM's together to form the outside multiplier

4x² (? - ?)

→ Complete the operations of 12x³ ÷ 4x² to find the first ? and 4x² ÷ 4x² to find the second ?

12x³ ÷ 4x² = 3x

4x² ÷ 4x² = 1

→ Therefore,

∴ 4x² (3x - 1)

type your equation into the desmos app and you can see the answer

Hope it helps :)

↓Graph Provided Below↓

Answer:

= (9/4) + (17/6)

= (61/12) / 2

= 61/24

Hope this helps you. Do mark me as brainliest.

The values of k for local maxima is k = 1 and k = -1

The given function is,

   f(x) = kx⁴ - 2k³x²

⇒ f'(x) = 4kx³ - 4k³x

⇒f''(x) = 12kx² - 4k³

To find a local maximum at x = 1, we need f'(1) = 0 and f''(1) < 0.

Therefore, set  f'(1) = 0,

⇒4k(1)³ - 4k³(1) = 0

⇒4k - 4k³ = 0

⇒4k(1 - k²) = 0

From this, we can see that either k = 0 or k = ±1.

However, we have to check the second derivative to determine if these are local maximums,

⇒f''(1) = 12k(1)² - 4k³

For k = 0, f''(1) = 0, which means there isn't a local maximum.

For k = 1, f''(1) = 8 < 0, which means there is a local maximum.

For k = -1, f''(1) = -8 < 0, which means there is also a local maximum.

Therefore,

The values of k that give a local maximum at x = 1 are k = 1 and k = -1.

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ12

Answer:

D. 48

Step-by-step explanation:

In the experiment, 16/40 landed exactly on heads. If you do 16/40 * 3/3 = 48/120.

This means that you can estimate 48 of the next 120 trials have 2 coins showing heads.

Answer:

0.0047

Step-by-step explanation:

there is no step by step explanation to this

It would be equal to 0.0047!

32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

To know more about integral visit

https://brainly.com/question/31433890

#SPJ11

Answer:

The Answer is P = (-2.5 , 1 )

Step-by-step explanation:

Let, the point is P(x,y)

then, \(x=\frac{m_{1}x_{2}+ m_{2}x_{1}}{m_{1}+m_{2}}\)

     =>\(x=\frac{5*(-1)+ 3*(-5)}{5+3}\)

     ∴\(x=-2.5\)

Again, \(y=\frac{m_{1}y_{2}+ m_{2}y_{1}}{m_{1}+m_{2}}\)

     =>\(y=\frac{5*7+ 3*(-9)}{5+3}\)

     ∴\(y=1\)

Thus, P = (-2.5 , 1 )

Answer:

240

Step-by-step explanation:

Answer:

It is 14 cents per minute

Step-by-step explanation:

We already have a ratio of

14:100

so we can divide it to get down to one to make it easier

.14:1

so it will be 14 cents per minute

hope this helps :)

Answer:

About 6 cents per minute

Step-by-step explanation:

Looking at the actual minutes and cost of the plan you can see this. Let's start with the first minutes given (100 with $14) which then goes to 200 with $20. There is a difference of 100 between the two and a difference of 6 with 14 and 20. If you would do 100*0.06 (6 cents) then you would see that for every 100 minutes there would be $6 being paid, in which is the difference between all the bottom numbers when going from left to right.

A more algebraic way to do this is by finding the slope from points we can make from the table (for example 100,14 , 200,20 , 300,26...). now let;s find the slope in which the two points (100,14) and (200,20) share. Using the slope formula \(\frac{y2-y1}{x2-x1}\) we substitute in our values so that the new equation would look like \(\frac{20-14}{200-100}\) which when adding like terms makes it \(\frac{6}{100}\) or in this case 0.06. The slope would be 0.06 and therefore every minute that is on the phone, $0.06 will be added to the bill.

Answer:

No, you should have learned this in 5th grade

Step-by-step explanation:

By the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverge

We are asked to determine whether the series ∑(1+9^n)/(4n) from n=1 to infinity is convergent or divergent.

We can use the ratio test to determine the convergence of the series. Let's compute the ratio of the (n+1)th term to the nth term:

[(1+9^(n+1))/(4(n+1))] / [(1+9^n)/(4n)]

= (1+9^(n+1))/(1+9^n) * (n/ (n+1))

As n approaches infinity, the term (n/(n+1)) approaches 1, and the ratio becomes:

(1+9^(n+1))/(1+9^n)

Since the ratio does not approach a finite value as n approaches infinity, the ratio test is inconclusive. Therefore, we cannot determine the convergence of the series using the ratio test.

However, we can use the limit comparison test with the series 1/n^p, where p=1/2. Let's compute the limit of the ratio:

lim n→∞ [(1+9^n)/(4n)] / [1/n^(1/2)]

= lim n→∞ (n^(1/2) * (1+9^n))/(4n)

= lim n→∞ (n^(1/2) + 9^n/ (4n^(1/2)))

Since the first term approaches infinity as n approaches infinity and the second term approaches zero, the limit diverges. Therefore, by the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverges.

Learn more about comparison test here

https://brainly.com/question/31474165

#SPJ11

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

To learn more about probability refer to:

https://brainly.com/question/13604758

#SPJ1

Rectangle ABCD is not similar to rectangle PQRS because their corresponding sides are not proportional, so rectangle ABCD cannot be dilated to fit exactly over rectangle PQRS.

Similar polygons are polygons that share these two features presented as follows:

The ratio between the equivalent side lengths is given as follows:

Due to the different ratios, they are not proportional, and hence the rectangles are not similar.

More can be learned about similar polygons at brainly.com/question/14285697

#SPJ1

Answer:

1/0.49

Step-by-step explanation:

Every pound = 1 pound

And for every one of this company spends 0.49pound

To express this in a ratio is 1:0.49

Which is also 1/0.49 in fraction.

A ratio tells us how many times a number contains another number. It compares two numbers in relation to each other.

Therefore 1/0.49 expresses the amount spent on advertising as a ratio

Answer:

Schalean paid about 13.6% sales tax

Sorry if i got it wrong

Answer:

9.36

Step-by-step explanation:

Answer:

\(m_{1} =1/2\\m_{2} =5\)

Step-by-step explanation:

\(2m^{2} -11m+5=0\)

\((2m-1)(m-5)=0\)

\(2m-1=0\\2m=1\\m_{1} =1/2\)

\(m-5=0\\m_{2} =5\)

Hope this helps