The value of all the integers are,
4, 5, 6
or, - 8, - 7, - 6
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Let three consecutive numbers are, (x - 1) , x , (x + 1).
Hence, By given condition we get;
⇒ (x - 1)² + 2 (x + x + 1) = 38
⇒ x² - 2x + 1 + 4x + 2 = 38
⇒ x² + 2x - 35 = 0
⇒ x² + 7x - 5x - 35 = 0
⇒ x (x + 7) - 5 (x + 7) = 0
⇒ (x - 5) (x + 7) = 0
⇒ x = 5 or x = - 7
When, x = 5
All the integers are,
x - 1 = 5 - 1 = 4
x = 5
x + 1 = 5 + 1 = 6
When x = - 7
All the integers are,
x - 1 = - 7 - 1 = - 8
x = - 7
x + 1 = - 7 + 1 = - 6
Thus, The value of all the integers are,
4, 5, 6
or, - 8, - 7, - 6
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-31.5 + 15x - 1.5x^2
The value of x for the given expression is x = 7 and x = 3.
What is a quadratic expression?A mathematical expression with the form ax² + bx + c, where a, b, and c are constants and x is a variable, is known as a quadratic expression. The graph of a quadratic expression can be represented by a U-shaped parabola. The y-intercept of the parabola is determined by the constant term c, whereas the coefficient a decides whether the parabola opens up or down.
The given expression is:
1.5x² - 15x + 31.5x = 0
The quadratic formula is given as:
x = -b ± √b² - 4ac / 2a
x = 15 ± √(15)² - 4(1.5)(31.5) / 2(1.5)
x = 15 ± 6 / 3
x = 15 + 6 / 3 and x = 15 - 6/3
x = 7 and x = 3
Hence, the value of x for the given expression is x = 7 and x = 3.
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7. What is the order of these numbers from least to greatest?
2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10¹2, 4.8 x 10²1
21
The order of these numbers from least to greatest is 2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10^12, 4.8 x 10^21
What are index forms?Index forms are simple described as the mathematical expressions or models used to represent numbers that are large or small in more appropriate ways.
They are also termed as scientific notations or standard forms.
Examples of index forms are;
2³ = 8
2 ² = 4
3 ³ = 27
From the information given, we have that;
2.7 x 10³
This is represented as; 2.7 × 10 × 10 × 10
Multiply the values
2700
2.3 x 10¹¹
This is represented as 2. 3 multiply by 10 in 11 times
6. 5× 10^12
This is represented by 6.5 multiplied by 10 in 12 places
4.8 × 10^21
This is represented by 4.8 multiplied by 10 in 21 places.
Hence, the exponent shows the greatest number
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please help:)))))))))))))))))))))))))))))
Answer:
The volume of the ice cream scoop is less than the volume of the cone. So, when the ice cream melts, it will fit in the cone without overflowing.
Mabel's salary is 1/3 higher than Lens. Lens salary is 1/4 higher than the hiring rate. how will you represent Mabel's salary (in terms of the original hiring rate h) if the hiring rate will be increased by 40%
Answer:
points cuzo
but if i find it out i will edit
Step-by-step explanation:
Which graph represents the solution to the inequality 0.5 is greater than or equal to the product of a number and −0.25?
A. number line with closed circle on 0.5 with arrow shaded right
B. number line with open circle on point on negative 0.5 with arrow shaded left
C. number line with closed circle on negative 2 with arrow shaded right
D. number line with open circle on 2 with arrow shaded left
Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
What is inequality?
An inequality is a comparison relationship between two or more mathematical expressions.
We are given an inequality as 0.5 is greater than or equal to the product of a number and −0.25.
Let the number be x.
So, from the above information, we get the inequality as
0.5 ≥ -0.25x
Now, on solving the above inequality, we get the following
0.5 ≥ -0.25x
On multiplying by -1, we get
⇒-0.5 ≤ 0.25x
On dividing both sides by 0.25, we get
⇒-2 < x
Hence, Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
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NONE OF THE APPS WORK BRO
Answer:
1 term (monomial).
Step-by-step explanation:
A term includes at least either a number, a variable, or both together, and can have more than one.
In this case, there is 1 term, which denotes that a variable, has an exponent of 9.
[tex]b^9[/tex] is one term.
Examples of more than 1 term can include:
[tex]b^9 + 1[/tex] , which is two terms (Binomial).
[tex]a^2 + b + 3[/tex] is three terms (Trinomial).
* One thing to note is to always simplify when possible.
~
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In this isosceles triangle,all the angles are equal what measure of angle x
120
360
We need more information to solve this problem
90
Answer:
D or B
Step-by-step explanation:
from my perspective, that doesn't look like a or b, and it looks like it's 90 degrees. But it could also be "We need more information to solve this problem, due to it all being x. i hope I'm correct, sorry if I'm not, and Goodluck!!!!!
A skateboard ramp is 4.1 feet high and 6 feet long along the horizontal. To the nearest
tenth of a degree, what is the measure of the angle that the ramp makes with a
horizontal line?
34.3°
55.7°
90°
46.9⁰
Answer: :)
Step-by-step explanation:
To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).
We can use the tangent function to find this angle:
tan(theta) = opposite/adjacent
In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:
tan(theta) = 4.1/6
Using a calculator, we can solve for theta:
theta = tan^-1(4.1/6)
theta ≈ 34.3°
Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.
If the sum of the measures of the three angles shown is 163
, what is the measure of
Answer:
See below.
Step-by-step explanation:
We are asked to find the measure of ∠CEB.
We already know that the 3 angles combined have a total sum of 163°.
Let's set the 3 angles equal to 163°.
[tex]x-10+4x +2x+5=163[/tex]
Now, we should Combine Like Terms.
What is Combining Like Terms?
Combining Like Terms is adding, or subtracting together 2 or more numbers or variables that are alike.
For example, if we were given the expression;
[tex]5x + 3 - 2x + 9[/tex]
We should combine 5x and 2x, 3 and 9 since they are like terms.
For our equation;
[tex]x-10+4x +2x+5=163[/tex]
We should combine x, 4x, and 2x. We also should combine -10, 5, and 163.
Afterwards, we should have:
[tex]7x=168[/tex]
Simplify:
[tex]x= 24[/tex]
Substitute 24 within the value of x in the given expression for ∠CEB.
Substitute:
[tex]-10 + 4(24) = 86[/tex]
The measure of ∠CEB = 86°
If f(x) = 2x(1-x)^2, then f(1) =
(A) 0
(B) 2
(c) 4
(D) 6
(E) 8
Answer:
0
Step-by-step explanation:
2(1)*(1-(1))²=0
plug in 0 for everywhere you see x
What is the area of 2 ft 2 ft and 6ft?
The Area would be 4ft because 2x2=4 its basic multiplication,
And I don't really understand why you also put 6ft but if you're saying 2ft x 6ft then that would be 12ft.
Hope that helps <3
how do I use order of operations
Answer:
pemdas
Step-by-step explanation:
pemdas means Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction
you always want to go left to right
when using pemdas.
example 4^5 • (9-8)
you start from left to right
we would work in parentheses because that is what pemdas said to do.
QUESTION 3 Read the extract below and answer the questions that follow. Cape Town- a thirteen-year-old-boy was arrested and released on warning after he was caught on video assaulting an assistant teacher on the body and on head using his closed fists. Published: Dec 7, 2021 By: Siphokazi Vuso The grade 12 pupil from Harmony Primary in Steenberg can be seen on the video assaulting an assistant teacher after she had confiscated a ball from another pupil. Spokesperson Captain Frederick Van Wyk said witnesses tried to keep the learner away from the teacher when he broke loose and assaulted her. He said the boy was arrested on December 3 and was released in the care of his parents on a warning to appear in the Wynberg Magistrate's Court on Wednesday. [Adapted from: https://www.iol.co.za Accessed on 02 January 2023] /15/ 3.1 Define the term 'conflict resolution' and explain how the above situation is an example of bad conflict resolution. (1+2)(3) 3.2 Suggest TWO strategies that learners and teachers could put in place to decrease the culture of violent within their schools.
These two situations are examples of poor conflict resolution because they do not offer a space for dialogue between the individuals involved, but rather there is only judgment by law without any mediation.
What is conflict resolution?Conflict resolution is a term that refers to the ability of individuals to resolve conflicts or differences with others in a peaceful manner agreed upon by all parties involved. In this case, these two examples are not examples of good conflict resolution because there is no space for dialogue between students and teachers, but rather there is only aggression and prosecution before the entities in charge of justice in each country.
Due to the above, we believe that some strategies to end the culture of violence in schools is to spread messages of dialogue and conflict resolution in a peaceful manner. Also, offer workshops for parents so that from home conflict resolution is reinforced through dialogue.
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In a blueprint, each square has a side length of 14
inch.
a. Ceramic tile costs $5 per square foot. How much would it cost to tile the bathroom?
It would cost $
to tile the bathroom.
b. Carpet costs $18 per square yard. How much would it cost to carpet the bedroom and living room?
Step-by-step explanation:
1 blue square on drawing is length 1/4 in but that means 4ft in reality.
so one blue square area correspongs to 4x4 = 16 square feet.
(a) there 6 tiles for the batrhroom = 6x16 sq.ft = 96 sq.ft and the cost will be $480
(b) bedroom + living area = 7x8-8 tiles = 48 tiles = 48 x 16 sq.ft. = 768 sq.ft = 85.33 sq. yards. So the cost will be 85.33*18=$1535.94
(c) unit cost for tile: $5/sq.ft
unit cost for carpet: $1535.94/768sq.ft = $2/sq.ft
The tile has a greater unit cost ($5 per sq.ft) than carpet ($2 per sq.ft)
Tiling the bathroom would cost $25. The price of five squares of tile, or the cost of tiling the bathroom, is: $5 x 5 squares is $25.
How much would it cost to tile the bathroom?a. To calculate the cost of tiling the bathroom, we must first calculate its square footage. Assume the restroom measures 8 feet by 10 feet. We now have the area of:
960 square inches are equal to 8 feet by 12 inches per foot and 10 feet by 12 inches per foot.
The area of the bathroom can be divided by the area of each square, which is 14 inches on the blueprint, to determine the number of squares required:
14 inches by 14 inches divided by 960 square inches equals 4.96 squares.
As we are unable to purchase a fractional quantity of tile, we will round up to 5 squares.
The price of five squares of tile, or the cost of tiling the bathroom, is:
$5 x 5 squares is $25.
Consequently, tiling the bathroom would cost $25.
How much would it cost to carpet the bedroom and living room?b. To calculate the cost of carpeting the bedroom and living room, we must first calculate the square footage of each space. Assume that the living room is 18 feet by 20 feet and the bedroom is 12 feet by 14 feet in size. These areas include:
Bedroom: 168 square feet (12 feet by 14 feet).
The living room is 360 square feet (18 feet by 20 feet).
Divide by 9 to convert square feet to square yards:
Bedroom 168 sq ft / 9 sq ft = 18.67 sq ft
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Calculate the cash discount and the net amount due the transaction (in $).
The cash discount is $353.20 and the net amount due is $17,306.80.
What are the purchase terms?Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.
We know that,
Cash discount = amount x discount rate
Net amount due = amount - cash discount
For 2/10:
Cash discount = $17,660 x 2% = $353.20
Net amount due = $17,660 - $353.20 = $17,306.80
Hence, the cash discount is $353.20 and the net amount due is $17,306.80.
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Please help with this problem
On the number line, the points that represent the values of x in - 1 < x < 3 are:
012What are the values of x ?The expression given is - 1 < x < 3 which means that x is any whole number that is greater than - 1 but less than 3. This means that on the number line given, the value of x would be any number that is more than - 1 but less than 3.
These numbers will include 0, 1, and 2. The line should therefore begin at -1 and go to 3 to show the values of x in - 1 < x < 3 . The line to use should be the open circle which shows greater than or less than
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Ms. Curtis Basham grows pears and plums on her
urban homestead. Two years ago she gathered 40
pounds of pears and 12 pounds of plums. The next
year the
pears declined by 25% and the plums
declined by 20%. By what percentage did the total
yield, by weight, of her fruit harvest decline?
A. 22.5%
B. 24%
C. 45%
D. 76%
The percentage did the total yield, by weight, of her fruit harvest declined by approximately 24%, which is option B.
what is percentage ?
Percentage is a way of expressing a number or quantity as a fraction of 100. It is often denoted by the symbol % (percent). For example, 50% means 50 out of 100, or 50/100, or the equivalent fraction 1/2.
Percentages are commonly used in many real-world situations, such as in finance, statistics, and everyday life. They are often used to express changes, differences, or ratios between two values.
According to the question:
To solve this problem, we need to calculate the total weight of fruit harvested in the first year and the total weight of fruit harvested in the second year, and then calculate the percentage decline.
Total weight of fruit harvested in the first year = 40 + 12 = 52 pounds
After a 25% decline, the weight of pears in the second year = 40 - 0.25(40) = 30 pounds
After a 20% decline, the weight of plums in the second year = 12 - 0.20(12) = 9.6 pounds
Total weight of fruit harvested in the second year = 30 + 9.6 = 39.6 pounds
Percentage decline in the total yield of fruit harvest = [(52 - 39.6)/52] x 100% = 23.8%
Therefore, the answer is approximately 24%, which is option B.
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Identify the solution for the system of equations and explain its meaning using the context from the real-world problem.
I GOT THE ANSWER BUT I NEED THE EXPLANATION
The linear equation in this situation is y=20x which will have its solution as per the values of 'x'.
Explain about the System of Linear Equations?A collection of more that two linear equations is known as a system of linear equations. It's possible for a linear equation to have a number of variables.There are numerous uses for a system of linear equations. Real-world problem like assessing cost, distance, lifespan, profit, etc., as an example. Every unknown quantity can be found for a given quantity by using it.For instance, the cost of a good for a certain amount can be determined using a linear equation.
If a unit of a single product costs $20, the equation would be y=20x.In this case, x is the quantity of items and y is the price.The linear equation in this situation is y=20x.
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Help me I dont know the answer
Answer: the length is 6
Step-by-step explanation:
3+3+6+6=18
3x6=18
tommmy earns $140 in interest after 5 years on a pricipal of $400 jane earned $132 after 4 years on principal of $600 use the intrest rate to justify which bank would you rather use tommys or janes
Comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for less principal amount.
What is meant by the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Given,
Interest earned by Tommy SI = $140
Time t = 5 years
Principal amount P = $400
Interest earned by Jane SI = $132
Time t = 4 years
Principal amount P = $600
Simple interest SI = (P × r × t)/100
where r = interest rate
For Tommy,
140 = ( 400 × r × 5) /100
r = 7%
For Jane,
132 = ( 600 × r × 4) / 100
r = 5.5%
Therefore comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for the less principal amount.
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what is the property to 3(4+n)=12+3n
11. Suppose Britta only paid the interest during her 2 years in school and the
6-month grace period. What will she pay in interest over the term of her loan
Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.
what is interest ?The sum of money that a borrower must give a lender as interest is compensation for the use of borrowed funds. It is typically computed as a percentage of the principal, which is the amount borrowed, and is repaid alongside the principal over a predetermined amount of time. The cost of the lender, the likelihood of a default, and the desire for credit in the economy are just a few of the variables that affect the interest rate, or the percentage charged for borrowing the money.
given
We can use the following method to determine the total interest paid:
Principal x Interest Rate x Duration equals total interest.
where Principal denotes the sum borrowed, Interest Rate denotes the annual interest rate (in decimal form), and Time denotes the number of years over which interest will accrue.
Assume Britta took out a $50,000 loan to pay for her schooling.
Therefore, the amount of her loan at the conclusion of that time frame would be:
$50,000 x 1.06^2 = $56,420
The interest that will be charged on this balance for the remaining 10 years and 6 months of the loan period needs to be calculated now. Using the above method, we obtain:
$56,420 multiplied by 0.06 times 10.5 equals the total interest, or $33,782.
Accordingly, if Britta only paid the interest during her two years of education, she would accrue about $33,782 in interest over the course of her loan.
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QUESTION 1
Consider the following argument: Either there is a massive, multi-million dollar conspiracy at work, or else the electorate
have decided that Senator Wiggins is the best candidate for the position. The electorate have decided that Senator
Wiggins is the best candidate for the position. So, there is not a massive, multi-million dollar conspiracy at work. What is
the logical form of this argument?
O a. Modus Tollens
b. Disjunctive Syllogism
O c. Affirming the consequent
O d. Affirming a disjunct
Oe. Modus Ponens
Since the electorate have decided that Senator Wiggins is the best candidate for the position. The logical form of this argument is option b. Disjunctive Syllogism
What is Disjunctive Syllogism?The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.
In this case, the two alternatives are:
There is a massive, multi-million dollar conspiracy at work.The electorate have decided that Senator Wiggins is the best candidate for the position.The argument concludes that the second alternative is true, which means that the first alternative must be false. Therefore, the argument logically deduces that there is not a massive, multi-million dollar conspiracy at work.Thus, the logical form of the argument is:
Either A or B.
Not A.
Therefore, B.
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Look at this series: 12, 11, 13, 12, 14, 13, … What number should come next?
series: 12, 11, 13, 12, 14, 13, … What number should come next? i believe its 12
12-11=1
13-11=2
So to get 11 you subtract 1 from 12 and to get 13 you add 2 to it
If you follow that procedure the next number should be 15 if you add 2 to 13
is 5x=7y linear equation
Yes, 5x=7y is a linear equatiοn.
What is linear equatiοn?First οrder equatiοns include linear equatiοns. In the cοοrdinate system, the linear equatiοns are defined fοr lines. A linear equatiοn in οne variable is οne in which there is a hοmοgeneοus variable οf degree 1 (i.e., οnly οne variable). Multiple variables may be present in a linear equatiοn. Linear equatiοns in twο variables, fοr example, are used when a linear equatiοn cοntains twο variables.
Linear equatiοn is an algebraic equatiοn in οne οr mοre variables where the pοwer οf each variable is less than οr equal tο 1.
Fοr example,
y = mx + c , an equatiοn in this fοrm can be called as linear equatiοn.
Sο in equatiοn 5x = 7y
We can write this equatiοn as 7y = 5x + 0.
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Consider the following figure.
(Note that the figure is not drawn to scale.)
74°
55°
63°
59°
Order the side lengths HI, IK, HJ, IJ, and KJ from least to greatest.
O
X
5
The side lengths from least to greatest are HJ, HI, IJ, JK and IK
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Angle H is 67 degrees
∠HIJ is 51 degrees
∠HJI is 61 degrees
Angle K is 63 degrees
∠KJI is 70 degrees
∠KIJ is 57 degrees
From least to greatest
HJ<HI<IJ<JK<IK
Hence, the side lengths from least to greatest is HJ, HI, IJ, JK and IK
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Airplane A traveled 1662 miles in six hours.
For Airplane B, y = [tex]\frac{922}{3}x[/tex]
x represents its rate of speed over the same six hours.
Compare the two airplanes to determine which airplane traveled at a faster rate?
Airplane A traveled at a faster rate. The solution has been obtained by using speed-distance-time relationship.
What is speed-distance-time?Speed is calculated by dividing the distance traveled by the time needed to complete the journey. Distance and speed are intimately associated but time and speed are not.
We are given that Airplane A traveled 1662 miles in six hours.
We know that Speed = Distance / Time
Using this, we get
⇒Speed = 1662 / 6
⇒Speed = 277 miles per hour
We are given for Airplane B that y = 922/3x , where x represents its rate of speed over the same six hours
So, from this we get,
⇒Speed = (922/3) / 6
⇒Speed = 922 / 18
⇒Speed = 51.22 miles per hour
Hence, Airplane A traveled at a faster rate.
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the triangle below is isosceles.find the length of side X in simplest radical form with a rational denominator.
the answer is r6 because of the end result
The mango mania drinks company has a new design for the juice boxes. Each box will have a square base of an area of 22 cm². The height will be 12 cm. What is the volume of one of these new juice boxes.
By answering the supplied question, we may infer that the response is square Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.
What is a square?
According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is sometimes referred to as a rectangle with two adjacent sides of the same length.
A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are those that are 90 degrees or straight.
The diagonals of the square are also equally spaced and divided at a right angle. a nearby rectangle with two sides of identical length.
a quadrilateral with four equal-length sides and four right angles. two neighboring, equal sides that create a right angle in a parallelogram. an equilateral rhombus.
By dividing the base area by the height, one may get the volume of a square-based box. Thus, we can use the following formula to determine the juice box's volume:
Volume equals base area times height.
We may enter the numbers 22 cm² for the base area and 12 cm for the height into the formula to obtain the following results:
Volume equals 22 x 12 cm²
These values are multiplied together to produce:
Size = 264 cm³
Hence, Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.
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Given that 224 hours of work need to be done to complete a project. (1) How long will it take 4 men, each working an 8-hour day to complete the project? (II) If each of them is paid 57-50 per hour, how much will it cost to employ them altogether? (iii) How many hours of overtime must they put in per day if the project is to be completed in 4 days? (iv) Given that the overtime rate of payment is l times as much as the regular hourly rate, find the cost of the project now.
If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:
Total number of hours of work / Number of hours of work done by 4 men in a day
= 224 / (4 x 8)
= 7
So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.
II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:
Total number of men x Total number of days x Number of hours worked by each man per day
= 4 x 7 x 8
= 224 hours
Therefore, the total cost of employing all 4 men is:
Total number of hours x Rate per hour
= 224 x $57.50
= $12,880
III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:
Total number of hours of work / Total number of days to complete the project
= 224 / 4
= 56 hours
Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:
Number of hours of work per day - Number of hours worked by each man per day
= 56 - 8
= 48 hours
Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.
IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:
l x $57.50
= $57.50l
Let the overtime rate of payment be $r per hour. Then:
r = $57.50l
The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:
Number of regular hours x Regular hourly rate
= 4 x 8 x 7 x $57.50
= $16,240
The cost of overtime hours is:
Number of overtime hours x Overtime hourly rate
= 4 x 6 x 7 x $57.50l
= $12,180l
So, the total cost of the project is:
Total cost = Cost of regular hours + Cost of overtime hours
= $16,240 + $12,180l
Answer:
Step-by-step explanation:
(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:
Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days
So it will take 4 men, each working 8 hours per day, 7 days to complete the project.
(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:
Total cost = 4 men x $57.50/hour x 56 hours = $12,320
(iii) If the project is to be completed in 4 days, each man will need to work for a total of:
224 total hours / (4 men x 4 days) = 14 hours per day
Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.
(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:
Overtime rate = $57.50 x 1.5 = $86.25/hour
To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:
Regular hours cost = 224 regular hours x $57.50/hour = $12,880
The cost of the overtime hours is:
Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour
= 96 x $86.25
Therefore, the total cost of the project is:
Total cost = Regular hours cost + Overtime cost
= $12,880 + $8,280
= $21,160
where the overtime rate is 1.5 times the regular hourly rate.
