The probability of event A is 5/18.
The probability of event B is 29/36.
What are the probabilities?Probability is used to determine how likely it is that a random event would happen. The probability that the random event would happen would lie between 0 and 1.
The probability that the sum is greater than 8 = sample space that have a sum greater than 8 / total number of sample space
sample space that have a sum greater than 8 = (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6, 4) (6,5) (6,6) = 10
Total number of sample space = 36
The probability that the sum is greater than 8 = 10 / 36 = 5/18
The probability that the number is not divisible by 5 = sample spaces that is not divisible by 5 / total number of sample spaces
= 29 / 36
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Here is the rest of the question:
Write your answers as exact fractions.
P(a)
P(b)
Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second – by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face.
Answer:
I 728.Two beetles sit at the verticesAandHof a cubeABCDEFGHwith edge length40√110 units. The beetles start moving simultaneously alongACandHFwiththe speed of the first beetle twice that of the other one.....ADCBEFGH✈s✈s. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................What will be the shortest distance between the beetles?29.In the diagram,4PQRhas an area of 960 square units. The pointsS,TandUare the midpoints of the sidesQR,RPandPQ, respectively, and the linesPS,QTandRUintersect atW.......PQRSUTNMLW✓✓✼. . . . . . . . . . . . . . .....................The pointsL,MandNlie onPS,QTandRU, respectively, such thatPL:LS= 1 : 1,QM:MT= 1 : 2 andRN:NU= 5 : 4.What is the area, in square units, of4LMN?30.A 40×40 white square is divided into 1×1 squares by lines parallel to its sides.Some of these 1×1 squares are coloured red so that each of the 1×1 squares,regardless of whether it is coloured red or not, shares a side with at most one redsquare (not counting itself). What is the largest possible number of red squares?
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
(b) Tickets for a raffle are placed in a box. The box contains 25 blue tickets and 20 red
tickets. Tickets are drawn at random from the box, one at a time and are not replaced.
What is the probability that:
(i) the first ticket drawn is red and the second ticket drawn is blue?
Probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.
As given in the question,
Number of blue tickets in a box is equal to 25
Number of red tickets in a box is equal to 20
Total number of tickets in a box = 25 + 20
= 45
Drawing a ticket one at a time and not replaced
Probability of drawing a ticket first is red and second drawn is blue
= ( 20 / 45 ) × ( 25 / 44 )
= ( 500 / 1980 )
= 0.2525..
= 0.253
Therefore, probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.
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for any integer p, show that p^3+11p will always be a multiple of 6
By the principle of mathematical induction, it has been proved that
[tex]p^3 + 11p[/tex] is divisible by 6
What is Principle of mathematical induction?
Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers
The given expression is [tex]p^3 + 11p[/tex]
For p = 1
[tex](1)^3 + 11 \times 1\\12[/tex]
which is a multiple of 6
Let it be true for p = m
[tex]m^3 + 11m[/tex] is a multiple of 6
[tex]m^3 + 11m = 6k[/tex], where k is any integer
For p = m + 1
[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]
Now,
[tex]m^3 + 11m[/tex] is divisible by 6
We know that the product of two consecutive integers are divisible by 6
[tex]3m(m+1)[/tex] is divisible by 6
12 is divisible by 6
[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6
So it is true for p = m + 1
By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers
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Which is the graph of y = 3¥x+2 + 3?
The graph of the equation y = 3x + 2 + 3 is shown below .
In the question ,
it is given that ,
the equation of the line is y [tex]=[/tex] 3x [tex]+[/tex] 2 [tex]+[/tex] 3 ,
we need to draw the graph of it .
Do draw the graph we need at least two points .
for the first point
put x = 0
we get ,
y = 3(0) + 2 + 3
y = 0 + 2 + 3
y = 2 + 3
y = 5
the first point is (0,5)
for the second point put y = 0,
we get ,
0 = 3x + 2 + 3
3x = - 2 - 3
3x = -5
x = -5/3 ,
So , the second point is (-5/3 , 0)
the graph of the given equation is shown below .
Therefore , The graph of the equation y [tex]=[/tex] 3x + 2 [tex]+[/tex] 3 is shown below .
The given question is incomplete , the complete question is
What is the graph of the equation y = 3x + 2 + 3 ?
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Assume the radius of a certain planet is 4790 km and the planet is a sphere. What is its surface area?
Answer:
A ≈ 2.88×108km²
Step-by-step explanation:
A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²
can someone
help with this
Step-by-step explanation:
let angles of a triangle a=86
b= 180-3z , c= 180-4z
a+b+c = 180 {angle sum property}
86 +180+180-3z-4z=180
446 -7z = 180
-7z = -266
[tex]z = \frac{ - 266}{ - 7} = 38[/tex]
so other angle are
3z = 3 x 38 = 114
4z = 4 x 38 = 152
log 4(x+8) + log 4(x+5) = 1
rewrite the equation
According to the product rule of logarithms, the given equation is written as, log₄(x² + 13x + 40) = 1
Product rule of logarithm
Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.
And it is the first law and it can be represented as;
logₐ(x) + logₐ(y) = logₐ(xy)
Given,
Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1
And we have to rewrite the equation.
Here we have the logarithmic equation,
=> log₄(x+8) + log₄(x+5) = 1
By using the product property of logarithms,
We have to rewrite the equation as,
=> log₄(x+8)(x+5) = 1
Now, we have to expand (x+8)(x+3) using the FOIL Method.
Then we get,
=> log₄(x² + 5x + 8x + 40) = 1
=> log₄(x² + 13x + 40) = 1
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John worked 18 hours last week. He earned $216. What was his hourly rate?
Add.
3/5+7/8+3/10
Enter as a mixed number in simplest form.
Answer:71/40 or 1 31/40 or 1.775
Step-by-step explanation:1 31/40 is the mixed number
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 −3.5%
Using technology, calculate the weighted dollar amount of the savings account.
−$58.63
$58.63
−$67.20
$67.20
The weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that An investment portfolio is;
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 -3.5%
The weighted dollar amount of the savings account is;
= 2.1% of $3200
= ( 2.1 / 100) × $3200
= ($6720) /100
= $ 67.20
Therefore, the weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
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Determine the x- and y-intercepts of the graph of x+2y=−4 .
Then plot the intercepts to graph the equation.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Answer:
Step-by-step explanation:
1) first we find the x and y intercepts. Remember the intercepts are where x=0 and y=0
2) To find the x-intercept, substitute y = 0 and solve for x.
given equation: x +2y= -4
then substitute y=0 so
x+ 2(0) = -4 -> any number multiplied by 0 it will always equal zero
then, it will be x=-4
the coordinates will be (-4,0)
3) To find the y-intercept, substitute x =0 and solve for y.
given equation: x +2y= -4
then substitute x=0 so
(0)+ 2y = -4 -> x disappears since is zero
then, it will be 2y=-4
then we multiply by 2 :
2y/2 = -4/2
y=-2
the coordinates for the y-intercept will be (0,-2)
graph:
A square with sides length x are cut out of each corner of a rectangular piece of cardboard measuring 5ft by 8ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed this way.
The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet
What is an extremum point in mathematics?An extremum of a function is the point where the value of the function is a maximum or a minimum.
The side length of the cut out squares = x
The width of the rectangular cardboard = 5 feet
The length of the rectangular cardboard = 8 feet
The length of the side of the cut square = 8 - 2·x
Width of the side of the cut square = 5 - 2·x
Height of the cut square = x
Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x
When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]
12·x² - 52·x + 40 = 0
3·x² - 13·x + 10 = 0
Which gives;
(3·x - 10)·(x - 1) = 0
The dimensions of the cut square that gives the maximum volume are therefore;
x = 1 or x = 10/3
When x = 10/3, we have;
V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0
When x = 1, we have;
V = (8 - 2×1) × (5 - 2×1) × 1 = 18
The value of x that gives the maximum volume is therefore, x = 1
The dimensions of the box that give the maximum volume are therefore;
Height = x = 1
Length = 8 - 2×1 = 6
Width = 5 - 2 × 1 = 3
The dimensions of the box that gives the maximum volume are;
Height = 1 ft
Length = 6 ft
Width = 3 ft
The volume of the largest box that can be formed is 18 cubic feet
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The equation y – 4 = 6(x + 7) represents a linear function. What is the y-intercept of the graph of the equation?
Step-by-step explanation:
In general equation, y = mx+c, c represents y-intercept.
So, y-4 = 6x+42
y = 6x+46
So, y intercept will be 46
A rectangular garden has an area of 72 square yards. The dimensions of the
garden are not prime numbers. What are the possible dimensions of the
garden
Answers:
1 yard by 72 yards
4 yards by 18 yards
6 yards by 12 yards
8 yards by 9 yards
==========================================================
Explanation:
Let's list out all the ways to multiply to 72 using two values
1*72
2*36
3*24
4*18
6*12
8*9
Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.
We're left with this list
1*72
4*18
6*12
8*9
which represent the possible dimensions of this rectangle.
Keep in mind that 1 is not prime.
on the coordinate plane, the number line that runs right and left is the?
A: x-coordinate
B: y-coordinate
C: x-axis
D: y-axis
Answer:
C: x-axis
Step-by-step explanation:
It is the x-axis.
2 market women shared a basket full of oranges in order to sell them.the share of the first woman is twice the other if the are 300 oranges in the basket what is the share of each women
Answer:
Step-by-step explanation:
no idea
The number of oranges with first women are 200 and the number of oranges with other women are 100.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, 2 market women shared 300 oranges.
The share of first woman is twice the other.
Let the number of oranges with other women be x.
Then, the number of oranges with first women will be 2x.
Now, x+2x=300
3x=300
x=100
So, 2x=200
Therefore, the number of oranges with first women are 200 and the number of oranges with other women are 100.
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Okay I think I'm going on to see if ur in
Answer:
21y-7/11
Step-by-step explanation:
First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11 that would equal to 21y-7/11
The names or notes of all the white notes on a piano are written in pieces of paper and placed in a cup. There are 7 sets of the notes D E F and G and 8 sets of the notes A B and C. If a person draws one note out of the cup without looking what are the chances of them getting a c
The probability that the person obtains a note with C written in it is of:
0.1538 = 15.38%.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
The total number of notes in this problem is composed as follows:
7 notes of each of D, E, F and G.8 notes of each of A, B and C.Hence the total number is of:
Total = 7 x 4 + 8 x 3 = 52 notes.
The desired number of outcomes is the number of notes with C, hence:
Desired = 8 notes.
Thus the probability is calculated as follows:
Probability = Desired/Total = 8/52 = 0.1538 = 15.38%.
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Joseph invested $7,850 in an account that pays 7.5% interest per year. How much interest will Juan have earned at the end of 36 months?
Juan have earned of interest after 36 months at the rate of 7.5% interest per year.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:
S.I = p×r×t
Where p is principle value, r is rate and t is time in years.
Here, the principle amount is $7,850 and rate is 7.5% i.e [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.
Now, putting the values,
SI = 7850×0.075×3
= $ 1766
Therefore, the interest Juan have earned in 36 months is $1,766.
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2. Which expression represents the simplest form of xy + 3xy?
3xy
3x²y^2
4x²²
4xy
The simplest form is 4xy
From the question, we have
xy + 3xy = 4xy
The simplest form is 4xy.
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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need help, preferably with solution
By evaluating f(x) in x = 0 we will see that the value is 1, then we will get:
f²⁰²³(0) = 1²⁰²³ = 1
How to evaluate the expression?Remember that 1 is the identity of the multiplication, this means that any number times 1, is equal to the same number.
Then, for any real value n, we know that:
1ⁿ = 1
Now we have the function:
f(x) = 1/(1 + x²)
Evaluating in x = 0, we get:
f(0) = 1/(1 + 0²) = 1
Now we can apply the exponent n = 2023 we will get:
f²⁰²³(0) = 1²⁰²³ = 1
The answer is 1.
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An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects. If the firm cuts the work year to 48 weeks but keeps the same rate of pay, how much should the architect expect his annual pay to decrease? Round your answer to the nearest dollar.
After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.
How to find the annual pay decrease?An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects
The company cuts the work year to 48 weeks but keeps the same rate of pay. The amount the architect should expect his annual pay to decrease can be calculated as follows:
Let's find the rate.
Therefore,
52 weeks = 47008
1 week = ?
cross multiply
rate = 47008 / 52
rate = 904 dollars per weeks
He collects the same rate after the company cuts the work year to 48 weeks.
Therefore,
annual pay of the architect after the cut = 48 × 904
annual pay of the architect after the cut = 43,392 dollars
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Let
U
be the universal set, where:
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
Let sets
A
and
B
be subsets of
U
, where:
A
=
{
4
,
8
,
9
,
10
}
and
B
=
{
2
,
3
,
4
,
6
,
7
}
Find
(
A
∩
B
)
c
:
{
}
Find
A
c
∪
B
c
:
{
}
Enter the elements as a list, separated by commas in order from smallest to largest. If the result is the empty set, enter DNE
The elements of set (AnB)' = {1,2,3,5,6,7,8,9,10} and The elements of A'uB' = {1,2,3,5,6,7,8,9,10}
What is complement of a set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. For example, if A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
Therefore if U={1,2,3,5,6,7,8,9,10} and A={4,8,9,10} B= {2,3,4,6,7} then,
(AnB) = {4}
(AnB)' = {1,2,3,5,6,7,8,9,10}
A' = {1,2,3,5,6,7} and B' = {1,5,8,9,10}
therefore A'uB'= {1,2,3,5,6,7,8,9,10}
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Let f(x) = 1 / 2+3x and point P = (2 , 1/8)
a.) Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at P.
m = lim f(a+h) - f(a) / h
tan h --> 0
b.) Determine an equation of the tangent line at P.
The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
f(x) = 1 / 2+3x and point P = (2 , 1/8)
f(x+h) = 1/(2 + 3a + 3h)
f(a) = 1/(2 + 3a)
m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h
After simplifying:
m(tan) = -3/[(2+3a)(2+3a+3h)]
h = 0
m(tan) = -3/(2+3a)²
The equation of the line:
y - 1/8 = [-3/(2+3a)²](x - 2)
Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
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Find the midpoint of the line segment with end coordinates of:
(0, 2) and (8,8)
The mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
Define the term mid point?A mathematical expression known as the midpoint formula is used to determine where two data points meet midway. This formula is also used in the study of economics to determine this same coefficient of elasticity, etc.The midpoint is the point on the center of the line that is equally distant as from 2 points if a line is created connecting the two points.For the given question;
The given coordinates are-
(x1, y1) = (0, 2)
(x2, y2) = (8,8)
The mid point is found by the formula;
x = (x1 + x2 )/2
y = (y1 + y2)/2
Put teh values,
x = (0 + 8)/2
x = 4
y = (2 + 8)/2
y = 5
Thus, the mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
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what is the volume of the recycling box shown in the diagram , 20cm, 40cm, 60cm can someone please help asap
write answers and working out.
Answer:
i got 48000
Step-by-step explanation:
20x40x60
when solving volume you multiply the length times width times height.
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9, so options A and E are correct.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The Balance on the gift card = $22.20,
The no of patches bought = 4,
The left balance on the card = $1.90.
The equation for the statement in the question is,
The no of patches bought × The price of patches + The left balance on the card = The Balance on the gift card
Let x be the price of one batch
Substitute the values,
4x + 1.9 = 22.20 or 22.2 – 4x = 1.9
Therefore, the equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9.
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PLEASE HELP ASAP!!! Find the volume of a cube with the given side length.
1/5b^3
The volume of the cube is 1/125b⁹
How to determine the volume of the cube?From the question, we understand that
Shape = Cube
Side length = 1/5b³
Rewrite the side length as
a = 1/5b³
The volume of a cube can be expressed as V = a³
where a is the length of any side
And v is the volume
Substitute the known values in the above equation So, we have the following equation
V = (1/5b³)³
Evaluate
V = 1/125b⁹
Hence, the volume is V = 1/125b⁹
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Find the image vertices for a dilation with center (0,0) and a scale factor of 4.
After dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
As given in the question,
From the given graph of quadrilateral the vertices of the given image is given by :
A and D are second quadrant , C is first quadrant and B is in fourth quadrant.
Each unit on both the axis represents 1 unit only.
Coordinates of each vertices are:
A = (-3 , 1) , B = (4 , -3) ,C = (2 , 3), D = (-1 , 4)
Now for dilation scale factor is equal to 4
Image vertices for a dilation with center (0 , 0) multiply the vertices by scale factor 4.
Required image vertices are given by:
A' = (-12 , 4),
B' = (16 , -12)
C' = (8 , 12)
D' = (-4 , 16)
Therefore, after dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
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Status:
Frank borrowed $56022 from the bank at 4.0% for 69 days to expand his bike shop.
Find the total amount Frank pays back to the bank.
The total amount Frank pays back to the bank = $210642.72
Assuming the given interest rate- that is the simple interest rate.
so the future value A for the simple interest rate is given by,
A = P(1 + rt)
here, P = $56022
r = 0.04
t = 69
Substitute these values in above formula.
A = 56022 (1 + 0.04 * 69)
A = 56022 * 3.76
A = $210642.72
Therefore, the total amount Frank pays back to the bank = $210642.72
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