Answer:
B. 60
Step-by-step explanation:
Since the digits 1, 1, 1, 2, 2, 3 are repeated, we use the concept of permutations with repetition. In this case, we can choose the first digit to be any one of the three, the second digit to be any one of the three, and so on. Therefore, the total number of distinct 6-digit numbers that can be made is 3 × 3 × 3 × 3 × 3 × 3 = 729.
However, we need to exclude the numbers that start with a 0 (i.e., numbers like 011112 or 001122). Therefore, the final answer is 729 - 3 = 726, which is the number of 6-digit numbers that do not start with a 0. The number of 6-digit numbers that start with a 0 is 3 (111120, 111202, 112102), so the total number of distinct 6-digit numbers is 726 - 3 = 60.
7. Write the decimal number 53.71 as a reduced fraction of two integers.
For the following exercises, line L is given.
a. Find point P that belongs to the line and direction vector v of the line. Express v in component form.
b. Find the distance from the origin to line -x=y+1, z=2
a. Point P on the line and the direction vector v of the line can be expressed as P = (x0, y0, z0) + t(a, b, c).
b. The distance from the origin to the line -x=y+1, z=2 is the shortest distance between a point and a line.
Here (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector. To find (x0, y0, z0) and (a, b, c), we need more information about the line.
This formula involves taking the dot product of the direction vector of the line and the difference between a point on the line and the origin. Again, we need more information about the line in order to calculate this distance.
Without more information about line L, it is not possible to find the point P or the distance from the origin to the line.
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10-2 eeaaasadaddadeeee
Answer:thwe answer is 8
Step-by-step explanation:
Answer:88
Step-by-step explanation:
The tables show functions representing the growth of
two types of bacteria on certain days within an
experiment that lasted a total of 10 days.
Bacteria A
Time (days)
Bacteria Count
Bacteria B
Time (days)
Bacteria Count
Mark this and return
0
60
2 4
240
960
0
1
3
90 180 720
6
3,840
5
2,880
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B.
Save and Exit
Next
Submit
The correct statement regarding the exponential functions is given as follows:
Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
How to model the situation?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.For Bacteria A, we have that:
The initial amount is of 60. (y-intercept).The amount doubles every 2 days.For Bacteria B, we have that:
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How can I find the area under the normal distribution between z= -0.30 and z=0.90?
To find the area under the normal distribution between z = -0.30 and z = 0.90, you can use a standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table:
Look up the area to the left of z = 0.90 in the standard normal distribution table. This will give you a value of 0.8159.
Look up the area to the left of z = -0.30 in the standard normal distribution table. This will give you a value of 0.3821.
Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:
Area = 0.8159 - 0.3821 = 0.4338
Using a calculator with a normal distribution function:
Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = 0.90. This will give you a value of 0.8159.
Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = -0.30. This will give you a value of 0.3821.
Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:
Area = 0.8159 - 0.3821 = 0.4338
Therefore, the area under the normal distribution between z = -0.30 and z = 0.90 is 0.4338.
A room addition requires 320 sq ft of wood floor Hardwood costs $5.59 per sq ft, while laminate costs $2.89 per sq ft. What is the total difference in cost between the
two types of flooring?
The difference in cost is $
(Round to the nearest dollar as needed.)
On solving the provided question, we can say that by bodmas, Hardwood cost = 5.59*320 = $1788.8 ; laminate cost = 2.89*320 = $924.8 and difference = 1788.8-924.8 = $864
what is bodmas?The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.
A room addition requires 320 sq ft
Hardwood costs $5.59 per sq ft.
laminate costs $2.89 per sq ft.
Hardwood cost = 5.59*320 = $1788.8
laminate cost = 2.89*320 = $924.8
difference = 1788.8-924.8 = $864
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50PTS. NEED HELP ASAP WILL MARK IF CORRECT!!!!!
Answer:
Step-by-step explanation:
PART A: No, the trinomial 4x^3 + 28x + 49 is not a perfect square trinomial. To be a perfect square trinomial, the first and last terms must be perfect squares and the middle term must be twice the product of the square roots of the first and last terms. In this case, the first and last terms are not perfect squares, and the middle term is not twice the product of the square roots of the first and last terms.
PART B: To factor the expression 6x^2 + 5x - 4, we need to find two binomials whose product is equal to this expression.
First, we can break down the coefficient of x into two numbers whose product is 6 * (-4) = -24 and whose sum is 5. These numbers are 8 and -3.
Next, we use these two numbers to split the middle term 5x into two terms:
6x^2 + 8x - 3x - 4
We can now factor the expression by grouping:
(6x^2 + 8x) - (3x + 4)
2x(3x + 4) - 1(3x + 4)
(2x - 1)(3x + 4)
Therefore, the area of the rectangle can be factored as (2x - 1)(3x + 4).
To determine the dimensions of the rectangle, we set each factor equal to one of the dimensions and solve for the other dimension:
2x - 1 = length
3x + 4 = width
Alternatively, we could switch the factors and get the same answer:
2x - 1 = width
3x + 4 = length
Either way, these are the dimensions of the rectangle, expressed in terms of x.
Another pond has an algae bloom that is also decreasing exponentially. The area of this
bloom in square meters is given by the function B(d) = 100 27, where d is days since
the first measurement of the bloom. Which of the two algae blooms was larger initially?
Which is decreasing more quickly? Explain how you know.
1. The algae blooms was larger initially is the first algae.
2. The first algae bloom is decreasing more quickly than the second algae bloom.
Math problems errors1. To determine which algae bloom was larger initially, we can compare the values of the functions at d=0.
For the first algae bloom, we have A(0) = 200.
For the second algae bloom, we have B(0) = 100*27⁰ = 100.
Therefore, the first algae bloom was larger initially.
2. To determine which algae bloom is decreasing more quickly, we can compare the rates of decrease of the two functions. The rate of decrease is given by the derivative of the function, which tells us how fast the area is changing with respect to time.
For the first algae bloom, we have A'(t) = -20e^(-0.2t).
For the second algae bloom, we have B'(d) = -100*27^(-1)d.
To compare these rates of decrease, we can evaluate them at the same point in time or days. Let's evaluate them at d=1, which means one day has passed since the first measurement.
For the first algae bloom, we have A'(1) = -20e^(-0.2) ≈ -15.24.
For the second algae bloom, we have B'(1) = -100*27^(-1) ≈ -3.70.
Therefore, we can see that the first algae bloom is decreasing more quickly than the second algae bloom. This is because the rate of decrease of the first bloom is more negative than the rate of decrease of the second bloom.
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you deal one friend a card at random. Then you deal a second friend a card at random. What is the possibility that both friends got diamonds?
Answer:
0.0588
Step-by-step explanation:
There are 52 cards total in a pack of cards.
There are 13 diamond cards in a pack of card
When the first card is dealt, it is NOT replaced. When the second card is dealt, it is NOT replaced
In probability:
AND = multiplication
OR = addition
Probability = [tex]\frac{Total number of diamond cards}{Total number of cards}[/tex]
Probability that both friends for diamonds:
First card is DIAMONDS AND second card is DIAMONDS:
= [tex]\frac{13}{52}[/tex]×[tex]\frac{12}{51}[/tex]
= [tex]\frac{156}{2652}[/tex]
= 0.0588 (Rounded off to 3 significant figures)
Jocelyn has 4/6 of her rectangular garden available for pla6vegerables she will plant carrots in 1/2of the portion available for vegetables
In 1/3 portion Jocelyn planted the carrots.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Jocelyn has 4/6 of her rectangular garden.
She plant carrots in 1/2of the portion available for vegetables.
So, the fraction of Carrot Jocelyn plants
= 4/6 x 1/2
= 2/6
= 1/3
Hence, 1/3 portion is used.
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$580 is invested for two years at a rate of 9% per year, compounding annually. complete the table below to determine the final value of the investment, roudning your answers to the nearest cent.
Answer:
Year | Rate | Interest (9%) | Principal Invested | Final Value
1 | 9% | 52.20 | 580.00 | 632.20
2 | 9% | 56.94 | 580.00 | 688.14
A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
The smallest number of blocks needed to build the wall is 350 blocks which are 1 foot high and either 2 feet long.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Dimension of the wall.
Length = 100 feet
Height = 7 feet
Area = 100 x 7 = 700 ft²
Dimension of the larger block.
Length = 2 feet
Height = 1 feet
Area = 2 x 1 = 2 ft²
Dimension of the smaller block.
Length = 1 feet
Height = 1 feet
Area = 1 x 1 = 1 ft²
Now,
The number of smaller blocks needed to build the wall.
= 700
The number of larger blocks needed to build the wall.
= 700 / 2
= 350
Thus,
The smallest number of blocks needed is 350 blocks which are 1 foot high and either 2 feet long.
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Mhlaba is planning on doing a baking course.she,therefore,decided to buy a food processor while browsing the internet,she came across the following special promotions
Based on the information, it can be inferred that Mhlaba food processor on offer is the right choice for Mhlaba due to its quality product.
Which food processor should Mhlaba buy?According to the information, Mhlaba should buy a home food processor because he only needs to make small portions for himself and his family.
Therefore, there is no need for Mhlaba to look for another more professional food processor since he will not work as a cook nor will he require a large-capacity machine. Then he should choose the one on offer.
Note: This question is incomplete. Here is the complete information:
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Wendy will have new carpet installed on her rectangular bedroom floor. The floor is 15 feet in length and 12 feet in width. The carpet costs $27.50 per square yard, and installation costs $4.15 per square yard. Which statement about the total cost of the carpet and installation is true?
a. The total cost is $379.80 since $31.65×12 = $379.80.
b. The total cost is $633.00 since $31.65×20 = $633.00.
c. The total cost is $474.75 since $31.65×15 = $474.75.
d. The total cost is $4,950.00 since $27.50×180 = $4,950.00.
Select all the coefficients of the product (5y − 3)2 .
The coefficients of the product are 25 and -30. Option A nd E
What are algebraic expressions?These are expressions that are composed of arithmetic or mathematical operations, such as;
AdditionBracketSubtractionDivisionParenthesesMultiplicationThey are also made up of variables, coefficients, terms, constants and factors.
Coefficients are numbers in the front of variables in the expression.
Given that;
(5y − 3)(5y -3 )
expand the bracket
25y² - 15y - 15y + 9
25y² -30y + 9
Hence, the coefficients are 25 and - 30
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express as a torinomial (2x-4)(x+8)
Answer:
2x²+12x-32
Step-by-step explanation:
Which type of wave is most affected by gravity from the Sun and the moon?(1 point)
Responses
water
water
electromagnetic
electromagnetic
sound
sound
seismic
Answer:A tidal wave is a regularly reoccurring shallow water wave caused by effects of the gravitational interactions between the Sun, Moon, and Earth on the ocean.
Im so confused could someone help me here:(
For the function y=f(x), the domain is (-2,2] and the range is (-2,3).
The corresponding values are -
f(-1) = -6, f(0) = -5, f(1) = 6, f(2) = 3.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph for function y = f(x) is given.
The collection of input or argument values for which a function is actual and defined is known as its domain.
In the graph it can be seen that the graph is intersecting x-axis at x = -2 and at x = 2.
So, the domain is (-2,2]. The ( symbol denotes empty circle whereas the ] symbol denotes a filled circle.
A function's range is the collection of values for which the dependent variable is defined.
The coordinates for the ending of the graph is (2,3). So, the range of the function is [-2,3].
The value for f(-1) as seen in the graph is -
x = -1, then y = -6.
The value for f(0) as seen in the graph is -
x = 0, then y = -5.
The value for f(0) as seen in the graph is -
x = 1, then y = 6.
The value for f(2) as seen in the graph is -
x = 2, then y = 3.
Therefore, the domain and range is (-2,2] and (-2,3) respectively.
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highest common factor 84,126 245
Answer: 7 is the common factor for ALL of these numbers.
5. If A=4 and B=6, then what is 6A plus 3B?
Answer:
42
Step-by-step explanation:
6*4+3*6= 42
Answer:
42
Step-by-step explanation:
6*4+3*6=42
which of the following statements about alpha is true? a. rows of alpha are numbered 0...24 and columns are numbered 0...9 b. rows of alpha are numbered 0...24 and columns are numbered 1...10 c. rows of alpha are numbered 1...24 and columns are numbered 0...9 d. rows of alpha are numbered 1...25 and columns are numbered 1...10
Rows of alpha are numbered 0...24 and columns are numbered 0...9 is the true statement about alpha.
What is alpha?
The first letter of the Greek alphabet is known as alpha. Alpha is typically used to signify an unidentified angle. Gamma, alpha, and beta are utilized as variables just as x, y, and z in mathematics. Mainly in quadratic problems, it is employed.
Since symbols are only meant for communication, you can create whatever you choose with them. It may take the form of a real number, vector, tensor, or index.
The rows of the alpha have to start from 0 so, the true statement lies in option a and option b.
Also, the columns are to be numbered till 9. So, the true statement lies in option a.
Hence, the true statement is that rows of alpha are numbered 0...24 and columns are numbered 0...9.
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Gallons of water in an area of .5 x 2 x 55 ft
Answer: It´s about 14.96 gallons per square foot with 55 square foot area and 2 feet height
Step-by-step explanation:
Convert to scientific notation.
0.000000032
Answer:
3.2 × 10⁻⁸
Step-by-step explanation:
Scientific notation is written in the form [tex]a \times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To convert a number into scientific notation, move the decimal point to the left or right until there is one non-zero digit to the left of the decimal point.
The number of times you have moved the decimal point is the power of 10 (the value of n).
If the decimal point has moved to the left, n is positive.If the decimal point has moved to the right, n is negative.Therefore, to convert 0.000000032 to scientific notation, move the decimal point 8 places to the right so that [tex]a[/tex] is 3.2.
As the decimal point has been moved 8 places the right, the exponent of 10 is -8.
Therefore, 0.000000032 = 3.2 × 10⁻⁸.
Bashir has a toy car collection. He keeps some in display case and the rest on the wall. 136 of his toys are on the wall and 15% of the toys are in the display what is the total number of toys in barshirs collection
The total number of toys in Bashir's collection is 160.
How to find the total number of toys in Bashir's collection?
A percentage is a number or ratio that can be expressed as a fraction of 100.
Let N represent the total number of toys in Bashir's collection
Since 136 of his toys are on the wall and 15% of the toys are in the display. We can write:
136 + (15% of N) = N
136 + (15/100 * N) = N
136 + 0.15N = N
N - 0.15N = 136
0.85N = 136
N = 136/0.85
N = 160
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The triangle shown below has an area
of 75 units²
what is the area of the triangle?
The triangle has an area of 75 units² then the area of triangle be 15 units.
What is meant by area of the triangle?The space bounded by a triangle's three sides is known as the area of a triangle. The total area that is bounded by a triangle's three sides is referred to as the triangle's area.
Area of triangle = 1/2 (b h), where b is the base and h is the height, is the fundamental formula for calculating a triangle's area. The type of the triangle and the known dimensions can affect other formulas that are used to calculate the area of a triangle.
Let x be base of triangle
height = 19 units
Area of triangle = 1/2 base × height
substitute the values in the above equation, we get
75 = 1/2 × x × 10
simplifying the equation, we get
75 = x × 5
x = 75/5
x = 15 units
Therefore, the area of triangle be 15 units.
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1/8 of the toys in a play area are yellow, and 1/4 are green. 3/5 of the remainder are red. The rest of the toys are blue. If there are 100 green toys, how many blue toys are there?
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To figure out what fraction of the toys are blue, we need to convert all of the fractions to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
Looking at the fractions, we can see that there are 3 fractions, [tex]\frac{1}{8}, \frac{1}{4}[/tex] and [tex]\frac{3}{5}[/tex].
To solve for the common denominator between [tex]\frac{1}{8}[/tex] and [tex]\frac{3}{5}[/tex], we first multiply the denominators, 8 and 5.
8 × 5 = 40We now know that the denominator is going to be 40.
[tex]\frac{?}{40} \frac{?}{40}[/tex]To get the numerators, we can use these equations:
1 × 5 = 58 × 3 = 24The new fractions look like this:
[tex]\frac{5}{40} \frac{24}{40}[/tex]To easily convert the last fraction ([tex]\frac{1}{4}[/tex]) we can multiply the numerator and denominator by 10.
1 × 10 = 104 × 10 = 40Why do we multiply by 10?We multiply by 10 because the denominator, which is 4, can be multiplied by 10 to get our common denominator of 40.
Now, we have our 3 fractions converted to have common denominators.
([tex]\frac{5}{40}, \frac{24}{40}[/tex] and [tex]\frac{10}{40}[/tex])
(Yellow, red, and green)
We can now add these up and see what fraction of blue is remaining.
[tex]\frac{5}{40}+ \frac{24}{40}+ \frac{10}{40} =\frac{39}{40}[/tex][tex]1 - \frac{39}{40} = \frac{1}{40}[/tex]Therefore, the fraction of blue toys compared to the total amount is [tex]\frac{1}{40}[/tex].
If there are 100 green toys resulting in [tex]\frac{10}{40}[/tex] of all the toys, we can divide 100 by 10 to get the number of blue toys.
Why do we divide by 10?We divide by 10 because [tex]\frac{1}{40}[/tex] is only [tex]\frac{1}{10}[/tex] of [tex]\frac{10}{40}[/tex], meaning we divide by 10.
100 ÷ 10 = 10Therefore, there are 10 blue toys.
Answer:
1/4=100
10/40=100
40/40=400
1/8=400/8=50
3/5=400/5*3=240
400-100-50-240=10
10 of the toys are blue
Hope this helped!!
Step-by-step explanation:
I. f(x) = f (x) = StartFraction 1 minus x squared Over x minus 1 EndFraction
II. f(x) = f (x) = StartFraction x squared minus x cubed Over x squared minus 1 EndFraction
III. f(x) = g (x) = StartLayout Enlarged left-brace First row StartFraction x squared minus 5 x + 6 Over x minus 3 EndFraction, x not-equals 3 Second row 5, x = 3 EndLayout
IV. f(x) = f (x) = StartLayout First Row StartFraction x squared minus 3 x + 2 Over x minus 1 EndFraction, x not-equals 1 Second Row negative 1, x = 1 EndLayout
For which function does the Limit of f(x) as x approaches 1 not exist?
For the function, [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex] the Limit of f(x) as x approaches 1 does not exist.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex], [tex]g(x) = \frac{x^2 - 5x + 6}{x - 3}[/tex].
We know, In a rational expression (p/q), q ≠ 0 as the expression would be undefined.
Therefore, The function for which the Limit of f(x) as x approaches 1 does not exist is [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex], as at x = 1, f(x) is undefined.
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Strategy-planning activity in which top management envisions different what if scenarios to anticipate plausible futures in order to derive strategic responses is definition of ?
Strategy-planning activity in which top management envisions different what if scenarios to anticipate plausible futures in order to derive strategic responses is definition of: Scenario planning.
What is Scenario planning?Scenario planning gives company decision-makers the ability to assess reactions, manage for both good and negative possibilities, and establish ranges of prospective outcomes and anticipated implications. Scenario planning is more than simply a financial planning tool; it's an integrated strategy for coping with uncertainty. It includes predicting financial results, calculating cash flow, and devising mitigation actions. But it goes beyond only being a means to identify and reduce risk or prepare for growth scenarios. Planning scenarios involves imagining several futures for an organisation based on various, sometimes positive, sometimes negative, assumptions about market dynamics. Scenario planning is a method pioneered by the United States military, which now conducts exercises looking up to 20 years in advance to direct R&D activities.
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A family drove a distance of 354 miles in 5 hours about how many miles did they travel each hour
Answer:
An average of 70.8 miles per hour
Step-by-step explanation:
Jack Fitzgerald wishes to purchase a used car that has a cash price of $11,000. The installment terms include a down payment of $2,000 and 48 monthly payments of $219.
a) What finance charge will Jack pay?
b) What is the APR to the nearest half percent?
The finance charge is $______?
The APR is_____%?
finance charge Jack will pay is $1,512.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Jack Fitzgerald wishes to purchase a used car that has a cash price of $11,000. The installment terms include a down payment of $2,000 and 48 monthly payments of $219.
a)
The amount that needs to be financed is = 11,000 - 2,000 = $9,000.
Amount repayment = 219 x 48 = $8,100.
=> Finance charge = Amount repayment - Amount needs to be financed
Finance charge = 10512 - 9000
Finance charge = 1,512$
b)
We apply the PV for annuity formula to find the interest rate per one month denoted as i:
Amount needs to be finance = (equal monthly installment x i) / [ 1 - (1+i)^-36 ]
or 9,000 = (219/i) x [1 - (1+i)^-48 ] <=> i = 0.911%.
APR = 12 x i
APR = 10.932% .
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