By first calculating the size of angle LMN,
calculate the area of triangle MNL.
You must show all your working.
I
+
M
4.8 cm
Answer cm²
38/43 Marks
L
8
7.2 cm
38°
14%
Not drawn
to scale
N

Answer:

To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.

Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.

So, dividing 32 by 4, we get:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.

Step-by-step explanation:

Emma's profit from selling the stock is $743.44.

To find out Emma's profit from selling the stock, we need to calculate the total cost of purchasing the stock and the total revenue from selling the stock. Then we can subtract the total cost from the total revenue to get the profit.

Total cost of purchasing the stock:

Emma bought 300 shares of the stock for $39.22 per share plus a 1 percent commission.

Commission = 1% of (300 x $39.22) = $117.66

Total cost = (300 x $39.22) + $117.66 = $11,871.66

Total revenue from selling the stock:

Emma sold 300 shares of the stock for $46.54 per share plus a commission of $49.95 plus $24 per share.

Commission = $49.95 + (300 x $24) = $7,449.95

Total revenue = (300 x $46.54) - $7,449.95 = $12,665.05

Profit:

Profit = Total revenue - Total cost - Commission

Profit = $12,665.05 - $11,871.66 - $49.95 = $743.44

Therefore, Emma's profit from selling the stock is $743.44.

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Emma received $6,512.05 after selling the 300 shares of stock in the fast food company.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To calculate the total amount Emma paid for the stock, we first need to calculate the commission she paid when she purchased it:

1% commission = 0.01 * 39.22 = 0.3922

Total cost per share = 39.22 + 0.3922 = 39.6122

So, Emma paid $39.6122 per share when she bought the stock.

To calculate the total amount she received for selling the 300 shares, we need to first calculate the commission she paid for selling it:

Commission per share = 24

Total commission = 300 * 24 + 49.95 = 7,449.95

The total amount she received for selling the shares is:

300 * 46.54 = 13,962

Therefore, the total amount of money Emma received after selling the shares and paying the commission is:

13,962 - 7,449.95 = 6,512.05

Therefore, emma received $6,512.05 after selling the 300 shares of stock in the fast food company.

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The cοοrdinates οf the image if triangle ABC is A′(0, 1), B′(8, 1), C′(4, 5).

A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.

A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with vertices A, B, and C is knοwn as triangle ABC. Any three pοints in Euclidean geοmetry that are nοt cοllinear result in a distinct triangle and a distinct plane.

The cοοrdinates οf the image if triangle ABC is translated 8 units tο the right are:

A′(0, 1), B′(8, 1), C′(4, 5).

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P(-2.33 ≤ z ≤ 2.33) = 0.98 for a standard normal random variable Z.

We are aware that the area under the curve between - and - is equal to 1 for a standard normal random variable Z.

The task of finding a number for z0 such that P(-z0 z z0) = 0.98 is given to us.

We can divide the area of 0.98 evenly between the two tails of the distribution since the normal distribution is symmetric around the mean.

(1 - 0.98 / 2) = 0.01 would be the area in each tail.

We can determine the z-score that corresponds to the area of 0.01 by using a calculator or a conventional normal distribution table. An area of 0.01 equates to a z-score of roughly -2.33.

Thus, z0 would have the value:

z0 = -(-2.33) = 2.33

Hence, for a typical normal random variable Z, P(-2.33 z z 2.33) = 0.98.

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The solution for the given system of equations is (1,0) using the addition method.

The addition method, also known as the elimination method, is a technique used to solve a system of linear equations by adding the two equations together in such a way that one of the variables is eliminated.

Multiply the first equation by -2:

-10x - 12y = -10

Add the second equation to the first:

-10x - 12y = -10

10x + 12y = 10

0 + 0 = 0

We can solve one of the original equations for x in terms of y and then replace into the equation to represent the solutions in terms of y. For instance, when we solve the first equation for x, we obtain:

5x + 6y = 5

5x = 5 - 6y

x = (5 - 6y)/5

By substituting this into the second equation, we get:

10x + 12y = 10

10((5 - 6y)/5) + 12y = 10

2(5 - 6y) + 12y = 10

10 - 4y = 10

-4y = 0

y = 0

So the solution to the system is (x, y) = ((5 - 6y)/5, y) = (1, 0)

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F1 = 1167.35N and F2 = 1932.65N are the contact support forces on the beam

For the torques, let the axis be at support 2 and consider torques and the counterclockwise rotation is positive.

Let m = mass of athlete and M = mass of beam.

Thus, the equilibrium of torques will be:

Mg(1.96) - mg(0.54m) - F1(3.92) = 0

Substitute the values and solve for F1:

(250 * 10 * 1.96) - (60 * 10 * 0.54) - 3.92F1 = 0

3.92F1 = 4900 - 324

3.92F1 = 4576

F1 = 1167.35N

Note: The weight of the beam is acting at the center and the distance from center to axis at support 2 is 1.96m.

Balancing forces in the vertical direction, we have:

F1 + F2 - Mg − mg = 0

1167.35 + F2 - (250 * 10) − (60 * 10) = 0

1167.35 + F2 - 2500 - 600 = 0

F2 = 1932.65N

Note: upward forces (supports) are positive and downward forces are negative.

Thus, the contact support forces on the beam are F1 = 1167.35N and F2 = 1932.65N.

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Answer: 9g+10

Step-by-step explanation:

Simple addition 6+3=9

Since 10 doesnt have a variable you just add it to the end of the equation, make sure to keep the sign = 9g-10

3.5

you plug in 1 in the x spot then solve

3.5 (1)

which then equals 3.5

that means that's what Y equals

Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.

Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:

=> s =√((h²) + ((w/2)²))

We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.

The following formula can be used to determine how much steel tubing is required:

=>  L = 3s + 3h

where h is the height of the frame and s is the length of each edge of the triangle.

Using the method instead of s, we obtain:

=> L = 3(√(h²) + ((w/2²))) + 3h

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The function values increase in size in a positive direction and decrease in size in a negative direction.

The following two statements can be used to describe how the function in the given graph ultimately behaves:

The function gets closer to positive infinity as x gets closer to negative infinity. This is the case since the graph's left end is pointed upward, showing that as x decreases, the function values increase in size in a positive direction.

The function becomes closer to negative infinity as x gets closer to positive infinity. This is the case since the graph's right end is pointing downward, showing that as x increases in value, the function values decrease.

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Given- Square root of 14 multiplied by square root of 10

To find - which is equivalent to the product below

Explanation - We can write the square root of 14 as

[tex]\sqrt{14} =\sqrt{2} \sqrt{7}[/tex]

and square root of 10 as

[tex]\sqrt{10} =\sqrt{2} \sqrt{5}[/tex]

Now

[tex]\sqrt{14} \sqrt{10} =\sqrt{2} \sqrt{5} \sqrt{2} \sqrt{7} =2\sqrt{35}[/tex]

Hence the choice is equivalent is D

Final answer - The final answer is D

Answer:

The distance between the student and the mirror is 7.5 feet.

Step-by-step explanation:

We can use similar triangles to solve this problem.

Let's call the distance between the student and the mirror "d". We can create a right triangle with the student's height as one leg, the distance "d" as the other leg, and the hypotenuse being the line from the student's eyes to the top of the school. Let's call the length of this line "h".

We can also create a second right triangle with the height of the school as one leg, the distance from the school to the mirror as the other leg, and the hypotenuse being the same line from the student's eyes to the top of the school.

Since these two triangles share an angle (the angle formed by the line from the student's eyes to the top of the school and the ground), they are similar triangles. This means that the ratios of their corresponding sides are equal.

We can set up the following proportion:

(student height) / d = (school height) / (distance from school to mirror)

Plugging in the given values, we get:

4.5 / d = 30 / 50

Simplifying, we get:

4.5 / d = 3 / 5

Cross-multiplying, we get:

3d = 22.5

Dividing by 3, we get:

d = 7.5

Therefore, the distance between the student and the mirror is 7.5 feet.

The distance of the student to the mirror, is 7.5 ft

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given that, a mirror is placed outside a school the distance from the school to the mirror is 50 ft and the height of the school is 30 ft we need to find the distance of the student to the mirror,

This arrangement is creating two similar triangles, here we will use the properties of the similar triangles, to find the distance of the student to the mirror,

Therefore,

30 / 4.5 = 50 / d

d = 50 x 4.5 / 30

d = 225 / 20

d = 7.5

Hence, the distance of the student to the mirror, is 7.5 ft

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The frequency distribution is calculated below

The dataset is given as

32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.

To construct a frequency distribution using class intervals, we calculate the class width as follows:

Class width = Range / Number of intervals

So, we have

Class width = (48 - 18)/5 = 6

Now we can construct the frequency distribution table:

Class Interval Frequency

18 - 23            9

24 - 29            8

30 - 35            9

36 - 41             7

42 - 47            6

48 - 53             1

The class mark for each class can be calculated as:

Class mark = (Lower limit + Upper limit) / 2

For the class boundaries, we use the following formula

Lower boundary = Lower limit - 0.5

Upper boundary = Upper limit + 0.5

For the cumulative frequency of the distribution, we need to add up the frequencies of each class and all the preceding classes.

Lastly, for the relative frequency we divide each frequency by the total frequency (40)

Using the above as a guide, we have

Interval Frequency   Boundaries Mark CF

18 - 23            9              17.5 - 23.5        20.5        9

24 - 29            8             23.5 - 29.5       26.5        17

30 - 35            9              29.5 - 35.5      32.5        26

36 - 41             7              35.5 - 41.5        38.5       33

42 - 47            6              41.5 - 47.5         44.5       39

48 - 53             1              47.5 - 53.5        50.5       40

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The exponential function that best models the value of the stock after n weeks is given as follows:

v(n) = 1600(1 + r)^n.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The initial investment was of 1600, hence the parameter a is given as follows:

a = 1600.

The rate of change is obtained multiplying two consecutive values on the table, and will have the following format:

b = 1 + r.

In which r is the growth rate.

The problem is incomplete, hence the general procedure to obtain the function is presented.

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The function P(t) = 3.5(0.91)^t is an exponential decay and the percentage rate of change is 9%.

option B.

The function P(t) = 3.5(0.91)^t is an exponential decay function because the base, 0.91, is between 0 and 1.

To find the percentage rate of change, we need to find the value of r in the exponential function;

P(t) = P(0) (1 + r)^t or

P(t) = P(0) e^(rt)

where;

In this case, the initial value is 3.5, and the function is P(t) = 3.5 (0.91)^t. Comparing this to the form P(t) = P(0) e^(rt),

we see that P(0) = 3.5 and r = ln(0.91) ≈ -0.094.

Therefore, the percentage rate of change is -9.4%, which means that the value decreases by about 9.4% with each unit of time.

So the correct answer is option B: Exponential decay; 9%.

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The complete question is below:

-Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of

change.

P(t) = 3.5 (0.91)^t

A) Exponential decay; 3.5%

B) Exponential decay; 9%

C) Exponential growth; 9%

D) Exponential growth; 3.5%

The proof of |x−6|+x>3 is shown below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have  |x−6|+x>3.

Now, opening the absolute value

|x−6|+x>3

-(x- 6) + x >3

-x + 6 +x > 3

6 > 3

Thus, |x−6|+x>3 has been proved.

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The statement missing in the proof is option D. m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘.

A triangle is classified as a geometric shape with three sides and three angles. It is one of the basic shapes in geometry, and is typically characterized by its three interior angles, which must add up to 180 degrees. The most common types are the equilateral triangle (all sides equal), the isosceles triangle (two sides equal), and the scalene triangle (no equal sides).

A proof involves logical deduction of the statements in order to arrive at a conclusion. In this case, the conclusion is that the angles 3, 5, and 7 are all congruent. To do this, the proof must show that the angles add up to 180 degrees, which is the sum of the angles in a triangle. Option D, m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘, is the statement that must be included in the proof to show that the angles are congruent. Without this statement, it is impossible to prove that the three angles are congruent. Therefore, Option D is the missing statement in the proof.

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According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.

%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.

Sam collects $150.00 each day for 6 days, so the total amount he collects is:

$150.00/day x 6 days = $900.00

The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):

$900.00 x 0.35 = $315.00

So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:

$900.00 - $315.00 = $585.00

$585.00 of the money that Sam collects will be used to buy cleaning supplies.

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Answer:

Step-by-step explanation:

midpoint of AC

[tex]x=\frac{1-1}{2} =0\\y=\frac{4-4}{2} =0\\mid ~point~of~AC=(0,0)[/tex]

midpoint of BD

[tex]x=\frac{4-4}{2} =0\\y=\frac{-1+1}{2} =0\\midpoint ~of~BD=(0,0)[/tex]

so diagonals bisect each other.

Gregor scored 65 points on the Stats exam.

We can use the formula for calculating z-score:

z = (x - μ) / σ

Where

We are given that the population mean (μ) is 75 and the population standard deviation (σ) is 5.

We are also given that Gregor's z-score (z) is -2.

We can plug these values into the formula and solve for x:

-2 = (x - 75) / 5

Multiplying both sides by 5, we get:

-10 = x - 75

Adding 75 to both sides, we get:

x = 65

Hence, the score is 65 points

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The total cost of painting his basement floor is $51.70.

To find the total cost of the paint including HST, we first need to calculate the total area of the basement floor that needs to be painted. We can do this by multiplying the length by the width:

Area of basement floor = length x width

Area of basement floor = 2.5 m x 2.3 m + 1.8 m x 2.3 m

Area of basement floor = 5.75 m² + 4.14 m²

Area of basement floor = 9.89 m²

Now, we can calculate the number of cans of paint needed:

Number of cans = Area of basement floor / Area covered by each can

Number of cans = 9.89 m² / 3.5 m²

Number of cans = 2.8257

Number of cans = 3

The total cost of the paint without HST would be:

Total cost = Number of cans x Cost per can

Total cost = 3 x $15.25

Total cost = $45.75

To calculate the HST, we need to multiply the total cost by the HST rate (13% or 0.13):

HST = Total cost x HST rate

HST = $45.75 x 0.13

HST = $5.95 (rounded to two decimal places)

Finally, we can find the total cost including HST by adding the total cost and the HST:

Total cost including HST = Total cost + HST

Total cost including HST = $45.75 + $5.95

Total cost including HST = $51.70

Therefore, the total cost of the paint including 13% HST is $51.70.

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Step-by-step explanation:

f(0):

f(0) = (0^2 - 9) / (0 + 5)

= -9/5

f(-1):

f(-1) = ((-1)^2 - 9) / (-1 + 5)

= (-8) / 4

= -2

f(1/k):

f(1/k) = ((1/k)^2 - 9) / (1/k + 5)

= (1/k^2 - 9) / (1/k) + 5

= (1 - 9k^2) / (k^2 + 5k)

Therefore, f(0) = -9/5, f(-1) = -2, and f(1/k) = (1 - 9k^2) / (k^2 + 5k).

Answer:

Step-by-step explanation:

To find the values of f(x) at the given points, we substitute the values of x into the expression for f(x) and simplify:

f(x) = (x^2 - 9)/(x + 5)

a) To find f(0), we substitute 0 for x:

f(0) = (0^2 - 9)/(0 + 5) = -9/5

Therefore, f(0) = -1.8.

b) To find f(-1), we substitute -1 for x:

f(-1) = (-1^2 - 9)/(-1 + 5) = (-10)/4

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 2:

f(-1) = -5/2

Therefore, f(-1) = -2.5.

c) To find f(1/k), we substitute 1/k for x:

f(1/k) = ((1/k)^2 - 9)/(1/k + 5)

We can simplify the numerator by multiplying out the square:

f(1/k) = (1/k^2 - 9)/(1/k + 5)

We can simplify the denominator by multiplying by k/k:

f(1/k) = (1 - 9k^2)/(1 + 5k)

Therefore, f(1/k) = (1 - 9k^2)/(1 + 5k).

Answer:

Step-by-step explanation:

Let's simplify - 4 - (-5):-

[tex]\tt -4 - (-5)[/tex]

[tex]\tt -4+5[/tex]

[tex]\tt 1[/tex]

Now, let's see which expression has the same value:-

F. -4 + (-5)

[tex]\tt -4 + (-5)[/tex]

[tex]\tt -4-5[/tex]

[tex]\boxed{\tt -9}[/tex]

________________

G. -4 +5

[tex]\tt -4 +5[/tex]

[tex]\boxed{\tt 1}[/tex]

_________________

H. -5 + (-4)

[tex]\tt -5 + (-4)[/tex]

[tex]\tt -5-4[/tex]

[tex]\boxed{\tt -9}[/tex]

_________________

J. -5-(-4)

[tex]\tt -5-(-4)[/tex]

[tex]\tt -5+4[/tex]

[tex]\boxed{-1}[/tex]

Therefore, we can say that G. -4 +5 has a similar value as

-4 - (-5).

________________________

Hope this helps! :)

Answer:

The inequality that represents the given statement is:

12 + w ≥ 45

Step-by-step explanation:

Answer:

4 + 36x

Step-by-step explanation:

4(1 + 9x)

= 4 + 36x

So, the answer is 4 + 36x

Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.

Two or more expressions with an Equal sign is called as Equation.

Assuming a month has four weeks, each with at least 20 workdays, we can calculate the total number of workdays in the month starting on a Monday as follows:

Week 1: Monday to Friday = 5 workdays

Week 2: Monday to Friday = 5 workdays

Week 3: Monday to Friday = 5 workdays

Week 4: Monday to Friday = 5 workdays

So the total number of workdays in the month is:

5 + 5 + 5 + 5 = 20

Therefore, Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.

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Answer:

a. Using a mortgage calculator with the given information, Marisa's monthly mortgage payment would be $1,088 to the nearest dollar.

b. The total cost of the house, including the down payment and all payments made over the 30-year mortgage period, would be $453,020. This is calculated by adding the $55,000 down payment to the total amount borrowed ($195,000) and then adding the total interest paid over the 30 years ($203,020) to get $453,020.

c. Marisa will have spent $203,020 in interest over the 30-year mortgage period. This is calculated by subtracting the total amount of the loan ($195,000) from the total amount paid over the 30 years ($398,020), which leaves $203,020 in interest paid.

The choice in the blank to make the statement true will be D. between $17 and $30)

Revenue = Price per book × Number of books sold = (745 - 30P) b

Since the store needs to sell at least 235 books, we have:

Revenue ≥ 235 × Price per book = 235(745 - 30P)

Simplifying this inequality, we get:

745b - 30Pb ≥ 235 × 745

P ≤ (745/30) - (235/b)

Since we want to find the minimum profit per book sold, we need to maximize the value of (235/b). The maximum value of (235/b) occurs when b is minimized

If we assume that the cost per book is constant, then the profit per book sold will increase as the price per book increases. Therefore, we can say that the minimum profit per book sold that would enable the store to sell at least 235 books is greater than $17.

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To have an effective safeguarding system, specific and detailed training of workers must also be included.

What constitutes the foundation of the safety system?

 Any portion of the operator's body, including the hands, arms, and other body parts, must not come into touch with potentially harmful moving parts.

                              A strong safety system completely avoids the chance of the operator or another worker putting their bodies in close proximity to dangerous moving parts.

What are the two main sorts of protection strategies?

There are primarily two types of safeguarding: hard guards and safeguarding gadgets. Hard guards act as a physical barrier between workers and moving parts.

                            Safeguarding devices, however, stop unintentional access to dangers. A machine that needs two hands to operate it, for instance, ensures that neither hand may enter the danger zone.

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We can simplify this expression by multiplying the cube roots together:

³√5 × ³√5 × ³√5 = ³√(5 × 5 × 5)

Simplifying the product inside the cube root, we get:

³√(125)

Therefore, the cube root of 5 × 5 × 5 is equal to:

³√5׳√5׳√5 = ³√125 = 5