Please help me with this exercise!

The monthly finance charge for the credit card transaction is $51.70.

We need to calculate the monthly finance charge for the given credit card transaction.

Credit card transaction means the purchase of goods or obtaining of services or cash against the use of the Credit Card, the Card number or in any manner authorised by the Cardholder for debit to the Credit Card Account or utilising of any services made available to the Cardholder by the Bank from time to time in respect.

Given that, $3,000 balance, 21% rate, 150 payments, average daily method

The particular month in question is 30 days long.

Your balance at the start of the month is $3,000.

Annual interest rate = 21%.

Payment = $150.00

When the payment is made in the month, it reflects on the tax amount you pay on both the average daily balance.

The average daily balance is $3000 from day 1 until day 10 (10 days)

The average daily balance is $2850 from day 11 until day 30 (20 days)

Average daily balance for the month = 10 × 3000 + 20 × 2850

= 87000 / 30

= $2900

Interest charge for the month = (0.21 × 2900× 30) / 365

The interest charge for the month = $50.05 rounded to the nearest penny

The average daily balance is $3000 from day 1 until day 29 (29 days)

The average daily balance is $2850 from day 30 until day 30 (1 day)

Average daily balance for the month = 3000 × 29 + 1 × 2850

= 89850 / 30

= $2995

Interest charge for the month = (0.21 × 2995 × 30) / 365

=51.6945≈$51.70

Therefore, the monthly finance charge for the credit card transaction is $51.70.

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Answer: c

Step-by-step explanation:

The  absolute difference is 492 people per square mile and Relative difference: 435.4%.

Thus, option (B) is correct.

To find the absolute difference between the two population densities, subtract the population density of country A from the population density of country B:

Absolute difference = Population density of country B - Population density of country A

                                 = 605 people per square mile - 113 people per square mile

                                 = 492 people per square mile

Now, the relative difference as a percentage, we use the formula:

Relative difference = (|Absolute difference| / Population density of country A) * 100

                                = (|492| / 113) * 100

                               = (492 / 113) * 100

                               = 4.35398230088 * 100

                               = 435.4%

Therefore, the absolute difference is 492 people per square mile

Relative difference: 435.4%

Thus, option (B) is correct.

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Answer:

The values of x are -6 + √5 and -6 - √5.

Step-by-step explanation:

It is given that we need to find all of the points of the form (x,-1) which are 3 units from the point (-6, 1).

Now, let us suppose that these points are in 2D coordinate system such as;

=> (x1, y1) = (-6, -1)

and let us suppose that the other point is;

=> (x2, y2) = (x, 1)

Further, the distance between both these points them is 3 units and we can write this as;

=> d = √(x1 - x2)² + (y1 - y2)²

=> 3 = √(-6 - x)² + (-1 - 1)²

After squaring both the sides;

=> 9 = 36 + x² + 12x + 4

=> 9 = x² + 12x + 40

On rearranging the equation;

=> x² + 12x + 31 = 0

Now, this is a quadratic equation of the form ax² + bx + c = 0 in which;

=> x = -b ± √(b² - 4ac) / 2a

After putting values in this for obtaining the value of x on comparing we get;

=> x = -12 ± √(12² - 4×31) / 2

=> x = -12 ± √(144 - 124) / 2

=> x = -12 ± √20 / 2

=> x = -12 ± 2√5 / 2

=> x = 2(-6 ± √5) / 2

=> x = -6 ± √5

Therefore, the values of x are -6 + √5 and -6 - √5.

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Answer:

EF = 32

Step-by-step explanation:

since the base angles D and F are congruent then the triangle is isosceles with both legs congruent , that is

EF = DE = 32

Answer:

32 units

Step-by-step explanation:

It is an isosceles triangle so two sides will be the same length opposite the equal angles     EF = 32

Answer:

true took the test on edge

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{-22})\qquad B(\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 8 +3}{2}~~~ ,~~~ \cfrac{ 4 -22}{2} \right) \implies \left(\cfrac{ 11 }{2}~~~ ,~~~ \cfrac{ -18 }{2} \right) \implies (5.5~~,~~\stackrel{\stackrel{y}{\downarrow }}{-9})[/tex]

The ways to know know which school has higher athletic achievements relative to budget per student are:

Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.

% of students in sports club divided by SAT average

the number of sports medals won divided by SAT average

To determine which school has higher athletic achievements relative to the SAT average, according to the two definitions will be that Did you get the same result for both definitions?

No. The definitions have opposite results.

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Analia wants to know which school has higher athletic achievements relative to the SAT average. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A % of students in sports club divided by SAT average (Choice B) B Graduation rate divided by SAT average (Choice C) C Number of sports medals won (Choice D) D Number of sports medals won divided by SAT average 2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average. (Choice B) B Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average. (Choice C) C No. The definitions have opposite results.

The inequality to determine the number of outfits Zendaya can purchase while staying within her budget is

     269.88 + 4*10.57 + 17.76 + 65.65x ≤ 540

And the number of outfits Zendaya can buy is 3 .

According to the question we have been given that the

 Total money Zendaya has = $540

  Cost of new bicycle = $269.88

   Cost of bicycle reflectors = $10.57

   Cost of bike gloves = $17.76

  Cost of biking outfits = $65.65

Let the number of outfits Zendaya purchases be x.

The inequality to determine the number of outfits Zendaya can purchase while staying within her budget is

     269.88 + 4*10.57 + 17.76 + 65.65x ≤ 540

Now solving this inequality for x we get

     269.88 + 42.28 + 17.76 + 65.65x = 540

    329.92 + 65.65x = 540

          65.65x = 210.08

              x = 3.2 ≈ 3

Thus number of outfits Zendaya can buy is 3

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Step-by-step explanation:

1. divide 10 with 5

2. using law indices, simplify the rest of the equation

3. you're done!

Answer: 5m³n³

Step-by-step explanation:

[tex]\frac{10m^5n^4}{2m^2n}[/tex] = [tex]\frac{5m^5n^4}{m^2n}[/tex]  

          = [tex]\frac{5m^3n^4}{n}[/tex]
          = 5m³n³

or
[tex]10m^{5} n^{4}[/tex] ÷[tex]2m^{2}n[/tex] = [tex]5m^{5-2} n^{4-1}[/tex]
                       = [tex]5m^{3} n^{3}[/tex]

Answer:

(2,7)

Step-by-step explanation:

we use the midpoint formula:

(3+-5/2 , 7+9/2)

(4/2, 14/2)

(2,7)

Answer: M(5,2)

Step-by-step explanation:

C(3,-5)    D(7,9)   the midpoint M(x,y)=?

x₁=3       x₂=7     y₁=-5      y₂=9

[tex]\displaystyle\\M(x,y)=(\frac{3+7}{2} ,\frac{-5+9}{2})\\\\M(x,y)= (\frac{10}{2},\frac{4}{2})\\\\ M(x,y)=(5,2) \\\\Thus,\ M(5,2)[/tex]

Given the change in altitude and time, the mean change of altitude of the airplane is -63 ft/min.

The mean change of altitude is simply know as the average rate of change.  

The average rate of change is the sum total of the change in altitude divided by the sum total of the change in time.

It is expressed as;

r = Δa/Δt

Where r is rate of change, Δa is total change in altitude and Δt is the total change in time.

Given the data in the question;

Plug the given values into the above formula and solve for r.

r = Δa/Δt

r = -378ft /  6min

r = -63 ft/min

Given the change in altitude and time, the mean change of altitude of the airplane is -63 ft/min.

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From calculations, the numbers of each type we should make are;

4 plain burgers

2 double burgers

5 regular burgers

Let us denote each of the types of the hamburgers as;

Plain burgers is p

double cheeseburgers is d

regular cheeseburgers is r

Thus;

For Beef patty, the equation is;

p + 2d + r = 13  -----(1)

For buns, the equation is;

p + d + r = 11   ------(2)

For cheese, the equation is;

0 + 2d + r = 9   -----(3)

Solving these three equations simultaneously using an online calculator gives;

p = 4; d = 2; r = 5

From calculations, the numbers of each type we should make are;

4 plain burgers

2 double burgers

5 regular burgers

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The number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.

Based on the information, the equation for last year will be:

A = 2B + 5

The number will be illustrated as:

A = B + 23

Therefore, it should be noted that we will equate the expression. This will be:

2B + 5 = B + 23.

Collect like terms

2B - B = 23 - 5

B = 18.

A = 23 + B = 23 + 18 = 41

Therefore, the number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.

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Last year, Singer A performed two times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 23. How many concert shows did each perform?

In order to be able to compensate to get the exact sum of the two prices, Kayla should subtract $0.05 from $55.75.

In order to be able to get the price of $55.75, Kayla rounded $34.95 up to $35 and then added $20.75.

To compensate for the rounding up and then get the exact sum of the prices of the sweaters, Kayla should subtract the difference between the $35 and the $34.95.

That difference is:

= 35 - 34.95

= $0.05

In conclusion, Kayla should subtract $0.05 from $55.75 to get $55.70.

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In mathematical expression the given expression is written as;

⇒ S + 12 = x² + 2x + 4

Where, S is area of square with side x.

What is Area of square?

A square is a two dimension figure in which all the sides are equal. Since all the sides are equal, the area would be two times the side of a square.

Let a side of square is x feet.

Then, Area of a square (S) = x²

When, The side of the square is increased by 2 feet. Then area is increase by 12 sq. ft.

Then, Side of a square = (x + 2)

Hence, Area of a square = (x + 2)²

                            s + 12  = x² + 2 * x * 1 + 2²

                            s + 12 = x² + 2x + 4

So, In mathematical expression the given expression is written as;

⇒ S + 12 = x² + 2x + 4

Where, S is area of square with side x.

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Answer:

5

Step-by-step explanation:

The distance between any two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

(x₁, y₁) = (1, 4) and (x₂, y₂)  = (4, 0)

So distance is

[tex]d = \sqrt {(4 - 1)^2 + (0 - 4)^2}\\\\d = \sqrt {(3)^2 + (-4)^2}\\\\d = \sqrt {(3)^2 + (-4)^2}\\\\d = \sqrt {25}\\\\d = 5[/tex]

Answer:

x = 4

Step-by-step explanation:

x - 6 = 2x - 10

-2x     -2x

-x - 6 = -10

    +6    +6

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

-x = -4

÷-1   ÷-1

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

x = 4

I hope this helps!

Answer:

n= -35 .................................

Answer:

is it is 10^4 - 11^2 + 6 then the answer will be 4

Step-by-step explanation:

Answer:

3. 7

5. 8

7. 15

9. 6

10. 1

Step-by-step explanation:

The expressions which Marika can use to find the total cost of the dinner, including the tip are:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to write and solve this word problem, we would assign a variable (x) to the cost and then evaluate the resulting algebraic expression. Therefore, let x represent the cost.

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The 100th line segment by using the nth term of a sequence is equal to 20200.

A sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.

Next, we would determine the differences between the terms in this sequence until all the differences are the same:

12 - 4 = 8

24 - 12 = 12

40 - 24 = 16

12 - 8 = 4

16 - 12 = 4

Since the differences are the same, the sequence is a quadratic function and it contains an n² term. Also, the coefficient of n² is one-half of the equal difference. This ultimately implies that, the coefficient of n² is equal to 2.

In order to determine the nth term of this sequence, we would develop a table to model increment:

n                    1       2       3      4

2n²                2       8      18    32

Operation    +2     +4     +6    +8

Sequence     4       12     24   40

By critically observing the table above, we can logically deduce that the nth term of this sequence is given by:

aₙ = 2n² + 2n

a₁₀₀ = 2(100)² + 2(100)

a₁₀₀ = 2(10000) + 2(100)

a₁₀₀ = 20000 + 200

a₁₀₀ = 20200.

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Answer:

The answer will be A.

Answer:

16

Step-by-step explanation:

4n -4 (pattern rule)

4x2 = 8-4 = 4

The solution using indices for the given equation is (x = 5/3).

For the given expression in question;

8 × 8⁴ˣ⁻³ = 512 × 8ˣ

By the property of indices, if the base is equal; then the powers are added with sign.

8⁴ˣ⁻³⁺¹ = 512 × 8ˣ

As, we know that 512 is the cube of 8.

8⁴ˣ⁻² = 8³ × 8ˣ

Apply the power law on right side;

8⁴ˣ⁻² = 8³⁺ˣ

As, the base on both side is equal, then the exponents are also equal.

Thus,

4x - 2 = 3 + x

Bring variables and constants on different sides.

4x - x = 3 + 2

3x = 5

x = 5/3

Therefore, the value of x is found as 5/3.

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Answer:

A (2x − 4)(4x2 + 8x + 16)

Step-by-step explanation:

A

(2x − 4)(4x2 + 8x + 16) =

8x3 + 16x2 + 32x - 16x2 - 32x - 64 =

8x3 - 64

B

(2x − 4)(4x2 − 8x + 16)

8x3 - 16x2 + 32x - 16x2 + 32x - 64

8x3 - 32x2 - 64

c

(2x + 4)(4x2 + 8x + 16)

8x3 + 16x2 + 32x + 16x2 + 32x + 64

8x3 + 32x2 + 64x + 64

D

(2x + 4)(4x2 + 8x − 16)

8x3 + 16x2 - 32x + 16x2 + 32x - 64

8x3 + 32x - 64

Answer:

66

Step-by-step explanation:

he will pay 66 dollars

Answer:

[tex]\frac{1}{2} - \frac{1}{6} = \frac{3}{6} - \frac{1}{6} = \frac{2}{6}[/tex]

Step-by-step explanation:

It does not say to simplify so 2/6 would be your answer.

The value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

The function definition is given as

f(x) = √(x - 9) + 6

We start by calculating the function f(x + a)

So, we have

f(x + a) = √(x + a - 9) + 6

The function definition f(x + a) - f(x) is calculated as

f(x + a) - f(x) = √(x + a - 9) + 6 - (√(x - 9) + 6)

Open the bracket

So, we have

f(x + a) - f(x) = √(x + a - 9) + 6 - √(x - 9) - 6

Evaluate the difference

So, we have

f(x + a) - f(x) = √(x + a - 9) - √(x - 9)

Hence, the value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

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Answer:

$320

Step-by-step explanation:

This answer is relieved by turning 40% into .4 and multiplying 800 by .4