Define a set of strings S by - a∈S - If σ∈S, then −σσσ∈S Prove that every string in S contains an odd number of a 's. Proof by Induction: Base case: a∈S. So, S has an odd number of a 's. Inductive Step: Consider the cases generated by a. Case 1: Consider aaa. It has an odd number of a 's Case 2: Consider aaaaaaa. It has 7 's and thus an odd number of a 's So by PMI this holds.

Answer:

f(x) = -5(2)-4     f(x) = -10-4      f(x) = -14

Step-by-step explanation:

You put in the number 2 for the variable x

Answer:

−590+5√5

^-^hope this helped^-^

Answer:

Step-by-step explanation:

Answer:

10kg-30g

10×1000g - 30g

(10000 - 30) g

9970g

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The slope of the secant line through the points (2, f(2)) and (2+h, f(2+h)) is  2h + 5.

To find the slope of the second line through the points (2, f(2)) and (2+h, f(2+h)), we need to use the slope formula which is given as:

\(m = (y_2 - y_1)/(x_2 - x_1)\)

So, substituting these values in the slope formula, we get:

m = (f(2+h) - f(2))/(2+h - 2)

Now, we need to find f(2+h) and f(2).

f(2+h) = 2(2+h)²- 3(2+h) - 5

= 2(4+4h+h²) - 6 - 3h - 5

= 8 + 8h + 2h² - 11 -3h

= 2h² + 5h - 3

f(2) = 2(2)² - 3(2) - 5

= 8 - 6 - 5

= -3

Substituting these values in the formula, we get,

m = (2h² + 5h - 3 + 3)/(2+h - 2)

= (2h² + 5h)/h

= 2h + 5

Hence, the slope of the secant line through the points (2, f(2)) and (2+h, f(2+h)) is  2h + 5.

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The complete question is

Let \(f(x) = 2x^2-3x-5\). show that the secant line through (2, f(2)) and (2+h, f(2+h)) has slope 2h+5. then use this formula to compute the slope of the secant line.

Answer:

2c + 3b= $

Step-by-step explanation:

if they make 2 dollars for every cupcake and 3 dollars for every brownie they just need to plug in however many cupcakes into C and however many brownies to B to find their product

The net financing need considering the three accounts is approximately $185,753.42.

To determine the average investment in accounts receivable, inventories, and accounts payable, we need to calculate the Inventory Period, Receivables Period, and Payment Period.

Inventory Period:

The Inventory Period is the average number of days it takes for finished goods to be sold. In this case, the average production process time is given as 40 days, and finished goods are kept on hand for an average of 15 days before they are sold. Therefore, the Inventory Period is the sum of these two periods:

Inventory Period = Production Process Time + Days Kept on Hand

Inventory Period = 40 days + 15 days

Inventory Period = 55 days

Receivables Period:

The Receivables Period is the average number of days it takes for accounts receivable to be collected. It is given that accounts receivable are outstanding for an average of 40 days. Therefore, the Receivables Period is 40 days.

Payment Period:

The Payment Period is the number of days the firm receives credit on its purchases from suppliers. It is given that the firm receives 40 days of credit. Therefore, the Payment Period is 40 days.

Now, we can calculate the average investment in accounts receivable, inventories, and accounts payable.

Average Investment in Accounts Receivable:

Average Investment in Accounts Receivable = (Net Sales / 365) * Receivables Period

Average Investment in Accounts Receivable = ($1,200,000 / 365) * 40

Average Investment in Accounts Receivable ≈ $131,506.85

Average Investment in Inventories:

Average Investment in Inventories = (Cost of Goods Sold / 365) * Inventory Period

Average Investment in Inventories = ($900,000 / 365) * 55

Average Investment in Inventories ≈ $142,191.78

Average Investment in Accounts Payable:

Average Investment in Accounts Payable = (Cost of Goods Sold / 365) * Payment Period

Average Investment in Accounts Payable = ($900,000 / 365) * 40

Average Investment in Accounts Payable ≈ $87,945.21

Finally, to calculate the net financing need, we subtract the average investment in accounts payable from the sum of the average investment in accounts receivable and inventories:

Net Financing Need = Average Investment in Accounts Receivable + Average Investment in Inventories - Average Investment in Accounts Payable

Net Financing Need = $131,506.85 + $142,191.78 - $87,945.21

Net Financing Need ≈ $185,753.42

Therefore, the net financing need considering the three accounts is approximately $185,753.42.

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we have derived the formula T = √(8R/2.5) for the time taken for a rope of length R to be rotated about a central point, made R the subject of the formula, and used the formula to calculate the length of a rope that takes 16 seconds for a single revolution and the time taken for a rope of length 18 metres to complete a revolution.

How to solve questions?

a) To make R the subject of the formula, we need to isolate it on one side of the equation. We start by rearranging the formula:

T = √(8R/2.5)

Squaring both sides of the equation, we get:

T²= 8R/2.5

Multiplying both sides by 2.5, we get:

2.5T²= 8R

Finally, dividing both sides by 8, we get:

R = 2.5T²/8

Therefore, R is given by the formula R = 2.5T²/8.

b) To find the length of rope if it takes 16 seconds for a single revolution, we can substitute T = 16 into the formula we derived in part (a):

R = 2.5T²/8 = 2.5(16)²/8 = 100

Therefore, the length of the rope is 100 metres.

c) To find the time taken for a rope of length 18 metres to complete a revolution, we can again use the formula we derived in part (a), but this time we substitute R = 18:

T = √(8R/2.5) = √(8*18/2.5) = √(115.2) ≈ 10.7 seconds

Therefore, the time taken for a rope of length 18 metres to complete a revolution is approximately 10.7 seconds, rounded to one decimal place.

In summary, we have derived the formula T = √(8R/2.5) for the time taken for a rope of length R to be rotated about a central point, made R the subject of the formula, and used the formula to calculate the length of a rope that takes 16 seconds for a single revolution and the time taken for a rope of length 18 metres to complete a revolution.

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In this situation, the teacher could use a hypothesis test for a population means to determine if the computer-based instruction led to a statistically significant improvement in the student's test scores. The population in this case would be the entire class of students, and the mean would represent the average difference in test scores between the pretest and posttest.

The teacher can use a hypothesis test for a population means in the following situation:

1. Determine the population: The teacher's population consists of all the students who participated in the experiment.

2. Calculate the mean pretest score: The teacher will compute the average score of all the students' pretest results.

3. Implement computer-based instruction: The teacher teaches a lesson using a computer program.

4. Conduct a posttest: After the lesson, the teacher administers a posttest to each student.

5. Calculate the mean post-test score: The teacher will compute the average score of all the students' post-test results.

6. Formulate a null hypothesis: The null hypothesis states that there is no significant difference between the pretest and posttest mean scores. In other words, computer-based instruction did not have a significant impact on the students' performance.

7. Conduct a hypothesis test for a population mean: The teacher will use a statistical test, such as a t-test, to compare the pretest and posttest mean scores. This test will determine whether there is a significant difference between the two means that suggests the computer-based instruction had a positive effect on the student's performance.

8. Interpret the results: If the hypothesis test shows a significant difference between the pretest and posttest mean scores, the teacher can conclude that the computer-based instruction likely had a positive impact on the students' learning. Otherwise, the null hypothesis cannot be rejected, and the teacher may need to explore other instructional methods or factors that could have influenced the results.

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Quadratic equations are equations that has a leading degree of 2. The value of x from the given quadratic equation is 2 or -12

Quadratic equations are equations that has a leading degree of 2

GIven the quadratic equation expressed as x^2 + 10x + 12 = 36

Rewrite

x^2 + 10x - 36 + 12 = 0

x^2 + 10x - 24 = 0

Factorize

x^2 + 12x -2x - 24 = 0
x(x+12) -2(x+12) = 0
x - 2 = 0 and x = -12

x =2 or -12

Hence the value of x from the given quadratic equation is 2 or -12

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Answer:

A on edge 23'

Step-by-step explanation:

because i said so

Answer:

just add all of the numbers that are around the shape and you will have your answer!

Answer:

so far if u add everything it should equal to 126

The amount of radioactive material left after half a day = 0.4883 g

Let us assume that function f(x) represents the amount of radoactive material and x represents the time in hour.

Initially the amount of radioactive material is a = 2000 g

A material decays by half every every hour.

This means that the rate of decay  = 1/2

So, we get an exponential decay function as:

f(x) = 2000 (1/2)^x

We need to find the amount of material after half a day.

The number of hours in half a day = 12

This means that we need to find the value of f(x) for x = 12

f(x) = 2000 × (1/2)¹²

f(x) = 0.4883 g

Therefore, the amount of  material is left = 0.4883 g

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Answer:

1 hour

Step-by-step explanation:

Answer:

After 2/5ths of a pizza is eaten, we have 3/5ths left.

Then, 3/4ths of the remaining (3/5) is eaten, so 3/5 multiplied by 1/4 = 3/20 slices left. If you're wondering why we multiplied it by 1/4th, there is one-fourth left after Sam eats it, so we might as well figure out what is 1/4th of 3/5.

Hari then eats his share, which is 3/4ths, so 3/20 times 1/4 = 3/80.

So, there is 3/80th of a pizza left.

Answer:

224 cm³

Step-by-step explanation:

Volume = Area of base x height

V = 32 x 7

V = 224 cm³

In this question, all the required information is given so we'll simply have to solve.

\(\large\boxed{\bold{V= \ base \ area× \ height}}\)

Now, substitute the values according to the formula.

\(V= \ 32 × 7\)

\(\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}\)

The answer is a whole number so we won't have to round off.

Hence, the volume of the given rectangular prism is 224 cubic centimeters.

The slope of a plot of ln k versus 1/t equal to: −E_a/R

The Arrhenius equation is one that describes the relation between the rate of reaction and temperature for many physical and chemical reactions.

Arrhenius equation is expressed as:

k = \(Ae^{-E_{a}/RT }\)

Taking natural log on both sides,

ln k = ln \(Ae^{-E_{a}/RT }\)

In k = In A - E_a/RT

In k = In A - (E_a/R * (1/T))

This equation is in the form of y = mx + c

The plot of ln k vs 1/T gives a straight line with negative slope.

Slope = −E_a/R

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We are told that the expression

represents the total cost of the transaction. The problem tells us that the customer purchased a single pair of yeans and an indeterminate amount of shirts. We also know that each shirt costs the same amount.

Since we know that they purchased various shirts at the same price, the total cost of the shirts is an unknown number times the price of the shirt. In the expression given, the only multiplication is 20*x, so 20x must be the total cost of the shirts.

Since they only bought a pair of jeans, and the only remaing part of the expression is 60, 60 must be the cost of the jeans.

Answer:

y = 3/2x + 2

Step-by-step explanation:

first things first write the equation is y = mb+b form which would be 2y  = 3x + 14 then divide everything by 2 to get y by itsself --> 3/2x + 7  for an equation to be paralle the equation needs the same slope which is -6 so 3/2(-6) = -9 so the next equation would also start with 3/2x,  so you would then do this:

-11 = -9 + b (y = mx+b)

b = -9 + 11 --> b = 2

so the equation is

y = 3/2x + 2

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The number of packs that should be bought should be considered as the 5.

Since

28 batteries for smoke alarm. Store sells them in 6 packs

So here we simply divide it

\(= 28 \div 6\)

= 5

hence, The number of packs that should be bought should be considered as the 5.

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If the probability of having a defect is 20%, then the probability that there is no defect is 0.8 or 80%.

The probability that there is no defect can be calculated by subtracting the probability of having a defect from 1. Since the probability of having a defect is 20%, the probability of no defect is:

1 - 0.20 = 0.80

Therefore, the probability that there is no defect is 80%.

In probability theory, the complement rule states that the probability of an event occurring is equal to 1 minus the probability of its complement. In this case, the event of interest is having no defect, and its complement is having a defect.

If the probability of having a defect is 20%, it means that out of every 100 cases, 20 cases would have a defect. Hence, the remaining 80 cases would not have a defect. This means that the probability of no defect is 80% or 0.80.

By subtracting the probability of having a defect (20%) from 1, we obtain the probability of no defect (80%). This is because the sum of the probabilities of mutually exclusive events must be equal to 1. Therefore, the probability that there is no defect is 80%.

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The midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

It follows from the task content that the midpoint of the line segment joining the two points (-3, 8) and (-8, 2) is to be determined.

Since the midpoint of a line is given by coordinates;

x = (x1 + x2)/2 and y = (y1 + y2)/2.

It follows that we have;

x = (-3+(-8))/2

x = -11/2

while; y = (8+2)/2

y = 10/2

y = 5.

Ultimately, the midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

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The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

From the question, we have the following parameters that can be used in our computation:

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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Step-by-step explanation:

I'll call the boxes at the bottom 1 through 6 from left to right.

1. The lines intersect

Answer: 2, 6

2. The lines are parallel

Answer: 3, 4

3. There is only one line

Answer: 1, 5

Answer:

Answer is in attachment, other guys is confusing?

Step-by-step explanation:

The least possible value for the mode is D=11

Let M be the median

According to the question, the two largest integers are M+2

Let a and b be the two smallest integers such that a<b

Accordingly, the sorted list can be concluded as a,b, M, M+2, M+2

Since the median is 2 greater than their arithmetic mean, we have,

{a+b+M+(M+2)+(M+2)/5 }+2 =M

OR, a+b+14=2M

Note that a+b must be even.

We minimize this sum so that the arithmetic mean, the median, and the unique mode is minimized.

Let a=1 and b=3

from which M=9 and

M+2=11

Therefore, The least possible value for the mode is D=11

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Answer:

2/3xy.

Step-by-step explanation:

8x/12x^2y

The 8 and 12 simplify to 2/3 and x and x^2 simplify to 1/x so we have:

= 2/3xy.