suppose that sum a n and sum b n are series with positive terms. prove that if lim n -> infty a n/b n does not exist, and sum b n diverges, then sum a n also diverges

Answer: As the loan is amortized, Boris will make a series of equal payments each month for the duration of the loan, with each payment comprising of both interest and principal. The amount of interest in each payment will decrease over time, while the amount of principal in each payment will increase.

To calculate the monthly payments, we can use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

Where:

M = monthly payment

P = the principal or the loan amount = 91500

i = interest rate as a decimal = 3.3%/12 = 0.00275

n = total number of payments = 40 years x 12 months/year = 480

By substituting the values in the formula:

M = 91500 [ 0.00275 (1 + 0.00275)^480 ] / [ (1 + 0.00275)^480 - 1]

M = $439.65

So the monthly payment that Boris will make is $439.65. This amount will stay the same throughout the loan term, but the proportion of interest to principal in each payment will change as the loan is amortized.

Step-by-step explanation:

answer: In this case, -0.50, -0.10, 0.60, 0.68, 0.98 are all correlation coefficients and -0.50 is the least and 0.98 is the greatest among the given correlation coefficients.

but why? The correlation coefficients can be ordered from least to greatest as:

-0.50, -0.10, 0.60, 0.68, 0.98

A correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. The value of the coefficient ranges from -1 to 1, where:

A coefficient of -1 represents a perfect negative correlation, meaning that as one variable increases, the other variable decreases.

A coefficient of 0 represents no correlation, meaning that there is no linear relationship between the two variables.

A coefficient of 1 represents a perfect positive correlation, meaning that as one variable increases, the other variable also increases.

From the given options, option B is the only statement that is not true is ∠C ≅ ∠E for congruent

What is the congruence theorem?

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If Δ ABC is congruent to Δ DEF, then its corresponding parts must be congruent.

segment AB ≅ segment DE

segment BC ≅ segment EF

segment AC ≅ segment DF

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Therefore, from the given options, option B is the only statement that is not true is ∠C ≅ ∠E.

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"Your question is incomplete, probably the complete question/missing part is:"

If triangle ABC is congruent to triangle DEF, which statement is not true?

A) Segment AB ≅ segment DE

B) ∠C ≅ ∠E

C) Segment BC ≅ segment EF

D) ∠A ≅ ∠D

From the given options, option B is the only statement - 1

The value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Given the following expression:

4 (1/2) - 1 (7/8)

Convert the mixed fractions into simple fractions:

9/2 -15/8

Take the LCM of the denominator:

36/ 8 - 15/8

21/8

2. 20% of x = 6.50

20/100 (x) = 6.50

20x = 650

x = 650/20

x = 32.5

Hence, the value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.

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This suggests that the data set has a skewed distribution with a long tail of larger values.

This suggests that the data set has a skewed distribution, meaning that the data is not evenly distributed. The mean being much larger than the median indicates that there are a few larger values in the data set that are pulling the mean up and creating a long tail of larger values.  This makes the distribution look lopsided, with a majority of the values being clustered around the median, and a few larger values that are skewing the mean higher.

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The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:

Quarts to gallons is 4 to 1.

1/4 x 60 = X

60/4 = X

15 = X

Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons

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Answer:

The number is 7

Step-by-step explanation:

1. Create the equation needed to solve this

Lets think of a number as x. We have a number multiplied by 6 and have 4 added to it.

We get:

6x + 4

Now this sum is equal to the product of 2 and 23. We connect this to get

6x + 4 = 2(23)

We can simplify this to

6x + 4 = 46

2. Solve for x

6x + 4 = 46

Subtract 4 from both sides

6x = 42

Divide both sides by 6

x = 7

Therefore the number is 7

The answers to all the parts is mentioned above.

Given are the geometrical figures as shown.

{ 9 } -

We can write the proportional relationship {since both triangles are similar} as -

5/8 = x/10

{x} = 50/8

{x] = 6.25

{ 10 } -

We can write the proportional relationship {since both triangles are similar} as -

x/20 = 10/16

{x} = 200/16

{x} = 12.5

TY = 20 - 12.5

TY = 7.5

Therefore, the answers to all the parts is mentioned above.

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Answer:

Step-by-step explanation:

the answer is 18 I think?

Answer:

18

Step-by-step explanation:

6 (legs) x 3 (ants) = 18 legs

It can also be represented as 6+6+6 (18)

hope this helps :)

The classification of the angles are;

a) ∠3 and ∠5; Alternate Angles

b) ∠1, ∠2 and ∠3; three interior angles of a triangle.

c) ∠2 and ∠3; Complementary angles

d) ∠4 and ∠5; Supplementary angles

We know that the sum of angles in a triangle is 180 degrees and as such it means that ∠1, ∠2 and ∠3 are classified as three interior angles of a triangle.

We know that alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size. Thus;

∠3 and ∠5 are alternate angles.

Since ∠1 is 90 degrees, then it means that ∠2 and ∠3 are complementary angles.

Similarly, ∠4 and ∠5 are called supplementary angles because they sum up to 180 degrees.

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The greatest sum that Gregory can get is given as follows:

1173.

When two three digit numbers are added, the numbers in the equivalent positions are added with each other, that is, the third digit is added with the third digit, the second with the second and the third with the third.

Hence the greatest sum would be obtained as follows:

Hence the sum would be given as follows:

642 + 531 = 1173.

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The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

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Answer:

all

Step-by-step explanation:

all of them

Step-by-step explanation:

83 in burn in 5 hours.

so, we have a 83/5 speed ratio.

directly proportional means

y = kx

with k being constant for all values of x.

83 = k×5 = 5k

k = 83/5

15 in burn in x hours.

therefore,

15 = 83/5 × x

75 = 83x

x = 75/83 hours

this can be also calculated like this :

because of the direct proportionality, 15/x must have the same ratio as the original 83/5.

83/5 = 15/x

83x/5 = 15

83x = 75

x = 75/83 hours = 0.903614458... hours

(a) List of variables is Years, Country, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.

(b) Each variable is numeric if the variable assumes number values and it will be categorical if it assumes labels.

(a) The list of variables is:

The variables that can be used in this visualization can be Years, Country, Percentage that said yes, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.

(b) Category of different variables:

Years: Numerical and discrete

years are number values but the voting has not been done in the same interval so it is a numerical and discrete variable.

Country: Categorical and not ordinal

country name assumes as labels hence it is a categorical variable.

The percentage that said yes: Numerical and continuous

The percentage indicates number values so it is a numerical value.

And following is also assumed as a label so these are also categorical values:

Arms control and disarmament: categorical and not ordinal

colonialism: categorical and not ordinal

economic development: categorical and ordinal

human rights: categorical and ordinal

Nuclear weapons and materials: categorical and not ordinal.

Palestinian conflict: Categorical and not ordinal

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The complete question is:

the visualization below shows voting patterns in the united states, Canada, and Mexico in the united nations general assembly on a variety of issues. specifically, for a given year between 1946 and 2015, it displays the percentage of roll calls in which the country voted yes for each issue. this visualization was constructed based on a dataset where each observation is a country/year pair.

1) List the variables used to create this visualization.

2) Indicate wheater each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, identify as the variable is ordinal.

If due to gravity, an object falls 16t^2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. The rock will hit the water in 2 seconds?

Given data:

Object falls = 16t² feet in t seconds

Rock from a bridge = 75 feet above the water

So,

72 =16t²

t² = 72/16

t²=  4.5

t = √4.5

t  =  2.12 seconds to hit the water

Therefore we can conclude that the rock will hit the water in 2 seconds.

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a) The expected annual rainfall is 15 million tons.

b) The standard deviation is the square root is 15 million tons.

c) Pgamma(4, shape = 3, scale = 5)

d) Pgamma(5, shape = 3, scale = 5) - Pgamma(2, shape = 3, scale = 5)

a) The expected annual rainfall accumulated in this lake is given by the mean of the gamma distribution, which is alpha * gamma. In this case, the expected annual rainfall is 3 * 5 = 15 million tons.

b) The standard deviation of the annual amount of rainfall in this lake is given by the square root of the variance, which is the square root of alpha * gamma². In this case, the standard deviation is the square root of 3 * 5² = 15 million tons.

c) To find P(X < 4), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(4, shape = 3, scale = 5)

This will return the probability that X is less than 4, which is the cumulative probability.

d) To find P(2 < X < 5), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.

pgamma(5, shape = 3, scale = 5) - pgamma(2, shape = 3, scale = 5)

This will return the probability that X is between 2 and 5, which is the cumulative probability.

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Let where is an integer greater than 9. compute the number of values of for which the sum of the squares of the digits of is at most 25.

The question asks us to count the number of values of for which the sum of the squares of the digits of is at most 25. To solve this problem, we can use a loop to iterate through all possible values of starting from 9 and up. For each value of , we can then calculate the sum of the squares of the digits of by using modulo and division operations to extract each digit and square it. If the sum of the squares of the digits of is at most 25, we can add 1 to the count of values. After the loop completes, we will have the total number of values of for which the sum of the squares of the digits of is at most 25.

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The following number is rational by writing it as a ratio of two integers. 52.4726172617261... = 52497370/999900.

In mathematics, any number that can be written as p/q where q ≠0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal.

The following number is rational by writing it as a ratio of two integers. 52.4726172617261...

let 52.4726172617261...=x

100x=5247.26172617.....

100x=5247+0.2617+0.00002617+....

S0, 0.2617+0.00002617+... is a geometric series,

[tex]S=\frac{a}{(r-1)}\\\\a=0.2617,r=0.0001\\\\s=\frac{0.2617}{0.9999}\\\\S=\frac{2617}{9999}\\\\now,\\100x=5247+\frac{2617}{9999}\\100x=\frac{52,467,370}{9999}\\\\x=\frac{52467370}{999900}[/tex]

So, 52.472617...can be written by x.

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Two equations that have the same solution as the given equation are;

2.3. p - 10.1 = 6.49. p - 4

230.p - 1010 = 650.p - 400 - p

The correct options are B and C.

The given equation is; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Both sides of an equation will remain equal, when both sides are multiplied by the same amount.

Multiplying both sides of the original equation by 100 gives the same solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

a. The initial quantity of radioactive material is 0.68 g.

b. It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

a. In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

the final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g * [tex](1 - 0.18)^4[/tex]

Initial Quantity = 1.52 g * 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

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The standard deviation of the total weight of the boxes that are shipped from this source is 3.02 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

Case A:

Standard Deviation= 0.3 pounds

mean weight= 1.5 pounds

Case B:

Standard Deviation= 0.1 pounds

mean weight= 0.5 pounds

Case C:

Standard Deviation= 3 pounds

mean weight= 12 pounds

let A is the Weight of boxes, B is the weight of packing and C is the weight of boxes.

ver(total)= ver A + ver B + ver C

Below is the Formula used:

SD = √variance

So, ver (total) = 0.3² + 0.1²+ 3²

ver (total) = 9.1 SD

ver (total) =√9.1

ver (total) = 3.02

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The complete Question is:

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

The area of the large pizza is approximately equal to 112.984 square inches.

Herein we need to determine the area occupied by a large pizza (A), in square inches, and based on given input by circumference of a small pizza (s), in inches. Then, we need the following formulas:

Circumference

s = π · D

Area

A = 0.25π · D²

Where D is the diameter, inches.

First, determine the diameter of the small pizza:

D = s / π

D = 12.56 / π

D ≈ 3.998 in

Second, calculate the diameter of the large pizza:

D' = 3 · (3.998 in)

D' = 11.994 in

Third, obtain the area of the large pizza:

A = 0.25π · (11.994 in)²

A ≈ 112.984 in²

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Answer: We can use trigonometry to solve this problem.

Let x be the length of the ladder, and h be the height of the ladder.

We can use the tangent function to relate the angle of elevation, the length of the ladder, and the height of the ladder:

tan(74°) = h / x

We know that x = 12 ft and we can find h.

We can cross multiply and solve for h:

x * tan(74°) = h

12 * tan(74°) = h

We can use a calculator to find the value of h, this will give us the height of the ladder.

Finally, we can use the Pythagorean theorem to find the length of the ladder:

x^2 = h^2 + 12^2

x = √(h^2 + 12^2)

Round your answer to the nearest tenth, we have x = √(h^2 + 12^2)

We can use the value of h to find the length of the ladder.

However, without the value of h it is not possible to find the length of the ladder.

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be a value is 55.

In mathematics, a percentage is a number any figure that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. The "%" symbol, however, is frequently used to denote it. The % amount has no dimensions and is flat. Because the numerator of percentages is 100, they are effectively fractions. To show that a number is a percentage, the percent sign (%) should be put in front of it. On a test, for instance, you would receive a 75% if you gave the answer 75 out of the total questions.

Here,

Given :

=> 20 /100 * a =11

=> a  = 11 *100 /20

=> a  = 1100 /20

=> a = 55

Thus , a is 55 .

Therefore , the solution of the given problem of percentage comes out to be a value is 55.

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The rate of change of the angle of elevation is approximately - 2.597 degrees per second (-0.045 radians per second). (Correct choice: C)

In this problem we find the case of a drone that travels horizontally, at constant height (h), in meters. The rate of change of the angle of elevation (θ'), in degrees per second, can be found from trigonometric functions and derivatives:

tan θ = y / x

Where:

By derivatives:

sec² θ · θ' = - y · x⁻² · x'

θ' = - (y · x⁻² · x') / sec² θ

Where x' is the speed of the drone, in meters per second.

If we know that y = 5 m, θ = π / 6 and x' = 5 m / s, then the rate of change of the angle of elevation is:

x = y / tan θ

x = (5 m) / tan (π / 6)

x ≈ 2.887 m

θ' = - [(5 m) · (2.887 m)⁻² · (5 m / s)] / sec² (π / 6)

θ' ≈ - 2.597 degrees per second (- 0.045 radians per second)

Note - Please notice that negative sign indicates that angle is decreasing.

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Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.

Using triangular inequality of triangle :

sum of two sides > third side

a. 3p - 1 + p² + 1 > 3p

⇒p² > 0

True result.

b. 3p + p² + 1 > 3p - 1

⇒ p² > -2

True result.

c. 3p - 1 + 3p > p² + 1

⇒ p² -6p + 2 < 0

Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)

                     = ( 6 ± √28 ) 2

                     = 5.6 or 0.35

Integer value of p are in between 0.35 to 5.6 are :

1, 2, 3, 4, 5

Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.

For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?

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The largest value of all four operations is 54

In order to determine the largest value of all the four operations, one needs to plug in the values into the different operations given and then generate their values. By so doing, the following deductions are made:

(f * g)(3) = 2 * (3^2) * (3 - 4 * (2 * 3)) = 54

(f - g)(4) = 2 * (4^2) - (4 - 4 * (2 * 4)) = 40

f(g(2)) = 2 * (2^2) = 8

(f + g)(1) = 2 * (1^2) + (1 - 4 * (2 * 1)) = -3

So, the largest value of all four operations is 54. Therefore, the correct answer is as given above

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