Pieceswise defined functions

An equation that represents a function that relates the value of Ethan’s car in dollars, g(t), and the time in years since he bought the car.

[tex]g(t) = P * e^{(-rt)[/tex]

Assuming that Ethan's car depreciates in value over time, a commonly used function to model such depreciation is an exponential decay function of the form:

[tex]g(t) = P * e^{(-rt)[/tex]

where:

[tex]g(t) = P * e^{(-rt)[/tex]

where P, r, and t are specific values based on the purchase price and depreciation rate of Ethan's car, as well as the time that has passed since he bought it.

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Every day, the number of views of the video increases by 80% of the previous day's views.

Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:

percent change = ((new value - old value) / old value) * 100

In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:

V(1) = 500*(1.8)^1 = 900

Substituting these values into the formula, we get:

percent change = ((900 - 500) / 500) * 100 = 80%

In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.

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Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

Answer:

2x-13

Step-by-step explanation:

First flip the operation to be (-10x^2+2x-10) + (10x^2-3).

Then you simplify it. The 10x^2 would get canceled out. You would then get 2x-13.

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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The probability of selecting no Independents is $\frac{{7 \choose 2} + {8 \choose 2}}{{20 \choose 2}} = \frac{91}{190} \approx 0.4789$.

The answer is   X = 10

⇒ Given [tex]\frac{2x}{3} + 1 = \frac{7x}{15} + 3[/tex]

⇒  [tex]\frac{2x+3}{3} = \frac{7x+45}{15}[/tex]

⇒ 15(2x + 3) = 3(7x + 45)

⇒ 30x + 45 = 21x + 135

⇒ 30x - 21x = 135 - 45

⇒ 9x = 90

⇒ x = [tex]\frac{90}{9}[/tex]

⇒ Therefore X = 10

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Weight cannot be represented as a function of height.

No, the weight of Karim's friends cannot be represented as a function of their height.

To represent weight as a function of height, there should be a consistent relationship between the height and weight values.

However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.

This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.

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If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64

We are given that y is proportional to the square root of x, or y ∝ √x.

Using the constant of proportionality k, we can write this relationship as:

y = k√x

To solve for k, we can use the values given in the problem

y = 60, x = 36

60 = k√36

60 = k × 6

k = 60 / 6

Divide the numbers

k = 10

Now that we know k, we can use the same equation to find x when y = 80

80 = 10√x

Squaring both sides, we get

6400 = 100x

x = 64

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The given question is incomplete, the complete question is:

y ∝ √x If y = 60 when x = 36, find x when y = 80​.

The correct option a. may.The data shown in the may histogram is more centered around a high peak.

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.

For the given two histograms,

May has the peak value for the frequency of day at 14.

July has the peak value for the frequency of day at 10.

Thus, The data shown in the may histogram is more centered around a high peak.

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Complete question-

which data set is more centered around a high peak??

a. may

b. july

c. neither

d. both

The diagram for the question is shown.

The H. C. F of 80,215,245 and 720 using long division method is 5.

The long division method to find the Highest Common Factor (H.C.F.) of 80, 215, 245, and 720.

Divide the largest number by the smallest number.

720 ÷ 80 = 9 with a remainder of 0

Divide the smallest number by the remainder from the previous step.

80 ÷ 40 = 2 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

40 ÷ 5 = 8 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

5 ÷ 5 = 1 with a remainder of 0

We have reached a remainder of 0, which means that 5 is the H.C.F. of the given numbers.

Therefore, the H.C.F. of 80, 215, 245, and 720 is 5.

We can also verify this by listing the factors of each number and finding the common factors:

80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

215: 1, 5, 43, 215

245: 1, 5, 7, 35, 49, 245

720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

The common factors are 1, 5, and 40.

The largest common factor is 5, which is the same as what we obtained using the long division method.

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1. The equation she was supposed to solve was sin(x) = cos(2x), but she mistakenly added an extra "= 0" term.

2. The correct answers are x = π/6 and x = 5π/6.

To find the correct answers, we will solve the correct trigonometric equation sin(x) = cos(2x).

Since cos(2x) = 1 - 2sin²(x), the equation becomes:

sin(x) = 1 - 2sin²(x)

Now we can rewrite this equation as a quadratic equation in sin(x):

2sin²(x) + sin(x) - 1 = 0

This equation can be solved using the quadratic formula:

sin(x) = [-b ± sqrt(b² - 4ac)] / 2a

where a = 2, b = 1, and c = -1:

sin(x) = [-1 ± sqrt(1² - 42(-1))] / (2*2)

sin(x) = [-1 ± sqrt(9)] / 4

sin(x) = (-1 ± 3) / 4

There are two possible solutions for sin(x):

sin(x) = 1/2

sin(x) = -1

For sin(x) = 1/2, we have:

x = π/6, 5π/6

For sin(x) = -1, there is no solution in the interval 0 < x < 2π because the sine function does not reach -1 within this range.

So the correct answers are x = π/6 and x = 5π/6.

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We have identified three parent functions that exhibit 180-degree rotational symmetry around the point (0,0): the constant function f(x) = 0, the odd power functions f(x) = x²ⁿ⁺¹ for any integer n, and the tangent function f(x) = tan(x) on the interval (-π/2, π/2).

A function f(x) exhibits 180-degree rotational symmetry around the point (0,0) if and only if f(-x) = -f(x) for all x. To see why, consider rotating the graph of f(x) by 180 degrees around the origin.

Using this criterion, we can identify the parent functions that have 180-degree rotational symmetry around the point (0,0). These functions are:

The constant function f(x) = 0. This function is symmetric about the origin, and any rotation around the origin preserves this symmetry.

The odd power functions f(x) = x²ⁿ⁺¹ for any integer n. These functions are also symmetric about the origin, and any rotation around the origin preserves this symmetry. To see why, note that f(-x) = (-x)²ⁿ⁺¹ = -x²ⁿ⁺¹ = -f(x) for all x.

The tangent function f(x) = tan(x) on the interval (-π/2, π/2). This function has vertical asymptotes at x = π/2 and x = -π/2, but these do not affect its rotational symmetry around the origin.

To see why, note that f(-x) = tan(-x) = -tan(x) = -f(x) for all x in the interval (-π/2, π/2).

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Answer:see below

Step-by-step explanation:

10.600

11.80000

12.17

13.48

14.4000

21. 1km=100m;0.5km=500m;0.1km=100m

22.50m=5000cm; 5m=500cm; 0.5m=50cm

Donna Mosier should use an Individuals control chart to set control limits for the data entry process.

An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.

To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:

By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.

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The next three terms of the sequence.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

To determine the next three terms of each sequence, we simply apply the rule or formula given above. For example, for sequence (a), the next three terms are 0, 1, 1, since the next term is 0 (since there are an even number of 1's so far), followed by two 1's (since there are now an odd number of 1's).

For sequence (b), the next three terms are 9, 10, 10, since the next term is 9 (since the next term in the pattern is odd), followed by two 10's (since the next two terms in the pattern are even). And so on for the other sequences.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

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Answer:

4028

Step-by-step explanation:

Answer:

4028

Step-by-step explanation:

You need to subtract 9,755 from 13,783 on a calculator and you get your answer.hope it helps

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

Standard error = (standard deviation) / sqrt(sample size)

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

[tex]Standard\  error = \frac{10} { \sqrt{(100)}} = 1[/tex]

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

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The probability that no more than 4 of the next 10 households that a student visits will purchase a raffle ticket is 1%.

Probability refers to the likelihood or chance of a particular event occurring, and it is usually expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain.

For example, if you toss a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5. If you roll a fair six-sided die, the probability of rolling a 6 is 1/6, and the probability of rolling any other number is also 1/6. Based on the information, the correct option is C.

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Answer:150°

Step-by-step explanation:

The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.

The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.

The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.

Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

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The tickets in the box model should be:
- 1 ticket with a value of $6 (representing a win)
- 4 tickets with a value of -$2 (representing a loss).

In this gambling game, you have a 4 to 1 payout and a 1 in 5 chance of winning.

To create a box model for this scenario, follow these steps:
Identify the possible outcomes:

In this game, there are two possible outcomes:

winning (with a 1 in 5 chance) and losing (with a 4 in 5 chance).
Determine the payout for each outcome:

If a player wins, they receive a 4 to 1 payout on their $2 bet, so they win $8.

However, they also lose the original $2 bet, so the net gain is $6.

If a player loses, they lose their $2 bet.
Assign tickets to the box model based on the probability of each outcome:

Since there is a 1 in 5 chance of winning, there should be 1 ticket representing a win (net gain of $6) and 4 tickets representing a loss (net loss of $2).

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The surface area of the cylinder is approximately 94.2 ft².

Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.

According to the given information:

The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.

The formula for the lateral surface area of a cylinder is given:

Lateral Surface Area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:

Lateral Surface Area = 2π * 3 * 2 = 12π ft²

The formula for the area of a circle (which represents the bases of the cylinder) is given:

Circle Area = πr²

Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:

Circle Area = π * 3² = 9π ft²

Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:

2 * Circle Area = 2 * 9π = 18π ft²

Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:

Total Surface Area = Lateral Surface Area + 2 * Circle Area

= 12π + 18π

= 30π ft²

As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²

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To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.

For the ordered pair (1, -5):

x - y = 6 becomes 1 - (-5) = 6, which is true.

y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.

Therefore, (1, -5) is not a point of intersection.

For the ordered pair (1, 5):

x - y = 6 becomes 1 - 5 = -4, which is false.

y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.

Therefore, (1, 5) is a point of intersection.

For the ordered pair (5, -1):

x - y = 6 becomes 5 - (-1) = 6, which is true.

y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.

Therefore, (5, -1) is not a point of intersection.

So the answer is:

(1,-5) - No

(1,5) - Yes

(5,-1) - No

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The probability that the average coyote weight for a sample of 20 coyotes is less than 13 kg is approximately 13.14%.

we need to know the mean and standard deviation of the coyote weight population. Let's assume that the population mean is μ = 13.5 kg and the population standard deviation is σ = 2 kg.

Since we are measuring a sample of 20 coyotes, we can use the central limit theorem to approximate the distribution of sample means. According to the central limit theorem, if the sample size is large enough (in general, if n > 30), then the distribution of sample means will be approximately normal, regardless of the distribution of the population.

The mean of the sample means will be equal to the population mean (μ) and the standard deviation of the sample means (also known as the standard error) will be equal to σ / √(n), where √(n) is the square root of sample size.

Using this information, we can calculate the z-score for a sample mean of 13 kg as follows;

z = (13 - 13.5) / (2 / √(20)) = -1.118

Next, we can use a standard normal distribution table (or a calculator or software that can calculate normal probabilities) to find the probability that a z-score is less than -1.118. The area to the left of this z-score is approximately 0.1314, or 13.14%.

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Answer:

C and D

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D

The formula for the general term of the arithmetic sequence is:

a) an = -10 + (n-1) * 6 and first-term = -10

b) an = -10 + (n-1) * 6 and first-term = 6

c) an = 36 + (n-1) * (-5) and first-term = 36

An arithmetic sequence is a sequence of numbers in which each term (after the first) is obtained by adding a fixed number called the common difference, d, to the preceding term. The first term of an arithmetic sequence is denoted by 'a'. The general formula for an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

where 'a' is the first term, 'd' is a common difference, and each term after the first is obtained by adding 'd' to the preceding term.

a) To find the common difference, we subtract any term from the term that comes after it. For example, we can subtract -10 from -4, or 2 from 8, and we get:

-4 - (-10) = 6

8 - 2 = 6

Since both of these subtractions give us the same result, we know that the common difference is d = 6. To find the first term, we can use any term and subtract the product of the common difference and its position in the sequence minus 1. For example, we can use the second term -4 and its position 2 to get:

a = -4 - (2-1) * 6 = -10

Therefore, the formula for the general term of the sequence is:

an = -10 + (n-1) * 6

b) The common difference between consecutive terms is -2 because each term is 2 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 8 and its position 2 to get:

a = 8 + (2-1) * (-2) = 6

Therefore, the formula for the general term of the sequence is:

an = 6 + (n-1) * (-2)

c) The common difference between consecutive terms is -5 because each term is 5 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 31 and its position 2 to get:

a = 31 + (2-1) * 5 = 36

Therefore, the formula for the general term of the sequence is:

an = 36 + (n-1) * (-5)

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Answer:

Step-by-step explanation:

5989.87

Answer:

The answer is 7 pens