Given the sequence 2 and one half comma 2 and one third comma 2 and one fourth comma and continues comma what is f (n)?

f of n equals 2 plus 1 over the quantity 1 plus n
f of n equals 2 plus 1 over n
f of n equals n plus 1 over the quantity 1 plus n
f of n equals 3 minus 1 over n

In a 45-45-90 triangle, the legs are always equal and the hypotenuse is always [tex]\sqrt{2}[/tex] times either leg.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angles of triangle= 45-45-90

Now,

This is a special case of a right triangle where the two acute angles are equal to 45 degrees each, and it has some unique properties, such as the fact that the two legs are congruent, and the hypotenuse is the square root of 2 times longer than each leg. This relationship can be expressed mathematically as:

If a and b are the lengths of the legs of a 45-45-90 triangle, and c is the length of the hypotenuse, then:

a = b

c = a * sqrt(2) = b * sqrt(2)

Therefore, in this right triangle the answer will be equal and [tex]$\sqrt{2}$[/tex] times.

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Due to the fact that they are both increased to the same power, the two functions are exponential. Both functions have distinct constants and rates.

A unit of code known as a function carries out a particular task. A function in mathematics is a relationship between a set of allowable inputs and outputs, having the condition that each input is connected to exactly one output.

As illustrated in the graphic that represents the posed question, the two functions that we are considering are all such that we can see that they are exponential in nature.

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A' is a dilation can only make the point bigger!

The coordinate plane movement of a point is referred to as dilation. To achieve this, find the horizontal and vertical distances from the center of dilation, multiply them by a scale factor, and then add those results to get the coordinates of the dilated point.

A dilatation is a kind of transformation that increases or decreases the size of a figure (referred to as the preimage) to produce a new figure (called the image). The size of the dilation image relative to the preimage is determined by the scale factor, r. k will always have a value larger than zero.

Therefore, the correct answer is option a) a dilation can only make the point bigger!

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The value of each variable include the following:

x = 5 units.

y = 5√2 units.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = 5.

Adjacent side = x.

Hypotenuse = y.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan45 = 5/x

x = 5Tan45

x = 5(1)

x = 5 units.

Next, we would determine the value of y by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

y² = 5² + 5²

y = √50

y = 5√2 units.

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The total height of the cake and candles is [tex]16\frac{1}{10}[/tex]

A fraction represents a part of a whole.

Ava's birthday cake is [tex]11\frac{7}{10}[/tex]

Her candles stick up from the cake an additional [tex]5\frac{4}{10}[/tex]

We need to find the total height of the  cake and candles

We have to add both the heights.

[tex]11\frac{7}{10}[/tex] +  [tex]5\frac{4}{10}[/tex]

107/10+54/10

161/10

[tex]16\frac{1}{10}[/tex]

Hence, the total height of the cake and candles is [tex]16\frac{1}{10}[/tex]

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Answer:

common multiples

Step-by-step explanation:

The value of the expression is 28.

An expression contains more than two variables or numbers with addition, subtraction, multiplication, and division.

Example: 4.4 + 3x + 9.9y = 7 is an expression.

We have,

12 + 13 + -1 + 4

All the terms are whole numbers.

= 25 + 4 - 1

= 29 - 1

= 28

Thus,

28 is the value.

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Answer:

(a) The height of the cubiod is 5cm.

(b) The volume of metal not used in making these spheres is 172cm^3.

Step-by-step explanation:

(a) 12*10= 120

     600/120= 5cm

(b) volume of 1120 spheres= (4/3*π*0.45^3)(1120)

                                              = 428cm^3 (to 3 s.f.)

    600-428= 172cm^3

The (x,y) coordinate points of the logarithmic function are as follows. (2, -5), (3, -4), (5, -3), (9, -2), (1, - 10).

The exponential function is thought of as the inverse of the logarithmic function because of its close relationship. The logarithmic function logaN = x is derived from the exponential function ax = N.

When seen as an exponential form, the logarithm of any integer N is the exponent to which the base of the logarithm needs to be raised in order to reach the value of N.

The fundamental logarithmic function has the notation f(x) = log_ax(r) y = log_a(x), where a > 0. Natural logarithm (ln) and common logarithm are examples of log functions (log).

From the given information, the logarithmic function y = log₂ (x − 1)- 5 is plotted on the graph and the following x,y points are obtained.

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Answer:

M = (2500 + 193.25) / 24 = $113.03

We can use the monthly payment to calculate the finance charge over the life of the loan, which is equal to 24 times the monthly payment minus the principal amount:

Finance charge = 24 * M - 2500 = 24 * 113.03 - 2500 = 193.25

Now that we have the finance charge, we can calculate the APR:

APR = (Finance charge / Principal amount) * (12 / Number of months) * 100%

APR = (193.25 / 2500) * (12 / 24) * 100%

APR = 7.73%

So, the APR of this loan is 7.73%.

Answer:

81, 144 and 19

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve for the first problem, we can use this equation:

For the second:

And the third:

Therefore, 81, 144 and 19 are the answers.

No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.

A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.

In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.

In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.

In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.

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Answer:

Avery can swim 3 laps in 3 minutes.

According to the given rate the incorrect option is Mason can swim 0.5 lap farther than Avery in 2 minutes.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Given that, Avery can swim 3 laps in 2 minutes. Mason can swim 5 laps in 4 minuets.

Their unit rates are =

Avery = 1.5 laps per minute

Manson = 1.25 laps per minute

Now checking the options,

a) Avery can swim 6 laps in 4 minutes :-

6/4 = 1.5 [correct]

b) Mason can swim 2.5 laps in 2 minutes :-

2.5/2 = 1.25 [correct]

c) Avery can swim 2 laps farther than Mason in 8 minutes :-

Avery laps in 8 minutes = 1.5 × 8 = 12 laps

Mason laps in 8 minutes = 1.25 × 8 = 10 laps

Therefore, Avery is 2 laps farther than Mason [correct]

d) Mason can swim 0.5 lap farther than Avery in 2 minutes :-

Mason in 2 minutes = 1.25 × 2 = 2.5 laps

Avery laps in 2 minutes = 1.5 × 2 = 3 laps

Since, Avery laps are 0.5 farther than Mason, so the option is incorrect.

Hence, the incorrect option is Mason can swim 0.5 lap farther than Avery in 2 minutes.

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The complete question is;-

Avery and Mason are both swimming laps in the same swimming pool.

Avery can swim 3 laps in 2 minutes.

Mason can swim 5 laps in 4 minutes.

Based on these rates, which statement is NOT true?

a) Avery can swim 6 laps in 4 minutes.

b) Mason can swim 2.5 laps in 2 minutes.

c) Avery can swim 2 laps farther than Mason in 8 minutes.

d) Mason can swim 0.5 lap farther than Avery in 2 minutes.

The price of the jeans after the markup is equal to $90.

Generally speaking, the markup price of a product can be calculated by multiplying the cost price by the markup value.

Markup price = 20/100 × 75

Markup\; price = 0.2 × 75

Markup price = $15

Now, we can find the new cost of the jeans after the markup is applied as follows:

New cost = Markup price + Cost price

New cost = $15 + $75

New cost = $90.

In conclusion, we can logically deduce that new cost of the jeans after the markup is applied is 90 dollars.

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No, the sample is random compared to the size of the shipment.

The number of individuals or observations included in a study is referred to as the sample size.

The sample is not large enough to be representative of the entire shipment, and therefore the manufacturer cannot assume the prediction is valid.

A random sample of 13 out of 5,000 MP3 players is too small to accurately predict the proportion of defective MP3 players in the entire shipment.

Additionally, the way the clerk generated the sample by using numbers 1 through 300 to represent defective MP3 players may have introduced a bias into the sample.

To accurately assess the proportion of defective MP3 players, a larger, more representative sample would be necessary.

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The biologist was checking the condition for inference that (d) the observations within each sample are close to independent.

This is concluded from the fact that the biologist was checking if the product of sample size and the proportion of deer with chronic wasting disease in each sample was greater than or equal to 10. This is a commonly used rule of thumb to ensure that each sample has enough data to provide meaningful information about the population, and it is based on the idea that the sample size should be large enough such that the expected number of success (deer with chronic wasting disease) is at least 10 and the expected number of failures (deer without chronic wasting disease) is at least 10.

This helps to ensure that the observations within each sample are close to independent, as the sample proportions are unlikely to be greatly influenced by any individual deer in the sample.

Correct Question :

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern colorado. to estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. the biologist checked for the following:

(200)(0.06)≥10

(200)(0.94)≥10

(197)(0.086)≥10

(197)(0.914)≥10

Which of the following conditions for inference was the biologist checking?

a. The population of deer within each region is approximately normal.

b. It is reasonable to generalize from the samples to the populations.

c. The samples are independent of each other.

d. The observations within each sample are close to independent.

e. The sampling distribution of the difference in sample proportions is approximately normal.

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Converting milliliters (mL) to ounces (oz) involves using a conversion factor. The conversion factor expresses the relationship between the two units of measurement and is given by 1 mL = 0.033814 oz

To convert milliliters (mL) to ounces (oz), you can use the following conversion factor:

1 mL = 0.033814 oz

This means that one milliliter is equivalent to 0.033814 ounces. To convert a given volume in milliliters to ounces, we can multiply that value by the conversion factor of 0.033814.

For example, let's say we want to convert 500 mL to ounces. We can do this by multiplying 500 mL by 0.033814 oz/mL:

500 mL x 0.033814 oz/mL = 16.907 oz

Therefore, 500 mL is equal to approximately 16.907 ounces.

Note that the conversion factor of 0.033814 is exact, meaning that it has an infinite number of decimal places. However, when we round off the final result, we should choose an appropriate number of decimal places based on the level of precision that we need for the particular application.

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In a bimodal histogram, the two highest bars will have the same height.

The above statement is TRUE that is n a bimodal histogram, the two highest bars will have the same height.

A histogram is said to be bimodal if it has two peaks. The only defining characteristic about this distribution is that it has 2 peaks of the same height. Bimodality sometimes occurs when the data set consists of observations from two different group of individuals. If this shape occurs, the two sources should be separated and analysed separately.

A bimodal histogram shape often reflects the presence of two different processes being "mixed" in the displayed data. For example, the data could contain information from two different machines, two shifts, weekdays and weekends, two offices, etc.

In some cases bimodal histogram indicates that the sample can be divided into two sub samples that differ from each other in some way.

Thus in a bimodal histogram, the two highest bars will have the same height.

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The pound is defined as 453.59237 grams. Using the formula to convert pounds to kilograms, you find that 190 pounds equals 86.18 kilograms.

We know that :

1 lb/ Pound = 0.453592 kilogram

therefore,

190 lbs/ Pound =  86.18 kilogram.

Using the formula to convert pounds to kilograms, you find that 190 pounds equals 86.18 kilograms

To convert 190 pounds (pounds) to kilograms (kg), you must use the conversion factor 1 pound = 86.18 kilogram.

Therefore,

we multiply 190 pounds by 86.18 kg/lb to get the equivalent weight in kilograms:

190 pounds x 0.45359237 kg/lb = 86.1825503 kilogram

Therefore,

190 pounds is 86.18 kilogram.

To understand the conversion factor, you need to know that pounds and kilograms are units of mass, but are used in many parts of the world. In the United States and some other countries, the accepted unit of mass is the pound, while most other countries use the kilogram.

A conversion factor connects the number of pounds to the number of kilograms, so you can easily convert from one unit of measure to another. It is important to use the correct conversion factor for accurate conversion.

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Based on the t-test assuming equal variances "Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

When conducting a t-test assuming equal variances, it is necessary to determine whether or not the variances of the two groups being compared are actually equal. This is important because the calculation of the t-statistic depends on the assumption of equal variances.

To assess the assumption of equal variances, one can examine the ratio of the variances of the two groups. Typically, if the ratio of the variances is greater than 2 or less than 1/2, then it is reasonable to conclude that the variances are unequal. In the absence of such evidence, one can assume that the variances are equal.

Therefore, it is not reasonable to assume that the variances are equal.

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Answer:

Step-by-step explanation:

If two vectors are perpendicular to each other then their scalar(dot) product must be zero.

Therefore,  

A

.

B

=0

(2

i

^

+2

j

^

​

+3

k

^

)⋅(3

i

^

+6

j

^

​

+n

k

^

)=0

6+12+3n=0

3n=−18

n=−6

The cell phone costs Rs 13,560 after a 20% discount and 13% VAT are applied.

First, we need to calculate the discount amount given on the market price of the mobile phone:

Discount = 20% of the market price

Discount = 0.20 x 15000

Discount = 3000

So, the discounted price of the mobile phone is:

Discounted Price = Market Price - Discount

Discounted Price = 15000 - 3000

Discounted Price = 12000

Now, we need to add the VAT amount to the discounted price:

VAT = 13% of the discounted price

VAT = 0.13 x 12000

VAT = 1560

Therefore, the final price of the mobile phone, including the discount and VAT, is:

Final Price = Discounted Price + VAT

Final Price = 12000 + 1560

Final Price = 13560

So, the price of the mobile phone, after allowing a 20% discount and levying 13% VAT, is Rs 13,560.

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The value of data that might affect the statistical measures of spread and center is B. There is a high data value that causes the data set to be asymmetrical for the males.

Outliers stretch out the data further, resulting in a wider range and a higher standard deviation. On the other hand, eliminating outliers reduces data spread, resulting in a lower range and standard deviation.

When an outlier is present, it might change the way the graph looks since it raises the mean. From the chart, there is a high data value in the males which will therefore make the data to be asymmetrical for the males as the larger spread for the males means the data set tilts towards them.

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The cost function for FedEx delivery is -

C{x} = 2x + 10

Given is that you want to deliver a package to Japan. The FedEx delivery service charges a $10 flat fee plus $2 per pound. You can also use the USPS Priority Mail service which charges a $2 flat fee plus $4 per pound.

For the FedEx delivery, we can write the cost function as -

C{x} = 2x + 10

Therefore, the cost function for FedEx delivery is -

C{x} = 2x + 10.

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The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The table is given below.

Number of hours               Total number of students

            0                                                 1

            1                                                  3

            2                                                 2

            3                                                 5

            4                                                 9

            5                                                 7

            6                                                 3

The total number of students is given as,

Total = 1 + 3 + 2 + 5 + 9 + 7 + 3

Total = 30

Then the probability that a student studied for 1 hour is given as,

P = 3 / 30

P = 0.10

The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.

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