What is the decay factor that corresponds to a 99% decrease?

The compound interest is $348,966.97 and the future value is $464,966.97.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest to calculate the future value of the investment:

\(FV=P(a1+r/n)^{nt}\)

where:

P = the principal amount (the initial investment)$116,000

r = the annual interest rate (as a decimal)=0.0429

n = the number of times the interest is compounded per year=52

t = the number of years=34

Plugging in these values, we get:

FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸

FV = $464,966.97

So the future value of the investment after 34 years is $464,966.97.

Compound interest = $464,966.97 - $116,000 = $348,966.97

Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.

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2x - 7 = 26 is the required equation representing the word problem

Third option is correct

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here

Let the number of miles Mary ran this week be x miles

Mary ran 7 miles less than twice the amount of miles she ran last week

Distance ran by Mary this week = 2x -7

By the problem,

2x - 7 = 26

This is the required equation representing the word problem

Third option is correct

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The number of whole cup of milk that Charlene would use for all 8 packages would be = 8 cups of whole milk.

A square is a type of quadrilateral that has four sides with four angle 90° at each edge.

The number of chocolate square mixture Charlene would use for the party = 8 packages.

The number of packages that require a cup of milk = 1

Therefore the number of whole cups of milk that would be used for the whole 8 packages would be = 8×1 = 8 cups of whole milk.

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Answer:

y = -400

Step-by-step explanation:

y = 350 - 25(x)​

Let x = 30

y = 350 - 25*30

y = 350 - 750

y = -400

Answer: d.12

Step-by-step explanation:

Answer: 185/8

Step-by-step explanation:

Area of triangle = Base x Height / 2

Convert numbers into improper fractions:

6 1/6 = 37/6

7 1/2 = 15/2

( 15/2*37/6 )/2 = 185/8

Answer:

2π(x+y+z)

is the factorization

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.

Let's calculate the expected value for each outcome:

Outcome 1: Roll a 1 and receive $55.

The probability of rolling a 1 on a fair die is 1/6.

Expected value = (1/6) × $55 = $9.17

Outcome 2: Roll a 2 and receive $10.

The probability of rolling a 2 on a fair die is 1/6.

Expected value = (1/6) × $10 = $1.67

Outcome 3: Roll a 3 and win nothing.

The probability of rolling a 3 on a fair die is 1/6.

Expected value = (1/6) × $0 = $0

Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.

The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.

Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)

Outcome 5: Roll a 6 and pay Señor Rick $25.

The probability of rolling a 6 on a fair die is 1/6.

Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)

Now, let's sum up the expected values:

Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17

= -$4.00

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

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In response to the given question, we can state that So the entire function factored expression is: 8x + 96y = 8(x + 12y)

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

To factor 8x + 96y, we can first factor out the greatest common factor, which is 8.

8x + 96y = 8(x + 12y)

So the entire factored expression is:

8x + 96y = 8(x + 12y)

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The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

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Answer:

C. 20.8

Step-by-step explanation:

Reference angle = 32°

Opposite side length opposite to reference angle = 13

Adjacent side length = x

We would apply the trigonometric function, TOA. Which is:

Tan 32 = Opp/Adjacent

Tan 32 = 13/x

Multiply both sides by x

x × Tan 32 = 13

Divide both sides by Tan 32

x = 13/Tan 32

x = 20.8043489

x = 20.8 (nearest tenth)

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

100%?

Step-by-step explanation:

Divide total distance of the race by the length each runner runs:

8 miles / 4/5

When dividing by a fraction flip the fraction over and multiply:

8 miles x 5/4 = (8x5)/4 = 40/4 = 10

There are 10 runners

Answer:

10 runners

Step-by-step explanation:

Is 8 Miles which equals to 40/5 miles. 40/5 miles divided by 4/5 = 10 so 10 runners.

Answer:

what is the answers is it multiple choice?

Step-by-step explanation:

Answer:

y = x

Step-by-step explanation:

So 1st we need to find the slope of the original line which is y = -x

(use slope formula)

2nd Now we just need to reverse the slope, and that gets us to y = x

Answer: 6

its obvious  

The rigid motion of the solid line figure is translated to the dotted line figure.

Translation describe a function that moves an object a certain distance.

In a translation, every point of the object must be moved in the same direction and for the same distance.

In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.

Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation

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The number of fruit flies on day 20 is approximately 213.

Given,

The population of fruit flies = p

Number of days = t

The given equation is:

p(t) = \(\frac{215}{1+52e^{-0.43t} }\)

We have to find the number of fruit flies on day 20.

That is, t as 20.

So,

p(20) = \(\frac{215}{1+52e^{-0.43(20)} }\)

p(20) = \(\frac{215}{1+52e^{-8.6} }\)

p(20) = \(\frac{215}{1+52(1.84)}\)

p(20) = \(\frac{215}{1+9.57}\)

p(20) = \(\frac{215}{1.009}\)

p(20) = 212.96

p(20) ≈ 213

That is, the number of fruit flies on day 20 is approximately 213.

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Answer:

Westbound = x;

Eastbourne = x-20;

So they will have the common rate: 360/2 = 180;

x+x-20 = 180

2x = 200;

x = 100;

So Eastbourne will be 100-20 = 80 miles per an hour;

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

There are 69120 total combinations.

Step-by-step explanation:

To find the total number of combinations, we multiply all these values. So

16 people

18 colors

12 shades

20 tertiary gradients.

How many combinations are there total?

16*18*12*20 = 69120

There are 69120 total combinations.

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04

The margin of error is a statistic that describes how much random sampling error there is in survey results.

Given in question,

n = 400

p = 317/400

  = 0.7925

Confidence Level = 95%

                          = 0.95

Formula for margin error, E = \(z\sqrt{\frac{p(1-p)}{n} }\)

Confidence level corresponding to 95 % confidence interval, z = 1.96

Therefore,

Margin Error, E = \(1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }\)

                         = 0.0397

                         ≈ 0.04

Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.

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Step-by-step explanation:

To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):

x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)

Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:

x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7

Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.

Note that this expression is defined for all values of x and y except for x=0.

Answer:

total amount donated when aaron walks n miles = $2 + $3(n-1)

Step-by-step explanation:

Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walks and then a certain dollar amount for each additional mile he walks. Based on this pledge, if Aaron walks 8 miles, the sponsor will donate a total of $23 to the charity.

Write a formula that can be used to determine the amount of money this sponsor donates when Aaron walks n miles.

total amount sponsor pays = base donations + (additional miles walked after first mile x amount paid)

when Aaron walks 8 miles

additional miles = 8 - 1 = 7

23 = 2 + 7x

23 - 2 = 7x

x = 3

additional amount paid is $3

total amount donated when aaron walks n miles = $2 + $3(n-1)

Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

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