What is the present value of ​$500 to be received 13 years from
now discounted back to the present at 11 ​percent?

Answer:

Step-by-step explanation:

2x+3

x=3divides2

After 75 minutes, a sample of 280 grams of radioactive goo has decayed to 17.5 grams. The half-life of the radioactive is 18.75 minutes.

The problem can be solved using decay model. The formula of decay system is given by:

Nt = No . e^(-λ . t)

Where:

Nt = quantity at time t

No = initial quantity

λ = decay constant = ln(2) / T

T = half life

The above formula can be rearranged to:

T = t . ln(2) / [ln(No/Nt)]

Parameters given in th problem:

No = 280 grams

t = 75 minutes

Nt = 17.5 grams

Plug these parameters into the formula:

T =  75 . ln(2) / [ln(280/17.5)]

  = 18.75 minutes

Hence, the half-life of the radioactive goo is 18.75 minutes.

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The number of miles driven per gallon is 401/20

Louie drove 5- 1/8 miles

He used 2.5 gallons for this journey

Therefore the number miles per gallon can be calculated as follows

401/8 = 2.5

x= 1

Cross multiply both sides

2.5x= 401/8

x= 401/8 ÷ 2.5

x= 401/8 × 1/2.5

= 401/20

Hence the number of miles per gallon is 401/20

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Answer:

\(\frac{68285}{44}\) or \(1551.93181818...\)

Step-by-step explanation:

\(\frac{9755}{2(\frac{22}{7})}\\\\\)

Answer:

C = .40n

Step-by-step explanation:

The line shows that the graph is proportional.  I know this because the graph is linear and goes through the origin (0,0).  This means that I can take any point and put it in the form y/x to find the slope.

I took the point (10,4) on the graph.  I put that in the form y/x = 4/10.  4/10 = .40 which is my slope.

C= .40n

Answer:

about $7.06

Step-by-step explanation:

Answer:

$7.06

Step-by-step explanation:

unit cost: $1.35/gram

5.23 grams * $1.35/gram = $7.0605

Answer: $7.06

The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.

A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.

Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.

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This describes the process of collecting a large sample size.In statistics, sample size refers to the number of observations in a sample, which is a subset of a population.

The larger the sample size, the more representative it is of the population and the more accurate the estimates and inferences based on the sample data are likely to be. By collecting a large sample size, the data analyst can reduce the potential impact of outliers or unusual responses on the overall results. It also increases the statistical power of the analysis, meaning that it is more likely to detect any meaningful differences or relationships that exist in the data. Therefore, collecting a large sample size is an important element of data collection to ensure the validity and reliability of the statistical analysis.

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The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.

If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:

Total number of People = 1000

Chances of winning the lottery = 1%

How many people would win 10 dollar lottery = 1000 * 1%

= 1000 * 0.01

= 10 People.

So there are chances that 10 out of 1000 people will win the lottery.

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Answer:

The mistake is that 4x+x = 5x  not 4x

Step-by-step explanation:

4x + x = 30 –6

Combine like terms

5x = 24

Divide each side by 5

5x/5 = 24/5

x = 24/5

The mistake is that 4x+x = 5x  not 4x

Answer: 2, 3, 5, 6, 9, 10,

Step-by-step explanation:

Answer:

The company can manufacture 135 boxes of stuffed animals for $5000

Step-by-step explanation:

To find b, substitute $5000 for c(x), so

Then subtract 2300 from both sides of the equation, so

Finally divide both sides of the equation by 20, so

To check your answer substitute 135 in as b...

Answer:

see below

Step-by-step explanation:

For every value of y, there can only be one value of x in order for it to be a function

D) is a function because every input has a unique output

E) is NOT a function because there are two values for one x value

F) is a function because even though there are two of the same values for one y value, each of the x values are unique

Answer: D is a function the other two are not.

Step-by-step explanation:

D: All the X's have there own individual y's

E & F: Some of the X's have different Y outputs which makes it faulty.

9514 1404 393

Answer:

  3x +2y +24 = 0

Step-by-step explanation:

In general, the equation of a perpendicular line can be found by swapping the coefficients of x and y, then negating one of them. The value of the constant will be what is required to make the line pass through the given point.

The equation will be of the form ...

  3x +2y +c = 0

At the given point, (x, y) = (-6, -3), we have ...

  3(-6) +2(-3) +c = 0 . . . . substitute the given point coordinates

  -18 -6 +c = 0 . . .simplify

  c = 24 . . . . . . . . add 24

The general-form equation for the line is ...

  3x +2y +24 = 0 . . . . . shown in blue in the attachment

Answer:

1.  3³

2.  (-5)⁴

3.  3¹⁰

4.  4⁰

Step-by-step explanation:

When multiplying exponents with the same base, you add the exponents.  When dividing exponents with the same base, you subtract the exponents.  When raising a number with an exponent to another power, multiply the exponents.

1.  \(\frac{3^4*3^6}{3^2*3^5} =\frac{3^{10}}{3^7}=3^3\)

2.  \(\frac{(-5)^{12}}{(-5)^3*(-5)^5} =\frac{(-5)^{12}}{(-5)^8}=(-5)^4\)

3.  \((3^2)^5=3^{10}\)

4.  \(\frac{4^0*4^4}{4^1 * 4^3} =\frac{4^4}{4^4}=4^0\)

Answer:

-10

Step-by-step explanation:

The constant is the part of the algebraic function or expression that does not change. In this case, as x changes, the constant -10 does not. Thus, -10 is the constant.

Answer:

a) y = 400(0.75) ^x

b) Exponential Decay

Step-by-step explanation:

An adult can take 400 mg of ibuprofen. Each hour, the amount of ibuprofen decreases by 25%.

a. Write an equation of this exponential situation for the total amount of ibuprofen, y, in terms of the number of hours, x.

This situation above is an exponential decay situation.

The forms is given as

y = a(1 - r) ^x

Where

y = the total amount of ibuprofen

a = initial amount of ibuprofen = 400mg

r = Decay rate = 25%

x = Time in hours

Hence, the Equation is written as

y = 400(1 - 0.25) ^x

y = 400(0.75)^x

b. Does this situation represent exponential growth or decay? Explain how you know

This situation represents an exponential decay because we are told in the question that each hour, the amount of ibuprofen DECREASES by 25%. Decrease in this context means Decay.

Answer:

3t (t²-7t-4t)

Step-by-step explanation:

The highest common factor was 3t

Answer: $122.64

Step-by-step explanation:

5% of $116.80 is $5.84

$116.80 + $5.84 = $122.64

There are 8! (factorial) ways for the eight students to stand next to each other. However, since no two professors can stand next to each other, we need to alternate professors and students. We can start with a professor, then a student, then a professor, and so on.

There are 5! ways to arrange the five professors among the eight spaces where a professor can stand. Once the professors are arranged, there are 8 - 5 = 3 spaces left for students to stand. There are 8P3 (permutations) ways to arrange the three students among the three spaces.

Therefore, the total number of ways for eight students and five professors to stand next to each other such that no two professors are standing next to each other is 5! * 8P3 = 5,760 ways.

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The Frequency will be "266.14 Hz" and the number of loops are "60".

For the given question-

The formula for the linear velocity is given as;

Linear density; μ = mass/length

Put the values,

μ = 4.5 x 10⁻³/0.6

μ = 7.5 x 10⁻³ kg/m

The formula for the fundamental frequency is;

F = (1/2L)√(T/ μ)      

F = (1/2x0.6)√(765/ 7.5 x 10⁻³)      

F = 266.14 hz

The number of loops  is;

n = f'/f

n = 16000/266.14

n = 60

Thus, a person who can hear frequencies up to f = 16 kHz would be able to hear the highest harmonic with number n equal to 60.

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The complete question is-

A piano tuner stretches a steel piano wire with a tension of 765 N . The steel wire has a length of 0.600 m and a mass of 4.50g .

What is the frequency (f_1) of the string's fundamental mode of vibration?

What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHzc?

Answer:

On a horizontal number line, going left means that temperatures are getting colder, while going right means that temperatures are getting warmer.

Answer:

Step-by-step explanation:

So it 22

Answer: 0.007

Step-by-step explanation:

Long answer: According to the International Telecommunication Union (ITU), there were an estimated 5 billion unique mobile phone users in the world as of January 2018. However, it is important to note that this number does not necessarily equate to the number of individual subscribers, as some people may have more than one mobile phone or SIM card. Additionally, the number of cell phone subscribers can vary by country and region. For example, according to Statista, the number of mobile phone users in the United States was approximately 266 million in 2018. Overall, while there is not a definitive global estimate for the number of cell phone subscribers in 2018, it is clear that mobile technology continues to have a significant impact on the way people communicate and access information worldwide.

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Answer:

70000000

Step-by-step explanation:

To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².

The first step is to substitute the given values into the formula:

29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).

Next, we simplify the equation and distribute the terms:

29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).

After combining like terms, we have:

29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.

Combining similar terms further, we get:

29,946 = 34x² + 40x - 6.

Now, we can rearrange the equation and set it equal to zero:

34x² + 40x - 29,946 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.

After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.

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Given:

5× ______ = - 35

• -35/5

• -7

5 x -7 = -35

Answer:

The answer is 7

Step-by-step explanation:

Divide each term in 5x=-35 by 5 and simplify.x=−7