Christie's Auction sold a painting for
$24,500. It charges all buyers a 15%
premium of the final bid price. How much
did the bidder pay Christie's?

The correct option is (d) i.e. log [ √x × (x-1)^3 / ∛ (x+1)^2 ] is as the single logarithm.

What is logarithm?

Logarithm is a mathematical operation which is used to determine the exponential power of a number. It is the inverse operation of exponentiation. Logarithm is commonly used in calculus, algebra, and other areas of mathematics. It can also be used to solve problems involving exponents, roots, and powers. Logarithm is denoted by the symbol log, and is read as "log to the base". The base is the number which the logarithm is taken to. For example, log2 10 is the logarithm to the base 2 of 10. This is equivalent to saying "2 to the power of what equals 10?" The answer is that 2 raised to the power of 3 (2^3) would equal 10.

Given, log x / 2 + 3 [ log(x-1) - 2/9 log(x+1) ]

        = log √x + 3 log(x-1) - 2/3 log (x+1)            {∵ log x^a = a log x }

        = log √x + log (x-1)^3 - log (x+1)^2/3

        = log √x + log [(x-1)^3 / (x+1)^2/3]              {∵ log a - log b = log a/b }

        = log [√x × (x-1)^3 / (x+1)^2/3 ]

        = log [ √x × (x-1)^3 / ∛ (x+1)^2 ]

Hence, (d) is the correct option.

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Answer:

52 is range

Step-by-step explanation:

Range is the 'y' values the function can have

 from 0 to 10 books would give a range of 0 - 52

Domain is the x-values  0, 1,2,3,4,56,7,8,9,10

    discrete, because you cannot have anything but the whole numbers listed for the values of 'x'

Answer:

The domain is the input.  It is the number of books.  You can have 0-10 books.  These would be the domains.  

The range is the outputs.  The outputs can be from 0 to 52 pounds.

The domain is discrete.  The domain is the number of books.  We cannot have half or a book or 3/4 of a book.  So this will be discrete.  The number of books can only be whole numbers up to 10.

Step-by-step explanation:

In the factorization, the bottom triangular matrix L is the only one.

The exponent of a number indicates how many times it has been multiplied by itself.

Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.

Given that A is a positively defined symmetric matrix with a Cholesky decomposition,

A = L[tex]L^{T}[/tex]  = [tex]R^{T} R[/tex]

Let A be our positive define symmetric matrix,

suppose A has Cholesky decomposition,

A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,

thus (A x ,x) = (Lx, Lx) = (Lx, Lx)

pick x = eₓ  the last coordinate vector,

then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²

Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,

The Kth entry is currently the last row.

given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)

so the last row of L₁, L₂ be the same,

we reduce our A to new (n - 1)x(n - 1) submatrix,

which will likewise be true, and then repeat the process to discover each row's unique value.

Thus, the inductive process shows that L1 = L2.

As a result, the factorization's bottom triangular matrix L is exclusive.

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Answer:

-6/6 or -1

Step-by-step explanation:

To find the equation of the line (or the slope, assuming that's what equation means, ) we need to write the formula Y1-Y2/X1-X2

So, we need to fill in the numbers, which gives us the fraction -6-0/-2-(-8)

When we solve for the numerator (-6-0), we get -6.

When we solve for the denominator (-2 - {-8}), we get 6.

So, we have -6/6, which, when simplified, is -1.

(If the problem is not asking for slope when it says equation, then sorry!)

Answer:

3/2 or 1.5 or 1 1/2 in mix number

The z-test statistic is used to test the claim that the proportions of the two populations differ. A normal test statistic, the z-test statistic can also be used to measure the proportion of a single population.

Let's say that:

p1: Liberal voters' proportion of the population who smoked cannabis, p. 2:

Conservative voters' proportion of the population who smoked cannabis The null hypothesis is H 0:

The alternative hypothesis is H 0: p 1 = p 2.

p 1 p 2 P-value = 0.00001 The P-value is less than the significance level of 1%. The null hypothesis is rejected at the 1% significance level.

We can conclude that conservative voters had a lower percentage of voters who regularly smoked cannabis.

Two distinct hypotheses are tested by all analysts using a random population sample: the alternative hypothesis and the null hypothesis. Typically, the null hypothesis is a hypothesis that all population parameters are equal; For instance, a null hypothesis might assert that the population mean return is zero.

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The inequality that shows the relationship between thier heights is g < r or r > g

From the question, we have the following parameters that can be used in our computation:

Reese is taller than Gage.

Also, from the question; we have

Reeses's height = r

Gage's height = g

Because Reese is taller than Gage, then it means that

The value of r is greater  than the value of g

So, we have the following inequality expression

r > g

Also, we have

g < r

Hence, the inequality is g < r

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Therease should take her 7th dose on Friday at 9:00AM

What is time ?

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.

The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.

If Theresa took her first dose at 9:00 AM on Monday,

Simply add 12 hours every time up to the 7th dose,

First dose  ----> 9:00 AM on Monday,

Second dose  ----> 9:00 PM on Monday,

Third dose  ----> 9:00 AM on Tuesday,

Fourth dose  ----> 9:00 PM on Tuesday,

Fifth dose  ----> 9:00 AM on Thursday,

Sixth dose  ----> 9:00 PM on Thursday,

Seventh dose  ----> 9:00 AM on Friday,

Hence, Theresa should take her 7th dose at 9:00 AM on Friday.

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Answer:

y = [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 10 ← is in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (10, 7 ) into the partial equation

7 = 5 + c ⇒ c = 7 - 5 = 2

y = [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line

Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9

First term, T(1) = 3

nth term, T(n+1) = T(n) +5 for n>1

Second term, T2 = T(n) +5

= 2 + 5

= 7

Third term, T3 = T(n) +5

= 3 + 5

= 8

Fourth term, T3 = T(n) +5

= 4 + 5

= 9

Therefore, the first four terms of the sequence are 3, 7, 8, 9

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The amount invested in the account that earns 8% interest is $6500

The amount invested in the account that earns 12% interest is $8500

a + b = $15,000 equation 1

0.08a + 0.12b = $1540 equation 2

Where:

a = amount invested in the account that earns 8% interest

b = amount invested in the account that earns 12% interest

The elimination method would be used to determine the required values:

Multiply equation 1 by 0.08

0.08a + 0.08b = 1200 equation 3

Subtract equation 3 from equation 2

0.04b = 340

Divide both sides of the equation by 0.04

b = 340 / 0.04

b = $8500

a + 8500 = 15,000

a = $15,000 - $8,500

a = $6500

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Answer:

y=12x+20

Step-by-step explanation:

Your question and a graph of picture are different. So I just considered your question.

m= (80-44)/(5-2) = 36/3=12

(y- y_1)=m(x-x_1)

(y-44)= 12(x-2)

y-44=12x-24

y= 12x-24+44

y=12x+20

Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly,

a) You will be refinancing $122536.

b) New monthly payment be after refinancing is

$794.1858 or 79 418.58 cents.

We have given that

Initial loan amount = $ 130,750

Number of year of loan = 30 year

Nomber of month of loan "n" = 30x12= 360

Annual interest rate = 6.6%

monthly rate "r" = 6.6% /12 =

monthly payment on the loan is

PMT= loan× r / [1 - (1+r)⁻ⁿ]

= $ 130750 X 12/(1 - (1+ 6.6%/12)⁻³⁶⁰)

= $719,125/(1- (1+0.0055) ⁻³⁶⁰

= $835.046

Monthly payment, $835.046 on initial loan.

Now after 5 years refinishing is done . So, amount and remaining balance is for 30-5 = 25 years and 25×12 = 300 months . The present value of unpaid monthly payment is

= PMT× ( (1 - (1+r)⁻ⁿ)/r)

= $835.046( 1 - (1+6.6%/12)⁻³⁰⁰/ 6.6%/12]

= $835.046× 196.74179

= $122536

Hence, amount refinanced is $122536.

b) New monthly payment will be on loan =$122536

Annual rate = 2.1%

monthly rate, r' = 2.1%/12

Number of years for refinancing = 15 years

Number of months , n' = 15× 12 = 180

Using the formula new monthly payment is

PMT = new loan× r'/ [1 - (1+r')⁻ⁿ´ ]

= $122536× 2.1%/12[ 1 - (1+2.1%/12)⁻¹⁸⁰]

= $214.43826/0.2700104

= $794.1858

Hence, new monthly payment is $794.1858.

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w=9/2 =4,5

Step-by-step:

:)

The amount earned by Damian on Friday, if The function f(x) = 12 x + 10, and he works for 2.75 hours, is $43.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function f(x) = 12 x + 10, where x is working hours,

Calculate the amount by putting the value of x = 2.75 in the function as shown below,

f(x) = 12 × 2.75 + 10

f(x) = 33 + 10

f(x) = $43

Thus, the amount earned is $43.

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For the quiz score of 100, the time will be equal to 5.26 hours.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.

Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.

At the score of the quiz of 100, the value of x will be calculated as,

y = 7.6x+60

100 = 7.6x + 60

40 = 7.6x

x = 40 / 7.6

x = 5.26 hours

The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.

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Answer:

Therefore, the area of the triangle with vertices at A(2, 2), B(4, 5), and C(7, 5) is approximately 4.5, to the nearest tenth.

Step-by-step explanation:

To find the area of a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can use the Shoelace Theorem.

The Shoelace Theorem states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by the following formula:

A = 1/2 * |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|

To apply the Shoelace Theorem to a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can plug in the coordinates of these vertices into the formula:

A = 1/2 * |(25 + 45 + 72) - (24 + 57 + 52)|

= 1/2 * |(10 + 20 + 14) - (8 + 35 + 10)|

= 1/2 * |44 - 53|

= 1/2 * |-9|

= 1/2 * 9

= 4.5

Answer:

  the product of 6 and 23 is more than 126

Step-by-step explanation:

You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.

When the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.

__

Additional comment

Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.

The following are binomial random variable,

A)A Roll a fair die 5 times and X = the number of rolls that land showing a "4", is a binomial random variable.

B) Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6), is a binomial random variable.

C) Roll 5 fair dice at once and let Y = the number of dice that land showing a "4" , is a binomial random variable.

A random binomial variable should satisfy the following conditions:

1. The number of trials are defined or fixed.

2. Each trial is independent of others.

3. The probability of success is same in all trials.

4. There should be only two outcomes in each trial.

Lets we evaluate the options based on the above conditions:

(A) Rolling fair dice 5 times have 5 trials, each rolling is independent, probability of 4 is 1/6 in all cases and the dice will either land 4 or will not land 4. So, X will have values from 0 to 5, 0 when dice doesn't land 4 even once in 5 rolls and 5 when dice land 4 in all rolls. This variable satisfies the condition to be a random binomial variable. So, X is a random binomial variable.

(B)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice with even number to all 5 dices with even number. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Z is a random binomial variable as it satisfies all the conditions.

(C)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice land with 4 to all 5 dices land with 4. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Y is a random binomial variable as it satisfies all the conditions.

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The value of the function G(-5 + h) - G(-5) in the simplest form -5h.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

G(t) = 9 - 5t            (1)

To find the value of expression G(-5 + h) - G(-5),

First, find the value of G(-5 +h) by substituting t = -5+h in equation (1),

G(-5 + h) = 9 - 5(-5 + h)

               = 9 +25 -5h

               = 34 - 5h

The value of G(-5)

G(-5) = 9 - 5(-5)

        = 9 + 25

        = 34

The required value,

G(-5 + h) - G(-5) = 34 - 5h - 34 = -5h.

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The correct answer is option D. 1/35. To count the number of rectangles that can be formed, we need to consider the two cases where the diagonals of the rectangle are parallel to the sides of the octagon, and where the diagonals are perpendicular to the sides of the octagon.

In the first case, there are four choices for which side the diagonals are parallel to, and once that side is chosen, there are two choices for which pair of vertices lie on that side. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.

In the second case, there are four choices for which vertex the diagonals intersect, and once that vertex is chosen, there are two choices for which pair of vertices lie on the same side of the intersection point as the chosen vertex. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.

Altogether, there are $8 + 8 = 16$ rectangles. Therefore, the probability that the quadrilateral formed by the four vertices is a rectangle is

                               = \frac{1}{{8 \choose 4}/16}

                               = \frac{1}{{8 \choose 4}/2^4}

                               = \frac{1}{{8 \choose 4}/2^4}

                               = \boxed{\text{(D) } 1/35}$.

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The discontinuity of our given function is at point (-6, -7).

The zero of our given function is, (1, 0).

What is discontinuity and zero of the function?

A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.

The x-intercept(s) of the function's graph represent the real zero of the function.

Consider the given function,

[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]

We know that a function is discontinuous, when its denominator is equal to zero.

To find the discontinuity for our given function, we will equate denominator to 0 as:

x + 6 = 0

    x = -6

Now simplify the given function.

[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]

Take  y = x - 1

Since the denominator term is cancelled out, so our give function has a removable discontinuity.

Now, we will find value of y by substituting  x = -6

⇒ y = -6 - 1

   y = -7

Therefore, the discontinuity of our given function is at point (-6, -7).

Now, we will find zero of our given function by substituting  f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:

⇒  0 = x - 1

x - 1 = 0

    x = 1

Therefore, the zero of our given function is, (1, 0).

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The expression of (a + b + c) is equivalent to 16.5.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given are two circles intersecting at each others centers at D and E.

We can write the area of the common region as -

[A] = 4 x {(θ/180) x (πr²/2) - (1/2)r²sinθcosθ}

Now, we can write θ as -

cos(θ) = (3/6) = 1/2

θ = 60°

[A] = 4 x {(60/180) x (π(6)²/2) - (1/2)(6)²sin(60)cos(60)}

[A] = 4 x {(1/3 x 36π/2 - (1/2) x 36 x [tex]\sqrt{\frac{3}{2} }[/tex] x 1/2}

[A] = 4 x {6π - 9 [tex]\sqrt{\frac{3}{2} }[/tex] }

[A] = 24π + (-  9 [tex]\sqrt{\frac{3}{2} }[/tex])

So, on comparing, with the expression below -

aπ + b[tex]\sqrt{c}[/tex]

We get -

a = 24

b = - 9

c = 3/2

So, we get -

a + b + c

24 - 9 + 3/2

24 - 9 + 1.5

24 - 7.5

16.5

Therefore, the expression of (a + b + c) is equivalent to 16.5.

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The value of x in the inequality, -13x < 65, is simplified as, x > 5.

Any inequality given can be solved by find the value of the variable in the inequality, which will make it a true statement. To do this, isolate the given variable to make it stand alone on one side.

Given the inequality, -13x < 65, solve as shown below:

-13x < 65 [given]

Divide both sides by -13:

-13x/-13 < 65/-13

x > -65/13 {the sign changes from < to > because we divided both sides by a negative quantity]

x > 5

The value of x is simplified as x > 5.

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Answer:

---------------------------------------

First, solve the inequality:

This is option C (you have chosen it correctly).

Now, graph it:

Answer:

x < -11  or  x > 8

Step-by-step explanation:

Given absolute value inequality:

[tex]|2x+3| > 19[/tex]

[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]

Apply the absolute rule:

[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex]            [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]

To graph the solution:

Answer: -64

Step-by-step explanation:

To solve this equation, you need to isolate the b term on one side of the equation. You can do this by dividing both sides of the equation by 16. This will give you:

b/16 = (-4)

You can then divide both sides of the equation by -4 to get:

b/16 = -4

b/16 * -4 = -4 * -4

b = -64

Therefore, the solution to the equation is b = -64.

Answer:

Step-by-step explanation:rate = minute/meter => 20/5

so, 5/1 for rate

so for 11 meter,  (5m/1min)(11)

The answer is 55 minutes

Answer:

R'>R

Step-by-step explanation:

To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.

We know the range is defined by R

R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.

Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5.  So, our range also becomes

R = X(n) + 5 - X(1)

So,  R'>R. Hence, the range of the new score will be greater than that of the original score distribution.

Answer:

the first option

Step-by-step explanation:

in an "and" statement both parts need to be true, so that the overall condition is true.

is x = 6 a valid solution ?

no, it violates both, x <= -8 and x <= 4

is a value between -8 and 4 a valid solution like x = -2 ?

no, it violates x <= -8, even though it is true for x <= 4.

only values that are smaller or equal to -8 (like -9) are true for both.

and therefore the first answer option is correct.