The solution is: 100! different ways can you draw all of the names from the hat.
Here, we have,
if we have n object, and as we know that arrangement given by = n!. (Permutation)
A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.
A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!
Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 100! Way.
So ANSWER IS 100!
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(a) In the figure below, m AB = 106° and m CD =66. Find mAEB
Answer:
[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]
Step-by-step explanation:
Given:arc AB = 106°
arc CD = 66°
Statement:According to angles of intersecting chords theorem, the measure of angle formed by two intersecting chords is half the sum of arcs intercepted by the angle.Mathematical form:[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]
Solution:Put the given data in the above formula.
[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The percentage of vehicles that are returned with less than 30000 miles are given as follows:
b) 2.5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 36400, \sigma = 3200[/tex]
The proportion is the p-value of Z when X = 30000, hence:
Z = (30000 - 36400)/3200
Z = -2.
Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.
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I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answer
[tex]\pink\sf{y=-1}[/tex]
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation [tex]\sf{y=0.5(6)-4}[/tex].
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
[tex]\sf{y=3-4}[/tex]
And now we just simplify the last part:
[tex]\sf{y=-1}[/tex]
∴ answer: y = -1
Given the net, what is the surface area of the rectangular prism below?
PLS HELP ASAP WILL MARK BRAINLIST
Answer:
Step-by-step explanation:
I'm sorry, but I cannot answer your question without a visual representation or description of the rectangular prism. Please provide more information or a picture so that I can assist you accurately.
Answer:
72 cm 2?? THERE Isn't anything bellow I am sorry?
Step-by-step explanation:
5 years ago the ratio of mark's age was 3:4 mark is 12 yr younger than francis how old is francis now.
5 years ago the ratio of Mark's age was 3:4 mark is 12 yr younger than Francis, now Francis is currently 53 years old
Let us suppose that age of him 5 years ago was 3x and Francis's age 5 years ago was 4x. According to the given information, Mark is 12 years younger than Francis.
So, we can set up the equation: 3x + 12 = 4x.
Simplifying the equation, we have: 12 = x.
This means that 5 years ago,
Mark age = 3 * 12 = 36 years old,
Francis age = 4 * 12 = 48 years old.
Now, to find out how old Francis is now, we add 5 years to both Mark and Francis. Thus, Francis's current age is 48 + 5 = 53 years.
Therefore, Francis is currently 53 years old.
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You have a bag of 12 blue marbles (numbered 1-12) and 12 red marbles (numbered 1-12). So you have 24 marbles in total (half blue and half red) with each of the numbers 1-12 appearing twice (once in each color). You draw one marble at random, replace it to the bag, mix up the marbles, and draw a second marble. Determine each of the following probabilities. P ( first marble is blue and second marble is red ) =
The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.
To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag
In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.
When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.
After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.
To find the overall probability, we multiply the probabilities of each event since they are independent events:
P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)
[tex]= (12/24) \times (12/24)[/tex]
[tex]= (1/2) \times (1/2)[/tex]
= 1/4.
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A circle has a center at C(2,7). The point A(8,17) lies on the circle. Which of the
following is the slope of the tangent to the circle at point A?
The slope of the tangent to the circle at point A is -3/2.
1. The equation of a circle with center C(2, 7) is given by (x - 2)² + (y - 7)² = r², where r is the radius of the circle.
2. Since point A(8, 17) lies on the circle, we can substitute the coordinates of point A into the equation of the circle to find the value of r.
(8 - 2)² + (17 - 7)² = r²
6² + 10² = r²
36 + 100 = r²
136 = r²
r = √136 = 2√34
3. Now that we have the radius, we can find the equation of the tangent line at point A.
The tangent to a circle at a given point is perpendicular to the radius at that point.
The slope of the radius can be found using the coordinates of the center and point A.
Slope of the radius = (17 - 7) / (8 - 2) = 10 / 6 = 5/3
The slope of the tangent line will be the negative reciprocal of the slope of the radius.
Slope of the tangent = -1 / (5/3) = -3/5
4. However, the question asks for the slope of the tangent to the circle at point A, so we need to consider the slope of the tangent line at point A, which is the negative inverse of the slope of the radius.
Slope of the tangent at point A = -1 / (5/3) = -3/5
5. The slope of the tangent to the circle at point A is -3/5.
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What is the area of this figure
Answer: i believe it’s 68
Step-by-step explanation:
My knowledge
Determine the lengths of the missing sides x and y in the triangle below:
x =
y =
2.6 2.1 4.2 3
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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please help its due today and I need a good grade on it!!!!
The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².
To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,
We can use the standard equation for a parabola in vertex form:
y = a(x - h)² + k
In this equation, (h, k) represents the coordinates of the vertex.
Since we want the vertex to be at the origin (0, 0), the equation becomes:
y = ax²
To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.
Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.
In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).
Plugging in the value of f (8) into the formula, we can solve for 'a':
8 = 1/(4a)
32a = 1
a = 1/32
Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = cos(5θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 1
Period = 2π/5
Evaluate
A = 1
Period = 2π/5
Hence, the amplitude is 1 and the period is 2π/5
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Fill in the table using this function rule.
y=-2x+3
x
-2
-1
0
1
y
0
1
0
10
X
Ś
The domain and range of the given function y = -2x + 3 are
Domain = 0, 1, 2, ,3 , 4, 5, 6
Range = 3, 1, -1, -3, -5, -7, -15
The table is given below.
We have,
y = -2x + 3
We can have domain as:
x = 0, 1, 2, 3, 4, 5, 6
For x = 0,
y = -2 x 0 + 3 = 3
For x = 1,
y = -2 x 1 + 3 = -2 + 3 = 1
For x = 2,
y = -2 x 2 + 3 = -4 + 3 = -1
For x = 3,
y = -2 x 3 + 3 = -6 + 3 = -3
For x = 4,
y = -2 x 4 + 3 = -8 + 3 = -5
For x = 5,
y = -2 x 5 + 3 = -10 + 3 = -7
For x = 6,
y = -2 x 6 + 3 = -18 + 3 = -15
The range are 3, 1, -1, -3, -5, -7, -15.
The table can be assumed as:
x y = -2x + 3
0 3
1 1
2 -1
3 -3
4 -5
5 -7
6 -15
Thus the domain and range of the given function y = -2x + 3 are
Domain = 0, 1, 2, ,3 , 4, 5, 6
Range = 3, 1, -1, -3, -5, -7, -15
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An alcohol was made by mixing 6fl. oz. of a 20% alcohol solution and 4fl. oz. of a 5% alcohol solution. What is the concentration of the mixture?
The concentration of the mixture made by mixing 6 fl. oz. of a 20% alcohol solution and 4 fl. oz. of a 5% alcohol solution will be; 14%
Consider that x represents the concentration of the mixture, hence:
(6 x 20%) + (4 x 5%) = x (4 + 6)
1.2 + 0.2 = 10x
x = 0.14 = 14%
The concentration of the mixture is made by mixing 6 fl. oz. of a 20% alcohol solution and
Thus 4 fl. oz. of a 5% alcohol solution = 14%
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Brian says the graph shows the circle with a center (-3, 2) and a radius of 3. Mia says the graph shows all possible centers for a circle that passes through (3, -1) with a radius of 4. Which student is correct? Explain.
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
The graph represents a specific circle with its own center and radius.
To find all possible centers for a circle passing through a given point, we need to consider the locus of points equidistant from the given point.
In this case, the locus of points equidistant from (3, -1) with a radius of 4 forms another circle with a different center and radius.
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
Therefore, neither student's claim is correct based on the given information.
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Find the measure of the red arc or chord in ⊙C
The calculated measure of the red arc in ⊙C is 5
How to find the measure of the red arc or chord in ⊙C.From the question, we have the following parameters that can be used in our computation:
The circle
From the circle, we have
Centers = C
Also, we have
Corresponding segments are equal segments
Using the above as a guide, we have the following:
UV = TU
Where
TU = 5
This gives
UV = 5
Hence, the value of UV is 5
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Math
82°F
Algebra 1 CC.20 Checkpoint: Quadratic equations NXG
2
x² - y + x = 16
y = 3x + 2
3x² - y + 32 = 22x
y = 2x - 16
Language arts
Decide whether each system of equations has two real solutions, exactly one real solution, or
no real solutions.
y = -x² + 6x + 12
y = -x +3
Answer:
x² - y + x = 16 is 1 real solution
3x² - y + 32 = 22x is 2 real solutions
y = -x² + 6x + 12 is 1 real solution
Step-by-step explanation:
sorry i am unsure about rest, they do not have a value. good luck :)
Amazon purchases an office chair for $63, and marks it up 28%.
Which equation can be used to find the selling price of the office chair?
$63 + ($63 · 0.28) = $80.64
[tex]f = p + pm[/tex] where:
[tex]f[/tex] = final price: $80.64,
[tex]p[/tex] = original price: $63,
and [tex]m[/tex] = markup percent (in decimal): 28% → 0.28.
stered comsident p43336280840
Save the expression by solating the variable Hemember to balance the equation in each step you take
2
0-6
The result of the expression 20 - 6 is 14.
To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.
Step 1: Start with the given expression, 20 - 6.
Step 2: Evaluate the subtraction operation: 20 - 6 = 14.
Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.
This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.
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What is the slope of the line that passes through the points (2,-4) and (5, 2)? Write
your answer in simplest form.
Answer:
undefined
Submit Answer
attempt 1 out of 2
Answer:
1/2
Step-by-step explanation:
Slope formula:
[tex] \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}[/tex]
P.S. Slope is denoted by letter m
We have;
[tex]x_{1}, y_{1}[/tex] = (2,-4)[tex]x_{2}, y_{2}[/tex] = (5,2)[tex] \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }[/tex]
[tex] \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }[/tex]
[tex] \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} [/tex]
find the value of x and y
The values of x and y in the figure are 3√2 and 3, respectively.
Identities in trigonometryThe diagram shown is a right triangle with a 45-degree acute angle.
The values of variables x and y must be determined.
Using the trigonometry identity, we get:
opposite/hypotenuse = sin 45
sin45 = 3/x
x = 3/sin45
x = 3(1/√2)
x = 3√2
Likewise,
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
As a result, the values of x and y in the figure are 32 and 3, respectively.
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6. Julie went to a family reunion at a restaurant. In total there were 8 families that attended. The bill at the restaurant was $1,060.32. How much does each family need to pay if they split the bill evenly? (WITHOUT TIP!)
Answer:
$132.54
Step-by-step explanation:
$1060.32 / 8 families = $132.54 / family
The diameter of a circle measures 28 cm. What is the circumference of the circle? Use 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.
Given a circle.
Also given that,
Diameter of the circle = 28 cm
We know that, radius of a circle is half the measure of the diameter of the circle.
Radius of the circle = 28 / 2 = 14 cm
The formula to find the circumference of the circle is,
Circumference = 2 πr
Here r is the radius of the circle.
Substituting the given,
Circumference = 2 π (14)
= 28π
= 28 × 3.14
= 87.92 cm
Hence the circumference is 87.92 cm.
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A sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But with a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive radiation (by failing to report excessive radiation even though the reactor is performing abnormally).
What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?
To reduce costly shutdowns caused by false alarms, management introduces a second completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sensors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors?
Being more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radiation. (According to this point of view, even a solitary report of excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?
1. The probability that the sensor will give an incorrect report is 0.03 or 3%.
2. The probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.
3. The probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.
1. Probability of the sensor giving an incorrect report (false alarm or miss):The probability of a false alarm is 0.02.
The probability of a miss is 0.01.
P(false alarm or miss)
= P(false alarm) + P(miss)
= 0.02 + 0.01 = 0.03
Therefore, the probability that the sensor will give an incorrect report is 0.03 or 3%.
2. Probability of simultaneous false alarms by both sensors:
P(false alarm by both sensors)
= P(false alarm by sensor 1) * P(false alarm by sensor 2)
= 0.02 * 0.02
= 0.0004
Therefore, the probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.
3. Probability of missing excessive radiation by both sensors:
P(miss by both sensors)
= P(miss by sensor 1) * P(miss by sensor 2)
= 0.01 * 0.01
= 0.0001
Therefore, the probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.
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A rental company charges $75 a day and 25 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill came to $243. How many miles did he drive?
The calculated total distance he drive is 372 miles
How many miles did he drive?From the question, we have the following parameters that can be used in our computation:
Charges $75 a day25 cents a mileSo, we have
Total charges = 75 * days + 0.25 * miles
For 2 days and total ot 243. we have
75 * 2 + 0.25 * miles = 243
So, we have
miles = 372
Hence, the total distance he drive is 372 miles
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5. 49% of adults say cashews are their favorite kind of nut. You randomly select 19 adults and ask
each to name his or her favorite nut. Find the probability that the number who say cashews are
their favorite nut is exactly four. (Round to the nearest thousandth as needed.)
6. According to the website nationalbikeregistry.com, at UCLA only 3% of stolen bikes are returned
to owners. If there are 335 bikes stolen at UCLA what is the probability that 12 or more stolen
bikes will be returned? (Round to the nearest thousandth as needed.)
The probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.
The probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).
To solve both of these probability problems, we can use the binomial probability formula:
P(X = k) = (n C k) × p^k × (1 - p)^(n - k)
where:
P(X = k) is the probability of getting exactly k successes
n is the total number of trials
k is the number of desired successes
p is the probability of success in a single trial
(1 - p) is the probability of failure in a single trial
(n C k) represents the binomial coefficient, calculated as n! / (k! x (n - k)!)
Let's solve each problem separately:
The probability that exactly four out of 19 adults say cashews are their favorite nut can be calculated as:
P(X = 4) = (19 C 4) ⁴(0.49⁴) (0.51¹⁵)
Using the binomial probability formula, we can calculate:
P(X = 4) ≈ 0.251
Therefore, the probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.
To find the probability that 12 or more stolen bikes will be returned out of 335 stolen bikes, we can use the binomial probability formula. Let's denote the probability of a stolen bike being returned as p = 0.03, the number of trials as n = 335, and the number of desired successes as k = 12 or more.
Using the complement rule, we can calculate the probability of not getting 11 or fewer successes:
P(X ≥ 12) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 11)]
To perform the calculation, summing up individual probabilities can be time-consuming. However, using statistical software or a binomial probability calculator can provide a convenient solution.
Using such a calculator, we find that the probability of 11 or fewer stolen bikes being returned is approximately 0.974. Therefore, the probability of 12 or more stolen bikes being returned is:
P(X ≥ 12) = 1 - 0.974 ≈ 0.026
Thus, the probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).
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A(2, 50°) is a point in a polar coordinate plane. Let O be the pole. 2 If B is another point in the same polar coordinate plane such that OA LOB and OB = 3 units, write down one possible answer for the coordinates of B.
Given statement solution is:- The coordinates of point B is (3, 50°).
In the given scenario, we have point A with polar coordinates (2, 50°) and the pole O. We need to find point B such that OA is parallel to OB and OB has a length of 3 units.
Since OA and OB are parallel, they have the same angle with the positive x-axis. Therefore, the angle between OB and the positive x-axis would also be 50°.
To find the coordinates of point B, we can use the polar coordinates system, where the distance from the pole is denoted by r and the angle with the positive x-axis is denoted by θ.
Since OB has a length of 3 units, the distance from the pole (r) would be 3. The angle between OB and the positive x-axis is also 50°. Therefore, the coordinates of point B would be (3, 50°).
So, one possible answer for the coordinates of point B is (3, 50°).
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Si un editor pone un precio de S/ 16 a un libro, se venderán 10,000 copias. Por cada dólar que aumente al
precio se dejarán de vender 300 libros. ¿Cuál debe ser el precio al que se debe vender cada libro para
generar un ingreso total por las ventas de S/ 129200?
Answer:
Step-by-step explanation:
Suppose that on January 1 you have a balance of $3100 on a credit card whose APR is 17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1
.a. Calculate your monthly payments.
b. When the card is paid off, how much will you have paid since January 1?
c. What percentage of your total payment from part (b) is interest?
a. Your monthly payments would be approximately $275.49.
b. When the card is paid off, you will have paid approximately $3,305.88 since January 1.
c. The percentage of your total payment that is interest is approximately 6.3%.
To calculate the monthly payments, we first need to determine the interest rate per month.
Since the APR is 17%, we divide it by 12 to get the monthly interest rate: 17% / 12 = 1.42%.
a. Monthly payments:
To pay off the credit card balance in one year (12 months), we divide the total balance by the number of months:
$3100 / 12 = $258.33 (approximately)
Therefore, your monthly payment should be approximately $258.33.
b. Total amount paid:
To calculate the total amount paid since January 1, we multiply the monthly payment by the number of months (12):
$258.33 * 12 = $3,099.96
Therefore, you will have paid approximately $3,099.96 since January 1.
c. Percentage of payment as interest:
To determine the percentage of the total payment that is interest, we subtract the initial balance from the total amount paid to find the total interest paid:
Total interest = Total amount paid - Initial balance
Total interest = $3,099.96 - $3100
Total interest = $-0.04 (approximately)
The negative value implies that the balance was paid off completely before the end of the year, resulting in a small overpayment.
As a result, there is no interest to calculate as it has been paid in full.
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your credit card has a balance of $3600 and an annual interest rate of 16%. you decide to pay off the balance over three years. if there are no further purchases charged to the card, you must pay $126.59 each month, and you will pay a total interest of $957.24. assume you decide to pay off the balance over one year rather than three. how much more must you pay each month and how much less will you pay in total interest?
You will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.
If you decide to pay off the balance over one year instead of three, the payment amount will be higher, but the total interest paid will be lower due to the shorter repayment period.
First, let's calculate the total interest paid over three years. The total payment made over three years will be the monthly payment of $126.59 times 36 months, which is $4,553.24. The total interest paid is the difference between the total payment made and the initial balance of $3600, which is $953.24.
Now, let's consider paying off the balance over one year. The total payment made over one year will be the monthly payment of $126.59 times 12 months, which is $1,519.08. To calculate the interest paid, we can use the formula:
Total interest paid = Balance × Annual interest rate × Time
where the time is expressed in years. Plugging in the values, we get:
Total interest paid = $3600 × 0.16 × 1 = $576
Therefore, if you decide to pay off the balance over one year instead of three, you will pay an additional amount each month equal to the difference between the monthly payment for one year and the monthly payment for three years, which is:
Additional monthly payment = ($4,553.24/12) - ($1,519.08/12) = $261.76
This means that you will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.
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Can I get help, please
Answer:
see attached
Step-by-step explanation:
You want the areas of the four triangles in the figure.
Triangle areaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is its height perpendicular to the base.
Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.
The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.
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Additional comment
If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.
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