A: The exponential function for the situation is P(t) = 36,000 × (1 + 0.15)^t.
B: The population in 2020 was 72,396.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The population of a city in 2015 is 36,000 and it is increasing at 15% per year.
Model this using an exponential equation of the form -
P(t) = P0 × (1 + r)^t
Where -
P(t) is the population after t years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
t is the number of years since 2015
So the exponential equation that models the population is -
P(t) = 36,000 × (1 + 0.15)^t
Part B:
To find the population in 2020, substitute t = 5 (2020 - 2015) into the equation -
P(5) = 36,000 × (1 + 0.15)^5
P(5) = 36,000 × 1.15^5
P(5) = 36,000 × 2.011
P(5) = 72396
Calculating this gives us a population of approximately 72,396 in 2020.
To obtain this answer, the exponential equation that models the population, P(t), is used where t represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for t.
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1. Which method would be the simplest way to solve the system? y= 1/2x 2x+3y=28 A) graphing B) substitution C)elimination D) distributive 2.How many solutions does this system have?
Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.
The system of equation are:
y = 1/2x...................(1)
2x + 3y = 28...................(2)
To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.
Now putting the value of y in equation 2.
2x + 3(1/2x) = 28
2x + 3/2 x = 28
7/2 x = 28
Multiply by 2 on both side, we get
7x = 56
Divide by 7 on both side, we get
x = 8
Now putting the value of x in equation 1
y = 8/2 = 4
The solution of the system of equation is (8, 4).
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Can someone please help me with this please?
Click on image for full view
Answer:
Obtuse and isosceles
Step-by-step explanation:
Cuz 2 sides and angles are equal and there is one obtuse angle
Answer:
obtuse and isoscelies
Step-by-step explanation:
120 is greater than 90 so obtuse
isoscelies means to sides of equal length and one of different length
2 sides are 3ft and one is 5ft
Given 450 grams of bacteria that decreases at a rate of 1/2 per year, what would be an appropriate range after 3 years?
The approximate range will be 56.25 gm. after the end of 3 years.
As per the question,
We have, the value of the weight of the bacteria = 450 gm
As the rate of bacteria is decreasing with rate of 1/2
So, after 1 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 1 year will be = 450 *(1/2)=225
As the rate of bacteria is again decreasing with the rate of 1/2
So, after 2 years the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 2 years will be = 225 *(1/2)=112.5
As the rate of bacteria is decreasing with the rate of 1/2
So, after 3 year the number of bacteria will be half as it was at the start of the year.
So, the number of bacteria after 3 years will be = 112.5*(1/2)=56.25
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Find the measure of angle A in the figure below.
Answer: 40°
Step-by-step explanation:
A professional pool player claims that she sinks at least one ball in a pocket on 80% of her opening break shots. In a recent set of 20 games, she sunk at least one ball on her break shot in only 14 of the games. A simulation of 100 trials was conducted to see how unusual these most recent games are. A dotplot titled the professional pool player has number of games with at least one ball made on the break on the x-axis, and frequency on the y-axis. 10, 1; 12, 3; 13, 11; 14, 12; 15, 17; 16, 25; 17, 16; 18, 9; 19, 5; 20, 2. Based on the dotplot of the simulation results and the pool player’s last 20 games, which conclusion can be drawn?
There is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games and no convincing evidence that her average is less than 80%.
Based on the dot plot of the simulation results, it appears that the player's true probability of sinking at least one ball on her break is not 80%. In the simulation, there were only 12 trials out of 100 where the player sank at least one ball on her break 14 or fewer times in 20 games. This corresponds to a probability of 12/100, or 12%.
Since the player's actual performance in the last 20 games (14 out of 20) is less likely to occur than what was observed in the simulation, we can get the conclusion that the player has a lower than 80% chance of sinking at least one ball during her break.
Therefore, the correct conclusion is, "there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. This result is not unusual and there is no convincing evidence that her average is less than 80%."
The question is incomplete. The complete question is 'The player’s true probability of sinking at least one ball on her break is 27%. another 100 simulated trials would show a much different outcome; therefore, we cannot draw any conclusions. it is most likely that she would sink at least one ball during her break exactly 16 times. there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. this result is not unusual and there is no convincing evidence that her average is less than 80%.'
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Answer:
d
Step-by-step explanation:
edge 2020
The smallest gecko on record is 0.8 inch long. Sarah's drawing has a scale factor of 1 inch to 0.1 inch. Which equation could be used to find g, the length of Sarah's drawing of the gecko?
The length of Sarah's drawing is given by the following equation:
0.1g = 0.8.
How to obtain the scale of the drawing?The scale of the drawing is obtained applying the proportions in the context of this problem.
The scale is defined as the division of the drawn length by the actual length.
Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.
The rule of three is defined as follows:
1 inch - 0.1 inches
g inches - 0.8 inches
Hence the equation is:
0.1g = 0.8.
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What do I put in the boxes?
The values in the result of the division operation, 7 ÷ 6 are as follows;
The quotient = 12
The remainder = 4
Please find attached the diagram with the correct values in the boxes created with MS Word
What is the quotient in a division operation?The quotient is the result following the complete division by the devisor. The remainder is the part of the dividend yet to be divided by the divisor.
The division operation is 76 ÷ 6
The quotient is the integer value obtained following the division operation of 76 by 6 which is 12 times. Therefore, the quotient is 12
The values in each box are therefore;
The value at the top left box, is 10
The value in the box below 2 and to the right of 60 is 12
The value outside to the top right of the rectangle is the remainder
The remainder is the difference between the dividend and the product of the quotient and the divisor as follows;
Remainder = 76 - 12 × 6 = 4
The remainder is 4
Please find attached a drawing of the figure, created with MS Word, showing the values that are to be placed in the boxes
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70%
60%
50%
40%
30%
20%
10%
0%
Federal Government Funding of Stem Cell Research
55%
58%
52%
Should fund
41% 39%
44%
Should not fund
4%
Total
Men
Women
3% 4%
No opinion
1. There are about 117,000,000 adult American men. About how many of these men
think the federal government should fund stem cell research?
Based on the given percentages, the number of adult American men who think the federal government should fund stem cell research is 67,860,000.
What is the percentage?The percentage is the ratio of a value in relation to another.
The percentage is determined as the quotient of the numerator divided by the denominator, multiplied by 100.
The percentage of men who approve of stem cell research = 58%
The percentage of men who do not approve of the research = 39%
The percentage of men who have no opinion on the research = 3%
The estimated number of adult American men = 117,000,000
Thus, based on the percentage of men who approve of stem cell research, the number is 67,860,000. (117,000,000 x 58%).
Federal Government Funding of Stem Cell Research
Total Men Women
Should fund 55% 58% 52%
Should not fund 41% 39% 44%
No opinion 4% 3% 4%
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on two tosses of a coin, what is the probability of head on 1st toss or head on 2nd toss (assume all outcomes are equally likely)
As an alternative, we could contend that the probability of the first coin coming up heads or tails is 1/2, the probability of the second coin coming up heads or tails is 1/2, and so on for the third and fourth coins.
This would reduce the probability of any given sequence of heads and tails to (1/2)x(1/2)x(1/2)x(1/2)=(1/16).
The curve achieves its greatest value for N=2 heads, which is the case where the outcome is most likely. This is exactly what you would anticipate: if each coin has an equal chance of landing heads or tails, then in four flips, half of the results should be heads, making N = 4x(1/2) = 2 the most likely result.
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Hector's net pay, after a $122.00 automatic savings withdrawal, is $1,413.00. Determine the percent of Hector's net pay that is automatically withdrawn for savings. a 7.9% b 8.0% c 9.1% d 9.5%\
The percent of Hector's net pay that is automatically withdrawn for savings is 7. 95 %
How to find the percentage ?To find the percentage of Hector's net pay that is being withdrawn for savings in an automatic manner, the formula is:
= Amount withdrawn for savings / Pay before amount is withdrawn x 100 %
Amount withdrawn for savings = $ 122
Pay before amount is withdrawn :
= 1, 413 + 122
= $ 1, 535
The percentage withdrawn is :
= 122 / 1, 535 x 100%
= 7. 95 %
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Help I can’t find the answer. Which math expression means "the product of 33 and 18"?
О A. 33 • 18
О B. 33 ÷ 18
O C. 33 + 18
• D. 33 - 18
Answer:
A. 33 • 18
Step-by-step explanation:
Product means multiplication
There are different symbols that are used for denoting multiplication and the dot (•) symbol is one of them
So 33 • 18 is same as 33 x 18 which is the product of 33 and 18
What expression and quotient does the diagram model?
Answer:
The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.
Which expression and quotient is depicted by the diagram model as in the task content?
It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).
Additionally, the dividend in the quotient by observation is the sum of terms as follows;
x² + x +x -x -1 -1 = x²+x -2.
Ultimately, the result of the division according to the model is; (x +2).
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Step-by-step explanation:
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow. Therefore, option D is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Here,
Probability of landing on orange is 1/8
Probability of landing on purple is 2/8 =1/4
Probability of landing on yellow is 2/8 =1/4
Probability of landing on blue is 3/8
Therefore, option D is the correct answer.
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need help algebra 2. write in rational exponent form
The rational exponent form is 5^3/5x. Option D
What is the rational exponent form?We know that a rational function would be the function that does not have the radical sign in it. We can see that we have the expression that have been written for us here as; 5√125x^5.
When we open up the radical we would have;
125^1/5 * 5^5/5
But we know that;
125 = 5^3
We now have;
5^3/5 * x
This becomes;
5^3/5x
Thus we are going to end up in the rational exponent form of the expression as 5^3/5x.
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if you are driving from vegas to los angeles, how fast would you need to drive to make it there in 3.5 hours?
You need to drive 122.86 km/ h to driving from Vegas to los Angeles in 3.5 hours
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 430 km (distance from Vegas to los Angeles)t = 3.5 hoursv = ?Applying the velocity formula, we get:
v = x /t
v = 430 km / 3.5 h
v = 122.86 km/ h
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Question 15 of 46
What identity can be used to rewrite the expression 4x² - 9?
A. Difference of Squares
B. Sum of Cubes
C. Difference of Cubes
D. Pythagorean Triples
SUBMIT
Answer:
A.
Step-by-step explanation:
4x² is a perfect square because it is (2x)²
9 is a perfect square with a value of 3
so if we factor 4x² - 9 we can use the difference of two squares to get:
(2x+3)(2x-3)
Radiotelescopes
reveal that space
is full of:
Answer: No real "space" exists. There is plenty of air all around us
Step-by-step explanation: I'm sorry If I am wrong tysm
-☈⊙⌘☿
Answer:
cosmic microwave background radiation
Step-by-step explanation:
suppose the die is tossed and we are told that the result is a number greater than 4 4 . based on this information, what is the probability that the result was a 6 6 ?
The probability that the result was a 6 is P(A)=1/3 the die is tossed and we are told that a result is a number greater than 4.
A standard 6-sided die numbered 1 to 6 has 2 sides that meet the criterion of greater than 4, which are 5 and 6. So out of 6, there are 2 ways.
A die has 6 faces with the numbers 1,2,3,4,5 and 6 on each of the six faces. Now consider an unbiased die and the probability of any of the faces appearing in a single roll is 1/6.
So,
P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6
The numbers that are greater than 4 are 5 and 6
So it can be P(5) or P(6)=
P(5)+P(6)=2/6=1/3.
If you had stated at least a 4, then there are three chances which are to be 4,5,6 that meet the criterion, and the chance would be 3/6=1/2.
Hence, by the classical definition of probability, the probability of getting a number more than 4 in a single throw of a die is 1/3.
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True or false
The following graph represents a maximum:
f(x)=3x^2+2
Answer:
False
Step-by-step explanation:
Answer come only two
Complete the table and write the question
A linear equation representing the data in table is t(n) = 12x + 23.
The missing values in table should be completed as follows;
n t(n)
4 71
5 83
How to write the equation and complete the table?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.
x and y are the data points.
Next, we would determine the linear equation representing the data in table which passes through the points (1, 24) and (2, 36) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 24 = (36 - 24)/(2 - 1)(x - 1)
y - 24 = 12(x - 1)
y = 12x - 1 + 24
y = t(n) = 12x + 23
When the value n = 4, the value of t(n) can be calculated as follows;
t(4) = 12(4) + 23
t(4) = 71.
When the value n = 5, the value of t(n) can be calculated as follows;
t(5) = 12(5) + 23
t(5) = 83.
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Find the average rate of change of y=0.5x-3 over the interval -3(equal to or <)x(equal to or <)4
The value of average rate of change of y = 0.5x - 3 over the interval
- 3 ≤ x ≤ 4 is, 0.5.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ y = 0.5x - 3
Now, The average rate of change is,
⇒ y = 0.5x - 3
⇒ dy / dx = 0.5
Hence, The value of average rate of change of y = 0.5x - 3 over the interval - 3 ≤ x ≤ 4 is, 0.5.
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Which recursive sequence would produce the sequence 5, -17, 71, ...?
The recursive sequence that would produce the sequence 5, -17, 71, is by multiplying the previous term by -4 and adding 3.
What is a sequence?A recursive sequence is a sequence where each term is defined as a function of the preceding term(s).
Given the sequence 5, -17, 71, ..., we can see that the next term in the sequence is obtained by multiplying the previous term by -4 and adding 3.
Therefore, the recursive sequence that produces this sequence is:
a_1 = 5
a_n = -4a_{n-1} + 3 where n > 1
This means that the first term of the sequence is 5, and each subsequent term is obtained by multiplying the previous term by -4 and then adding 3.
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For the given region, calculate the shaded area. You can assume right angles.
The area of the shaded region is equal to 116 sq units.
It is given that we can assume the angles to be right angle. So from the fig we can see that it is a quadrilateral and length and breadth for the given figure are different. So the given fig is a rectangle.
The area of a rectangle = length × breadth
∴ The area of the bigger rectangle = 10×20=200 sq units
Similarly,
The area of the smaller rectangle = 14 × 6 = 84 sq units
Now,
The area of the shaded region = Bigger rectangle - Smaller rectangle
⇒ 200 - 84 = 116 sq units
Therefore, The area of the shaded region is equal to 116 sq units.
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Lawrence worked 12 days for a total of 112.8 hours. How many hours did he average per day?
Answer:
112.8 hours / 12 days
112.8/12 = average of 9.4 hours per day
David wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 37 ft from the tree, and
David is standing 9.3 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
(The figure is not drawn to scale.)
6 ft
9.3 ft
37 ft
X
David's method to find the height of the tree is the use of the properties of similar triangles. The height of the tree is approximately 24 feet
Laws of ReflectionAccording to the laws of reflection, we have;
Angle of incidence of the light from the top of the tree = Angle of the reflected light ray David sees.
The possible values in the question are;
Distance of the mirror from the tree = 37 feet
Distance from where David is standing to the mirror = 9.3 ft.
Height of his eyes above the ground = 6 ft.
Required: Height of Tree
Therefore;
The triangle formed by David's height, the reflected ray from the mirror and his distance from the mirror is similar to the right triangle formed by the tree, which by the relationship of similar triangles, gives;
[tex]\frac{9.3}{37}[/tex] = [tex]\frac{6}{Height of the Tree}[/tex]
Height of the tree × 9.3 = 6 × 37
Height of the tree = [tex]\frac{6 X 37}{9.3}[/tex] = 23.87 ≅ 24 feet
Therefore, the tree is approximately 24 feet tall
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Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank.
Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent. What is the total price he has to pay for the clothes?
Step 1: (Original Price)(Tax Percent) = Amount of Tax
Step 2: Original Price + Amount of Tax = $
The total price he has to pay for the clothes is 27.83
What is Percentage ?
Percentage can be defined as the product ratio of given value, total value and hundred.
Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank.
Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent.
If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05)
which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.
Therefore, The total price he has to pay for the clothes is 27.83
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Solve the quadratic equation using the square root method:
-108 = (x-11)^2 +13
Answer:
[tex]\sf x=11+11i\\x=11-11i[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]\sf -108=(x-11)^2+13[/tex]
Subtract 13 from both sides:
[tex]\implies \sf -108-13=(x-11)^2+13-13[/tex]
[tex]\implies \sf -121=(x-11)^2[/tex]
Switch sides:
[tex]\implies \sf (x-11)^2=-121[/tex]
[tex]\textsf{For $(g(x))^2=f(a)$ the solutions are $g(x)=\pm\sqrt{f(a)}$}[/tex]
[tex]\implies \sf x-11=\pm \sqrt{-121}[/tex]
Rewrite -121 as 11² · -1 :
[tex]\implies \sf x-11=\pm \sqrt{11^2 \cdot-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sf x-11=\pm\sqrt{11^2} \sqrt{-1}[/tex]
[tex]\implies \sf x-11=\pm11\sqrt{-1}[/tex]
[tex]\textsf{Apply\;imaginary\;number\;rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \sf x-11=\pm11i[/tex]
Add 11 to both sides:
[tex]\implies \sf x=11\pm11i[/tex]
Therefore, the solutions are:
[tex]\implies \sf x=11+11i[/tex]
[tex]\implies \sf x=11-11i[/tex]
An architect is designing a new windmill with four sails. In his sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point Upper R,
has coordinates (2,-4).
He wants to make another sketch that shows the windmill after the sails have rotated 180 degrees about their center of rotation. What would be the coordinates of Upper R prime ?
The coordinates of Upper R prime would be ______?
The coordinates of upper R prime are (-2, 4).
Now, According to the question:
Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.
The sails center of rotation is the origin (0,0)
The top of one sails point R(2, -4).
A 180 degree rotation make you turn (x, y) into (-x, -y),
So, the point turn (2,-4 ), into (-2, 4).
Therefore the coordinates of R are (-2, 4).
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Can you help me please thank you so much.
Answer: It is the last one on he far right.
Step-by-step explanation:
;)
Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for X, Y, and Z
The value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft. The solution has been obtained by using the properties of triangle.
What is a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to a total of 180 degrees.
We know that if a line is parallel to the third side of the triangle, then the ratio of the sides is equal.
So,
⇒10/6 = x/8
⇒80/6 = x
⇒40/3 = x
Similarly,
⇒y/10 = 9/(40/3)
⇒y/10 = 27/40
⇒y = 27/4
Similarly,
⇒y/(y+10) = 7/z
⇒(27/4)/((27/4)+10) = 7/z
⇒469/27 = z
Hence, the value of X is 40/3ft, Y is 27/4ft and Z is 469/27ft.
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