The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced three times. What is the voltage in exponential form?

The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.

Explain function?

A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.

The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]

To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]

So, the corrected version of the solution is:

Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.

Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]

Step 3: The decay factor is [tex]0.3.[/tex]

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As per the combination method, there are 12 people with a triple citizenship.

To find out how many people have a triple citizenship, we need to first find out how many people have two citizenships. We can do this by adding up the number of people with each combination of citizenship:

US-Mexican: 4

US-Canadian: 5

Canadian-Mexican: 6

Total number of people with two citizenships = 4 + 5 + 6 = 15

Next, we need to find out how many people have only one citizenship. We can do this by subtracting the number of people with two citizenships from the total number of people:

Total number of people = 53

Number of people with two citizenships = 15

Number of people with only one citizenship = 53 - 15 = 38

Now, we can use combinations again to find out how many people have a triple citizenship.

However, we need to subtract out the people who have only two citizenships, since we don't want to count them twice:

n(US-Mexican-Canadian) = n(US-Mexican) + n(US-Canadian) + n(Canadian-Mexican) - n(with 2 citizenships)

                      = 4 + 5 + 6 - 3   (since 3 people have 2 citizenships)

                      = 12

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The order of rotational symmetry of an equilateral triangle is 3.

The order of rotational symmetry of the isosceles triangle is 1.

What is an equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

When an object is rotated around its own axis, its shape stays the same, which is explained by the rotational symmetry of a shape.

All sides of an equilateral triangle are equal.

When an equilateral triangle rotates 120⁰, then its shape remains the same.

The order of rotational symmetry of an equilateral triangle is 360⁰/120⁰ =3.

All sides of an isosceles triangle are not equal.

When an isosceles triangle rotates 360⁰, then its shape remains the same.

The order of rotational symmetry of an isosceles triangle is 360⁰/360⁰ =1.

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Answer:

[tex]\frac{25}{11}[/tex]

Step-by-step explanation:

an improper fraction is one where the value on the numerator is larger than the value on the denominator.

2 [tex]\frac{3}{11}[/tex] is a mixed number, that is a whole number and a fraction

this can be converted to an improper fraction by summing the 2 parts , that is the whole number and the proper fraction as

2 + [tex]\frac{3}{11}[/tex]

= [tex]\frac{22}{11}[/tex] + [tex]\frac{3}{11}[/tex]

= [tex]\frac{22+3}{11}[/tex]

= [tex]\frac{25}{11}[/tex]

or

multiplying the whole number by 11 and adding 3 , over 11

[tex]\frac{2(11)+3}{11}[/tex]

= [tex]\frac{22+3}{11}[/tex]

= [tex]\frac{25}{11}[/tex]

Answer:f(x-5)=x

Step-by-step explanation:To evaluate f(x-5) we need to subtitute x - 5 for x in the expression for f(x):

f(x-5) = (x-5) + 5

The +5 and -5 cancel out, so we are left with f(x-5)=x

Renaming 1 foot to equivalent fraction in yards as  1/3 yards

We multiply the number of feet by 1/3 to convert this to yards, and then we need to identify the two elements of this equation that have a functional relationship.

As we are aware,

1 foot equals 3 yards.

As a result, we must multiply the unknown numbers, denoted by the letter x, by 1/3 in order to get the feet.

Let's say that the variables in this situation are x and y, where x stands for feet and y for yards.

To get the unit in yards, multiply the unit in feet by a factor of three-quarters. x = 1/3y

Hence, the renaming of 1 feet as 1/3 yards, where the fraction is 1/3.

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Answer:  y = 2x + 8

Step-by-step explanation:

3y - 6x = 24

      3y = 6x + 24

        y = (6x + 24) / 3

        y = 2x + 8

Answer:

Step-by-step explanation:

To find the benchmarks between which 3/8 falls, we need to identify the nearest fractions with denominators that are multiples of 8.

The fraction 3/8 is halfway between 1/4 and 1/2, which can be written as 2/8 and 4/8 respectively. So, we know that 3/8 is greater than 2/8 and less than 4/8.

Therefore, the benchmarks between which 3/8 falls are 2/8 and 4/8. Alternatively, we can express these fractions as decimals and say that 3/8 falls between 0.25 and 0.5.

If Atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, then he has 1 nickels and 4 dimes.

Let x be the number of nickels and y be the number of dimes. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, we can write two equations:

x + y = 10 (since he has 10 coins in total)

5x + 10y = 70 (since the combined value of the coins is 70 cents)

We can simplify the second equation by dividing both sides by 5:

x + 2y = 14

Now we can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x + y = 10x = 10 - y

Now we can substitute this expression for x into the second equation:

x + 2y = 14(10 - y) + 2y = 14

Simplifying, we get:

10 + y = 14

y = 4

Therefore, Atharv has 5 - 4 = 1 nickel and 5 - 1 = 4 dimes.

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Lydia used a total of approximately 16.33 pints of paint to paint her bedroom walls, with 6.2 pints being blue and 10.33 pints being white.

We know that 3/5 of the total paint used is blue, and the remaining 2/5 must be white.

Let x be the total amount of paint used in pints. Then, we can write:

3/5 x = 6.2 (pints of blue paint used)

2/5 x = ? (pints of white paint used)

To solve for the pints of white paint used, we need to isolate the variable x in the second equation:

2/5 x = (2/3) * 3/5 x (multiply both sides by 2/3 to simplify)

2/5 x = 6.2 * 2/3

2/5 x = 4.1333...

Now we can solve for x by multiplying both sides by 5/2:

x = (5/2) * (2/5) x = (5/2) * 4.1333... = 10.3333...

Therefore, Lydia used approximately 10.33 pints of white paint and  6.2 pints of blue to paint her bedroom walls.

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The probability that no student will withdraw from the course is approximately 0.008 or 0.8%, assuming a binomial distribution with n=90 and p=0.05.

Since each student's decision to withdraw or not is independent of others, we can model the number of students who withdraw as a binomial random variable with n=90 and p=0.05.

To find the probability that no student will withdraw from the course, we want to find P(X=0), where X is the number of students who withdraw. This is given by the binomial probability mass function:

P(X=0) = (n choose 0) * p^0 * (1-p)^(n-0) = (90 choose 0) * 0.05^0 * 0.95^90

Using a calculator or software, we find:

P(X=0) ≈ 0.008

Therefore, the probability that no student will withdraw from the course is approximately 0.008 or 0.8%.

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Answer:

-0.06666666666

hope it helps :)

A' is complement of A, A∩B is intersection of A and B, A∪B is union of A and B.

In set theory, the complement of a set is the set of all elements in the universal set that are not in the given set. In other words, it is the set of all elements in the universal set that are outside of the given set.

Ω = {2, 3, 4, 5, 6, 7, 8, 9} (whole numbers from 2 to 9)

A = {4, 6, 8} (even numbers from Ω)

B = {2, 3, 5, 7} (prime numbers from Ω)

a. A' (complement of A, i.e. elements in Ω that are not in A)

A' = {2, 3, 5, 7, 9} (odd numbers and 9 are not in A)

b. A∩B (intersection of A and B, i.e. components found in both A and B)

A∩B = {2} (the only even prime number is 2)

c. A∪B (union of A and B, i.e. elements that can be found in A, B, or both)

A∪B = {2, 3, 4, 5, 6, 7, 8} (all the even numbers and prime numbers from Ω).

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The complete question is:

ASAP

Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:

a. A’

b. A∩B

c. A∪B

A. The equation of the line is expressed as: y = (-5/2)x + 13.

B. The x-intercept of the equation is calculated as: 26/5.

A. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to find the equation of a line passing through the point (4,3) with a slope of -5/2.

Substituting the values, we get y - 3 = (-5/2)(x - 4), which simplifies to y = (-5/2)x + 13 by expanding and adding 3 to both sides.

B. To find the x-intercept of the equation y = (-5/2)x + 13, we set y to 0 and solve for x. 0 = (-5/2)x + 13, which simplifies to x = 26/5 by multiplying both sides by -2/5 and adding (26/5) to both sides.

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Answer:1, -.66 repeating, 1.25

Step-by-step explanation  i turned them into decimals

24/8x-1/3= -1

-2/5x5/3= -.66 repeating

-5/6x-3/2= 1.25

The value of x for the angle 100 + x under the top parallel line is equal to -10.

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.

The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:

100 + x = 90

subtract 100 from both sides

x = 90 - 100

x = -10.

Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.

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Answer:

Step-by-step explanation:

We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:

(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3

(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3

4 = (linear dimension of image / linear dimension of original)^3

Taking the cube root of both sides, we get:

(cube root of 4) = (linear dimension of image / linear dimension of original)

Simplifying, we have:

2 = (linear dimension of image / linear dimension of original)

Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.

The probability that an ugly splice is weak is 2/3.

This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).

In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).

The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.

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Answer:

54 degrees

Step-by-step explanation:

180-126=54

Answer:

The cost price of each shirt is $8.

They mark up the shirts 25%, which means they increase the price by (25/100) * $8 = $2.

So, the selling price of each shirt becomes $8 + $2 = $10.

At the end of the year, they sell the shirts for 25% off, which means they reduce the price by (25/100) * $10 = $2.50.

Therefore, the selling price of each shirt after the discount becomes $10 - $2.50 = $7.50.

The profit made on each shirt sold at the end of the year is the difference between the selling price and the cost price, which is $7.50 - $8 = -$0.50.

Since the profit is negative, it means that the Spirit Club is making a loss of $0.50 on each shirt sold at the end of the year.

The measure of angle R in ΔSRT which is drawn inside the circle is 77.5°.

Circle is a two-dimensional shape that is defined as the set of all points that are equidistant from a central point. It is often represented as a round shape with a curved boundary.

Since SR is a diameter of the circle, it follows that angle STR is a right angle (90°). Therefore, we can find the measure of angle SRT using the following equation:

∠SRT + ∠STR = 180°

(2x-23°) + 90° = 180°

2x + 67° = 180°

2x = 180° - 67°

2x = 113°

x = 56.5°

∠TRS = 5x-97°

∠TRS = 5(56.5°)-97°

∠TRS = 192.5°

Finally, we can find the measure of angle SRT:

∠SRT = 180° - ∠STR - ∠TRS

∠SRT = 180° - 90° - 192.5°

∠SRT = -102.5°

Therefore, to find the measure of angle R, we need to add 180° to angle SRT:

∠R = ∠SRT + 180°

∠R = -102.5° + 180°

∠R = 77.5°

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Answer:  The answer is 32.

Step-by-step explanation: Yes since you did 9.5+13.6+5.7+3.2 is 32.00 or 32.

To find the number of machines that minimize the unit cost, we need to find the value of x that minimizes the function C(x). We can do this by finding the critical points of C(x) and determining which one corresponds to a minimum.

First, we take the derivative of C(x) with respect to x:

C'(x) = 1.2x - 372

Then, we set C'(x) equal to zero and solve for x:

1.2x - 372 = 0

1.2x = 372

x = 310

So the critical point is x = 310.

To determine whether this critical point corresponds to a minimum or a maximum, we need to examine the second derivative of C(x):

C''(x) = 1.2

Since C''(x) is positive for all values of x, we know that the critical point x = 310 corresponds to a minimum.

Therefore, the number of machines that must be made to minimize the unit cost is 310.

The probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.

The probability of getting a head on the 5th flip is still 50%. This is because each coin flip is an independent event, and each coin flip is not affected by the outcome of the previous coin flips. Thus, the probability of getting a head on the 5th coin flip is 0.5, regardless of the previous 4 coin flips.

To summarize, the probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.

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Answer:

The mean increases by 1.4

A statement that must be true according to the dot plot include the following: A. the data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the number of e-mails that Darren received from one of his customers each day for 14 days, we can reasonably infer and logically deduce that the data set is skewed left, which ultimately implies that that on half of the days (7 days), Darren received a total of 11 or 12 e-mails from this customer.

In conclusion, the dot plot is skewed left because it has a long tail on its left side and 7 days is the half of 14 days.

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Answer:

Step-by-step explanation:

every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get

85.184in^3 per second

Answer:

Step-by-step explanation:

the answer is

z=0.625