Match the letter with the transformation that it controls in the graph of an exponential.
f(x) = ab-h + k
h
[Choose ]
[Choose ]
horizontal shift
vertical shift
negative shift
reflection over asymptote
reflection over y axis
Answers
In the equatiοn [tex]f(x) = ab^{(x-h)}+ k:[/tex]
The letter h cοntrοls the hοrizοntal shift οf the graph.
What is hοrizοntal shift ?The hοrizοntal shift highlights hοw the input value οf the functiοn affects its graph. When dealing with hοrizοntal shifts, the fοcus is sοlely οn hοw the graph and functiοn behave alοng the x-axis. Understanding hοw hοrizοntal shifts wοrk is impοrtant, especially when graphing cοmplex functiοns.
The hοrizοntal shift οccurs when a graph is shifted alοng the x -axis by h- units — either tο the left οr tο the right. Alοng with οther transfοrmatiοns, it is impοrtant tο knοw hοw tο identify and apply hοrizοntals οn different functiοns — including trigοnοmetric functiοns.
What is an equatiοn?A mathematical equatiοn is a fοrmula that uses the equals sign (=) tο express the equality οf twο expressiοns. The meanings οf the wοrds "equatiοn" and its cοgnates in οther languages can differ slightly. Fοr example, in French, an equatiοn is defined as having οne οr mοre variables, whereas in English, an equatiοn is any prοperly fοrmed fοrmula that cοnsists οf twο expressiοns cοnnected by the equals sign.
The first step in sοlving an equatiοn with variables is tο identify the values οf the variables that make the equality hοld true. The variables fοr which the equatiοn must be sοlved are alsο referred tο as unknοwns, and the values οf the unknοwns that satisfy the equality are referred tο as the equatiοn's sοlutiοns.
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Related Questions
Rosalind drew a rectangle with a width of 11 centimeters and a length of 14 centimeters. Which equation can be used to determine P, the perimeter of this rectangle in millimeters
Answers
Answer:
P=(1100+1400)2
Step-by-step explanation:
PLEASE HELP!!!!
All I need to know is the area.
Answers
Answer:
45
Step-by-step explanation:
Draw an imaginary line from F to S. We then break this into 2 parts:
1. Evaluate the area of triangle SFN
The base of the triangle is FS, who has length 9. The height is the vertical line that passes through point N and FS, and that line has length 6. The area would then be 9*6/2=27.
2. Evaluate the area of rectangle SCWF
WC has length 9. FW has length 2. The area would then be 9*2=18.
Find the median of 16 even number
Answers
Answer:
17
Step-by-step explanation:
To find the median of 16 even numbers, we need to arrange the numbers in order from least to greatest, and then find the middle value.
Since the numbers are even, the middle two values will need to be averaged to find the median.
Let's assume the 16 even numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32
Now, we arrange them in order from least to greatest:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32
The middle two numbers are 16 and 18. So, we need to average them to find the median:
Median = (16 + 18) / 2 = 17
Therefore, the median of 16 even numbers is 17.
Match each area to the correct polygon on the coordinate plane. Drag the Items on the left to the correct location on the right.
A 6 square units
B 12 square units
C 4 square units
D 5 square units
(33 points and giving brainilest)
Answers
C goes to the Purple Polygon
D goes to the Orange Polygon
B goes to the Blue Polygon
A goes to the Green Polygon
Pls help!!!
A home has a rectangular kitchen. If listed as ordered pairs, the corners of the kitchen are (7, 6), (−4, 6), (7, −9), and (−4, −9). What is the area of the kitchen in square feet?
Answers
Using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.
What is a rectangle?The internal angles οf a rectangle, which has fοur sides, are all exactly 90 degrees. At each cοrner οr vertex, the twο sides cοme tοgether at a straight angle.
Here, Pοints (7,6) and (7.-9) lie οn the same hοrizοntal line as the x values are the same
Sο the distance between these pοints can be taken as the length οf the rectangle.
The distance can be fοund using the distance fοrmula.
Length l = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
= [tex]\sqrt{(7-7)^2 + (6--9)^2} = \sqrt{15^2} = 15[/tex]
Nοw the pοints (7,6) and (-4,6) lie οn the same vertical line as the y values are the same.
Sο the distance between these pοints can be taken as the breadth οf the rectangle.
Breadth b = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] = [tex]\sqrt{(7--4)^2 + (6-6)^2} = \sqrt{11^2} = 11[/tex]
Since it is a rectangle, the οppοsite sides will have the same measurements.
Nοw the area = l * b = 15 * 11 = 165 sq. feet.
Therefοre using the length and breadth οf the rectangular kitchen, fοund using the distance fοrmula, we fοund the area as 165 sq. feet.
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What is the resulting costant when (2 - 4/3) is subtracted from (-3/5 plus 5/3)
Answers
The resulting constant is 2/5 when (2-4/3) is subtracted from (-3/5 plus 5/3).
What is subtraction?Mathematical subtraction includes calculating the difference between two numbers. It is the inverse of addition and is denoted by the symbol "-". When we subtract one number from another, we are essentially finding out how much smaller the second number is than the first number.
According to question:We can simplify the expressions inside the parentheses first:
2 - 4/3 = 6/3 - 4/3 = 2/3
-3/5 + 5/3 = -9/15 + 25/15 = 16/15
So the expression (-3/5 + 5/3) - (2 - 4/3) becomes:
(16/15) - (2/3)
To subtract these fractions, we need to find a common denominator, which is the least common multiple of 15 and 3, which is 15. Then we can rewrite both fractions with this denominator:
(16/15) - (2/3) = (16/15) - (10/15)
Now we can subtract the numerators and keep the denominator:
(16/15) - (10/15) = 6/15 = 2/5
Therefore, the resulting constant is 2/5.
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10
9
=
k
10
start fraction, 9, divided by, 10, end fraction, equals, start fraction, 10, divided by, k, end fraction
k =
Answers
The value of k that solves the proportion is given as follows:
k = 100/9.
How to solve the proportion?The proportional relationship for this problem is defined as follows:
9/10 = 10/k.
Then we cross-multiply, that is we multiply the numerator of one ratio by the denominator of the other ratio, and vice versa, hence:
9k = 10 x 10
9k = 100.
Then we solve for the unknown variable k, applying the division, which is the inverse operation of the multiplication, hence the value of k that solves the proportion is given as follows:
k = 100/9.
Missing InformationThe proportional equation for this problem is defined as follows:
9/10 = 10/k.
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Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer: -2
Step-by-step explanation: Find the midpoint of both points so they are equidistant meaning that the ratios between them are 1:1.
To do so, add both quantities given and divide by 2.
[tex](-7+3)/2\\(-4)/2\\-2[/tex]
Which is the answer!
Answer:
plot the point at -2
Step-by-step explanation:
Which is a recursive formula for this geometric sequence?
-18, -14, -12, -1, . . .
A. a1 = -1/8
an = (an – 1)(1/8)
B. a1 = -1/8
an = (an – 1)(1/2)
C. a1 = 2
an = (an – 1)(-1/8)
D. a1 = -1/8
an = (an – 1)(2)
Answers
A recursive formula for this geometric sequence is;
Option C:
a₁ = -1/8
aₙ = (-1/8)a⁽ⁿ⁻¹⁾
How to find the recursive formula?The geometric sequence is given as;
-1/8, -1/4, -1/2, -1, . . .
The general formula used to find the nth term of a geometric sequence is;
aₙ = a(r)⁽ⁿ⁻¹⁾
where;
a is first term
d is common ratio
where;
r = (-1/4)/(-1/8)
r = 2
Thus;
aₙ = -1/8(2)⁽ⁿ⁻¹⁾
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(Help ASAP pls/50 points) Solve the equation by completing the square. Show your work on the canvas.
x^2- 8x - 20 = 0
(canvas is a piece of paper btw)
Answers
Alvin is 12 years younger than Elga. The sum of their ages is 66 . What is Elga's age?
Answers
According to the problem, Alvin is 12 years younger than Elga, and the sum of their ages is 66. So, we have to use algebra to find Elga's age.
Step-by-step explanation:
Let's assume Elga's age to be x.
Alvin's age can be found as: x - 12
The sum of their ages is 66. So,
x + (x - 12) = 66 ⇒ 2x - 12 = 66
⇒ 2x = 78
⇒ x = 39
Therefore, Elga's age is 39 years old.
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What is the length of are AB? Give an exact value
Answers
The length of arc AB for the given circle is found to be 13.60 units.
Explain about the arc of the circle?Plotting two lines from the arc's ends to the circle's center, measuring the angle at the point where the two lines intersect the center, and then solving for L by cross-multiplying are useful methods for calculating an arc's length.
And use the arc length method, one may determine a circle's arc length given its radius and center angle.
Length of an Arc = θ × r,in which θ is in radian.Length of an Arc = θ × (π/180) × r,in which θ is in degree.So,
Radius r = 13 units
Central Angle Ф = 60 degree.
Arc length AB = 60 * 3.14 * 13 /180
Arc length AB = 13.60
Thus, the length of arc AB for the given circle is found to be 13.60 units.
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in a small county, there are 150 people on any given day who are eligible for jury duty. of the 150 eligible people, 80 are women. (a) determine whether the following statement is true or false. this is an example of sampling without replacement. true false (b) if four potential jurors are excused from jury duty for medical reasons, what is the probability that all four of them are women? (round your answer to four decimal places.)
Answers
a) True. This is an example of sampling without replacement because once a person is selected for jury duty, they are no longer available for selection again.
b) 0.5238 is the probability.
a) Sampling without replacement is the technique of choosing a sample from a population without replacing the selected individuals in the population after each selection. In this case, once an eligible person is chosen, they cannot be chosen again.
Hence, the given statement is true.
b) We have to find the probability of all four of the excused jurors being women. We are picking four people out of 70 men and 80 women, or 150 people in total. Since we are dealing with independent events, we may use the multiplication principle for probabilities.
There are 80 women in the 150-person sample, so the probability of selecting one woman is 80/150.
After the first woman is selected, there are 79 women remaining in the 149-person sample, so the probability of selecting another woman is 79/149.
Similarly, the probabilities of selecting a third and fourth woman are 78/148 and 77/147, respectively.
Therefore, the probability that all four excused jurors are women is:
P(4 women) = (80/150) × (79/149) × (78/148) × (77/147)
P(4 women) = 0.5238 (rounded to four decimal places)
The probability that all four of the excused jurors are women is 0.5238.
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what value of x makes the two expressions equal (image)
Answers
Answer:
[tex]\huge\boxed{\sf x = 6.5 }[/tex]
Step-by-step explanation:
Given that, both the expressions are equal.
So,
7x - 5 = 5x + 8
Subtract 5x from both sides7x - 5x - 5 = 8
2x - 5 = 8
Add 5 to both sides2x = 8 + 5
2x = 13
Divide both sides by 2x = 13/2
x = 6.5[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex] \sf \: x = 6.5[/tex]
Step-by-step explanation:
Given expressions,
→ 7x - 5
→ 5x + 8
Now we have to,
→ Find the required value of x.
Forming the equation,
→ 7x - 5 = 5x + 8
Then the value of x will be,
→ 7x - 5 = 5x + 8
→ 7x - 5x = 8 + 5
→ 2x = 13
→ x = 13 ÷ 2
→ [ x = 6.5 ]
Hence, the value of x is 6.5.
if you multiply by 1/3 in front of a exponential function what would happen to the graph
Answers
Answer:
If you multiply a function by a constant value, it will result in a vertical scaling of the graph. In this case, multiplying by 1/3 would compress the graph vertically by a factor of 3. Specifically, the y-coordinates of each point on the graph would be multiplied by 1/3, resulting in a graph that is one-third as tall as the original.
Brainliest will be rewarded+ 100 points!!
Take a screen shot of the work and do the work on the ss
Answers
Answer: When do you need it done?
Step-by-step explanation: ?
Answer:
Step-by-step explanation:
x+y=17
x-y = 7
From equation 2, x = 7 + y
put this in equation 1.
(7+y) + y = 17
7+2y = 17
2y = 10
y = 5.
We said that x = 7+y
thus, x = 7 + 5
x = 12.
2x+2y=36
2(x+y) = 36
Thus, x + y = 18.
x+y = 18
x-y=6 using elimination (literally simplifying this)
2x = 24 (y-y=0. ELIMINATED!)
x = 12
When x = 12,
x+y=18
12+y=18
y=6.
3x = y
x + y = 20
From 1, y = 3x.
x + (3x) = 20
4x = 20
x = 5.
when x = 5,
y = 3x
y = 3(5)
y = 15.
x+y = -4
xy = -21
from 1, x = -4-y
=> y(-4-y)= -21
-y²-4y = -21
Therefore,
y² + 4y -21 = 0
y= 3 or -7.
When y = 3,
x + 3 = -4
x= -7.
When y = -7,
x + (-7) = -4
x-7=-4
x = 3.
Hope these help! :)
*fingers cracking*
If PR = 14 find ST and QR
Answers
The values of ST and QR based on the information regarding the square will be 7 and 9.9
How to calculate the valueThe square is a geometric figure that belongs to the parallelograms. The square has the following properties:
All four sides have the same length. The four angles measure 90. The sum of its angles is equal to 360
The diagonals are congruent. The diagonals bisect each other.
We get a PQRS square with PR=14. We are required to find ST and QR.
First, since the figure is a square, we must know that the diagonals are congruent. Therefore, we are required to find ST and QR:
PR = SQ = 14.
ST = 14/2 = 7
QR = sin 45 × 14
QR = 9.9
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HELP PLSSS....The table shows the result of spinning a color spinner (purple, blue, yellow, and green) in an experiment. PART A: Using the results in the table, what is the experimental probability of a spinner landing on purple (P) in Experiment A? Write your answer as a fraction and as a decimal.
Answers
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
part A)
the table shows that in 10 attempts
Blue was hit 5 times
Yellow was hit 2 times
Green was hit 2 times
Purple was hit 1 time
so the experimental probabilities are
Blue 5/10 = 1/2 = 0.5
Yellow 2/10 = 1/5 = 0.2
Green 2/10 = 1/5 = 0.2
Purple 1/10 = 0.1
part B)
the theoretical probability of Purple with an equally spaced spinner of 4 colors is 1/4 = 0.25
Okay, I really need some help with my math questions
1. At a local ballgame the hamburgers sold for 2.50 each and the cheeseburgers sold for 2.75 each. there were 131 total burgers sold for a total value of 342. how many of each kind of burger were sold?
2. Bradford bought a total of 20 medium and large bags of chips. If he spent $53 and bought 6 more large bags of chips as medium bags of chips, how many large and medium bags of chips did he buy? HELP: chips; large-$3, medium-$2, and small-$1
please help I will make you brainliest! Answer the questions fully and show how did you do it.
Answers
Answer: Let's use the following system of equations to represent the given information:
h + c = 131 (the total number of burgers sold is 131)
2.5h + 2.75c = 342 (the total value of the burgers sold is $342)
where h represents the number of hamburgers sold and c represents the number of cheeseburgers sold.
We can use the first equation to solve for one of the variables in terms of the other:
h + c = 131
h = 131 - c
Substituting this into the second equation, we can solve for c:
2.5h + 2.75c = 342
2.5(131-c) + 2.75c = 342
327.5 - 2.5c + 2.75c = 342
0.25c = 14.5
c = 58
So, 58 cheeseburgers were sold. We can use the first equation to find the number of hamburgers sold:
h + c = 131
h + 58 = 131
h = 73
Therefore, 73 hamburgers were sold.
Let x be the number of medium bags of chips that Bradford bought. Then, he bought 20 - x large bags of chips.
According to the problem, the total cost of the chips was $53. We can set up an equation for the total cost in terms of x:
diff
2x + 3(20-x+6) = 53
2x + 54 - 3x + 18 = 53
-x = -19
x = 19
So, Bradford bought 19 medium bags of chips and 20 - 19 = 1 large bag of chips.
Enjoy!
Step-by-step explanation:
What is the value of j?
can some one help me please
Answers
Answer: 130 degrees
Step-by-step explanation:
The line equals 180 degrees
50+j=180
180-50=130
Answer:
130 Degrees
Step-by-step explanation:
180-50 = 130
Point m is on line segment ln. given ln=20 and lm=7,determine the length mn
Answers
27 mn is the length of line segment .
What in mathematics is a line segment?
A line segment has two unique points on the line defining its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.
In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.
The value of the line segment will be calculated as:-
Point M is on the line segment MN.
In = 20
Im = 7
MN = In+ Im
= 20 + 7
= 27
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[CALCULATOR OK] Many years back, Mr. Yang invested a sum of $1000 into a savings account that earned interest at 6% compounded semiannually (twice per year). This sum is now worth $1435.77. How long ago did he invest that $1000? Round to two decimal places.
Answers
Mr. Yang invested the $1000 approximately 8.55 years ago
To calculate the time that Mr. Yang invested the money, you can use the formula for compound interest: A=P(1+r/n)^nt where A is the amount of money after t years, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. We are given A= $1435.77, P=$1000, r=0.06, and n=2 (since interest is compounded twice per year). We want to solve for t, so we will rearrange the formula to solve for t:t=ln(A/P)/(n ln(1+r/n))Plugging in the values, we have: t= ln(1435.77/1000)/(2 ln(1+0.06/2)) ≈ 8.55 years, rounded to two decimal places.Therefore, Mr. Yang invested the $1000 approximately 8.55 years ago.
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A circular watch has a minute hand that is 2.5 cm long.
(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes?
Answers
Answer:
a) 20 minute=2pi/3 rad
angle=arc length/radius
arc length= angle×radius
=2pi/3×2.5
=5pi/3 cm
b)area= pi(radius)²/2
=pi×6.25
=25pi/4cm²
i hope you find it helpful
Step-by-step explanation:
Answer:
[tex]L=\frac{5}{3} \pi cm. \\ A=3.125\pi cm^{2}[/tex]
Step-by-step explanation:
a)
L - is how far does the tip of the hand move in diameter.
m - is how much time does the tip of the hand move in minutes.
m=20
r =2,5cm
[tex]L=\frac{m}{60} *2\pi r\\L=\frac{20}{60} *2\pi *2,5cm\\L=\frac{5}{3} \pi cm[/tex]
In a formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. L = 2πr is a formula for the full length of a circle.
b)
A- Area
r=2,5cm
m - is how much time does the tip of the hand move in minutes.
[tex]A=\frac{m}{60} *\pi r^{2} \\A=\frac{30}{60} *\pi *(2,5cm)^{2} \\A=\frac{1}{2} *\pi *6.25cm^{2} \\A=3.125\pi cm^{2}[/tex]
In the formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. The formula for the full area of a circle is A=πr².
Write the polynomial in standard form. Then classify its degree and by number of terms
7x²+10+4x³
Answers
Step-by-step explanation:
4x^3 + 7x^2 + 10 <====standard form
degree is 3 (this is the largest exponent) and there is three terms
Due to the pandemic, there was a huge fluctuation in the real estate industry in Dubai. Now back to normal & it is increasing at a rate of 7% p a. What is the price of a villa after 3 years if it is purchased at Dollar 15,000?
Answer with steps please
Need it ASAP!!!
Answers
In three years, the villa would cost roughly $18,375.64.
We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:
[tex]A = P(1 + r)^t[/tex]
What is the principal amount?The principal is the sum that was either lent or borrowed. It is the initial sum of money borrowed or lent in a loan, exclusive of interest or other costs. It serves as the baseline from which interest is determined. The total sum that must be repaid at the conclusion of the loan term is known as the principal amount. It is often referred to as the loan's face value or par value.
from the question:
We can apply the compound interest formula if a villa's price is rising at a pace of 7% annually:
[tex]A = P(1 + r)^t[/tex]
where A represents the overall sum, P represents the initial sum, r represents the annual interest rate in decimal form, and t is the number of years.
In this case, P = $15,000, r = 0.07, and t = 3. Plugging in these values, we get:
A = $15,000[tex](1 + 0.07)^3[/tex]
= $15,000[tex](1.07)^3[/tex]
= $15,000(1.225043)
= $18,375.64 (rounded to two decimal places)
As a result, the villa's price would be roughly $18,375.64 after three years.
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Work out the surface area of the solid cuboid.
3cm, 4cm and 6cm
Answers
Answer:
The formula for the surface area of a cuboid is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the cuboid, respectively.
In this case, l = 6 cm, w = 4 cm, and h = 3 cm. Substituting these values into the formula, we get:
SA = 2(6)(4) + 2(6)(3) + 2(4)(3)
SA = 48 + 36 + 24
SA = 108
Therefore, the surface area of the cuboid is 108 square centimeters.
Step-by-step explanation:
Answer: Surface Area is [tex]72cm^2[/tex].
Step-by-step explanation: Let surface area be a.
[tex]a= 2(5*4)+(5*2)+(4*2)\\a= 2(20+10+8)\\a=2(38)\\a=72 cm^2[/tex]
This means the surface area of the solid cuboid is [tex]72cm^2[/tex].
Hope this helps!
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The dimensions of a rectangle are 14 centimeters by 48 centimeters. Find, in centimeters, the length of the diagonal of the rectangle
Answers
We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle with legs of length a and b and hypotenuse of length c, we have:
a^2 + b^2 = c^2
In this case, the rectangle has dimensions of 14 centimeters by 48 centimeters, so we can let the length and width of the rectangle be the legs of a right triangle, and the diagonal be the hypotenuse. Then:
a = 14 cm b = 48 cm c = ?
We can plug these values into the Pythagorean theorem and solve for c:
14^2 + 48^2 = c^2 196 + 2304 = c^2 2500 = c^2 c = sqrt(2500) c = 50
Therefore, the length of the diagonal of the rectangle is 50 centimeters.
Answer:
50 cm
Step-by-step explanation:
the equation is d=sqrt(w^2+l^2)
so you get sqrt(14^2+48^2) which equals 50.
Christopher borrows 7,500$ to build a garage. He agrees to pay 475$ a month for 24 months but pays off the loan after 18 months.
Part A: Determine the amount of unearned interest.
Part B: Determine the amount needed to repay the loan using the Rule of 78.
Part C: Show your work to support your answers to Part A and Part B.
Answers
Part A: The amount of unearned interest is $3,225.
Part B: The amount needed to repay the loan using the Rule of 78 is $8,443.75.
Part C: To support our answers to Part A and Part B, the total interest that Christopher would have paid, which is 3,900$. the amount needed to repay the loan using the Rule of 78, which is $8,443.75.
What is an interest?
To determine the amount of unearned interest, we need to find out how much interest Christopher would have paid if he made all 24 payments.
First, we can calculate the total amount he would have paid if he made all 24 payments:
Total amount paid = 475 x 24 = 11,400$
Next, we can subtract the amount borrowed from the total amount paid to find the total interest:
Total interest = Total amount paid - Amount borrowed
Total interest = 11,400$ - 7,500$
Total interest = 3,900$
Since Christopher paid off the loan after 18 months instead of 24 months, he did not pay the full amount of interest he would have paid if he made all 24 payments. The unearned interest is therefore:
Unearned interest = Total interest - (Number of remaining payments / Total number of payments x Total interest)
Unearned interest = 3,900 - (6 / 24 x 3,900)
Unearned interest = 3,225$
Therefore, the amount of unearned interest is $3,225.
What is repay?
Part B:
To determine the amount needed to repay the loan using the Rule of 78, we need to calculate the proportion of the total interest that has been earned by the lender up to the point when Christopher repays the loan.
The Rule of 78 is a method of allocating interest charges based on the sum of the digits of the loan term. In this case, since the loan term is 24 months, the sum of the digits is:
1 + 2 + ... + 4 + 5 = 15
We can use this sum to calculate the proportion of the total interest earned by the lender up to the point when Christopher repays the loan:
Proportion of earned interest = (Number of payments made / Total number of payments) x (Sum of digits of loan term / Total sum of digits)
Proportion of earned interest = (18 / 24) x (15 / 120)
Proportion of earned interest = 0.09375
The total interest paid is 3,900$, so the amount needed to repay the loan using the Rule of 78 is:
Amount needed to repay loan = Amount borrowed + Total interest x Proportion of earned interest
Amount needed to repay loan = 7,500$ + 3,900$ x 0.09375
Amount needed to repay loan = 8,443.75$
Therefore, the amount needed to repay the loan using the Rule of 78 is $8,443.75.
Part C:
To support our answers to Part A and Part B, we calculated the total interest that Christopher would have paid if he made all 24 payments, which is 3,900$. We also calculated the unearned interest, which is the difference between the total interest and the interest that Christopher actually paid when he paid off the loan early.
Using the Rule of 78, we calculated the proportion of the total interest earned by the lender up to the point when Christopher repaid the loan, which is 0.09375. We then used this proportion to calculate the amount needed to repay the loan using the Rule of 78, which is $8,443.75.
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Decrease R1400 in the ratio 7:3
Answers
Based on the given task content; the decrease of R1400 in the ratio 7:3 is R980 and R420 respectively.
How to solve ratio:Ratio refers to the number representing a comparison between two different quantities. It is expressed as a quotient which is the relative magnitudes of two quantities.
Amount given = R1400
Ratio = 7 : 3
Total ratio = 7 + 3 = 10
Rate 1 for 7:
= 7/10 × R1400
= 0.7 × R1400
= R980
Rate 2 for 3:
= 3/10 × R1400
= 0.3 × R1400
= R420
In conclusion, R1400 decreased in the ratio 7:3 is R980 and R420.
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Lourdes garage is in the shape of a square pyramid. The garage is shown, with dimensions given in feet (ft).
Lourdes is replacing the roof and installing shingles. What is the surface area of the roof?
The slant height of the roof is 18ft the base of the roof is 40ft
Answers
Since Lourdes garage is in the shape of a square pyramid, the surface area of the square pyramid roof is 1440 ft²
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The surface area (SA) of a pyramid is given as:SA = B + (1/2)Ph
where B is the base area, P is the perimeter and h is the slant height
Since the roof is a square pyramid with base 40 feet and slant height of 18 ft, hence:
h = 18 ftP = 40 + 40 + 40 + 40 = 160 ft.
Surface area of only roof = (1/2)Ph
Therefore, Substituting:
SA = (1/2)(160)(18) = 1440 ft²
The surface area of the roof is 1440 ft²
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