An exponential function would be more appropriate than a linear function, as exponential growth
the best function for the dataTo determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.
Differences between consecutive y values:
16,357.04 - 14,944.54 = 1,412.50
17,974.72 - 16,357.04 = 1,617.68
19,891.18 - 17,974.72 = 1,916.46
The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.
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I need help please
here is the picture is about Row Ops
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
From the given information, the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
We are to carry out the operation
Add -4(row 1) to row 3
This means we should multiply row 1 by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result to row 3
4 -1 6 | -8
-4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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f(x)=4x-3
g(x)-3x+3
find f(9)/g(9)
For the following exercises,
(a) find the angle between 0 and 2π in radians that is coterminal with the given angle.
(b) find the reference angle of each one.
a)32π/13 b)-17π/6
The reference angle of given angles are -6π/13 and -5π / 6
To get coterminal angles, you simply have to add or subtract 2π.
a) 32π/13 =
= -32π/13 + 2π
= -32π + 26π / 13
= -6π/13
b) -17π/6 + 2π =
= -17π + 12π / 6
= -5π / 6
Hence the reference angle of given angles are -6π/13 and -5π / 6
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when the sun is 35° above the horizon. how long is the shadow cast by a building 15 metres high?
Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.
What is trigonometry?Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).
Here,
When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).
Let x represent the desired shadow's length. Next, we have
=> tan 35° = 15/x
When we multiply both sides by x, we obtain:
=> x tan 35° = 15
By dividing both sides by 35° of tan, we obtain:
=> x = 15 / tan 35°
We may calculate the value of the tangent of 35 degrees using a calculator:
=> tan 35° ≈ 0.7002
Next, we have
=> 15x/0.702x=21.424 metres
Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.
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Ignatio and his two friends each bought a ticket to play lazer tag and each spent $15 on game tokens at Fun Mountain. Let t represent the cost of a lazer tag ticket. Enter an expression that represents the total amount that Ignatio and his friends spent.
The expression that represents the total amount that Ignatio and his friends spent is 15t
From the question, we have the following parameters that can be used in our computation:
Each spent $15 on game tokens at Fun MountainEach cost = tAfter spending on t games, we have
f(t) = Rate * t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 15 * t
Evaluate
f(t) = 15t
Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t
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Help Please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answer:
the number is even
Step-by-step explanation:
an even number plus an even number will aalways be even. adding 6 to an odd number will never be even. Therefore the number will be even
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²
where k is the proportionality constant.
In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.
In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:
Strength = k * width * depth² = k * x² * (d/2 - x)²
where x is the width and depth of the beam.
In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:
Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²
where θ is the angle at which the beam is cut from the log.
In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:
w = d sinθ
d = (d/2)cosθ
Then we can express the strength of the beam as:
Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²
Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.
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Complete question is:
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
El perímetro de un campo rectangular es 300 m . Si la longitud del campo es 88 , ¿cuál es su anchura?
Based on the above, the width of the field is 62 meters.
What is the width?Based on the question, Let's say that the width of the field is denoted with 'w'.
Note that the formula for the perimeter (P) of a rectangle is:
P = 2(l + w)
where"
l = length
w = width.
Fixing the values into the equation, it will be:
300 = 2(88 + w)
So, Divide both sides by 2:
150 = 88 + w
Subtract 88 from both sides:
w = 150 - 88
w = 62
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Se text below
The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?
Suppose a city with population 500,000 has been growing at a rate of 4.3% per year. If this rate continues, find the population of this city in 10 years
In the Show Your Work box, must have the following:
- 1 pt- Formula used
- 1 pt- Variables and what they stand for
- 3 pts- Full solving process
Answer:
t = time in years
p(t) = population at time t
[tex]p(t) = 500000( {1.043}^{t} )[/tex]
[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]
An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.
To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.
Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.
To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.
The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.
Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.
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The complete question is:
An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
In the diagram below, BE intersects AD at C, AB | DE. If CD = 4.2 and AB = 9.6, what is the length of
BC to the nearest tenth of a centimeter?
Dont mind the writing
The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.
How to Find the Length of the Indicated Side?Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:
AC/CE = BC/CD
Given the following:
AC = 7.2 units
CE = 2.4 units
CD = 4.2 units
BC = ?
Plug in the values:
7.2/2.4 = BC/4.2
Cross multiply:
BC = 7.2 * 4.2 / 2.4
BC = 12.6 cm
Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.
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15 POINTS!! ASAP TYYY
Answer:
A
Step-by-step explanation:
She earns $15 per poinsettia.
3. Find the solution to each equation mentally.
a. 30+ a = 40
b. 500+ b = 200
C. -1+c= -2
d. d +3.567=0
Answer:
[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]
hope it helps:)
A meter in a taxi calculates the fare using the function f(x) = 2.56x + 2.40. If x represents the length of the trip, in miles, how many miles can a passenger travel for $20?
A passenger can travel 6.875 miles for $20 using the given taxi fare function.
To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.
The equation we need to solve is:
2.56x + 2.40 = 20
To solve for x, we can start by subtracting 2.40 from both sides of the equation:
2.56x = 17.60
Next, we can divide both sides by 2.56:
x = 6.875
This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.
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Help please connect the left to the right for each component
f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.
What is a linear equation?An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:
ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.
The given situation can be expressed in the form f(x) = mx + b.
Where,
f(x) = the total cost for detailing the car.
x = the number of minutes it takes to detail the car.
m = The cost per minute for the detailing in car.
b = the flat fee for detailing the car.
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Use Chebyshev’s inequality and the value of W to decide whether there is statistical evidence, at the significance level of α=0.05 , that D, the average proportion of all lightbulbs that are defective, is greater than 0.10.
Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.
Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.
Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,
P(|X - μ| ≥ kσ) ≤ 1/k²,
where μ and σ are the mean and standard deviation of X, respectively.
Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.
Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,
P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,
where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,
P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².
To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.
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James answered 14 lems correctly
an a 16-item quiz. what percentage did he answer correctly
Answer:
14/16 = 0.875
(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
she needs to clean 15 uniforms to break even
Which expression is equivalent to (x-3)(2x^(2)-3x-1)
The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.
In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).
We have to find the equivalent-expression for (3x-1)-2(x+2);
⇒ (3x-1)-2(x+2),
⇒ (3x - 1) - 2x - 4,
Combing the like-terms together in the above expression,
We get,
⇒ 3x - 2x -1 - 4,
⇒ x - 5,
Therefore, the correct equivalent expression is Option (c).
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The given question is incomplete, the complete question is
Which of the following expression is equivalent to (3x-1)-2(x+2)?
(a) x+3
(b) x+1
(c) x-5
(d) x-3
Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment
Answer:
$640
Step-by-step explanation:
You want to know the income tax reduction resulting from investing $3200 in a defined-contribution account when the marginal tax rate is 20%.
Tax exemptThe money invested in a defined-contribution account is not subject to income taxes when it is invested. The tax savings is ...
20% × $3200 = $640
Jermaine lowered his taxes by $640.
Using the GCF, what is the factored form of 75 - 3x?
please i need help!!!
u will get 100 points!!!
The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. In this case, we can find the GCF of 75 and 3 by listing their factors and finding the largest one they have in common. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 3 are 1 and 3. The largest factor they have in common is 3. Therefore, the GCF of 75 and 3 is 3.
We can use the GCF to factor the expression 75 - 3x by dividing each term by the GCF and writing the expression as a product. In this case, we can divide both terms by 3 to get 75/3 - (3x)/3, which simplifies to 25 - x. We can then write the original expression as a product by multiplying this simplified expression by the GCF: 3(25 - x).
Therefore, the factored form of 75 - 3x using the GCF is 3(25 - x).
Answer:
3(25-x)
Step-by-step explanation:
First we find the GCF of 75 and -3x, which is 3
3 is the highest number we can divide both 75 and -3
Hence, the answer is 3(25-x)
Identify the null and alternative hypotheses
Statistics!
The null and the alternate hypothesis are:
H₀: p ≤ 0.5H₁: p > 0.5How to write the hypothesisIn hypothesis testing, we take the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is the opposite of the claim , while the alternative hypothesis states the claim.
In this case, the null hypothesis is that a majority of adults would not erase their personal information online if they could (i.e., 50% or less of them would do so). The alternative hypothesis is that a majority of adults would erase their personal information online if they could (i.e., more than 50% of them would do so). In symbolic form:
H₀: p ≤ 0.5
H₁: p > 0.5
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determine the values of the six trigonometric functions of (- pi / 2 )
with work shown please.
Answer:
[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = -1\\\\[/tex]
[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)= 0\\\\[/tex]
[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = -\dfrac{1}{0}[/tex] is not defined
[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) =-1\\\\[/tex]
[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac {1}{0}\\[/tex] is not defined
[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) =\:0[/tex]
Step-by-step explanation:
[tex]\text{Values of trig functions for $-\dfrac{\pi}{2}$ are: }\\\\[/tex]
[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = - sin\left(\dfrac{\pi}{2}\right) = -1\\\\[/tex]
[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)=\cos \left(\dfrac{\pi }{2}\right) = 0\\\\[/tex]
[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = \dfrac{sin\left(-\dfrac{\pi}{2}\right)}{cos\left(-\dfrac{\pi}{2}\right) } = \dfrac{-1}{0}[/tex]
This is undefined since division by zero is undefined
[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{sin\left(-\dfrac{\pi }{2}\right)} = \dfrac{1}{-1} =-1\\\\[/tex]
[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{\cos\left(-\dfrac{\pi }{2}\right)} = \dfrac {1}{0}[/tex]
This is undefined
[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) = \dfrac{cos\left(-\dfrac{\pi }{2}\right)}{sin\left(-\dfrac{\pi }{2}\right)}\:=\:\dfrac{0}{-1\:}=\:0[/tex]
Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been if she had worked the problem correctly?
Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.
How is the correct value determined?The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:
(x - 9) ÷ 3 = 43
x = 43 x 3 + 9
x = 138
With the certain number, x = 138, the correct mathematical operations can be performed as follows:
Correction Operation:(138 - 3) ÷ 9
135 ÷ 9
= 15
Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.
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Girish left his home at 7 45 and travelled to Muar, which was 120 km away. He arrived
at Muar 2 h later. After staying 1 2/3 hours in Muar, he travelled from Muar back to his home
along the same route at a speed which was 20 Km/h slower than his previous speed.
At what time did Girish reach home?
Answer:
2:35
Step-by-step explanation:
it takes 2 hours to get to Muar so 9:45
he spends 1 hour 40 in muar so 11:35
he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35
Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
A population of values has a normal distribution with a mean of 246 and a standard deviation of 89.7. You intend to draw a random sample of size m = 158.
Answer the following, rounding your answers to three decimals where appropriate.
Find the probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4.
P(M>242.4) = ???
The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.
How to calculate the probabilityz = (x - μ) / (σ/√n)
where x is the sample mean.
Substituting the values, we get:
z = (242.4 - 246) / (89.7/√158) ≈ -0.670
We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.
P(z > -0.670) ≈ 0.751
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Which of these expressions is equivalent to log (128^)?
OA. log (8) - log (12)
OB. 8 log (12)
C. log (8) log (12)
D. log (8) + log (12)
.
The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.
The likelihood that the first question will be true is equally likely and unlikely.
Interpreting the likelihood that the first question will be true.From the question, we have the following parameters that can be used in our computation:
The teacher gave a true and false quiz where P(true) = 0.5 for each question.
This means that
P(true) = 0.5
As a percentage,, we have
P(true) = 50%
When the probability of an event is 50%, then the event is equally likely and unlikely.
Hence, the liikelihood is (c) qually likely and unlikely.
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Encik Halim bought 108 lemons to sell at his grocery shop. He packed 3 lemons in small packets and sold at the price of RM6.80 per packet. If he made a total profit of RM88.20, calculate the price of each lemon bought by him.
Answer:
the price of each lemon bought by Encik Halim is RM1.45.
Step-by-step explanation:
Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.
Let's assume that the cost of each lemon bought by Encik Halim is x RM.
The total cost of 108 lemons would then be 108x RM.
Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.
We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:
Total cost = Total revenue - Profit
Total cost = RM244.80 - RM88.20
Total cost = RM156.60
We know that Encik Halim bought 108 lemons, so we can write:
Total cost = Number of lemons bought x Cost per lemon
RM156.60 = 108x
Therefore, the cost per lemon bought by Encik Halim is:
x = RM156.60/108
x = RM1.45
So the price of each lemon bought by Encik Halim is RM1.45.