The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.
What is the inverse function f-¹(x)?It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.
Therefore, let f(x) = y; so that we have;
y = (x - 7)³
make x the subject so that we have;
³√y = x - 7
x = ³√y + 7
By switching the variables; we have;
y = ³√x + 7
Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.
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18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
In the critical value method, we find the area in the tail end and compare it to alpha to determine whether to reject or fail to reject the null hypothesis.
The critical value strategy entails deciding whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true in order to determine whether something is "likely" or "unlikely."
How do you determine the rejection zone and the crucial value?
The rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .
To execute any hypothesis test, the critical value technique entails four specific phases, which are as follows:
The null and alternative hypotheses should be specified.Calculate using the sample data and the null hypothesis as the default. the test statistic's value Using the t-statistic t=m−μ÷s/√n which follows a t-distribution with n - 1 degrees of freedom, we may test the population mean hypothesis.By determining the value of the known distribution of the test statistic such that the likelihood of making a Type I mistake is low, also known as the "significance level of the test," or (greek letter "alpha"), the crucial value can be found (typically 0.01, 0.05, or 0.10).Assess the critical value against the test statistic. Reject the null hypothesis in favor of the alternative hypothesis if the test statistic is more extreme in the alternative direction than the crucial value. When the test statistic falls inside the acceptable range,To know more about critical value method visit:
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Last year Kristen had $ 20 , 000 to invest. She invested some of it in the first account that paid 7 % simple interest per year, and she invested the rest of it in a second account that paid 8 % simple interest per year. After one year, she received a total of $ 1 , 540 in interest. How much did she invest in each account?
The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 20,000 equation 1
0.07a + 0.08b = 1540 equation 2
Where:
a = amount invested in the account that earns 7% interest
b = amount invested in the account that earns 8% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.07
0.07a + 0.07b = 1,400 equation 3
Subtract equation 3 from equation 2
0.01b = 140
Divide both sides of the equation by 0.01
b = 140/ 0.01
b = 14,000
Substitute for b in equation 1:
a + 14,000 = 20,000
a = 20,000 - 14,000
a = 6,000
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A function has the following properties:
• It is increasing and linear when the value of x is between -5 and -3.
• It remains constant when the value of x is between -3 and 0.
• It is decreasing and linear when the value of x is between 0 and 3.
• It is increasing and nonlinear when the value of x is between 3 and 5.
Which graph best represents this function?
Answer:
c
Step-by-step explanation:
trust me
Complete the table.
q=p+7
Р
q
0
1
8
2
3
4
11
Given expression q=p+7
Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.
Simply put the p values in the expression. solve it and get the q values.
q=p+7 in the place of p submit p=0
q=0+7
q=7
q=p+7 in the place of p submit p=2
q=2+7
q=9
q=p+7 in the place of p submit p=3
q=3+7
q=10
Therefore, The values of q are 7,9,10
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The missing numbers are:
7,9 and 10 when 0, 2, and 3 respectively.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
An equation,
q = p + 7.
Substituting the values of p:
When p = 0,
q = 0 + 7
q = 7.
When p = 2,
then q = 9.
And when p = 3,
q = 10
Therefore, all the required values are given above.
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ite the equations of the lines with the following properties Two points, (1, 3) and (9,8)
The linear equation that passes through the two given points is:
y = (5/8)*x + 19/8
How to write the linear equation?We want to find the equation of a line that passes through (1, 3) and (9, 8).
Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:
slope = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (1, 3) and (9, 8).
Then the slope is:
slope = (8 - 3)/(9 - 1) = 5/8
We can write the line as:
y = (5/8)*x + b
To find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:
3 = (5/8)*1 + b
3 = 5/8 + b
3 - 5/8 = b
24/8 - 5/8 = b
19/8 = b
The linear equation is:
y = (5/8)*x + 19/8
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PLEASE ANSWER QUICKLY!
For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?
A. 0.15
B. 0.21
C. 0.45
D. 0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given data we get,
The categories are mutually exclusive, so we have ...
P(≥21) = P(21-30) +P(31-40) +P(41-50)
= 45% +19% +15%
P(≥21) = 79%
=0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
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A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within 0.15 ounces of that amount. Which inequality shows all the possible actual bottle volumes (v) that the manufacturer would be able to advertise as 21 ounces?
Answer:
Step-by-step explanation:
the Answer is b
Help quick!! Which of the following tables represents a relation that is a function?
Explained answer please
D because none of the inputs (x) are repeated. All the others have the same input with two or more different outputs.
A total of tickets were sold for the school play. They were either adult tickets or student tickets. There were fewer student tickets sold than adult tickets. How many adult tickets were sold?
There were 375 adult tickets sold and 316 student tickets for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the question, we have a system of equations:
x + y = 691 ....(i)
x = y - 59 ....(ii)
Substitute the value of x = y - 59 in equation (i),
y - 59 + y = 691
2y = 691 + 59
2y = 750
y = 375
Substitute the value of y = 375 in equation (ii), and solve for x:
x = 375 - 59
x = 316
Thus, there were 375 adult tickets sold.
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The complete question would be as:
A total of 691 tickets were sold for the school play. There were 59 fewer student tickets sold than adult tickets. How many adult tickets were sold?
1) Find the 9th term of the sequence:
60, 30, 15, ...
*
Answer:
Step-by-step explanation:
Let me explain step by step:
Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.
Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:
a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.
Plug in the values: We want to find the 9th term, so we plug in the values into the formula:
a_9 = 60 * (1/2)^(9-1)
Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:
a_9 = 60 * (1/2)^8
Divide the result by 256: We can simplify the expression further by dividing both sides by 256:
a_9 = 60 * 1/256
a_9 = 60 / 256
Get the final answer: We divide 60 by 256 to get the final answer:
a_9 = 0.234375
So the 9th term of the sequence is approximately 0.234375.
Select the correct answer.
A right angle triangle where ABC angle is 90° and angle ACB is 45°.
Which trigonometric ratio will not have the same value as sin A?
A.
cos A
B.
sin C
C.
tan C
D.
cos C
Reset Next
Trigonometric Ratios: Mastery Test
© 2023 Edmentum. All rights reserved.
Trigonometric ratio in option (c) tan C will not have the same value as sin A.
What are Trigonometric Functions?Trigonometric functions are defined as the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given a right angled triangle ABC given below.
ABC angle is 90° and angle ACB is 45°.
Then angle BAC = 180° - (90° + 45°) = 45°
Since two angles are equal, it is an isosceles triangles.
So opposite sides to the equal angles are equal.
AB = BC
AC is the hypotenuse.
Sin A = Opposite side / Hypotenuse = BC / AC
(a) Cos A = Adjacent side / Hypotenuse = AB / AC = BC / AC
(b) Sin C = AB / AC = BC / AC
(c) Tan C = Opposite side / Adjacent side = AB / BC = BC / BC = 1, not equal to Sin A
(d) Cos C = BC / AC
Hence the option (c) is not equal to sin A.
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2. The population of chickadees in a certain region is smaller by 30% than the population of
phoebes, and the population of blue jays is 30% of the population of phoebes.
The population of phoebes is 12,000.
Find the sizes of the chickadee and blue jay populations in the region.
The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):
Population of chickadees = 0.7 x 12,000 = 8,400
Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:
Population of blue jays = 0.3 x 12,000 = 3,600
Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.
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the answer to this question
Answer is B.
y= 2x -3 y= -2x + 1
step by step
First I found the y intercepts at (red line) -3 and (green line) +1.
There is only one answer that shows these two y intercept values.
To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.
Slope was found on the graph finding rise over run and compared to the number next to x in the equations.
See attached graph.
A boat has a top speed of 26 knots and a displacement of approximately 81,000 tons. Express the top speed in miles per hour and the displacement in metric tons. The boat has a top speed of approximately______mile(s) per hour. (Round to the nearest tenth as needed.)
The boat has a top speed of approximately 29.7 miles per hour and a displacement of approximately 73,934 metric tons.
Answer:
[tex]29.9[/tex] miles per hour
[tex]73482[/tex] metric tons
Step-by-step explanation:
We are given:
top speed of 26 knots
displacement of 81,000 tons
It is asking us to convert knots to miles per hour.
It is asking us to convert tons to metric tons.
We can use conversion factors to complete the unit conversions.
1 knot (kt) = 1.15077945 miles per hour (mph)
1 ton = 0.907185 metric tons
Numerical Evaluation
Lets convert our top speed.
We can set up an equation like this
[tex]\frac{1}{1.15077945} =\frac{26}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=26*1.15077945[/tex]
Evaluate [tex]26*1.15077945[/tex].
[tex]26*1.15077945 =29.9202657[/tex]
Round to the nearest tenth.
[tex]29.9[/tex] miles per hour
Lets convert our displacement.
We can set up an equation like this
[tex]\frac{1}{0.907185 } =\frac{81000}{x}[/tex]
Lets solve for [tex]x[/tex].
Cross multiply.
[tex]1x=81000*0.907185[/tex]
Evaluate [tex]81000*0.907185[/tex].
[tex]81000*0.907185=73481.985[/tex]
Round to the nearest tenth.
[tex]73482[/tex] metric tons
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I Given that x is an Intergen write down the three lowest values of x in each of the Following. al 10-3x > 8 62 5x-27 > 7x solution
The lowest values of x are;
1. x = 1/2, x = 2/4, x = 3/6
2. x = 14, 15, 16
How to determine the valuesFrom the information given, we have that;
10-3x > 8
collect the like terms, we get;
-3x > 8 - 10
subtract the values
-3x > -2
Make 'x' the subject
x > 2/3
5x-27 > 7x
collect the like terms
5x - 7x> 27
subtract the like terms
-2x> 27
Make 'x' the subject
x > -27/2
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Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares.
The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units
The radius of the base = 4 units
The length of the side of the square = 2x
The area of the square = a^2
Where a is side of the square
The area of the square = (2x)^2
= 4x^2
The equation of the circle is
x^2 + y^2 = 16
x^2 = 16 - y^2
The area = 4(16 - y^2 )
= 64 - 4y^2
The volume of the square
V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]
= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]
= 64×4 - 4×(4^3/3)
= 256 - 256/3
= 512/3 cubic units
Therefore, the volume of the solid is 512/3 cubic units
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Which is stronger? 3 scoops of coffee for 4 cups of water, or 4 scoops of coffee for 6 cups of water? Show Your Work.
The stronger one is 4 scoops of coffee for 6 cups of water.
How strong coffee is made?Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.
In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.
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Please see attached photo thanks
The single payment 2 years from now will be of $13,287.26
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.
To calculate investments or debts with compound interests.
Where:
V(n) is the value of the debt after n years,
R is the annual interest rate,
t is the number of times the debt is going to be compounded annually,
n is the number of years the debt is going to be compounded,
P is the principal amount being owed.
we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.
Then you have that t = 4, because the debt is compounded quarterly.
We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.
And finally we have that R = 7.74.
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 2,370 / (1 + 7.74/365)(365)^(2)
P = $13,287.26
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The triangles are similar. What is the missing length?
8
18
72
16
The answer is B. 18
When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.
33/44 = x/24
Once finished solving the proportion, you are left with 18
The missing length of triangle is 18.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.Equilateral Triangle - A triangle has three sides that are of the same length.A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.Triangle with a Right Angle - A triangle with one of its angles equal to 90°.Now,
As these triangles are similar that means
we can find the proportion of sides from given sides and
from that find x.
So, here AC/AM=AL/AB
44/33=24/x
AL=24*33/44
AL=18
Hence,
The missing length AL of triangle is 18.
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The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 feet, what are the lengths of the three sides?
Answer:
the solution is done in the given picture..
thank you
Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?
Step-by-step explanation:
(x-2)(x-2)-4x
x²-2x-2x +4-4x
x²-4x-4x +4
x²-8x+4
Answer:
4x - (x - 2)² = 4x - x² + 4 = 3x + 4
Step-by-step explanation:
A 10-ft board is cut into 2 pieces so that one piece of 6 feet longer than 3 times the shorter piece. If the shorter piece is x feet long find the lengths of both pieces
The lengths of the pieces are 1ft and 9ft
How to determine the length of sides
From the information given, we have that;
The shorter side = x
The longer side of the board = 6 +3x
The total length = 10
Substitute the values, we have;
x + 6 + 3x = 10
collect the like terms
x + 3x = 10 -6
Add or substract the like terms, we have;
4x = 4
Now, make 'x' the subject of formula by dividing by 4, we get;
4x/4 = 4/4
x = 1 ft
The longer side = 9ft
Hence, the values are 1 and 9
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The figure below shows a rope that circles the Earth. The radius of the Earth is
6371
63716371 kilometers.
Assuming the rope makes a perfect circle, what is the length of this rope?
Give your answer in terms of pi.
Answer:
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Where r is the radius of the circle.
Plugging in the value for the radius of the Earth, we have:
Circumference = 2π(6371 km) = 12,742 km
So the length of the rope, assuming it makes a perfect circle around the Earth, would be 12,742 km = 2π(6371) kilometers.
Step-by-step explanation:
2x+3y=102, x, plus, 3, y, equals, 10
In the xyx, y-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
Any line of the form:
y = (3/2)x + b
Is perpendicular to the given line.
Which equation is perpendicular to the given one?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the product between the slopes is -1.
Here we want to find a line perpendicular to:
2x + 3y = 10
We can rewrite this as:
3y = 10 - 2x
y = (10/3) - (2/3)*x
Then the slope of the perpendicular line must be such that:
a*(-2/3) = -1
a = 3/2
Then any line of the form:
y = (3/2)*x + b
Is perpendicular to the given line.
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The value of a car deprecates by 35% each year.at the end of 2007 the value of the car was £5460. Work out the value of the car at the end of 2006
Answer:
£3549
Step-by-step explanation:
The value of the car depreciates by 35% each year, so we can calculate the depreciation for 2006 as follows:
Depreciation for 2006 = 0.35 * £5460 = £1911
The value of the car at the end of 2006 is:
£5460 - £1911 = £3549
Answer:
The depreciation rate:
Step-by-step explanation:
Step 1: Total depreciation = 35% x 2 years = 70%
Step 2: Find the value of the car at the end of 2006:
Value at the end of 2006 = 5460 x (100 - 70)/100 = 1638
Therefore, the value of the car at the end of 2006 was £1638.
Which is NOT a liability?
A. Debt owed by a business
B. Debt that must be paid within the current year
C. Debt that must be paid after the current year
D. Machines, vehicles, furniture and appliances
Answer:
D. Machines, vehicles, furniture, and appliances are not considered liabilities. Liabilities are obligations or debts that a business owes to others. They are usually in the form of loans or accounts payable and represent money that must be paid in the future.
Machines, vehicles, furniture, and appliances are assets, which are resources that a business owns and that have monetary value. Assets can be sold to generate cash or used to produce goods or provide services. While assets can be used to secure loans, they do not represent a debt or obligation that must be paid in the future like a liability
Answer:
D
Step-by-step explanation:
current liability is money owed to suppliers in the form of accounts payable . Current liabilities are typically settled using current assets, which are assets that are used up within one year.
Isaac Newton sat under an apple tree to drink some tea and think. While he was thinking, an apple fell off a branch of the tree. The equation v=(19.8d)12
can be used to find the velocity, in meters per second, of the apple after dropping a distance , in meters. If the apple was connected to a branch 9 meters above the ground, what was the velocity of the apple, to the nearest hundredth, when it hit the ground?
The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
How to determine the velocity of the apple?From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:
Velocity = (19.8d)^{1/2}
Where:
d represents the distance in meters.
Velocity = (19.8 × 9)^{1/2}
Velocity = (178.2)^{1/2}
Velocity = 13.35 meters per seconds.
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A student's course grades and their corresponding weights are given in the table.
What is the minimum grade needed on the final exam to earn an overall grade of 83% in the class
Answer: 75%
Step-by-step explanation: To calculate,
(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%
the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022
Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022, a total number of liters supplied is 3,380,000 liters.
What is the rationale for the above response?
To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).
Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:
14 water tankers/day x 23 weekdays = 322 water tankers
On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:
4 water tankers/day x 4 Saturdays = 16 water tankers
Therefore, the total number of water tankers to be supplied in March 2022 would be:
322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.
Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:
338 water tankers x 10,000 liters/tanker = 3,380,000 liters
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Full Question:
The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022
