find the closed formula for each of the following sequences by relating them to a well known sequence. assume the first term given is a1. (a) 2; 5; 10; 17; 26; : : : (b) 0; 2; 5; 9; 14; 20; : : : (c) 8; 12; 17; 23; 30; : : : (d) 1; 5; 23; 119; 719; :

The transformation performed on f(x) = x² to create h(x) = 1/5f(x) is the graph is compressed horizontally by the factor 1/5

Transformations are mathematical operations performed on a graph or function to change the shape, size or orientation of the graph or function.

Given that we have the function f(x) = x² and it is transformed into the graph h(x) = 1/5f(x).

So, the graph is  compressed horizontally by the factor 1/5

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Increasing the sample size leads to a more accurate estimation of the population mean.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

As the sample size, n, increases, the center of the sampling distribution of sample means becomes more precise and closer to the true population mean. This is known as the central limit theorem, which states that as the sample size increases, the distribution of sample means becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In other words, as we take larger and larger samples, we are more likely to obtain sample means that are closer to the true population mean. This is because larger samples are less affected by random fluctuations and more likely to provide a representative picture of the population as a whole.

Therefore, increasing the sample size leads to a more accurate estimation of the population mean.

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The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.

Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.

The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:

Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)

The cost of 1 gallon of apple juice is $4.49.

So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:

Total cost = Cost of bananas + Cost of apple juice

Total cost = $2.96 + $4.49

Total cost = $7.45

Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.

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Answer:

The constraints are:

Plot the graphs of the constraints

From the graph (see attachment), the only optimal point is (3,4)

Substitute 3 for x and 4 for y in the objective function.

So, we have:

Hence, the maximum value of C is 17

Step-by-step explanation: Hope this helps!!!

Answer:

88

Step-by-step explanation:

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You need 1.8 lbs of the type of chocolate that sells for $2.50/lb and 6.6 lbs of the type of chocolate that sells for $3.60/lb.

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these problems. The intersection of two lines represents the system of equations' solution.

let

x = lbs of the type of chocolate that sells for $2.50/lb

y = lbs of the another type of chocolate that sells for $3.90/lb

You would like to have 8.4 lbs of a chocolate mixture that sells for $3.60/lb

x + y = 8.4

2.50x + 3.90y = 8.4 x 3.60

2.50x + 3.90y = 30.24

Putting the value of x = 8.4 - y in equation 2.

2.50( 8.4 - y) + 3.90y = 30.24

21 - 2.5y + 3.9 y = 30.24

1.4y = 9.24

y = 6.6

Putting y in x equation we get,

x = 1.8

by solving the above system of equations we find:

x = 1.8 lbs

y = 6.6 lbs

Therefore, each chocolate will you need to obtain the desired mixture is 1.8 lbs and 6.6 lbs.

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Glenn orders the same drink every time. This can be answered by the Simple intelligence.

The logic behind this conclusion is as follows:

Brian orders tea: In this case, John must order the same drink as Glenn. According to statement 4, if Brian orders tea, John orders the drink that Glenn orders. However, Glenn's choice is not dependent on Brian's choice, so Glenn will always order the same drink. Therefore, Glenn is the only person who orders the same drink every time.

Therefore, Glenn orders the same drink every time.

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The table showing the distance traveled by the boat at various times should be completed as follows;

Time (h)                  0      0.5     1      1.5     2     2.5      3

Distance (mi)          0       1        2      3       4      5        6

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1.5

Constant of proportionality, k = 2.

When x = 0.5, the distance is given by;

y = 2x

y = 2(0.5) = 1 mile.

When x = 1, the distance is given by;

y = 2x

y = 2(1) = 2 miles.

When x = 2, the distance is given by;

y = 2x

y = 2(2) = 4 miles.

When x = 2.5, the distance is given by;

y = 2x

y = 2(2.5) = 5 miles.

When x = 3, the distance is given by;

y = 2x

y = 2(3) = 6 miles.

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Missing information:

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

The given statement "if we take a simple random sample from a normal distribution, the probability that the sample mean is equal to the population mean is 1 (i.e., 100%)" is false.

The probability that a sample mean is equal to the population mean is actually zero, since any given sample will differ slightly from the population mean due to sampling error. However, as the sample size increases, the sample mean is likely to be close to the population mean, and the probability of it being equal approaches 1 (i.e., 100%).

To explain further, the population mean is the mean of the entire population and is calculated by adding up all the values of the population and dividing them by the total number of individuals in the population. A sample mean, on the other hand, is the mean of a sample taken from the population and can be calculated by adding up the values of the sample and dividing them by the total number of individuals in the sample. Since the sample size is usually smaller than the population size, the sample mean is likely to be slightly different from the population mean due to sampling error.

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The probability of drawing a second card as an ace after drawing one card and putting it aside without looking at it depends on the outcome of the first draw and whether the card was replaced or not.

The possibility of drawing an ace from a general deck of 52 playing cards is 4/52, or 1/13. But, the probability of drawing an ace as the second card relies upon whether or not the first card drawn turned into an ace or now not, in addition to whether the first card was replaced lower back into the deck or no longer.

If the primary card becomes an ace and it was now not replaced, then there are only three aces left inside the deck out of fifty-one cards, so the opportunity of drawing another ace as the second card could be 3/51.

However, if the primary card becomes an ace and it is turned into changed, then the opportunity of drawing any other ace as the second one card would nonetheless be 4/52, or 1/13 because the deck could be efficiently reset.

Then again, if the primary card was now not an ace, then there might be 4 aces left inside the deck out of fifty-one cards. Consequently, the opportunity of drawing an ace as the second card could be 4/51.

In precis, the opportunity of drawing a 2nd ace from a well-known deck of cards could rely on the outcome of the primary draw and whether the cardboard was replaced or no longer.

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At alpha equal to 0.01 there is enough evidence to reject the claim that is the chance of a false positive.

When reducing the alpha from 0.05 to 0.01 reduces the chance of a false positive also called a Type I error, it makes it harder to detect differences with a t-test and with any significant results one might obtain would be more trustworthy but there would probably be less of them.

We know that:

probability > 0.1: no evidence,

then, probability between 0.05 and 0.1: weak evidence

then, probability between 0.01 and 0.05: evidence

then, probability between 0.001 and 0.01: strong evidence

and probability < 0.001: very strong evidence

The alpha level set relates to the formal decision made rather than this informal interpretation, but both can be reported together.

Lower alpha levels are sometimes used while carrying out multiple tests at the same time and a common approach is to divide the alpha level by the number of tests being carried out.

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From the given information provided, the surface area and volume of cylinder is 1130.97 and 3816.85 respectively.

To find the surface area and volume of the cylinder, we can use the following formulas:

Surface Area = 2πr² + 2πrh

Volume = πr²h

Substituting the given values, we get:

Surface Area = 2π(9)² + 2π(9)(15) = 1130.97 square inches (rounded to the nearest tenth)

Volume = π(9)²(15) = 3816.85 cubic inches (rounded to the nearest tenth)

Therefore, the surface area of the cylinder is approximately 1130.97 square inches, and the volume is approximately 3816.85 cubic inches, both rounded to the nearest tenth.

Question - A cylinder has a height of 15 in and a radius of 9 in. Find area and volume. Round to the nearest tenth.

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Answer: x = 24

Step-by-step explanation:

21 + 3= 24

Using the identity sin² 0 + cos² 0 = 1, the value of cos 0 is 0.951 (to the nearest hundredth)

Using the identity sin² 0 + cos² 0 = 1, we can solve for cos 0:

cos² 0 = 1 - sin² 0

cos² 0 = 1 - (-0.31)²

cos² 0 = 1 - 0.0961

cos² 0 = 0.9039

Taking the square root of both sides, we get:

cos 0 ≈ ±0.951

Since 0 is in the interval ³ < 0 < 2π, we know that cos 0 must be positive. Therefore, to the nearest hundredth, cos 0 ≈ 0.95.

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So the coordinates of point X' after dilation are (15, 11).

Polygon WXYZ is dilated by a scale factor of 3, with vertex W as the center of dilation. This means that the distances from vertex W to the other vertices are multiplied by 3, while W remains unchanged. Given the coordinates of point W are (3,2) and point X are (7,5), we can find the coordinates of point X' after dilation.

To do this, first determine the change in the x and y coordinates from point W to point X:

Δx =[tex]7 - 3 = 4\\[/tex]
Δy =[tex] 5 - 2 = 3[/tex]

Now multiply these changes by the scale factor of 3:

Δx' =[tex] 4 * 3 = 12[/tex]
Δy' =[tex] 3 * 3 = 9[/tex]

Now add these new changes to the original coordinates of point W to get the coordinates of point X':

X'(x) =[tex] W(x) + Δx' = 3 + 12 = 15[/tex]
X'(y) = [tex]W(y) + Δy' = 2 + 9 = 11[/tex]

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It would be: D) Increased recycling of waste

Your Welcome

The frequency table would have three classes, one for each digital music player option.

When summarizing the consumer responses with a frequency table, the frequency table would have 3 classes.

Frequency table:

A frequency table is a statistical tool that is used to organize raw data in a clear and concise manner.

It is a way of representing the information contained in the data so that it can be easily interpreted and analyzed.

A frequency table is often used to summarize categorical data, such as the data collected in a marketing study like the one mentioned in the question.

The marketing study in this question involved asking 100 consumers to select the best digital music player from three options:

the iPod Touch, Sony Walkman, and Zune HD.

To create a frequency table from this data, we would need to count the number of times each option was chosen by the consumers.

This can be done by grouping the data into classes, which are categories that are created based on the values in the data.

For this particular study, there are only three options to choose from, so there are only three possible classes:

iPod Touch, Sony Walkman, and Zune HD. We would simply count the number of times each option was chosen and record it in the appropriate class.

The resulting frequency table would look something like this: Digital Music Player Frequency i Pod Touch 45 Sony Walkman 28 Zune HD27

Total 100

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The greatest integer m for which n is an integer is 40.

This is because the product of all multiples of 3 between 1 and 100 (n) is equal to the product of all integers from 3 to 99, which is equal to 3^39*2^20.

By using the prime factorization of n, we can see that the greatest integer m is equal to the sum of the exponents of the prime factors, which is 39 + 20 = 40.

To solve this problem, we must first factor n, which is the product of all multiples of 3 between 1 and 100. n can be expressed as a product of prime factors 3^39*2^20.

This can be further expressed as 3^39*2^20 = (3*2)^39*2^20 = 6^39*2^20. To find the greatest integer m for which n is an integer, we must add the exponents of the prime factors, which gives us 39 + 20 = 40. Therefore, the greatest integer m for which n is an integer is 40.

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The function f(x) = sec(x) has no x-intercepts.

The y-intercept of the graph of f(x) = sec(x) is (0, 1).

From the question, we are to identify any x-intercepts and y-intercepts of the graph of f(x) = sec(x).

The function f(x) = sec(x) is defined as the reciprocal of the cosine function, that is:

f(x) = 1 / cos(x)

The cosine function has a zero at x = π/2 + nπ, where n is an integer.

At these values of x, the denominator of the secant function becomes zero, and the function becomes undefined.

Therefore, the function f(x) = sec(x) has no x-intercepts.

To find the y-intercept, we need to evaluate the function at x = 0, which gives:

f(0) = 1 / cos(0) = 1 / 1 = 1

Hence, the y-intercept of the graph of f(x) = sec(x) is (0, 1).

The graph of the function f(x) = sec(x) is shown below.

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Answer:

Part A:

Assuming that Morgan kicks the ball at an angle that will allow it to clear the crossbar, we can use the following formula to determine how far she must kick the ball:

Distance = Height / tan(θ)

where θ is the angle at which the ball is kicked.

Since the field goal is 16 feet off the ground and we want the ball to clear the crossbar, we can assume that Morgan needs to kick the ball at an angle of approximately 45 degrees. Therefore, plugging in the given values, we get:

Distance = 16 / tan(45)

Simplifying the equation, we get:

Distance = 16 / 1

Therefore, Morgan must kick the ball a distance of 16 feet to make the extra point if she stands 30 feet from the field goal.

Part B:

To arrive at this conclusion, we used the formula for the distance of a projectile when given the initial velocity, angle, and height of the object. However, since we were not given the initial velocity, we assumed that Morgan would need to kick the ball at an angle of approximately 45 degrees to clear the crossbar. This is a common assumption in football, as it allows for the ball to travel the farthest distance possible while still clearing the crossbar. Additionally, we assumed that there was no wind or other external factors that could affect the trajectory of the ball. With these assumptions, we were able to determine that Morgan would need to kick the ball a distance of 16 feet to make the extra point if she stood 30 feet from the field goal.

Answer:

Step-by-step explanation:

9to12

Answer:

b = 12 units

Step-by-step explanation:

In a right angled triangle,

Base² + Perpendicular² = Hypotenuse²

b² + 16² = 20²

b² = 20² - 16²

b² = 400 - 256

b² = 144

b = √144

b = 12 units

Answer:

Step-by-step explanation:

To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.

The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:

($0.06 ÷ $20.00) x 100% =

0.003 x 100% =

0.3%

Therefore, Dylan has 0.3% of the original amount remaining on his gift card.

Answer:

the amswer is five apples

The equation of the circle is with the diameter given is x² + y² = 9.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

We can quickly determine the circle's centre and radius thanks to this form. We must first square the x and y terms before rearranging the components in order to transform a circular equation into standard form.

The endpoints of the diameter is (-3,0) and (3,0).

Now, using the section formula the coordinates of radius are:

((-3+3)/2, (0+0)/2) = (0,0

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

Substituting the values:

(x - 0)² + (y - 0)² = 3²

Hence, the equation of the circle is x² + y² = 9.

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The mean retirement age in the census report is 68.3 years.

The given information states that the population mean retirement age is 68.3 years, and a random sample of retirement age has a sample mean of 65.8 years. We can use this information to estimate the population mean with a certain level of confidence.

However, the question asks us to find the mean of 68.3 years, which is simply the given population mean. Therefore, we can state that the mean of 68.3 years remains the same, as it is not affected by the sample mean or any other sample statistic.

In other words, the population mean of 68.3 years is a fixed value, and it does not change based on the sample mean or any other sample statistic. Therefore, we can simply state that the mean retirement age is 68.3 years, which is the given information provided in the question.

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so, the BEST supported conclusion is option D: "A majority of visitors had a favorite attraction."

Percentage is a way of expressing a number as a fraction of 100. The symbol used to represent percentage is "%". For example, if we say that 75% of students passed a test, it means that 75 out of every 100 students passed the test.

To calculate a percentage, you can use the following formula:

[tex]percentage = (part/whole) * 100[/tex]

Here, "part" refers to the number that is being expressed as a percentage of the "whole" number. For example, if we want to find out what percentage of 80 is 20, we can use the formula as follows:

percentage = (20/80) x 100 = 25%

So, 20 is 25% of 80.

According to the results of the sample, 40% of the visitors responded that they had no favorite attraction, while the remaining 60% did have a favorite. Among those who had a favorite attraction, the percentages for each attraction were: 15% safari, 20% aquarium, and 25% panda bears. Therefore, no conclusion can be made about which attraction was the most popular among all visitors. However, it is possible to conclude that a majority of visitors (60%) had a favorite attraction, so the BEST supported conclusion is option D: "A majority of visitors had a favorite attraction."

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