There are 24 ways to pick two green marbles first and one red marble last.
The probability of picking a green marble on the first draw is 4/10, and then 3/9 on the second draw since there are only 3 green marbles left out of 9 total marbles remaining.
The probability of picking a red marble on the third draw is 4/8 since there are 4 red marbles left out of 8 total marbles remaining.
So the probability of picking two green marbles first and one red marble last is (4/10) x (3/9) x (4/8) = 2/45.
To calculate the number of ways to pick two green marbles first and one red marble last, we need to use combinations.
There are [tex]^4C_2[/tex] = 6 ways to choose two green marbles from four, and there are 4 ways to choose one red marble from four.
So there are 6 x 4 = 24 ways to pick two green marbles first and one red marble last.
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Find the two perfect squares that each Integer is between. Then approximate the square root to one decimal place.
√47
pls i need it quick
Answer:
[tex] 36 < 47 < 49[/tex]
[tex] \sqrt{36} < \sqrt{47} < \sqrt{49} [/tex]
[tex]6 < \sqrt{47} < 7[/tex]
√47 is approximately 6.9
Which set of data contains two outliers?
113, 115, 103, 114, 109, 111, 119
141, 151, 138, 142, 149, 140, 150
99, 113, 91, 104, 109, 114, 97
101, 135, 131, 99, 138, 136, 140
Answer:
D.
Step-by-step explanation:
The set of data that contains two outliers is: 101, 135, 131, 99, 138, 136, 140. An outlier is a value that is significantly different from other values. In this set, both 99 and 138 are outliers because they are much lower and higher respectively than the other values. In the other sets, all values are relatively close to each other with no extreme deviations, thus they do not contain any outliers. Outliers can skew statistical analyses and should be removed or treated with caution.
Step-by-step explanation:
The set of data containing two outliers is the last one: 101, 135, 131, 99, 138, 136, 140. This can be determined by analyzing the range and distribution of the data. Two values, 99 and 140, are significantly different from the other values in the set and fall outside the typical range. These two extreme values are considered outliers and can impact the accuracy of any analysis or Scalculations based on the data.
Which value is a solution of the inequality 1/4y>8?
The solution of the inequality is y > 32.
We have the inequality,
1/4 y > 8
Now, solving the inequality for y
Multiply both side by 4 we get
1/4 y(4) > 8 (4)
y > 32
Thus, the solution of the inequality is y > 32.
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Crown Heights Ceramics collects 6% sales tax on all sales. If total sales including tax are $2739.45 , find the portion that is the tax amount. (Show your work)
$165.60
$164.37
$155.06
$2584.39
If total sales including tax are $2739.45 , the portion that is the tax amount is $155.06. So, correct option is C.
To find the portion that is the tax amount, we need to first determine the portion of the total sales that is the cost of the item before taxes. To do this, we can use the fact that the sales tax is 6%, which means that the total sales including tax is 106% of the cost before taxes.
Thus, we can set up the equation:
total sales including tax = cost before taxes + tax amount
Or, in terms of percentages:
106% cost before taxes = cost before taxes + tax amount
Simplifying this equation, we get:
0.06 cost before taxes = tax amount
Now we can substitute the given information into this equation. If total sales including tax are $2739.45, then the cost before taxes is:
cost before taxes = total sales including tax / 1.06
cost before taxes = $2584.39
Finally, we can calculate the tax amount:
tax amount = 0.06 * $2584.39
tax amount = $155.06
Therefore, the answer is option C, $155.06.
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Simplify
2x5
-
O-4x³+4
○ 2x5 - 6x³ +4-x-2
O 2x5 - 6x³ +4+x=²
2x³
6x + 4x 2
-
-
6x³ +4
x²
○ 2x5 6x³+4x2
< Previous
Your answer should not have any fractions.
The simplified expression is determined as 2x³ - 6x + 4x⁻².
What is the simplification of the expression?The expression is simplified by applying the principle of exponent rules of division as shown below;
The given function = 2x⁵ - 6x³ + 4 / x²
So we will divide each of the numerator with the denominator as shown below;
2x⁵/x² = 2x⁵⁻² = 2x³
6x³/x² = 6x³⁻² = 6x
4/x² = 4x⁻²
The simplified expression = 2x³ - 6x + 4x⁻²
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The graph below was obtained by transforming the graph of the
square root function. Write the equation for the function the
graph represents.
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x-1)} +2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.Therefore, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 2) + 2
[tex]g(x) = -\sqrt{9(x-1)} +2[/tex]
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A: A statement about rational numbers is shown.
The product of two negative rational numbers is greater than either factor. Is the statement always true, sometimes true, or never true? Explain your answer. Provide at least two examples to support your answer.
Part B: A different statement about rational numbers is shown. The product of two positive rational numbers is greater than either factor. Provide at least two examples to show that this statement is only sometimes true.
The statement "the product of two negative rational numbers is greater than either factor" is never true.
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
We have,
Part A:
The statement "the product of two negative rational numbers is greater than either factor" is never true.
This can be proved by considering a negative rational number, say -1/2, and multiplying it by a negative rational number that is greater in magnitude, say -2/3.
The product of these two negative rational numbers is 1/3, which is less than either factor.
Another example is -3/4 multiplied by -1/2 which results in 3/8, again less than either factor.
Part B:
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
For example, if we take 1/2 and 2/3, the product is 1/3 which is less than either factor.
Similarly, if we take 3/4 and 4/5, the product is 3/5 which is less than either factor.
Therefore, the statement is only sometimes true and not always true.
Thus,
The statement "the product of two negative rational numbers is greater than either factor" is never true.
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
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The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.22
.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99%
confidence level with an error of at most 0.03
? Round your answer up to the next integer.
A sample size of 176 tenth graders would be needed in order to estimate the fraction of students with reading skills at or below the eighth grade level at a 99% confidence level having an error of at most 0.03.
To calculate the sample size required for estimating the fraction of tenth graders with reading skills at or below the eighth grade level, we can use the formula for sample size estimation for proportions;
n = (ZZ × p × (1 - p)) / (EE)
where; n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, the Z-score for a 99% confidence level, which is approximately 2.626)
p = estimated population proportion (in this case, 0.22)
E = desired margin of error (in this case, 0.03)
Plugging in the given values;
n = (2.6262.626 × 0.22 × (1 - 0.22)) / (0.030.03)
n = 0.15774 / 0.0009
n ≈ 175.27
Since we need to round up to the next integer, the sample size required would be 176.
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collection of rivers of Nepal is a well defined or not well defined
The collection of rivers of Nepal is a well defined value.
Why is this collection well defined ?Nepal boasts a finite number of well-defined rivers, each identified and named for easy reference. Given the geographically diverse landscape of Nepal with intricate topography, the task of accurately delineating the sources and tributaries of its waterways is challenging.
Further compounding such complexity are seasonal variations that cause some rivers to dry up at specific times—rendering the precise marking of their borders an especially arduous undertaking.
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___ less than 60 greater than ___
Answer:
less than 60 is 59 and greater than 60 is 61
Answer:40 and 20
Step-by-step explanation: Mathematically the first fill in the blank can be any number less than 60 here in I have taken it as 40.In the second fill in the blank the it can be any number less than 40 so 20 can be answer I hv chosen here.
3/10+63/100 what is this
Answer:
The answer would be 0.93!
Step-by-step explanation:
What's the solution to the inequality x^2 + 2x < or equal to 24?
a) (-infinity, -6] union [4, +infinity)
b) (-6, 4)
c) (-infinity, -6) union (4, +infinity)
d) [-6, 4]
The solution to the inequality x² + 2x ≤ 24 is D. [-6, 4].
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
x² + 2x ≤ 24
x² + 2x - 24 ≤ 0
x² + 6x - 4x - 24 ≤ 0
x(x + 6) - x(x + 6) ≤ 0
(x + 6)(x - 4) ≤ 0
x = -6 or x = 4.
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Find the value of x for the following
The length x in the similar triangle is 7.06 units.
How to find the side of similar triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Therefore, let's use the similarity of the triangle to find the value of x in the triangle.
Hence, using the proportion,
y / 8 = 8 / 17
cross multiply
17y = 64
y = 64 / 17
y = 3.76470588235
y = 3.76
Therefore,
17 - 3.76 = 13.24
Hence,
13.24 / x = x / 3.76
cross multiply
x² = 49.7824
x = √49.7824
x = 7.05566439111
Hence,
x = 7.06 units
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Determine the measure of the arc CED
Answer:kbef;eohrjkvoubwe
cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?
A.
Kendall might be determined to be insane and not qualified to testify.
B.
The evidence in Kendall’s case is inconclusive and doesn’t prove anything.
C.
Kendall is an expert witness who has testified many times before.
D.
The police think it will hurt their case if Kendall chooses to testify.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Arc length= [tex]\frac{interior angle}{360} 2\pi r[/tex]
If a player bets 3$ on the 5$ denomination, find the players expectation
The player can expect to win 1.67$ for each 3$ bet placed on the 5$ denomination.
In probability theory, the expected value or expectation is the value that a player would expect to receive on average if they repeated the same game many times under the same conditions.
To find the player's expectation, we need to use the formula:
Expectation = (Probability of Winning x Amount Won) - (Probability of Losing x Amount Lost)
Assuming that the player wins if the bet is successful, the probability of winning on a 5$ denomination bet is 1/3, since there are three possible outcomes (win, lose, or push). The probability of losing is 2/3, since the player will lose if the bet is unsuccessful or if the outcome is a push.
If the player bets 3$ on a 5$ denomination, there are two possible outcomes: they either win 5$ or lose 3$. Therefore, the player's expectation can be calculated as:
Expectation = (1/3 x 5$) - (2/3 x 3$) = 1.67$
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The following data sets show the number of shoppers on four weekends in a month at different hours of the day. Identify the weekend whose data best shows asymmetric distribution.
First: 9, 7, 8, 6, 7, 8, 7, 6, 8, 7, 9, 7, 8, 5, 10, 5, 10, 8, 7, 7
Second: 15, 13, 12, 15, 14, 13, 15, 16, 14, 13, 15, 15, 15, 17, 18, 12, 18, 15, 17, 16
Third: 11, 18, 17, 14, 15, 9, 16, 12, 13, 15, 14, 12, 15, 17, 16, 14, 13, 11, 10, 9
Fourth: 18, 17, 18, 19, 18, 17, 16, 18, 17, 19, 18, 17, 17, 16, 16, 15, 15, 16, 15, 17
The second data set best shows asymmetric distribution.
To identify the weekend whose data best shows asymmetric distribution, we need to look for the data set that is skewed, or "lopsided", meaning it has a longer tail on one side than on the other.
We can begin by creating a histogram for each of the data sets to visualize their distributions
The second data set, however, shows a clear skew to the left, with a longer tail of observations on the left side of the center than on the right side.
This makes the second data set the one that best shows asymmetric distribution.
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I'll MARK THE BRAINLIEST!
The line plots show the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week. A) Which statement is true about the range? B) Which statement is true about the mean?
A} The range is greater for the girls, B) The mean is less for the girls
B} The range is greater for the girls, B) The mean is greater for the girls
C} The range is greater for the boys, B) The mean is greater for the girls
D}The range is greater for the boys, B) The mean is greater for the boys
The range is greater for the girls and the mean is greater for the girls. So, correct option is B.
A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.
Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.
B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:
(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours
To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:
(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours
Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".
So, correct option is B.
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The radius of a circle is decreasing at a constant rate of 2 centimeters per second. What is the rate of change of the area of the circle, in square centimeters, at the instant that the radius, r=5 centimeters
The rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.
Use the formula A=pi*r^2 to calculate the area of the circle when the radius is 44cm.
A=pi*r^2
A= 3.14159*(44 cm)^2
A= 6081.816 cm^2
Use the formula A'=2pi*r*r' to calculate the rate of change of the area.
A'=2pi*r*r'
A'= 2*3.14159*44 cm*(7 cm/s)
A'= 97.636 cm^2/s
The area of a circle is calculated by the equation A=pi*r^2, where r is the radius of the circle. At the instant when the radius of the circle is 44 centimeters, the area is 6081.816 cm^2.
To calculate the rate of change of the area, we use the equation A'=2pi*r*r', where r' is the rate of change of the radius.
In this case, the radius of the circle is decreasing at a rate of 7 cm/s, so r'=7 cm/s. Plugging these values into the equation, we get A'=2*3.14159*44 cm*(7 cm/s), which equals 97.636 cm^2/s.
Therefore, the rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.
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complete question:
the radius of a circle is decreasing at a constant rate of 7 centimeters per second. at the instant when the radius of the circle is 44 centimeters, what is the rate of change of the area? round your answer to three decimal places.
) F= {mango, apple) is a given set of fruits. (i) Find the number of subsets of the set F by using formula. (ii) Write all possible subsets of the set F (iii) Among these subsets, which one is the improper subset? Write with reason.
The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.
Given :
The set of days of the week.
The following steps can be used in order to determine the number of subsets and the number of proper subsets:
Step 1 - According to the given data, the set is given below:
S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Step 2 - Now, the total number of subsets is given by the formula where 'n' is the number of elements of the set.
The total number of subsets is 128.
Step 3 - Now, the total number of proper subsets is given by the formula where 'n' is the number of elements of the set.
The total number of proper subsets is 127.
a) The total number of subsets is 128.
b) The total number of proper subsets is 127.
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complete question:
Find (a) the number of subsets and (b) the number of proper subsets of the set.
The set of days of the week.
(a) The number of subsets is
(b) The number of proper subsets is
PQ is tangent to Circle O at Point P with arc lengths 160° and 60° as shown below.
The measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula. So option A is correct.
What is the secant tangent angleThe secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:
θ = 1/2 (arc EB - arc BD)
where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.
From the question,
θ = m∠PQR
arc EB = 160°
arc BD = 60°
m∠PQR = 1/2(160° - 60°)
m∠PQR = 1/2 × 100°
m∠PQR = 50°
Therefore, the measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula.
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4. The scale drawing of a baby blanket has the dimensions of 6 inches by 10 inches. The dimensions of the actual baby blanket are 30 inches by 50
inches.
What is the scale of the drawing?
The scale factor of the given drawing is expressed as: 1:5
How to find the scale factor?We are given the dimensions of the scale drawing of the blanket as:
Length = 10 inches
Width = 6 inches
We are given that the actual dimensions of the baby blanket are:
Length = 50 inches
Width = 30 inches
The size by which a shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. If y = Kx is an equation, then K is the scale factor for x.
The scale factor is:
50/10 = 30/6 = 5
Thus, we have 1:5
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It is possible to have a function f:A→B with an element b∈B so that f does not assign any element to b?
Answer:
Yes, it is possible to have a function f:A→B with an element b∈B so that f does not assign any element to b. This happens when b is not in the range of f 1.
I hope this helps!
How does Tom's ploy to get other boys to do his work
for him create suspense?
OA. through Tom's explanation the difficult parts of
work
O B. through Tom's use of persuasion and trickery to
get the work done
O C. through Tom's consideration of exchanging toys
and marbles for the work
O D. through Tom's description about completing the
work and doing a good job
Tom's ploy to get other boys to do his work: through Tom's use of persuasion and trickery to get the work done. Option B
How does Tom's ploy to get other boys to do his workThe reader is left wondering if Tom will be caught and punished for his conduct because he uses persuasion and deceit to persuade other lads to perform his work for him.
The reader is also left wondering whether the other lads will finally grasp what Tom is up to and cease assisting him, or whether they will continue to be duped by him. The use of persuasion and cunning adds a sense of danger and risk-taking to the situation, heightening the story's tension.
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un automóvil que se desplaza en una pista recta aumenta su velocidad de 15 m/s a 45 m/s utilizando para ello un
po de 10 segundos. Consideremos que la aceleración fue uniforme, calcula:
aceleración en dicho tiempo.
The acceleration of the car at that time was 3 m/s².
We have,
From the kinematic equation to find the acceleration:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Initial velocity u = 15 m/s
Final velocity v = 45 m/s,
Time t = 10 s
We can rearrange the equation to solve for acceleration:
a = (v - u) / t
Substituting the values, we get:
a = (45 m/s - 15 m/s) / 10 s
a = 3 m/s^2
Therefore,
The acceleration of the car at that time was 3 m/s².
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The complete question in english.
A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a
po of 10 seconds. Assuming that the acceleration was uniform, calculate:
acceleration at that time.
Points S and T are midpoints of the sides of trisngle FGH.
The length of GF is 4 cm minus half the length of side FH.
To do this, we can use the fact that point S is the midpoint of FH. This means that FS = 1/2 FH. Similarly, point T is the midpoint of GH, so TG = 1/2 GH. We can now use these equalities and the fact that SG = 4 cm and HT = 6 cm to set up an equation involving FH:
SG + GF + HT = ST + TG + FH
Substituting the given values and using the fact that TG = GH - TG = GH - 1/2 GH = 1/2 GH, we get:
4 cm + GF + 6 cm = 8 cm + 1/2 GH + FH
Simplifying and substituting FS = 1/2 FH and TG = 1/2 GH, we get:
10 cm + GF = 8 cm + FS + TG
GF = 8 cm + FS + TG - 10 cm
GF = 1/2 FH - 1/2 GH
Now, substituting the values we know, we get:
GF = 1/2 FH - 1/2 GH
GF = 1/2 (FS + SH) - 1/2 (GH)
GF = 1/2 (8 cm + SH) - 1/2 (GH)
GF = 1/2 (8 cm + FS) - 1/2 (GH)
GF = 1/2 (8 cm + 1/2 GH) - 1/2 (GH)
GF = 3 cm - 1/4 GH
We can now substitute TG = 1/2 GH and solve for GH:
TG = 1/2 GH
8 cm - FS = 1/2 GH
GH = 16 cm - 2 FS
Substituting this value into the expression for GF, we get:
GF = 3 cm - 1/4 (16 cm - 2 FS)
GF = 3 cm - 4 cm + 1/2 FS
GF = 1/2 FS - 1 cm
Finally, substituting FS = 8 cm - SH, we get:
GF = 1/2 (8 cm - SH) - 1 cm
GF = 4 cm - 1/2 SH
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Complete Question:
Points S and T are midpoints of the sides of triangle FGH
when HT = 6cm, ST = 8 cm, SG = 4CM
what is GF ?
A total of $7000 is invested: part at 8% and the remainder at 12%. How much is invested at each rate if the annual interest is $580
?
The amount of $5000 is invested at 12% and $2000 is invested at 8%.
Let x be the amount invested at 8% and y be the amount invested at 12%. We know that the total amount invested is $7000, so we have:
x + y = 7000
We also know that the annual interest earned is $580. The amount of interest earned from the investment at 8% is 0.08x, and the amount of interest earned from the investment at 12% is 0.12y. So we have:
0.08x + 0.12y = 580
We now have two equations with two variables. We can solve for one variable in terms of the other in the first equation and substitute it into the second equation:
x = 7000 - y
0.08(7000 - y) + 0.12y = 580
560 - 0.08y + 0.12y = 580
0.04y = 20
y = 500
So $5000 is invested at 12% and $2000 is invested at 8%.
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A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $6,299.59. The
cardholder makes a payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much
interest did the credit card holder pay?
O$123.02
O$562.73
O $211.04
O$559.56
The total interest that the credit card holder paid at 11.99% APR for $6,299.59 is D. $559.56.
How the interest is determined:The total interest is a function of the APR, the principal, and the period involved.
The total interest can be determined using an online finance calculator with some adjustments.
N (# of periods) = 11 months
I/Y (Interest per year) = 11.99%
PV (Present Value) = $6,299.59
PMT (Periodic Payment) = $-350
Results:
FV = $-2,979.39
Sum of all periodic payments = $-3,850.00
Total Interest = $529.80
12th Month Interest = $29.76 ($2,979.39 x 11.99% x 1/12)
Total interest up to the 12th month = $559.56 ($529.80 + $29.76)
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Question in picture. Solve please.
Answer:
[tex] \frac{1}{3} \pi( {3.5}^{2} )(11) = 44.9\pi[/tex]
C is the correct answer.
Ayudaaaaaaaaaaaa
Porfi y gracias
Answer: option b
Step-by-step explanation:
a density graph for all the possible speeds bwtween 0 and 160 is in the shape of a triangle. what’s the height of the triangle
Answer:
0125
Step-by-step explanation:
The answer is equal to 0125