The expected value of the life insurance policy is $864.77.
To calculate the expected value, we first need to determine the payout in the event that the policyholder dies before reaching age 100. Since the policy costs $1000 and the probability of dying before age 100 is 0.14, the expected payout, in this case, would be:
Payout = $1000 * 0.14 = $140
Next, we need to determine the value of the policy if the policyholder lives to age 100. In this case, the policy would pay out the face value of $1000, but the present value of that amount is less than $1000 due to the time value of money. Assuming an interest rate of 5%, the present value of $1000 payable in 50 years would be:
PV = $1000 / (1 + 0.05)^50 = $54.26
The probability of living to age 100 is 0.86, so the expected value of the policy, in this case, would be:
Expected Value = $54.26 * 0.86 = $46.72
Finally, we can calculate the overall expected value of the policy by adding the expected payouts in both scenarios:
Expected Value = $140 + $46.72 = $186.72
Rounding to the nearest cent, the expected value of the life insurance policy is $864.77.
In conclusion, even though the probability of living to age 100 is high, the expected value of the policy is not very high due to the time value of money and the relatively low payout in the event of death before age 100.
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PLEASE HELP MEEEEEEEEEEE!
What is the measure of the unknown angle?
A straight angle divided into a fifty-eight-degree angle and an unknown angle.
100°
112°
120°
122°
Therefore , the solution of the given problem of angles comes out to be the right response is option d 122°.
An angle meaning is what?Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.
Here,
180 degrees is the length of a straight circle. It has been split into a 58-degree angle and an unidentified angle, as far as we are aware. So that we can determine the size of the undetermined angle, let's use subtraction:
=> Angle unknown = 180 degrees minus 58 degrees
=> Angle unknown = 122 degrees
As a result, the undetermined angle is 122° in size.
The right response is (d) 122°.
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4cm 12 cm 7cm ___square centimeters
Answer:
7cm to square centimeters is 2.6458 centimeters
Step-by-step explanation:
a car dealership pays $8,350 for a car, they mark up the price by 17.4% to get the retail price. What is the retail price of the car at this dealership
divide the circumference of a pumpkin by its diameter and what do you get?
Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)
When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.
This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.
Mathematically, this can be represented by the formula
pi ≈ circumference / diameter
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circle project represented in a graph
1. Draw a point at (1,-2).
2. Draw a long radius of 8 units.
3.Using a compass, draw a circle with your point from step one as its center and the point from step two as the side.
4.Using a protractor, draw a 70 degree arc
5. draw a central angle that intersects your arc
6. Draw an inscribed angle that intersects an arc of 40 degrees
7.draw a tangent line
8. draw a secant line
9. write the equation of your circle
Answer:
search up the answers
Step-by-step explanation:
I just need help with this, please! 10 points!
The given data comprises of a right triangle in which the base is denoted by x whose value is found to be 10.01.
Define trigonometric identity of sine?It states that the ratio of the length of the side opposite to the angle to the length of the hypotenuse is equal to the sine of the angle.
The given data comprises of a right triangle in which the base is denoted by x and the perpendicular is 8. The angle formed between the base and hypotenuse is 53 degree.
To solve this problem, we can use the trigonometric identity of sine.
Mathematically, it can be expressed as:
sin 53° = Perpendicular/Hypotenuse
8/x = sin 53°
x = 8/sin 53°
x = 8/ 0.7986
x ≈ 10.01
Hence, the value of x is 10.01.
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PLEASE HELP
find the equation of the line
using exact numbers
Answer: y = -3x + 7
Step-by-step explanation:
slope = -3
y intercept = 7
Which of the following sets of numbers could not represent the three sides of a triangle?
1. 11,25,35 2. 15,24,39
3. 9,20,26 4. 9,13,21
Reason:
a+b = 15+24 = 39 is NOT larger than c = 39
Since a+b > c is false, a triangle is NOT possible.
The sum of any two sides must exceed the third side for a triangle to be possible. For more information, check out the triangle inequality theorem.
Use the given information to prove the following theorem.
Answer: two right-angled triangle, equilateral triangle
Step-by-step explanation:
It is a combination of two right-angled triangle or it is an equilateral triangle.
Explanation:
You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.
Statement . . . . Reason1. PX is the perpendicular bisector of YZ . . . . given
2. angles at X are right angles . . . . definition of perpendicular
3. YX = XZ . . . . definition of bisector
4. PX = PX . . . . reflexive property of congruence
5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem
6. YP ≅ ZP . . . . CPCTC
scores on an iq test are normally distributed with a mean of 100 and a standard deviation of 15. what is the z-score for an iq score of 122?
The z-score for an IQ score of 122 is 2.
This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.
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Dante collects baseball cards. He would like to keep the cards in an album. He has 10 cards for each of 24 teams. How many album pages will he need if each page can hold 8 cards? Show your work. Draw a picture if it helps.
Answer: 30 album pages
Step-by-step explanation:
cards = 10
teams = 24
total cards = 240
240 / 8 = 30
For 5 days mr fransico had a total 10. 5 hours of overtime in the office what was his average daily overtime?
Mr. Fransico had average overtime in a day is 2.1 hours.
In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.
For 5 days Mr fransico had a total of 10. 5 hours of overtime in the office
Then the average daily overtime is-
10.5÷5 = 2.1 hours
Hence Mr. Fransico had total overtime in a day is 2.1 hours.
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Last sentence was find the volume of the larger pyramid
a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.
what is volume ?
Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.
In the given question,
a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:
(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²
Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:
25/9 = (h₁/h₂)²
Taking the square root of both sides, we get:
h₁/h₂ = 5/3
Therefore, the ratio of the heights of the pyramids is 5:3.
b. Since the volume of a pyramid is proportional to the cube of its height, we have:
(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27
Substituting the given volume of the smaller pyramid, we get:
108 / (volume of larger pyramid) = 125/27
Solving for the volume of the larger pyramid, we obtain:
volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)
Therefore, the volume of the larger pyramid is 23.04 cm³.
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Alanna goes to the pet store to buy fish for her new 15-gallon fish tank. Each large fish costs $8 and requires 2 gallons of water. Each small fish costs $3 and requires 0.5 gallon of water. She has $100 to spend on fish at the pet store. Which combinations of large and small fish can Alanna purchase for her fish tank?
Let's set up the cost constraint inequality.
x = number of large fish, some nonnegative integer
y = number of small fish, some nonnegative integer
8x = cost of just the large fish only
3y = cost of just the small fish only
8x+3y = total cost
The total cost must be $100 or smaller, so Alanna keeps to her budget.
We form the inequality 8x+3y ≤ 100 as the cost constraint.
Because x and y are nonnegative, this means x ≥ 0 and y ≥ 0
----------------
Now let's form the water constraint inequality.
x = number of large fish
y = number of small fish
2x = amount of water needed for the large fish only
0.5y = amount of water needed for the small fish only
2x+0.5y = total amount of water needed
This total must be 15 gallons or fewer.
2x+0.5y ≤ 15
Let's multiply both sides by 2 to make that 0.5 turn into a whole number.
2x+0.5y ≤ 15
2*(2x+0.5y) ≤ 2*15
4x+y ≤ 30
This represents the water constraint.
----------------
Here are the inequalities we found
8x+3y ≤ 100
4x+y ≤ 30
x ≥ 0
y ≥ 0
The first two items represent the cost constraint and water constraint in that order. The last two items make sure that x and y can't be negative.
Valid (x,y) solutions will be found in the shaded region of that system of inequalities. Points on the boundary are included in the shaded region due to the "or equal to" as part of each inequality sign.
Below is the graph of this system of inequalities. I used Desmos to make the graph. GeoGebra is another good choice. Let me know if you need to make the graph by hand rather than use technology.
The purple shaded region represents all possible (x,y) solutions.
For example, (5,5) is in that shaded region. I've marked it in the drawing below. This means x = 5 large fish and y = 5 small fish can be bought. Alanna will stick to her budget and she'll have enough water to go around.
On the other hand, (5,25) is NOT in the shaded region. This means Alanna cannot buy x = 5 large fish and y = 25 small fish (she'll either go over budget or she won't have enough water, or both happens).
A number cube is rolled
twice. What is the probability
of getting a 6 on the first roll,
then a number less than 5
on the second roll?
A) 1/9
B) 2/3
C) 5/36
D 5/12
E) 1/36
Therefore , the solution of the given problem of probability comes out to be the response is A 1/9.
What is probability exactly?The primary goal of the systems inside a procedure known as criteria is to determine the average possibility that a statement is true or that a specific occurrence will occur. Any value from 0 to 1, when 0 is frequently utilized to denote that something is likely and 1 is typically used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
If a 6 is rolled on the first roll, the probability of spinning a number less than 5 on the second roll is 2/3,
since there are the four possible outcomes on the third roll that are less than 5 (rolling a 1, 2, 3, or 4) out of an overall of six possible outcomes (rolling any plenty from 1 to 6),
so the probability of a favorable outcome is 4/6, which simplifies to 2/3.
As a result, the likelihood that a 6 will be rolled on the first roll and a figure less than 5 will be rolled on the second roll is:
=> (1/6) x (2/3) = 1/9
As a result, the response is A) 1/9.
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S(t) = 2t^3 -3t^2-12t+8
(a) Find the velocity and acceleration functions
(b) Determine the time intervals when the object is slowing down or speeding up
The time interval when the object is speeding up is t > 2, and the time interval when the object is slowing down is 1 < t < 2.
The the velocity and acceleration functions
Given that
S(t) = 2t³ - 3t² - 12t + 8
Differentiate to get the velocity function
v(t) = 6t² - 6t - 12
Differentiate to get the acceleration function
a(t) = 12t - 6
The intervals of slowing down or speeding upTo determine the time intervals when the object is slowing down or speeding up, we need to examine the sign of the velocity and acceleration functions.
The object is speeding up when the velocity function is positive and the acceleration function is also positive.
This occurs when t > 2 (graphically)
Similarly, the object is slowing down at t < 2
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Factor out the GCF from the polynomial.
3x³y² - 9xz4 + 8y²z
The expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
What is (GCF) greatest common factor?The GCF defines the highest common factor present in between given two or more numbers or algebraic expressions.
we shall determine the GCF greatest common factor for the algebraic expression 3x³y² and 8y²z as follows:
3x³y² = y² × 3x³
8y²z = y² × 8z
both terms 3x³y² and 8y²z have y² common to them, so we can write;
3x³y² + 8y²z = y² × 3x³ + y² × 8z
3x³y² + 8y²z = y²(3x³ + 8z)
In conclusion, the expression 3x³y² - 9xz⁴ + 8y²z have no GCF greatest common factor but the terms 3x³y² and 8y²z have GCF equal to y².
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PLEASE ANSWER AS QUICKLY AS YOU CAN!!!!!!
Answer:
(x+6)(x+6)
[tex]x^2+12x+36[/tex]
(x+8)(x-5)
[tex]x^{2}+3x-40\\[/tex]
(x-5)(x-2)
[tex]x^{2}-7x+10[/tex]
Step-by-step explanation:
Brainliest pls hope it helped^^
Answer:
a) x^(2)+12x+36
b) x^(2)+3x-40
c) x^(2)-7x+10
Step-by-step explanation:
What did I do wrong? (#11)
Answer:
It's not "wrong", per se, it just didn't quite include the info that your teacher wanted! I personally would have said "Rotate 180 degrees about F", so I think that may be it.
Let me know if this helped by hitting the thanks button/marking brainliest! If not, please comment and I'll get back to you ASAP.
Please help me this is due after class (20 mins) (I-Ready Math)
YOU GET 20 POINTS!!!!
Here's the picture
The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.
In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.
To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:
Area = base x height
Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:
72 = 12 x h
h = 72/12
h = 6
Therefore, the value of h in the parallelogram is 6 units.
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Kyle is playing a game where he rolls a number cube twice and flips a coin twice. The number cube is labeled 1 to 6. The coin can land on heads or tails.
If the number cube lands on 5 both times and the coin lands on heads both times, Kyle wins a prize. What is the probability that Kyle wins the prize?
The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]
What is the probability?The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.
Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:
P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)
[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]
[tex]= 1/144[/tex]
Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately [tex]0.0069[/tex] (rounded to four decimal places).
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Which expression is equivalent to
-5
28p9q5
12pq
7 ? Assume P≠0,q≠0.
The expression -5 + 28p9q5 - 12pq + 7 is equivalent to 7. Since all the terms except the last one contain variables, we can use algebra to solve for the value of the expression.
What is algebra?Algebra is a branch of mathematics which deals with the manipulation of equations, inequalities, and other mathematical expressions. Algebra is used to solve equations, simplify expressions, and model real-world problems.
To begin, we can add -5 and 7 to obtain 2. This means that the expression is now equal to 2 + 28p9q5 - 12pq. We can then simplify this expression by combining like terms.
Since 28p9q5 and -12pq are both products of the same variables, we can add them together. When we do so, we obtain 16p9q5, which means that the expression is now equal to 2 + 16p9q5.
Finally, we can simplify the remaining term by breaking down the product. We can divide 16 by 8 to obtain 2, and then divide 9 by 3 to obtain 3. This means that the expression is now equal to 2 + 2p3q5. Since there are no more terms to simplify, we can conclude that the answer is 2.
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Jackson is making lemonade for a class party. He uses 3 tablespoons (tbsp. ) of lemonade mix for each 6 ounces of water. He wants to make 4 quarts of lemonade. How much lemonade mix does Jackson need?
A
2 tbsp. B
16 tbsp. C
32 tbsp. D
64 tbsp
As per the unitary method, Jackson needs 64 tablespoons of lemonade mix to make 4 quarts of lemonade. (option D).
First, we need to convert the 4 quarts of lemonade into ounces since we know the ratio in terms of ounces. One quart is equal to 32 ounces (8 oz per cup and 4 cups per quart). So, 4 quarts would be equal to 128 ounces (32 oz x 4).
Next, we need to determine how much lemonade mix is needed for every 6 ounces of water.
Therefore, the ratio of lemonade mix to water is 3 tablespoons/6 ounces.
Now that we have the ratio, we can use it to find out how much lemonade mix is needed for 128 ounces of water (4 quarts). We can set up a proportion using the ratio we just found:
3 tbsp / 6 oz = x tbsp / 128 oz
We want to solve for x, which represents the amount of lemonade mix needed for 128 ounces of water. To solve for x, we can cross-multiply and simplify:
3 tbsp x 128 oz = 6 oz x
384 tbsp oz = 6x
x = 64 tbsp
So the answer is D) 64 tbsp.
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650 of those surveyed said their favorite color was blue. if 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answer:
let X be the value of the total students
[tex] \frac{65}{100} \times x = 650 \\ \\ \frac{65x}{100 } = 650 \\ if \: w \:e \: crossmultipl \\ 65x = 65000 \\ x = 65000 \div 65 \\ x = 1000[/tex]
a large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, find the probability of selecting 3 red marbles
A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.
The probability of selecting 3 red marbles is 1/54.What is a probability?
Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.
A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.
There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:
[tex]10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120[/tex]
There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:
[tex]22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540[/tex]
Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54
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ten identical protein samples were analyzed by the bradford method for protein analysis. the following values for protein concentration were obtained. observation number protein concentration (mg/ml) 1 1.02 2 0.98 3 0.99 4 1.01 5 1.03 6 0.97 7 1.00 8 0.98 9 1.03 10 1.01 calculate sample mean
The sample mean protein concentration obtained using the Bradford method for protein analysis is 1.00 mg/ml.
We must add together all the protein concentrations and divide the total by the number of observations in order to determine the sample mean for the protein concentrations acquired using the Bradford technique for protein analysis.
We have ten identical protein samples in this instance, and the measured protein concentrations are as follows:
Protein concentration (mg/ml) observations: 1: 1.02, 2: 0.98, 3: 0.99, 5: 1.01, 6: 0.97, 8: 1.00, 9: 1.03, and 10: 1.01.
We add up the protein concentrations and divide the total by the number of observations to determine the sample mean:
[tex](1.02 + 0.98 + 0.99 + 1.01 + 1.03 + 0.97 + 1.00 + 0.98 + 1.03 + 1.01) / 10[/tex] is the sample mean.
= 1.00 mg/ml
As a result, the Bradford method for protein analysis yielded a sample mean protein content of 1.00 mg/ml.
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Can someone please help me answer these I’m gonna have a lot of these on my test I just need help answering this one and if you could please try to explain it to me to that would be great
The formula for percent from the board can be expressed this way:
The total number of students that like pineapple pizza * 100.
The total number of students
A (i). The part is the number of students that like pineapple pizza which is 5.
(ii). The whole is the total number of students namely; 7 + 12+ 5 + 3 + 6 = 33.
(iii). Plugging the part and whole into the equation, we will have: 5/33 * 100
(iv). Final answer is = 15.15%
What is a percentage?A percentage is a mathematical expression that is aimed at calculating the proportion of a given quantity out of 100. In the question, we are requested to find what proportion of students like pineapple pizza.
To get the answer, we first have to determine the number of students that like pineapple pizza which is 5 according to the table. Next, we get the sum of students which is 33. The percentage will then get the fraction and multiply the result by 100. The final answer is 15.15%.
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while shopping, sofia noticed that her favorite bag of chips were on sale for $5 for 2 bags. how much would 7 bags cost?
Sofia's favorite bag of chips were on sale for $5 for two bags. If she wanted to buy seven bags, the cost would be $17.50.
To calculate this, we need to use the formula for finding the total cost of a given number of items: Total Cost = Number of Items x Cost Per Item.In this case, we need to find the total cost of seven bags, so the equation looks like this: Total Cost = 7 x $5.
We can solve this equation by multiplying the two numbers together. 7 multiplied by 5 equals 35. However, the question is asking us to find the total cost of seven bags, which is $17.50. To convert the answer from 35 to 17.50, we need to divide 35 by two: 35 divided by 2 equals 17.50.
Therefore, the cost of seven bags of Sofia's favorite chips would be $17.50.
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7. Javier shared $280.00 among his siblings Juan, Micah and Savi. Savi received 4 times as much as Juan and Micah received 1/2 of Savi's share and Juan got the balance Calculate Micah's share.
Micah received 1/2 of Savi's share and Juan got the balance.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
total amount = $280=x
savi= 4*juan= 11
micah= 1/2 savi= 1/2*280/100= 1.4
juan got balance= 267.6
Hence, Micah received 1/2 of Savi's share and Juan got the balance.
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A certain amount of money is shared between rui feng and vishalin the ratio of 5:9 if rui feng gets 44 dollar less than vishal find total amount of money shared between the two boys
The total amount of money shared between Rui Feng and Vishal is 154 dollars.
Let's assume that the amount of money shared between Rui Feng and Vishal is x dollars.
According to the given ratio, the amount of money received by Rui Feng is 5/14 of the total amount, and the amount received by Vishal is 9/14 of the total amount.
We are also given that Rui Feng receives 44 dollars less than Vishal. We can express this as:
9/14 x - 5/14 x = 44
Simplifying the equation, we get:
4/14 x = 44
Multiplying both sides by 14/4, we get:
x = 154
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