The probability that the A-rated bond defaults given that the AA-rated bond defaults is approximately 0.74.
What is probability?
Probability is a branch of mathematics in which the chances of experiments occurring are calculated.
a. To find the probability that at least one of the bonds defaults, we can use the complement rule: the probability that neither bond defaults is (1 - 0.53) * (1 - 0.47) = 0.27, since the events are independent. Therefore, the probability that at least one bond defaults is 1 - 0.27 = 0.73. So the answer is 0.73.
b. The probability that neither bond defaults is (1 - 0.53) * (1 - 0.47) = 0.27, as calculated above.
c. We want to find the conditional probability that the A-rated bond defaults given that the AA-rated bond defaults, which can be expressed as P(A defaults | AA defaults). We can use Bayes' theorem to calculate this probability:
P(A defaults | AA defaults) = P(AA defaults and A defaults) / P(AA defaults)
From the problem statement, we know that P(AA defaults) = 0.53 and P(AA defaults and A defaults) = 0.39. Therefore,
P(A defaults | AA defaults) = 0.39 / 0.53 ≈ 0.74
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Greatest common factor of 14b with a exponent of 3 and 5b with a exponent of 2
The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
Define common factor.The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.
The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.
To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both
[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]
[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]
Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
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Ruby sold art supplies but it's on her website she bought the art supplies bundles of drawing paper and utensils for $75 each and included 70% markup to get the selling price what's the retail price including the marker for the art supply bundles
The retail price of each art supply bundle, including the markup, would be $127.50.
What is a markup, and how is it calculated?The gross or whole profit on a certain item or service is what is meant by markup. Moreover, it can be shown as a % of the cost price. For instance, if a product costs Rs. 100 and is sold for Rs. 150, the markup in this case will be 50%.
In studying the fundamentals of business, students come across the words selling price and cost price. A commodity's cost price is the amount paid when buying it from a retailer. The selling price, however, is the cost at which it is offered for sale.
Given that, the products were marked them up by 70%, then the selling price would be:
Selling price = $75 + 70% of $75
Selling price = $75 + $52.50
Selling price = $127.50
Therefore, the retail price of each art supply bundle, including the markup, would be $127.50.
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A concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, what is the exact length of each side?
In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.
How can the exact length of each side be known?Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.
Then we can formulate as 24/2
= 12 feet.
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y=x^2-8x-8 quadratic function in vertex form
Answer:
[tex]y=(x+4)^2-8[/tex]
Step-by-step explanation:
[tex]y=x^2-8x-8[/tex]
complete the square.
[tex](x+4)^2-8[/tex]
set y equal to the new right side.
[tex]y=(x+4)^2-8[/tex]
Hope this helps!
Brainliest is much appreciated!
Answer:
Answer is Below!Step-by-step explanation:
a = 1
c = -8
b= -8
the formula of vertex form is a(x-h)^2 +k = y
First find H and k using the formula -b/2a = h
h = 4
so, k = -24
y =1(x-4)^2 -24
mike has these marks on his report card ; english =82% , french=75% , history =78% , science=80% what mark will he need in math if he wants to earn a mean mark of 80% across all these subjects ?is it possible for him to earn a mean mark of 85%
Mike cannot attain a mean grade of 85% for every one of his studies since a grade higher than 100% is not feasible.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from of the median) of a dataset. This central tendency is usually referred to as the "average".
How can you calculate the mean?Just dividing the total amount of information in a data collection even by sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table can be used for the computation.
mean = (sum of all numbers) / (number of numbers)
80% = (82% + 75% + 78% + 80% + m) / 5
85% = m
The another equation is,
85% = (82% + 75% + 78% + 80% + m) / 5
425% = 315% + m
110% = m
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ACTIVITY (EXPERIMENTAL PROBABILITY) 50 trials
The dice i roll: 2, 3, 4, 4, 4, 4, 6, 5, 2, 4, 2
What is the probability of rolling a sum of even number?
What is the probability of rolling a sum of odd number?
What is the probability of rolling a sum of greater than 5?
This is for statistics ok? Ty!U,,w,,U♡
And please answer now thank you!:D
Answer:
1st=3/50
2nd=2/50
3rd=1/50
thats is if the only possible number you can roll are only from 2,6 not 1,6
classfify each number below as a rational or irrational number
Answer:
Step-by-step explanation:
-14.76: Rational
-sqrt(64): 64 is a perfect square so it is rational
1.4444444… rational numbers repeat their decimal digits at one point or another, so this is rational
pi is irrational, so 19pi is irrational.
sqrt(2)*sqrt(2) is rational, but not 2sqrt(2). Irrational.
**PLEASE SOMEONE ANSWER IM STRUGGLING** To the nearest hundredth, what is the value x ?
Answer:
A answer that is not yet known.
Step-by-step
For example x is to sub in 21 but you do not know that yet
until you solve the question.
Find the value of x, y, and z. (Round to the 3rd decimal place if possible)
Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
values of x, y, and z, we can use the system of equations
3x - 2y + z = 1
2x + y - z = 0
x + 2y + 3z = -1
We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:
3x - 2y + z = 1 (eq. 1)
2x + y - z = 0 (eq. 2)
x + 2y + 3z = -1 (eq. 3)
3x - 2y + z = 1 (eq. 1)
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
-0.3333y + 2.3333z = -1.3333 (eq. 3')
3.3333x - 0.3333z = 0.1667 (eq. 1')
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
2.1667z = -1.0833 (eq. 3')
z = -0.5
y = 0.1667
x = 0.5
Therefore, the solution to the system of equations is:
x = 0.5, y = 0.1667, z = -0.5
x = 0.500, y = 0.167, z = -0.500
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is this statement true sometimes always or never ??
The statement: If ∠F is a 60° angle, then cos (F) = sin (F), is never true.
What are sine and cosine functions?Two of the six trigonometric functions used to connect angles to the sides of a right triangle are sine and cosine. The length of the opposite side of an angle divided by the length of the hypotenuse of a right triangle is known as the sine function. The length of the adjacent side of an angle divided by the length of the hypotenuse of a right triangle is known as the cosine function.
We know that,
If angle F is 60 degrees, then the value of cos F = 1/2 and sin F = sqrt(3)/2.
Therefore, cos F is not equal to sin F and the statement is never true.
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Glenn has 2/5 of a granola bar. If he eats 7/8 of it, how much of the granola bar is left.
Glenn has 1/20 of the granola bar left.
How to find?
If Glenn has 2/5 of a granola bar and eats 7/8 of it, we need to find out how much is left.
First, we need to find out how much Glenn ate. To do this, we can multiply the fraction of the granola bar that Glenn had (2/5) by the fraction that he ate (7/8):
2/5 × 7/8 = (27)/(58) = 14/40
Simplifying this fraction, we get:
14/40 = 7/20
So, Glenn ate 7/20 of the granola bar.
To find out how much is left, we can subtract the fraction that he ate from the fraction that he had:
2/5 - 7/20
To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 20 is 20, so we can convert both fractions to have a denominator of 20:
2/5 = 8/20
7/20 = 7/20
Now we can subtract the fractions:
8/20 - 7/20 = 1/20
So, Glenn has 1/20 of the granola bar left.
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You pay $3.00 to play. The dealer deals you one card. If it is a spade, you get $10. If it is anything else,
you lose your money. Is this game fair?
The game is fair in the sense that the expected value is not negative.
What is expected value?The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.
The probability of getting a spade is 13/52 or 1/4.
The probability of getting anything else is 3/4.
he expected value of playing the game can be calculated as:
Expected value = (probability of winning x amount won) - (probability of losing x amount lost)
Expected value = (1/4 x $10) - (3/4 x $3)
Expected value = $2.50 - $2.25
Expected value = $0.25
Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.
Hence, game is fair in the sense that the expected value is not negative.
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The lenght of a rectangle is twice its breath. if the perimeter of a rectangle is 60cm, find the dimension of the rectangle.
Answer:
L = 20 , B = 10
Step-by-step explanation:
L = 2B
we know perimeter of rectangle = 2( L + B )
By substitution , 2( 2B+ B) =60
4B + 2B = 60
6B = 60
B= 10
L = 2 * B = 2 * 10 = 20
Rosa is using a balance scale. She has a set of weights which consists of two one-gram, six two-gram, four eight-gram, and two thirty-two gram pieces. What could she use to balance a mass of 45 grams?
The combination of weights listed above would balance a mass of 45 grams on the balance scale.
How exactly does a balancing scale operate?A instrument used to determine an object's mass is a balancing scale. It is made out of a beam suspended from a fixed point, with two pans or trays hanging from either end. The beam is balanced when the mass of the objects on one tray equals the mass of the objects on the other tray. The principle of moments, according to which, when the beam is in equilibrium, the moment of force on one side of the balance is equal to the moment of force on the other, governs how a balancing scale functions.
Given that, Rosa can balance a mass of 45 grams using the given combinations.
Thus, total weight on the two sides are:
Left side: 32g + 6g + 6g + 1g = 45g
Right side: 8g + 8g + 2g + 2g = 20g
Hence, the combination of weights listed above would balance a mass of 45 grams on the balance scale.
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Mr. champion storage container is 4 feet long 3 feet wide and 7 feet tall can fit 88 boxes that each has a volume of 1 ft.³ in his container explain your answer
Answer:
because 7*3*4 is 88 ft^3
where would [-8,-6] be graphed on a coordinate grid
The point [-8,-6] would be graphed 8 units left and 6 units down from the origin (0,0) on a coordinate grid.
What is a coordinate grid?A coordinate grid, also called a Cartesian plane, is a two-dimensional plane formed by a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). It is used to graph and locate points in a two-dimensional space by their x- and y-coordinates.
The coordinate grid is formed by two perpendicular lines, the horizontal x-axis and the vertical y-axis.
The point [-8,-6] represents an ordered pair where -8 is the x-coordinate and -6 is the y-coordinate.
To graph this point on a coordinate grid, start at the origin (0,0), which is where the x-axis and y-axis intersect. Then, move 8 units to the left along the x-axis since the x-coordinate is negative.
After that, move 6 units down along the y-axis since the y-coordinate is negative. The point where you end up after moving left 8 units and down 6 units is the point (-8,-6).
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A city is building a new pool. A scale drawing of the pool is shown below.
Scale,
1 in: 3 ft
What is the area, in square feet, of the pool?
4 in.
A.16n
B.24n
C.48n
D.144n
After answering the provided question, we can conclude that As a result, expression the answer is D. 144n.
what is expression ?In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators. Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
According to the scale, 1 inch on the drawing equals 3 feet in real life. As a result, the pool's length is 4 inches x 3 feet/inch = 12 feet. Similarly, the pool's width is 4 inches x 3 feet/inch = 12 feet.
As a result, the pool's area equals the length multiplied by the width, which is:
144 square feet = 12 feet x 12 feet.
As a result, the answer is D. 144n.
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To approach the runway, a pilot of a small plane must begin a 7 degrees descent starting from a height of 1069 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?
The airplane is approximately 1.7 miles from the runway at the start of the approach.
What is trigonometry?
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry
To solve this problem, we need to use trigonometry. The angle of descent is 7 degrees, which means that the angle between the horizontal ground and the plane's flight path is 7 degrees. We can use the tangent function to find the distance from the runway:
tangent (7 degrees) = opposite / adjacent
The opposite side is the height of the plane above the ground, which is 1069 feet. The adjacent side is the distance from the plane to the runway, which we need to find.
tangent (7 degrees) = 1069 / adjacent
We can solve for the adjacent side by multiplying both sides by the denominator:
adjacent = 1069 / tangent(7 degrees)
Using a calculator, we get:
adjacent = 1069 / 0.122173048
adjacent = 8743.3 feet
To convert this to miles, we divide by the number of feet in a mile:
adjacent = 8743.3 / 5280
adjacent = 1.655 miles
Rounding to the nearest tenth of a mile, we get:
The airplane is approximately 1.7 miles from the runway at the start of the approach.
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Let S = {-4, 0, 2, 3}. A new sequence of numbers is formed by repeating the numbers in S, IN ORDER from lowest to highest, until 80 numbers have been listed in the new sequence, i. E. , NEW_SEQUENCE = {-4, 0, 2, 3, -4, 0, 2, 3,. }. What is the sum of the first 31 terms in the new sequence?
The sum of the first 31 terms in the new sequence is 5.
Let S = {-4, 0, 2, 3}
New Sequence = {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............}
The four terms are repeatedly separated, as we can see above. Below are some of the first four terms = -4 + 0 + 2 + 3 = 1
Now, first four terms sum = 1
Next four terms sum = 1.
So sum of first 28 terms is given as
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
Now we find sum of first 31 terms = 7 - 4 + 0 + 2 = 5
So, sum of first 31 terms of new sequence {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............} is 5.
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A serving of skinny popcorn has 4 grams of fiber. This is about 16% of the recommended daily amount of fiber. How many grams of fiber are in the recommended daily amount?
A serving of skinny popcorn has 4 grams of fiber, which is about 16% of the recommended daily amount of fiber. The recommended daily amount of fiber is 25 grams.
If a serving of skinny popcorn has 4 grams of fibre and provides 16% of the necessary daily fibre intake, we can apply a proportion to calculate the entire recommended daily fibre intake:
If x is the required daily fibre intake in grams, we may calculate the following proportion:
4 / x = 16 / 100
We may cross-multiply and simplify to find x:
4 × 100 = 16 × x
400 = 16x
x = 25
As a result, the daily fibre recommendation is 25 grams.
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The cost of 4 chairs is the same as the cost of 3 tables. If the
cost of one chair is Rs. 48, find the cost of one table.
Answer: 64 Rs
Step-by-step explanation:
Let x be the number of tables
4 x 48 = 3x
192 = 3x
x = 64
Find product of face values of all digits in
the number 91250
To find the product of the face values (the values of the digits as they appear in the number) of all digits in 91250, we can simply multiply the face values of each digit together.
The face value of a digit is simply the value of the digit itself, regardless of its position in the number.
So, we have:
9 * 1 * 2 * 5 * 0 = 0
Note that the face value of the digit 0 is 0, so any product that includes a 0 will also be 0.
Therefore, the product of the face values of all digits in 91250 is 0.
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7.1 Calculate: -24÷-8-13 (1)
Answer:
-10
Step-by-step explanation:
BODMAS
Brackets
Of
Division
Multiplication
Addition
Subtraction
●When simplifying an equation follow the above order.
•Since division comes before subtraction, first divide -24 by -8 to get 3
•Then subtract 13 from 3 to give you -10.
What is the median of the following data values? 10, 14, 15, 17, 20, 21, 22, 25
Answer:
The median of the data set is 18.5
Step-by-step explanation:
To find the median of this set of data values, we need to first arrange them in numerical order:
10, 14, 15, 17, 20, 21, 22, 25
The middle value is the median. If there is an odd number of values, there will be exactly one middle value, and if there is an even number of values, the median will be the average of the two middle values.
In this case, there are 8 values, which is an even number. So, we take the average of the sum of the 2 middle numbers:
Median of Data Set = (17 + 20)/2 = 18.5
Therefore, the median of the data set is 18.5.
HELP ASAP
i will mark you brainleast (30 points)
graphing quadratic functions in vertex form
*please answer correctly*
5. Vertex: (2, 2)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
What is quadratic functiοns?A quadratic functiοn is a pοlynοmial functiοn οf degree 2, where the highest pοwer οf the variable is 2. It has a parabοlic graph and is cοmmοnly used tο mοdel real-wοrld phenοmena.
5. Vertex: (2, 2)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
7. Vertex: (2, 3)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
Range: y ≥ 3
6.Vertex: (-2, -4)
Vertical shift: -4 units
Hοrizοntal shift: -2 units
Width: Cοmpressed hοrizοntally by a factοr οf 1/3
Reflected: Nο
8. Vertex: (-2, -2)
Vertical shift: -2 units
Hοrizοntal shift: -2 units
Width: Stretched by a factοr οf 3 in the vertical
Reflected: Nο
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hi i don't get this question pls HELP! calculate the monthly repayments for the house loan(total cost divided by number of months) so for example i got my total cost that is 15,393,86 and i divided by the per month which is 12 so basically i did this and here is the answer:
(15,393,86 ÷ 12= 128282.1667) is this correct?
pls correct me and guid me
Yeah, it seems fine so you're doing great so far! ^^
Without graphing, tell whether the slope of a line that models the linear relationship is positive, negative, zero, or undefined. Then find the slope.
A laptop battery has 85% power after 1 hour of use and 40% after after 4 hours of use
Answer:
its a negative slope because the battery is going down, not staying the same, or going up
Step-by-step explanation:
22. At a wedding, guests are given cone-
shaped cups filled with flower petals. The cups
have a radius of 5 centimeters and a height of
10 centimeters. If there are 150 cups, what is
the total volume of petals that all the cones will
hold? Round to the nearest whole number.
Answer:
The volume of one cone-shaped cup can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height. Substituting the given values, we get:
V = (1/3)π(5 cm)^2(10 cm)
V ≈ 261.8 cm^3
Therefore, one cup can hold approximately 261.8 cubic centimeters of flower petals.
To find the total volume of petals that all 150 cups will hold, we can multiply the volume of one cup by the total number of cups:
Total volume = 150 cups × 261.8 cm^3/cup
Total volume ≈ 39,270 cm^3
Rounding to the nearest whole number, we get that the total volume of petals that all the cones will hold is approximately 39,270 cubic centimeters.
Answer:
I forgot how to do this sorry
OFERING BRAINLIEST! Step by step explanation please!
Answer:
600ft²
Step-by-step explanation:
Volume of a cube V = a³
a³ = 1000
Cube root of both sides
a = 10ft
Surface area A =6a²
A = 6 x 10 x10 ft²
Answer:
600 feet²
Step-by-step explanation:
1) Break down the info
To answer this question we have to figure out the values of the sides. As it is a cube all sides should have the same area and length!
We know that the equation for volume is...
volume = area of cross-section x heightThis means that to simply find the sides, we can cube root 1000
[tex]\sqrt[3]{1000}[/tex] = 10Let's check...
10 x 10 x 10 = 10002) Find the surface area
We now know that the sides are 10 feet each so to find the surface area is [tex]6a^2[/tex] where a is the length of one side!
We can solve the question by plugging our numbers into the equation...
[tex]6[/tex] × [tex]10^{2}[/tex] = [tex]600[/tex]Our surface area is 600 feet!
Hope this helps, have a lovely day! :)
Aysha and ahmed are going to dubai shopping festival next week. The table
shows the amount that each person spent on snacks ,games and sovenirs the last
time they went to shopping festival. Aysha wants to spend money using the same ratios as on her last trip to shopping
snacks games Souvenirs
Aysha Dh. 20 Dh25 Dh10
Ahmed Dh40 Dh20 Dh15
festival. If she spends Dh 100 this time on games how much she will spend on
souvenirs
As per the unitary method, Aysha will spend Dh45.45 on souvenirs if she spends Dh100 on games, using the same ratios as on her last trip to the shopping festival.
Now, let's use the unitary method to solve the problem at hand. We know that Aysha wants to spend money using the same ratios as on her last trip to the shopping festival. So, let's find out the ratio of the amount she spent on games to the total amount she spent on all three items (snacks, games, and souvenirs) on her last trip:
Amount spent on games = Dh25
Total amount spent on all three items = Dh20 + Dh25 + Dh10 = Dh55
So, the ratio of the amount spent on games to the total amount spent on all three items is:
Dh25/Dh55
Now, we know that Aysha wants to spend Dh100 on games this time. Let's use the unitary method to find out how much she will spend on souvenirs, given the ratio we just found.
If Dh25 is spent on games, then the total amount spent on all three items will be:
(Dh25/Dh55) * Total amount spent
And we know that the total amount spent is Dh100 (the amount Aysha wants to spend on games). So, substituting this value, we get:
(Dh25/Dh55) x Dh100
Simplifying this expression, we get:
Dh45.45
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