Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.

log₄3 x

l o o k    i t   u  p     o n    g a u t h m a t h      c o p y   u r    q e s t i o n   t h e r e

Step-by-step explanation: You're welcome

A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.

If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.

Current Balanced Owned =$785

APR = 24.42%

Let’s suppose the billing cycle is 30 days, then

Finance charge = $15.76

The new balance you owe = $800.76.

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Using addition, Total length of wire used by the electrician is 76 feet.

Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

We will use simple addition here,

Total length used by electrician is

(9 + 13 + 42 + 12) feet.

= 76 feet

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Answer:

Step-by-step explanation:

If a polygon does not have 5 sides, then it is not a pentagon.: TRUE

Answer:1 hour 30 minutes

Step-by-step explanation:8 kilometres are compete in an hour, plus another 4 kilometres (to make 12 total) is half of that, so adds another half an hour

The time it will take the man 1.5 hours to cover a distance of 12 km, travelling at the same speed.

Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.

The speed formula is speed = distance / time.

We are given that;

Distance = 12 km

Speed = 8 km/h

Now,

Plugging these values into the formula for time, you get:

time = 12 / 8

time = 1.5 hours

Therefore, by the given speed the answer will be 1.5 hours.

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The coordinate of the point R' after translation will be (0, - 4).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

If ∆PQR is translated left 2 and down 6. Then the translation rule is given as,

(x', y') → (x - 2, y - 6)

From the graph, the coordinate of point R will be at (2, 2). Then the coordinate of the point R' after translation will be

(x', y') → (2 - 2, 2 - 6)

(x', y') → (0, - 4)

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Answer:  f(x) = | x |

Step-by-step explanation:

when transforming and translating a function, you use the form a | x - h | + k  

a= vertical shrink/stretch factor

h = horizontal movement ( right or left)  

k = vertical movement ( up or down )

So a = 1/2  h = 0 and k =2

g(x) = 1/2 | x-0 | + 2

g(x) = 1/2 | x | + 2    [which means vert shrink of 1/2 and up 2 units ]

the range of the function in the graph is:

-4 ≤ y ≤ 2

For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.

Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.

If we look at the graph, we can see that the minimum value of y is:

y = -4

And we can see that the maximum value of y is:

y = 2

Then the range of the function in the graph is:

-4 ≤ y ≤ 2

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The step 2 should  be m∠p + m∠o  = 180 degrees(supplementary angles)

The external angle theorem  states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles(remote interior angles) .

Therefore,

Step 1

m∠m + m∠n + m∠o = 180°(sum of angles of a triangle)

It's very correct

Step 2

m∠p - m∠o = 90 degrees(Alternate angles)

This is incorrect.

It should be m∠p + m∠o  = 180 degrees(supplementary angles)

The angles  m∠p  and  m∠o are supplementary angles. This simply implies the angles add up to 180 degrees.

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The simplified form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).

An algebraic expression (or variable expression) is a term that has been combined with operations like addition, subtraction, multiplication, and division.

To simplify an algebraic expression, we simply combine like terms. As a result, variables that are similar will be combined. The same abilities will now be combined from the similar variables.

The given expression is (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y).

As we know [tex]x^{a}[/tex] + [tex]x^{b}[/tex] = [tex]x^{a+b}[/tex]

So, (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (3×[tex]2^{3}[/tex])([tex]x^{2}[/tex]×[tex]x^{3}[/tex])([tex]y^{-1}[/tex]×y)

(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])([tex]y^{0}[/tex])

(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])

As a result, the abbreviated form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).

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Answer: 6.30

Step-by-step explanation:

Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.

It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.

In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.

Therefore, it should be noted that 8.33 will be:

= 8 + 1/3

It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...

Therefore, the appropriate fraction for 8.33 will be 8 1/3.

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The probability that a string of 15 people passes through screening successfully before an individual is caught with a questionable object is 0.3040 and the expected number of people to pass through be- fore an individual is stopped 49

3% of people whose luggage is screened at an airport have questionable objects in their luggage i.e

P(x)=3/100=0.03

The probability of people whose luggage is screened at an airport and have no questionable object in their luggage is

〖P(x)〗^1=1-P(x)

〖P(x)〗^1=1-0.03

〖P(x)〗^1=0.97

Using Binomial probability which states that

P(x)=(nCx) (p)^x (q)^(n-x)

N= 16 total number in consideration

p= probability with no questionable luggage

q= probability with questionable luggage

P(15)=(16C15) (p)^15 (q)^(16-15)

P(15)=(16C15) (0.97)^15 (0.03)^(16-15)

16C15=16!/((16-15)!(15!))

15C15=15!/((1)!(15!))

16C15=20922789888000/((1)(1307674368000))

16C15=20922789888000/1307674368000

16C15=16

P(15)=(16) (0.97)^15 (0.03)^1

P(15)=(16)(0.63325)(0.03)

P(15)=0.3040

P(x) =(Required outcome)/(Total outcome)

0.3040 =15/(Total outcome)

Total outcome=15/0.3040

Total outcome=49.34

Total outcome=49

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The questions tests on indices. Write 27 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 27 = 3×3×3

27 = 3^3

(27^3)^(1/3) = 3^(3×1/3) = 3

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Answer:

i’m pretty sure it’s 6,039

Step-by-step explanation:

12,078 divided by 2

Answer to this question is:

Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,0)

Set-Builder Notation:{x|x<0}

The set of all valid y values constitutes the range.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (2x - y)⁴

By using binomial expansion theorem, we get

(2x - 3)⁷ = 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187

(2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.

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The sum in scientific notation will give:

7.76*10⁶

Here we want to find the sum between the numbers (7.3*10⁶) and (4.6*10⁵).

To sum these numbers, we need to have the same exponent in the "10", then we can rewrite:

7.3*10⁶ = 73*10⁵

Now the sum will be:

73*10⁵ + 4.6*10⁵

Taking a common factor we get:

73*10⁵ + 4.6*10⁵ = (73 + 4.6)*10⁵ = 77.6*10⁵

Now we want to go back to scientific notation, so we need to move the decimal point one time to the left, we will get:

77.6*10⁵ = 7.76*10⁶

That is the outcome of the sum.

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The third term of the expansion is 6a^2b^2

The binomial term is given as

(a - b)^4

The r-th term of the expansion is calculated using

r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)

So, we have

3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)

Evaluate the sum and the difference

3rd term = C(4, 2) * (a)^2 * (-b)^2

Evaluate the exponents

3rd term = C(4, 2) * a^2b^2

Evaluate the combination expression

3rd term = 6 * a^2b^2

Evaluate the product

3rd term = 6a^2b^2

Hence, the third term of the expansion is 6a^2b^2

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The simplest form of the expression is 4   .

We have given an expression √2 . √8 .

On multiplying , we get

√2 . √8 = √16

On simplifying , we get

√16  =  √ 4 × 4

           = 4

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Based on the amount that Scott borrowed for the new TV and game system, and the interest paid, the simple interest rate is 15.7%

The simple interest rate can be found by the formula:

= Interest paid by Scott on the loan / Amount Scott borrowed x 100%

Solving for the simple interest rate gives:

= 155 / 985 x 100%

= 0.1573604060913705583756345177665 x 100%

= 0.157 x 100%

= 15.7%

This means that Scott paid 15.7% on the loan he borrowed.

In conclusion, Scott's simple interest rate is 15.7%.

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Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{14}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +14}{2}~~~ ,~~~ \cfrac{ y +21}{2} \right) ~~ = ~~\stackrel{midpoint}{(41~~,~~50)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +14}{2}=41\implies x+14=82\implies \boxed{x=68} \\\\\\ \cfrac{ y +21}{2}=50\implies y+21=100\implies \boxed{y=79}[/tex]

Answer: 1.3

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

9 is the hundredth and we round up with 8 so we’d round up 1 and we get 1.3

The required solution of the given expression is -2/5 as a simplified form.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

The given expression is

2/5÷(−5/5)

According to given question we have

The expression is

2/5÷(−5/5)

=2/5÷(-1)

=2*(-1)/5

=-2/5

Therefore, the required solution of the given expression is -2/5 as a simplified form.

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The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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Answer:

Step-by-step explanation:

Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7