8. If a=-10, b-4, show that a - b ≠ b - a
​

Use the change-of-base identity and the exponent property for logarithms.

[tex]\log_b(a) = \dfrac{\log_c(a)}{\log_c(b)} \implies \log_b(a) = \dfrac1{\log_a(b)}[/tex]

[tex]\log_c(a^b) = b \log_c(a)[/tex]

This lets us rewrite

[tex]\log_{(k+1)^{2k-1}} (k+2)^{2k} = \dfrac{2k}{\log_{k+2}(k+1)^{2k-1}} = \dfrac{2k}{(2k-1) \log_{k+2}(k+1)}[/tex]

[tex]\log_{(k+2)^{2k-1}} (k+1)^{k^2} = \dfrac{k^2}{\log_{k+1} (k+2)^{2k-1}} = \dfrac{k^2}{(2k-1) \log_{k+1}(k+2)}[/tex]

It follows that

[tex]a_k = \dfrac2k \dfrac{\log_{k+2}(k+1)}{\log_{k+1}(k+2)} = \dfrac2k \left(\ln^2(k+1)}{\ln^2(k+2)}[/tex]

so that the product of [tex]a_k[/tex] telescopes:

[tex]\displaystyle \prod_{k=1}^{n-1} a_k = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(2)}{\ln^2(3)}\cdot\frac{\ln^2(3)}{\ln^2(4)}\cdot\frac{\ln^2(4)}{\ln^2(5)} \cdots \frac{\ln^2(n-1)}{\ln^2(n)} \cdot \frac{\ln^2(n)}{\ln^2(n+1)} \\\\ ~~~~~~~~ = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(n+1)}{\ln^2(2)}[/tex]

We can similar reduce the coefficient of [tex]P_n[/tex] to write

[tex]\log_{(n+1)^{2n-1}}(2^{2n}) = \dfrac{2n}{(2n-1) \log_2(n+1)}[/tex]

[tex]\log_{2^{2n-1}}(n+1)^{n^2} = \dfrac{n^2}{(2n-1)\log_{n+1}(2)}[/tex]

[tex]\implies \dfrac{\log_{(n+1)^{2n-1}}(2^{2n})}{\log_{2^{2n-1}}(n+1)^{n^2}} = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)}[/tex]

Then the expression for [tex]P_n[/tex] reduces significantly to

[tex]P_n = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)} \cdot \dfrac{2^{n-1}}{(n-1)!} \dfrac{\ln^2(n+1)}{\ln^2(2)} = \dfrac{2^n}{n!}[/tex]

and we ultimately find

[tex]\displaystyle \sum_{n=2}^\infty P_n = \sum_{n=0}^\infty \frac{2^n}{n!} - \frac{2^1}{1!} - \frac{2^0}{0!} = \boxed{e^2 - 3}[/tex]

where we recall the power series

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

Answer:

circumference=44cm

44cn

Area=154cm

200cm

Answer:

Step-by-step explanation:

90 - 65 = 25

x = 25 degrees

90 - 25 = 65

y = 65 degrees

The required value of the standard deviation is 0.04.

Given that,

1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers is to be determined. Where s = 5

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
1 miles = 1.60934 Km
Given
1 mile = 1.6
Standard deviation = 1.60934 - 1.6000
                                = 0.00934
S = 5
Standard deviation = 5 * 0.00934
                                = 0.04670

Thus, the required value of the standard deviation is 0.04.

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Answer: 6

Step-by-step explanation:

7+2+5+10= 24
24 divided by 4 equals 6

[tex] \sqrt{15} \approx3.873\\ \\ \sqrt{15} < 3.9[/tex]

Answer: The answer is play on words, or a pun - a row of large animals separating two yards is called an elefence.

Step-by-step explanation: The first part of the word, ele-, obviously refers to elephants, which are large animals. The second part is a fence, which separates two yards. So this is intended to have a humorous effect (I got this from go.ogle....)

The statements which are true about parallel lines are;

Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.

Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.

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Reason:

32 = 8*4

56 = 8*7

We see that 8 is the largest common factor, aka GCF, of 32 and 56

So this is the greatest number of guests possible.

Each guest will get 32/8 = 4 cookies and 56/8 = 7 slices of pizza.

The  profit or loses  change should he receive​ is $19.5

Given,

The price of Dozen of mangoes is $.15

Robert gives $20

The change should be is $20-$.15 =$19.5

When a person buys an item at one price and later sells it at a different one, he either earns a profit or loses money. There are several phrases that are involved with the complete transaction procedure. For instance, cost price (C.P. ), selling price (S.P. ), discount, marked price, profit, and loss. Let us go through the definitions of these terminologies one by one.

Price Cost

For example, if Neil purchased an umbrella for $8, the cost price of the umbrella is $8. The abbreviation is C.P.

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The amount taken from Jim's check for FICA taxes is $75.51.

FICA (Federal Insurance Contributions Act) taxes are of two types: Social Security tax and Medicare tax.

FICA taxes simply mean United States federal payroll (or employment) taxes imposed on both employees and employers.  The purpose of FICA taxes is to fund Social Security and Medicare.

These two federal programs benefit retirees, the disabled, and the children of deceased workers.

The rate for the Social Security tax is 6.2% of the taxpayer's gross pay.

The rate for the Medicare tax is 1.45% of the income earner's gross pay.

The FICA taxes rate is 7.65%.

Gross pay for the week = $987

FICA taxes = 7.65%

FICA taxes in dollars = $75.51 ($987 x 7.65%)

Thus, the amount Jim paid in FICA taxes is $75.51.

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Answer: B. 60.96

Step-by-step explanation:

27% of 48 is 12.96

12.96+48=60.96

The thermometer show the temperature at 73°F when there is a percentage error.

From the information, the thermometer has a percent error of 3% and the actual temperature is 75°F.

Therefore, the temperature down on the thermometer will be:

= 75 - (3% ×75)

= 75 - 2.25

= 72.75

= 73 approximately.

Therefore, the thermometer show the temperature at 73°F when there is a percentage error.

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The proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.

From the information, two out of every fifteen trick-or-treaters that came to the house last Halloween were dressed as Spiderman.

Therefore the fraction is represented as 2/15.

Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be:

= 1 - 2/15

= 13/15.

Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.

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Answer:

Hello,

Answer: B   : y=(m-3)*(x+1)²3

Step-by-step explanation:

The parabola with vertex (-1,3)

is y=k(x+1)²+3

(0,m) is a point of the parabola:

m=k*(0+1)²+3 ==> k=m-3

So, y=(m-3)*(x+1)²+3 is the correct equation.

x = 40 is the value of vertical angles .

What is vertical opposite angles?

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.

The total of the two vertical angle pairs, or four angles, is always 360 degrees. Angles that come from each pair of vertical angles are supplementary and are referred to as neighboring angles (the angles sum up to 180 degrees).

(3x + 2)° and (5x-78)° are equal .

because of they are  vertical opposite angles.

3x + 2 = 5x - 78

5x - 3x = 78 + 2

2x = 80

x = 40

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The equation that states the sum of the tickets sold is -

30x + 45y = 60900.

We have concert promoter.

We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.

The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.

According to the question -

Money earned from $30 tickets = $30x

Money earned from $45 tickets = $45y

Total money from 1780 tickets = $60,900

Therefore -

30x + 45y = 60900

Hence, the equation that states the sum of the tickets sold is -

30x + 45y = 60900.

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[ The given question is incomplete, the complete question is

A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]

The set of numbers is S = { x ∈ N ; x > 22 }.

We have the statement:

Set of natural numbers greater than 22.

We need to make the set from it.

A set is a collection of different things objects or elements that are used to represent a situation or a function in a concise form.

For example a set of real numbers can be denoted by x ∈ R.

There can be finite or infinite sets. In finite sets, the number of elements are limited whereas in infinite sets it is not limited.

Here, the set that will be formed can be written as:

S = { x ∈ N ; x > 22 }

Therefore, the set of numbers is S = { x ∈ N ; x > 22 }.

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Answer:

71.62

Step-by-step explanation:

[tex]A = \frac{C^2}{4 \times \pi }\\A = \frac{30^2}{4 \times 3.14 }\\A = 71.62[/tex]

The given geometric series, the first term is a₁ = 2 and the common ratio is r = -1

What are some examples of geometric series?

We are given to find the values of  a₁ and r of the following geometric series

2 - 2 + 2 - 2 + 2 - ........

We know that

a₁ is the first term and r  is the common ratio of the given geometric series.

We can see that the first term of the given geometric series is 2.

So. we must have

            a₁ = 2

Also, common ratio is found by dividing a term by its preceding term.

Therefore, the common ratio r  of the given geometric series is

r = -2/2 = 2 / -2 = ...... = -1

Thus, for the given geometric series, the first term is a₁ = 2 and the common ratio is r = -1.

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Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.

A linear function is modeled by:

y = mx + b

In which:

One example of function is:

y = 4x + 3.

When x = 1:

y = 4 + 3 = 7.

When x = 2:

y = 8 + 3 = 11.

The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.

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Answer:

a. = 1

b. = 0

c. = 2

d. = 7

Hopefully this helps

Answer:

Q1: Plane

Q2: Point

Q3: line

                                  I hope this helps!

Answer: $63

Step-by-step explanation:

so you put 6 where the w is to find out the answer

45+3(6)=45+18=63

Answer:

Binomial

Step-by-step explanation:

There are only 2 terms

Answer:

1 in 6

Step-by-step explanation:

The probability of getting the original green is 1 in 7 (1 green pencil and 7 total)

If you take it out, there will be 6 pencils left

The required solution is correct. AB = 5.5.

Given that,

AB=[1+4.5]=5.5

To describe the expression and to determine whether the expression is correct or not.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
Simplifying the given expression, AB = 1 + 4.5
AB = 1 + 4.5
Addition property of alike terms
AB = 1.00 + 4.50
AB = 5.50

AB = 5.5

Thus, the required solution is correct. AB = 5.5

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Carl calculates the z-score corresponding to the weight 255oz= -1.5.

Now, Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.

Given that,

In an orchard, apple weights are typically distributed. Fred the farmer concludes from a sample that the average weight of a box of apples is 270 ounces, with a standard deviation of 10 ounces.

He is interested in knowing what proportion of the apple boxes he has gathered for sale will weigh less than 255 oz.

Mean is 270

Standard deviation is 10

x = 255

Formula for z-score,

z = (x - mean)/SD

z = (255 - 270) / 10

=> z = -15 / 10

=> z = -1.5

Hence, by using z-table,

-1.5 equates to 0.0668, which suggests that 0.07

Therefore, 7% of Apple boxes weigh less than 255 oz.

The ratio of boxes is between 255 oz and 270 oz,

Calculating the proportion

Now,

50% - 7% = 43%.

Therefore, Carl calculates the z-score corresponding to the weight 255oz= -1.5.

Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.

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It means that if you rotated the figure 60 degrees (clockwise or counterclockwise) about its center, then the figure does not change.

The "before" and "after" are identical. In other words, the preimage and image are the same.