Answers
(i) The mean is
\(\displaystyle E(X) = \sum_x x \, P(X = x) \\\\ E(X) = 1\cdot0.175 + 2\cdot0.315 + 3\cdot0.211 + 4\cdot0.092 + 5\cdot0.207 \\\\ \boxed{E(X) = 2.839}\)
The variance is
\(V(X) = E((X - E(X))^2) = E(X^2) - E(X)^2\)
Compute the second moment \(E(X^2)\) :
\(\displaystyle E(X^2) = \sum_x x^2 \, P(X = x) \\\\ E(X) = 1^2\cdot0.175 + 2^2\cdot0.315 + 3^2\times0.211 + 4^2\times0.092 + 5^2\times0.207 \\\\ E(X^2) = 9.997\)
Then the variance is
\(\boxed{V(X) \approx 1.9171}\)
(ii) For a random variable \(Z=aX+b\), where \(a,b\) are constants, we have
\(E(Z) = E(aX+b) = E(aX) + E(b) = a E(X) + b\)
and
\(V(Z) = E((aX+b)^2) - E(aX+b)^2 \\\\ V(Z) = E(a^2 X^2 + 2ab X + b^2) - (a E(X) + b)^2 \\\\ V(Z) = a^2 (E(X^2) - E(X)^2) \\\\ V(Z) = a^2 V(X)\)
Then for \(Y=\frac{X+3}2\), we have
\(E(Y) = \dfrac12 E(X) + \dfrac32 \\\\ \boxed{E(Y) = 2.918}\)
\(E(Y^2) = E\left(\left(\dfrac{X+3}2\right)^2\right) = \dfrac14 E(X^2) + \dfrac32 E(X) + \dfrac94 \\\\ \boxed{E(Y^2) \approx 9.0028}\)
Related Questions
Derivative using direct definition of derivative 2-x/2+x
Answers
Let f(x) = (2 - x)/(2 + x). By definition of the derivative,
\(\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h\)
\(\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{2-(x+h)}{2+(x+h)}-\frac{2-x}{2+x}}h\)
\(\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{(2-x-h)(2+x)-(2-x)(2+x+h)}{(2+x+h)(2+x)}}h\)
\(\displaystyle f'(x)=\lim_{h\to0}\frac{-4h}{h(2+x+h)(2+x)}\)
\(\displaystyle f'(x)=-4\lim_{h\to0}\frac1{(2+x+h)(2+x)}=\boxed{-\frac4{(2+x)^2}}\)
The following Frequency Table describes the number of garages in a house.
What is the average number of garages in a house?
X
1
2
3
4
Frequency
15
23
35
10
Answers
The average number of garages in a house, based on the given frequency table, is approximately 2.48.
The average number of garages in a house, we need to calculate the mean using the frequency table provided.
First, we calculate the product of each value of X (the number of garages) with its corresponding frequency.
This will give us the sum of the products.
Sum of products = (1 × 15) + (2 × 23) + (3 × 35) + (4 × 10)
= 15 + 46 + 105 + 40
= 206
Next, we calculate the total frequency by summing up all the frequencies.
Total frequency = 15 + 23 + 35 + 10
= 83
Finally, we divide the sum of products by the total frequency to find the average.
Average number of garages = Sum of products / Total frequency
= 206 / 83
≈ 2.48
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hay 1230 personas, entre hombres y mujeres. Si se sabe que el número de mujeres, supera en 150 al número de hombres. ¿Cuántos hombres están habitando la mini ciudad?
Answers
There are 540 men living in the mini city.
x + (x + 150) = 1230
Simplifying this equation, we get:
2x + 150 = 1230
Subtracting 150 from both sides, we get:
2x = 1080
Dividing both sides by 2, we get:
x = 540
Therefore, there are 540 men living in the mini city.
To check our answer, we can substitute x = 540 into our original equation:
540 + (540 + 150) = 1230
690 = 1230
This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.
We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:
x + (x + 150) = 1230
Simplifying this equation, we get:
2x + 150 = 1230
Subtracting 150 from both sides, we get:
2x = 1080
Dividing both sides by 2, we get:
x = 540
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Tessa feeds her dog,Roscoe 3 3/4 cups of dog food per day.if she buys a bag of food that contains 165 cups, how many days will the bag last?
Answers
I need the answers for the table below.
Answers
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
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I WILL GIVE THE BRAINIEST
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Answers
An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
How to write an equation to determine the number of students that went on this trip?In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;
Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;
\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
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Complete Question:
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.
Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Student Council has 1,064 flowers. They want to divide the flowers evenly among 28 centerpieces. How many flowers will be in each centerpiece?
Answers
To find out how many flowers will be in each centerpiece, we can divide the total number of flowers by the number of centerpieces:
Total number of flowers: 1,064
Number of centerpieces: 28
Number of flowers in each centerpiece = Total number of flowers / Number of centerpieces
Number of flowers in each centerpiece = 1,064 / 28 = 38
Therefore, there will be 38 flowers in each centerpiece.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Answer: 38
Step-by-step explanation:
The question is asking you to divided.
1064 divided by 28 = 38
So there will be 38 flowers in each centerpiece
What are the like terms in the expression 6x + 9 – 4x – y - 8
Answers
Answer:
6x and -4x
9 and -8
Step-by-step explanation:
As you can see, both of the numbers at the top have a variable x. Both of the numbers at the bottom have no variable. These are two pairs of like terms because they either have the same variable or no variable at all.
A firm’s monthly cost for paying cleaners’ wages is $47 250. Under a new pay deal each cleaner earns $375 more each month. If the new pay deal goes through, the firm realises that it will need to reduce the number of cleaners by 3 if it is to cover its costs within the existing budget. What is the monthly salary of a cleaner before the pay rise?
Answers
Answer:
Answer attached in images below.
here are three fractions: 2/3, 4/5,6/9. Two of these fractions are equivalent to each other. Which two? Explain your reasoning in a complete sentence.
Answers
Answer:
The two fractions equivalent to eachother are 2/3 and 6/9
Step-by-step explanation:
These fractions are equivalent because 6/9 can be reduced into 2/3. Also 6 is a multiple of 2 and 9 is a multiple of 3.
The fractions 2/3 and 6/9 are equivalent to each other after simplifying the fractions.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The three fractions are:
2/3, 4/5, 6/9
The above fractions can be written in the form of decimals:
After dividing:
2/3 = 0.666
4/5 = 0.8
6/9 = 0.66
The fractions 2/3 and 6/9 are equivalent to each other because its decimal forms are equal.
Or
2/3 = 6/9
Thus, the fractions 2/3 and 6/9 are equivalent to each other after simplifying the fractions.
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What is the formula for net cost price
Answers
Answer:
Hope this helps lol !
Step-by-step explanation:
This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.
Two friends work at the same store. One friend works 32 hours and earns $17 each hour, and the other works 26 hours and earns $15 each hour.
Answers
Answer:
The difference between the first and second friends' total earnings is $154.
BRAINLIEST, PLEASE!
Step-by-step explanation:
32 x $17 = $544
26 x $15 = $390
$544 - $390 = $154
consider a circle of radius 2 centered at the origin. find parameterizations of this curve under the following assumption. clearly state any restriction on the variable of parametrization
Answers
As per the given radius, the parameterizations of this curve is 4
The term curve in math is defined as an abstract term used to describe the path of a continuously moving point
Here we have given that consider a circle of radius 2 centered at the origin.
And we have to find the parameterizations of this curve under the following assumption.
Here we have know that we need to find a parameterization for the circle of radius 2 in the xy-plane that one is centered at the origin at the direction of clockwise.
=> x(t) = 2cos(t) ------------------(1)
and
=> y(t) = −2sin(t) -----------------(2)
Here we have to note that the given expression is written as,
=> x²(t) + y²(t)
When we apply the values on it then we get
=4cos²t + 4sin²t
Then it can be written as,
=> 4(cos²t + sin²t)
=> 4
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Which of the following is a polynomial?
OA. 5+x2²/X
OB. √x+2x-1
OC. 8x²+x+3
OD. 7x
Answers
Answer:
C. 8x²+x+3.
Step-by-step explanation:
A and B are not polynomials as they contain a division (A) and a square root (B).
D is a monomial ( just one term).
oc.8x²+x+3
Step-by-step explanation:
Which of the following is a polynomial?
OA. 5+x2²/X
OB. √x+2x-1
OC. 8x²+x+3
OD. 7x
what is compliance?
come here fast
dwdduizgga
Answers
Answer:
the property of a material of undergoing elastic deformation or (of a gas) change in volume when subjected to an applied force. It is equal to the reciprocal of stiffness.
Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank contains 19140 L at 4:47 PM and 8097 L at 5:05 PM the same day, how many liters will the tank contain at 5:11 PM that day?
Answers
Answer:
The liters that the tank will contain at 5:11 PM that day are:
4416 Liters.Step-by-step explanation:
Firstly, you must identify the outlet flow of the water pumped from the tank, for this, you must subtract the last volume given from the first volume:
19,140 L - 8,097 L = 11,043 LAnd the minutes that passed from the first volume until the last volume given (18 minutes from 4:47 PM to 5:05 PM), so, you must divide that two values to obtain the outlet flow:
Outlet flow = \(\frac{Volume}{Time}\) Outlet flow = \(\frac{11,043 L}{18 min}\) Outlet flow = 613.5 \(\frac{L}{min}\)Now, you must see the next hour given (5:11 PM), if you see, from 5:05 PM to 5:11 PM has passed 6 minutes, taking into account this, you replace the equation of outlet flow to clear the volume:
Outlet flow = \(\frac{Volume}{Time}\) Volume = Outlet flow * timeAnd replace the values to obtain the new volume pumped:
Volume = 613.5 \(\frac{L}{min}\) * 6 minVolume = 3681 L.At last, you must subtract these liters from the last volume identified in the tank:
New Volume in the tank = 8097 L - 3681 LNew Volume in the tank = 4416 LThe volume in the tank at 5:11 PM is 4416 Liters.
The tank will contain 4416 L of water at 5:11 PM .
Rate of discharge of water:Given that, the tank contains 19140 L at 4:47 PM and 8097 L at 5:05 PM
It means that, in 18 minutes the amount of water discharge is,
\(=19140-8097=11043L\)
The rate of flow is,
\(=\frac{11043}{18}=613.5L/min\)
From 5:05 PM to 5:11 PM , six minutes are passes.
Water discharge in that six minute is ,
\(=613.5*6=3681L\)
The tank will contain at 5:11 PM is,
=\(8097-3681=4416L\)
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Please help, this is on final. I need how you got the answer and what the answer is.
Answers
Answer:
Angle 1 is congruent to the angle that is supplementary to angle 2. Angle 2 is also congruent to angle 3 due to the Corresponding angles theorem. Since angle 2 is supplementary to angle 1 and angle 3 is congruent to angle 2. This shows that angle 1 and angle 3 are supplementary.
Step-by-step explanation:
Answer:
I can't see it that wel..?m
Can you please find and solve the unknown variable.
Answers
The value of x is; x = 3.14
Here, we have,
from the given diagram, we get,
there is a right angle triangle.
we have to find the value of x.
we know that,
Let the angle be θ , such that
cos θ = base / hypotenuse
here, we get,
cos 17 = 3/x
so, we have,
0.956 = 3/x
so, x = 3.14
Hence, The value of x is;x = 3.14
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James planted a bush in his yard. The year he planted it, the bush produced 17 flowers. Each year the branches of the bush split, so the number of flowers doubles. The input is the year after planting, and the output is the number of flowers. Does this represent a linear equation? Why or Why not?
Answers
Answer:
No
Step-by-step explanation:
The function is growing exponentially since each output is the previous input multiplied by 2.
The equation for the given condition will be N = 17× \(2^{x-1\\\) and it will be a geometric progression function, not a linear function.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
Given that,
Number of flowers in 1 year = 17
Let's say the number of flowers is N and x is the number of years
Since saying that number of flowers going double
17, 34, 68....
So, it will create a geometric series with a common ratio of 34/17 = 2
The general term for geometric series will be the number of flowers in that year
So,
N = 17× \(2^{x-1\\\)
where x is representing year and N is the number of flowers.
Hence "The equation for the given condition will be N = 17× \(2^{x-1\\\)".
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ABC is a straight line, work out the size of angle x
Answers
The value of x is: 180° - 100° - 45° = 35°
EXPLORE ACTIVITY 2
TEKS 7.13.8
Analyzing a Family Budget
One way to present a budget is in a circle graph. You can see at a glance which
categories take the greatest part of the family's resources. You can also work
backward from a circle graph to figure out exactly how much money is in each
category.
Use the circle graph to complete
the table for the Baker family's
monthly budget. Their net
monthly income is $4,000.
STEP 1)
STEP 2
STEP 3
STEP 4
STEP 5
432 Unit 7
Enter the income in the table.
Enter the percent or amount of money for each
category from the circle graph in the table.
Calculate the amount of money or the percent
for each category in the table.
Determine which expenses are fixed and
which are variable. Place X's in the appropriate
columns.
Complete the Amount Available column.
Item
Net monthly income
means how much
income the family
has after taxes.
Net monthly
Income
Housing cost
Food
Savings
Entertainment
Clothing
Medical
Transportation
Emergency
fund
Amount
($)
Percent
(%)
Baker Family's Monthly Budget
Emergency fund
Transportation
(car expense,
bus passes)
$400
Medical
(insurance
and
additional
expenses)
$600
Clothing
8%
Entertainment
Savings
$320
Fixed
Variable
Amount
Expense Expense Available
($)
Housing
cost (house
payment and
Insurance!
$1,400
Food
15%
Answers
Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.
What happened during emergency repair of $305?4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.
5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.
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Full Question:
See attached image.
Reflect
4. Analyze Relationships One month, the family must make an
emergency car repair for $305. Are they able to pay for it out of the
fixed emergency fund for that month? If not, how can they afford it?
5. The family wants to make a trip to Houston to visit the NASA Space
Center. What are some ways they can save without using all of the
allotted $160 for entertainment
What is the diameter of a hemisphere with a volume of
8582
m
3
, to the nearest tenth of a meter?
Answers
Answer: The volume of a hemisphere is given by the formula:
V = (2/3)πr^3
where V is the volume and r is the radius.
However, in this case, we are given the volume of the hemisphere, not the volume of the full sphere. The volume of a hemisphere is half the volume of the full sphere, so we can find the volume of the full sphere and then use that to find the diameter.
The volume of the full sphere is:
V_sphere = 2V_hemisphere = 2(8582) = 17164 m^3
Using the formula for the volume of a sphere, we can solve for the radius:
V_sphere = (4/3)πr^3
17164 = (4/3)πr^3
r^3 = (3/4)(17164/π)
r ≈ 14.1 m
The diameter of the sphere is twice the radius, so:
d ≈ 2r ≈ 28.2 m
Therefore, the diameter of the hemisphere with a volume of 8582 m^3, rounded to the nearest tenth of a meter, is approximately 28.2 meters.
Step-by-step explanation:
Answer: 32
Step-by-step explanation: V=4/3pi r^3
17164(double the hemisphere)=4.1887902r^3
4097.6031648 = r^3
r=16.0
Diameter=32.0
The mean age of 7 boys is 12yrs. What is the total age of the boys?
Answers
Answer:
total age = 84 years
Step-by-step explanation:
mean is calculated as
mean = \(\frac{total}{count}\)
here count = 7 and mean = 12 , then
\(\frac{total}{7}\) = 12 ( multiply both sides by 7 )
total = 7 × 12 = 84 years
Antonio burns 75 calories for every 15 minutes
Answers
Answer is 5 calories/min
75 divided by 15 is 5
Answer:five cal per min.15 in five groups equals ''75''
Which equation is true?
Answers
An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication law of exponents for powers to each of the expressions, we have the following:
4 × n × n × n × n = 4n⁴
4 × n⁴ = 4n⁴
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match each equation to the number of distinct, real solution it has
Answers
a) We have the equation
\(\begin{gathered} x^2=49 \\ x=\sqrt[]{49} \\ x=\pm7\text{ (two real solutions: -7 and +7)} \end{gathered}\)b) This equation is similar to a), and have 2 real solutions.
\(\begin{gathered} x^2-74=0 \\ x^2=74 \\ x=\sqrt[]{74} \\ x\approx\pm8.6 \end{gathered}\)c) This equation can be factorized as:
\(\begin{gathered} x^2-10x+25 \\ x^2-2\cdot5x+5^2 \\ (x-5)^2 \end{gathered}\)It has one real solution (x=5).
d)
\(\begin{gathered} 3x^2-6x=29 \\ 3x^2-6x-29=0 \\ x=\frac{6\pm\sqrt[]{36-4\cdot3\cdot(-29)}}{2\cdot3}\text{ \lbrack{}applying the quadratic equation for the roots\rbrack} \\ x=\frac{6}{6}\pm\frac{\sqrt[]{36+348}}{6} \\ x=1\pm\frac{\sqrt[]{384}}{6}\longrightarrow\text{ Two real solutions.} \end{gathered}\)e)
\(\begin{gathered} 2x^2-6x+10=0 \\ 2(x^2-3x+5)=0 \\ x^2-3x+5=0 \\ x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot1\cdot5}}{2\cdot1} \\ x=\frac{3}{2}\pm\frac{\sqrt[]{9-20}}{2} \\ x=\frac{3}{2}\pm\frac{\sqrt[]{-11}}{2} \\ x=\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}\cdot\sqrt[]{-1} \\ x=\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}i\longrightarrow\text{ Two complex solutions (not real)} \end{gathered}\)In ΔGHI, g = 240 cm, m m∠H=157° and m m∠I=17°. Find the length of h, to the nearest 10th of a centimeter.
Answers
Check the picture below.
\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)
Make sure your calculator is in Degree mode.
Joy made a scale drawing of a tower using a scale of 1 foot = 218 millimeters. If the actual height of the tower is 56 feet, then what is the tower's height in Joy's drawing?
Answers
Answer:
its 119
Step-by-step explanation:
Mary, Margaret, Ron, and Nick are to share a scholarship. Ron receives 1/3 of the scholarship; Nick gets 1/4 of the scholarship; Mary receives the same as Nick, and Margaret receives $72,000.
Find each person's share in the scholarship as well as the original scholarship amount
Answers
Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.
Let's denote the original scholarship amount as "P."
According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.
Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).
Now, we can sum up all the shares to equal the original scholarship amount:
Ron's share + Nick's share + Mary's share + Margaret's share = P
(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P
To simplify the equation, we can combine like terms:
(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P
Combining the fractions and constants:
(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P
16P/12 - $48,000 = P
Multiplying both sides of the equation by 12 to eliminate the denominator:
16P - $576,000 = 12P
Subtracting 12P from both sides of the equation:
4P = $576,000
Dividing both sides of the equation by 4:
P = $144,000
Therefore, the original scholarship amount is $144,000.
Ron's share: (1/3)($144,000 - $72,000) = $24,000
Nick's share: (1/4)($144,000 - $72,000) = $18,000
Mary's share: (1/4)($144,000 - $72,000) = $18,000
Margaret's share: $72,000
Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.
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100 points!!!
Solve the following equation:
8x + 3 = 2x + 9
Answers
Answer:
\(\Huge \boxed{\boxed{ x = 1}}\)
Step-by-step explanation:
Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.
To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.
Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.
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SolutionStep1: Subtract \(\bold{2x}\) from both sides
\(8x + 3 = 2x + 9\)\(8x - 2x + 3 = 2x - 2x + 9\)\(6x + 3 = 9\)Step 2: Subtract 3 from both sides
\(6x + 3 - 3 = 9 - 3\)\(6x = 6\)Step 3: Divide both sides of the equation by 6
\(\frac{6x}{6} = \frac{6}{6}\)\(x = 1\)So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).
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