If a man stands 6ft tall and stands 30 ft from a tree of unknown height and also 5 ft away from a steak in the ground tied to the top of the tree how tall is the tree ?

Answer:

E =53.1

Step-by-step explanation:

sin=opposite ÷ hypotenuse

opposite side of E = 4

hypotenuse = 5

4÷5=0.8

sin^-1 (0.8) = 53.1

E=53.1

Answer:

k=32

Step-by-step explanation:

One root of x^2 + 12x + k = 0 is twice the other root. Find k

k will be the product of the two roots

12 will be the sum of the two roots

12/3=4

4*2=8

The two roots are 4,8

Multiply 4 and 8, you get 32.

k=32

The expression which is equivalent to [tex](\frac{3}{2})^8[/tex] is [tex]$\frac{3^6}{2^8}$[/tex] . So, correct option is C.

An exponential expression is a mathematical expression that involves a base raised to an exponent. The base is usually a fixed number, and the exponent represents the number of times the base is multiplied by itself. For example, in the expression [tex]2^3[/tex] the base is 2 and the exponent is 3. This means that 2 is multiplied by itself three times, resulting in the value of 8.

Exponential expressions are commonly used in many areas of mathematics and science, as well as in everyday life. For example, they can be used to represent growth rates, decay rates, population growth, radioactive decay, and compound interest.

Exponential expressions can be simplified using the laws of exponents, which allow us to combine or simplify expressions with the same base. Some common laws of exponents include:

Product law: [tex]a^m x a^n = a^(m+n)[/tex]

Quotient law: [tex]a^m / a^n = a^(m-n)[/tex]

Power law: ([tex]a^m)^n = a^(mn)[/tex]

Negative exponent law: [tex]a^(-m) = 1 / a^m[/tex]

Zero exponent law: [tex]a^0 = 1[/tex]

Exponential expressions can also be graphed on a coordinate plane, producing a curve called an exponential function. The shape of the curve depends on the value of the base and the sign of the exponent, and can be used to model a wide range of real-world phenomena.

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Answer:

(1,5)?

Step-by-step explanation:

The three points that are solutions to the linear inequality y < 0.5x + 2 are (-3, -2), (-1, -2), and (1, -2)

To check which points are solutions to the linear inequality y < 0.5x + 2, we can substitute the coordinates of each point into the inequality and check whether the inequality is true or false.

For the point (-3, -2):

y < 0.5x + 2

-2 < 0.5(-3) + 2

-2 < -0.5

This inequality is true, so (-3, -2) is a solution.

For the point (-2, 1):

y < 0.5x + 2

1 < 0.5(-2) + 2

1 < 1

This inequality is false, so (-2, 1) is not a solution.

For the point (-1, -2):

y < 0.5x + 2

-2 < 0.5(-1) + 2

-2 < 1.5

This inequality is true, so (-1, -2) is a solution.

For the point (-1, 2):

y < 0.5x + 2

2 < 0.5(-1) + 2

2 < 1.5

This inequality is false, so (-1, 2) is not a solution.

For the point (1, -2):

y < 0.5x + 2

-2 < 0.5(1) + 2

-2 < 2.5

This inequality is true, so (1, -2) is a solution.

Therefore, the three points that are solutions are (-3, -2), (-1, -2), and (1, -2).

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The given question is incomplete, the complete question is:

Which points are solutions to the linear inequality y < 0. 5x +2? Select three options. (-3,-2) (-2,1) (-1,-2) (-1, 2) (1,-2)

Answer:

1:3 is your rate for dollars per soda

Step-by-step explanation:

The population of India in 2020 was approximately 1.38x10^9 people, while the population of Estonia in 2020 was approximately 1.33x10^6 people. This means that India was approximately 103 orders of magnitude more populated than Estonia in 2020.
To calculate the difference in orders of magnitude between India and Estonia, divide India's population (1.38x10^9) by Estonia's population (1.33x10^6). This gives a result of 1.03x10^3, or 103 orders of magnitude.
In other words, India's population was 103 times bigger than Estonia's population in 2020. This difference can also be expressed as India being 10,300,000,000 times more populated than Estonia in 2020.

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37.70/12

MARK ME AS BRAINLIEST :)

Step-by-step explanation:

The proportion of similar triangles are

[tex] \frac{3}{4} = \frac{9}{r} [/tex]

Solving for r

[tex] \frac{4}{3} = \frac{r}{9} [/tex]

[tex] \frac{9 \times 4}{3} = r[/tex]

[tex]12 = r[/tex]

The unit rate is 8.4 miles per hοur.

Distance and displacement are twο quantities that seem tο mean the same but are distinctly different with different meanings and definitiοns. Distance is the measure οf “hοw much grοund an οbject has cοvered during its mοtiοn” while displacement refers tο the measure οf “hοw far οut οf place is an οbject.”

Tο find the unit rate in miles per hοur, we need tο divide the distance by the time.

The distance is 1 2 2 1  miles and the time is 1 4 4 1  hοurs.

Sο, the unit rate in miles per hοur is:

(1 2 2 1  miles) / (1 4 4 1  hοurs) = 8.4 miles per hοur (rοunded tο οne decimal place)

Therefοre, the unit rate is 8.4 miles per hοur.

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The Construction of line MN and perpendicular at point N as well as angle MNP = 60°such that NP would be 6.3 cm is given below as image.

In Euclidean geometry, an angle is a shape made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed in the plane where two rays are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what they are called.

In geometry, two lines are considered to be perpendicular if they meet or intersect at right angles of 90°. The Latin term "perpendicularis," which denotes a plumb line, is where the word "perpendicular" originally made its appearance.

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x ≈ 17.8 cm (rοunded tο 1 decimal place).

The trigοnοmetric functiοns in mathematics are real functiοns that relate the angle οf a right-angled triangle tο the ratiοs οf its twο side lengths. They are alsο knοwn as circular functiοns, angle functiοns, οr gοniοmetric functiοns.

All geοsciences, including navigatiοn, sοlid mechanics, celestial mechanics, geοdesy, and many οthers, use them extensively. They are sοme οf the mοst straightfοrward periοdic functiοns, and as a result, Fοurier analysis is frequently used tο study periοdic phenοmena.

Tο sοlve fοr x, we can use the trigοnοmetric functiοn cοsine since we have the adjacent side and the hypοtenuse.

cοs(θ) = adjacent/hypοtenuse

cοs(38°) = x/hypοtenuse

We knοw that the perpendicular is y = 11 cm, sο we can use the Pythagοrean theοrem tο find the hypοtenuse:

[tex]\rm hypotenuse^2 = perpendicular^2 + base^2[/tex]

[tex]x^2 = y^2 + (adjacent)^2[/tex]

[tex]x^2 = 11^2 + (x cos(38^\circ))^2[/tex]

[tex]x^2 = 121 + (x 0.7880107536)^2[/tex]

[tex]x^2 = 121 + 0.6201117996x^2[/tex]

[tex]0.3798882004x^2 = 121[/tex]

[tex]x^2 = 318.5022183[/tex]

x ≈ 17.84 cm (rounded to 1 decimal place)

Therefore, x ≈ 17.8 cm (rounded to 1 decimal place).

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In our proof, as the trapezium are congruent and the rest of the sides are equal ∴AC = BD. Hence, the cyclic trapezium is isosceles and its diagonals are equal.

Step 1:

The diagonals are AC and BD, and the line CE is parallel to AD.

We know that a parallelogram's opposite angles are equal.

∠D = ∠AEC......(1)

We also know that the sum of a cyclic quadrilateral's opposite angles is 180 degrees.

∠D + ∠ABC = 180..........(2)

We can deduce from (1) and (2) that

AEC + ABC = 180....... (3)

AEC and CEB are now a linear pair.

AEC + CEB = 180................. (4)

We can conclude from (3) and (4) that,

CEB = ABC

The sides opposite the equal angles are also equal, as we know.

CEB = ABC

CE = CB ... (5)

However, because AECD is a parallelogram, opposite sides must be equal.

∴CE = AD ... .(6)

From equation (5) and (6), we can conclude that

AD = CB ......(7)

As a result, the cyclic trapezium ABCD is isosceles.

Step 2:

Establishing that its diagonals are equal.

We have AC and BD as diagonals.

In triangle DBA and CBA,AD = CB from (7)⇒AB = AB (common side).

ADB + ACB (angles in the same segment of a circle are equal). As a result of the SAS rule, ABD and ABC are congruent.

Because they are congruent and the other sides are equal, AC = BD. As a result, a cyclic trapezium is isosceles and has equal diagonals.

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h(2) + j(−7) = −7(1 + j)

Suppose that f(x) = h^−1(x) and that both j and h are defined for all values of x. Let h(11) = 2 and f(12) = −7. We need to evaluate the following. h(2) + j(−7)For finding the value of h(2), we can use f(x) = h^−1(x) where x = h(2)f(h(2)) = 2h(2) = f^−1(2)We need to find h(2). Therefore, we need to find f^−1(2). We know f(12) = −7f(h(2)) = 2⟹ h(2) = −7Substitute h(2) = −7 in h(11) = 2h(11) = h(2 + 9) = h(2) + 9 = 2 + 9 = 11Therefore, h(2) = −7 and h(11) = 2.h(2) + j(−7) = −7 + j(−7) = −7(1 + j)Therefore, h(2) + j(−7) = −7(1 + j).

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Answer:

19

Step-by-step explanation:

Product of 5 and a number is 5a

5a - 26 = 69

Add 26 to both sides

5a = 69+26

5a = 95

Divide both sides by 5

A = 19

Check

(5× 19) - 26 = 65

In response to the given question, we can state that We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.

A sequence is a collection of numbers (or "terms"). Examples of words are 2, 5, and 8. Certain sequences may be made infinitely long by takes advantage of a specific pattern they follow. To continue the sequence, use the case of 2,5,8 or add 3. There are formulae that show where to seek for words in a sequence. A sequencing in mathematics is a collection of items that are in some order (or events). It is similar to a set in that it has components (also called elements or terms). The length of a sequence is defined as the total, possibly unlimited number of ordered items. the act of arranging two or more elements in a logical sequence.

To get the common ratio of a geometric series, divide any phrase by the term before it.

Let us divide the second term by the first term:

4 ÷ (-1) = -4

Let us now divide the third term by the second term:

(-7) ÷ 4 = -1.75

Lastly, let us divide the fourth term by the third term:

10 ÷ (-7) = -1.42857142857 (rounded to 11 decimal places) (rounded to 11 decimal places)

We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.

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On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.

a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb

Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)

Energy saved in one day = 300 watt-hours - 80 watt-hours

Energy saved in one day = 220 watt-hours

To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:

Energy saved in one day = 220 watt-hours / 1000

Energy saved in one day = 0.22 kWh

b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Energy saved in one year = Energy saved in one day x Number of days in one year

Energy saved in one year = 0.22 kWh/day x 365 days/year

Energy saved in one year = 80.3 kWh

c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Cost savings in one year = Energy saved in one year x Cost per kWh

Cost savings in one year = 80.3 kWh x $0.10/kWh

Cost savings in one year = $8.03

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Therefore , the solution of the given problem of coordinates comes out to be the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).

By utilising one or even more variables or coordinates, a coordinate system is able to precisely locate points or other mathematical items on such a room, including Euclidean space. Coordinates, which seem to be pairs of integers, are used to locate a point or object on a double plane. The y and x vectors are used to represent the position of a point on a two-dimensional surface. a group of figures used to designate particular places.

Here,

G(3, -2) will have the following coordinates after being reflected across the y-axis:

=> (-3, -2).

A point's x-coordinate changes sign when it is reflected across the y-axis, but its y-coordinate stays the same.

Consequently, the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).

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The coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2) and The coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).

A reflection on the coordinate     plane (x , y ) is a type of transformation. It takes a geometric figure such as a line,    segment, point or shape and transforms it into a congruent   geometric figure called the image.

a. It is given that a point (-3, 2) reflected   across the y - axis.

Now, when any given coordinate    is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.

Therefore, the coordinates of the resulting    point after the reflection across the y - axis    will be G'(3, 2)

b. It is given that a point (3, -2) reflected   across the x - axis.

Now, when any given coordinate    is reflected across the x - axis then, the sign of the y - coordinate is inverted and the x - coordinate remains same.

Therefore, the coordinates of the resulting    point after the reflection across the x - axis    will be G'(3, 2).

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The probability that the small business owner's annual profit will not exceed $100,000 is about 0.0571

We can use the central limit theorem to approximate the distribution of the annual profit. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed.

Let X be the daily profit, then the annual profit, Y, is given by Y = 105X. The mean of Y is:

μY = 105μX = 105(975) = 102375

The variance of Y is:

σY^2 = 105σX^2 = 105(129)^2 = 2244385

The standard deviation of Y is:

σY = sqrt(2244385) ≈ 1498.12

We want to find the probability that the annual profit will not exceed $100,000, which is equivalent to finding the probability that Y ≤ 100000. We can standardize Y using the formula:

Z = (Y - μY) / σY

Substituting the values, we get:

Z = (100000 - 102375) / 1498.12 ≈ -1.58

We can use a standard normal distribution table or calculator to find the probability that Z ≤ -1.58. This probability is approximately 0.0571.

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The given question is incomplete, the complete question is:

A small business owner estimates his mean daily profit as $975 with a standard deviation of $129. His shop is open 105 days a year. What is the probability that his annual profit will not exceed $100,000?

This means that the Mt. Rinjani eruption was approximately 20 times larger and more powerful than the Mt. Pinatubo eruption.

An exponent is a mathematical operation that involves raising a base number to a certain power. The exponent tells how many times the base number should be multiplied by itself. For example, in the expression 2³, 2 is the base number and 3 is the exponent, and it means that 2 should be multiplied by itself three times: 2 x 2 x 2 = 8. Exponents are commonly used in algebra, calculus, and other branches of mathematics.

Here,

The Volcanic Explosivity Index (VEI) is a logarithmic scale used to measure the relative size and power of volcanic eruptions. Each increase of 1 on the VEI scale represents a tenfold increase in the eruption's size and power.

The difference in VEI between the Mt. Rinjani eruption and the Mt. Pinatubo eruption is 7.3 - 6.0 = 1.3.

To calculate the difference in size and power, we need to raise 10 to the power of 1.3:

10¹.³ = 19.95

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The width of Averi's area model is 4 units.

The area model for factoring 4x²+20x-16 is shown above. The width of Averi's area model is 4 units. To factor the given expression, Averi used an area model.

In this model, the width represents the greatest common factor of the given expression while the length represents the remaining factors of the expression. Averi determined that the greatest common factor of 4x²+20x-16 was 4.

Therefore, she created a rectangle with a width of 4 and a length of (x²+5x-4). The dimensions of the rectangle are determined by the factors of the given expression.

The area of the rectangle represents the original expression. Therefore, the area of the rectangle can be calculated by multiplying the width and length of the rectangle. The area of the rectangle is equal to: Area of rectangle = width x length Area of rectangle = 4(x²+5x-4)Area of rectangle = 4x²+20x-16

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The volume of the given solid above which is a triangular prism would be = 510 ft³.

To calculate the volume of the given prism the formula should be used such as;

Volume = 1/2 × base× height × length

Where base = 10ft

height = 6 ft

length = 17ft

Volume = 1/2 × 10×6×17

= 5×6×17

= 510 ft³

Therefore the volume of the given shape above would be = 510 ft³ when the formula for triangular prism is used.

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(a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.

(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position.

This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.

(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role.

For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.

For further information on (a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.

(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position. This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.

(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role. For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.

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G is 215° North from H in bearing terms. This means that to get from point H to point G, one must travel in a northerly direction at an angle of 215°.

The bearing of G from H is 215° North. This means that to get from point H to point G, one must travel in a northerly direction at an angle of 215°. Bearings are typically measured in degrees, where north is 0° and east is 90°. To calculate the bearing of G from H, you must first draw a line from H to G. After that, calculate the angle between the line you drew and north.. This angle is the bearing of G from H. Bearings can also be expressed as a three-letter compass direction (such as NNE or SW). To calculate the three-letter compass direction, divide the bearing into four quadrants (0-90° = N, 90-180° = E, 180-270° = S, 270-360° = W) and then divide each quadrant further into three sections. For example, if the bearing of G from H is 215°, it would be expressed as SW, since it falls within the 270-360° quadrant. Bearings are useful for navigation, determining the direction of a destination from a starting point, and for plotting points on a map.

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The equatiοn οf the line οf best fit is ŷ= 0.96x+3.79

The slοpe is 0.96

The y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches is 67.15 inches and the heights οf peοple that have arm spans οf 74 inches is 74.83 inches.

When the line tοuches the y-axis, it fοrms a y-intercept. Find the y when x = 0 tο find these. The y-intercept pοint will have the shape οf (0,y) When the line tοuches the x-axis, it fοrms an x-intercept.

We have the fοllοwing cοmputatiοn summary frοm the graphing calculatοr:

Sum οf X = 486

Sum οf Y = 506

Mean X = 44.1818

Mean Y = 46

Sum οf squares (SSX) = 1225.636

Sum οf prοducts (SP) = 1171

Hence, the fοrmula fοr the line οf best fit is ŷ= 0.96x+3.79

A linear regressiοn equatiοn is mentiοned

ŷ=mx+b

Where m is the slοpe, and b is the y-intercept

Sο, the slοpe is 0.96 and the y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches and 74 inches

This means that:

x = 66 and x = 74

When x = 66,

y=0.96*66+3.79=67.15

When x = 74,

y=0.96*74+3.79= 74.83

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A system of equations to determine the number of home versions and professional versions of the software the company sold is given by:

20h + 45p = 38,075

h + p = 1000

The number of home versions sold is 277 and the number of professional versions sold is 723.

In order to write a linear equation to describe this situation, we would assign variables to the number of home versions sold and the number of professional versions sold respectively, and then translate the word problem into a linear equation as follows:

Since a home version of their photo editor cost $20, and a professional version, cost $45, a linear equation that models the situation is given by:

20h + 45p = 38,075

Additionally, the company sold 1000 copies of the photo editing software;

h + p = 1000

Solving the equations simultaneously, we have:

20h + 45(1000 - h) = 38,075

20h + 45,000 - 45h = 38,075

25h = 6,925

h = 277 home versions.

p = 1000 - h

p = 1000 - 277

p = 723 professional versions.

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The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.

The total distance covered can be calculated using the formula:

distance = rate × time

From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:

March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31

Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.

The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:

distance = rate × fuel capacity

= 5 km/l × 460 litres

= 2300 km

So, the total distance covered by the water tanker in March 2022 is:

distance = 23 days × 2300 km/day

= 52,900 km

Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:

quantity of fuel = distance ÷ rate

Using the values we have calculated, we get:

quantity of fuel = 52,900 km ÷ 5 km/l

= 10,580 litres

Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.

To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:

total cost = quantity of fuel × fuel price

From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:

total cost = 10,580 litres × R19.55/litre

= R206,929.00

Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

Complete question:

Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022​. Quantity of fuel utilized by water tanker March 2022

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Answer:

yes, a triangle with the side lengths 12, 5, and 12 does exist.

Step-by-step explanation:

side a = 12

side b = 5

side c = 12

area = 29.34In

Max needs 54 horizontal rails to build a fence with 27 vertical posts.

The problem states that each section of the fence uses 3 vertical fence posts and 6 horizontal rails. This means that for every section of fence, there are 3 vertical posts and 6 horizontal rails.

To find out how many horizontal rails Max needs for a fence with 27 vertical posts, we need to figure out how many sections of fence Max needs to build.

Since each section of fence has 3 vertical posts, apply unitary method, we can divide the total number of vertical posts by 3 to find out how many sections of fence Max needs to build:

27 / 3 = 9

So Max needs to build 9 sections of fence.

Since each section of fence has 6 horizontal rails, we can multiply the number of sections by 6 to find out how many horizontal rails Max needs in total:

9 x 6 = 54

Learn more about unitary method here

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