The minimum value of the expression 3x² + 6x + 6 is 3.
Therefore the answer is 3.
A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.
Minimum value of a quadratic equation of form ax² + bx + c is when
x = -b/ 2a
Then minimum value is
a( -b/ 2a )² + b( -b/ 2a ) + c
= (b²a + -2ab² + 4a²c)/ 4a²
= ( - b² + 4ac)/ 4a
= c - b²/4a
In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is
= 6 - 6²/ (4×3)
= 3
--The question is incomplete, answering to the question below--
"What will be the minimum value of the expression 3x² + 6x + 6?"
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Select all the expressions that are equivalent to 16x - 12- 24x+ 4 16 x − 12 − 24 x + 4. Explain or show your reasoning.
1. 4+16x-12(1+2x)4 + 16 x − 12 ( 1 + 2 x )
2. 40x-1640 x − 16
3. 16x-24x-4+1216 x − 24 x − 4 + 12
4. -8x-8- 8 x − 8
5. 10 (1. 6x - 1. 2 - 2. 4x + 4)
1) 16x - 12(1 + 2x) + 4 is the expression that are equivalent to 16x-12-24x+4.
what is expression?An expression is a mathematical phrase that can contain numbers, variables, and operators. It can be a combination of these elements and can be evaluated to a specific value or a mathematical function.
An expression can be a simple mathematical statement such as 2x+3, or a more complex one involving multiple operations such as
(3x^2 - 4x + 5) / (2x +1). Expressions are used to represent mathematical operations, equations and relations between variables.
so we need to evaluate option 1 :
16x - 12 -24x +4
=> 16x - 12 -24x +4
the above expression is same as the expression mentioned in the question so option 1 is correct.
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Complete question :
Select all expressions that are equivalent to 16x−12−24x+4. Show or explain your reasoning.
1. 16x - 12(1 + 2x) + 4
2. 40x - 16
3. 4 - 12 + (2x - 3x)
4. -8(x+1)
Find the measures of the angles
Answer:
（1）：
angle1/2/3/4=90
angle6=51
angle7=40
angle8=89
angle9=51
angle10=40
angle12=50
angle13=130
angle14=50
Step-by-step explanation:
Q1：
angle1 2 3 4 divided 360 into four equal parts
so 360/4=90
angle11=110degree
so angle12 is 180-130=50 degree
because angle 12 3 10 are in triangle
their sum is 180
so angle 10=180-90（angle3）-50（angle12）=40
because angle 10 5 6 sum is 180
so angle 6 is=180-89（angle5）-40（angle10）=51
because angle 5 6 7 sum is 180
angle7=180-51（angle6）-89（angle5）=40
angle8=angle5=89
angle9=angle6=51
angle12 &13sum is 180
so angle13=180-50=130
angle14=angle12=50
30% of n = 84
please help I'll put as brainlisest
Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
30100 of 84 = 30100 × 84Therefore, the answer is 25.2
If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.
a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help explanation required
Answer:
$68
Step-by-step explanation:
Let x = original price.
The sale price is 75% of the original price, so the sale price is 75% of x.
75% as a decimal is 75/100 = 0.75
75% of is the same as 0.75x
We are told the sale price is $51, so 0.75x must equal $51.
0.75x = 51
Divide both sides by 0.75 to find the value of x.
x = 51/0.75
x = 68
Answer: $68
Answer:
Step-by-step explanation:
$51 is 75% of 100%
75% = 3/4
51 / 3 = 17
17 = 1/4
51 + 17 = 68
$68 is the original price of the shoes
HI!!
can someone help with ts
Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.
x is the input and f(x) is the output
This question is essentially asking what is the output of the function when the input is equal to 5.
[tex]f(5) = (5)^2-2(5)[/tex]
[tex]f(5) = 25-10[/tex]
[tex]f(5) = 15[/tex]
How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together
On solving the provided question, we can say that the permutation will bw , N = (4!)(5!)(3!)(3!)= 103,680
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
we can put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together will be , N = (4!)(5!)(3!)(3!)= 103,680
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Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality.
Answer:
It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.
To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:
5(-0.3) + 1.5 ≥ 4
This simplifies to:
-1.5 + 1.5 ≥ 4
Which further simplifies to:
0 ≥ 4
Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.
Step-by-step explanation:
You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $\sqrt{z}$. If the value of $x$ is 3 when $z$ is $12$, what is the value of $x$ when $z$ is equal to $75$
The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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100 points + Brainliest Let C represents the cost in dollars and R represents the revenue in dollars. What is the break-even point? Use a table to help if necessary.
C=36x+200
R=76x
Break-even point: (,)
Answer:
(x, {C and/or R}) = (5, 380)
Step-by-step explanation:
You want the break-even point when cost (C) and revenue (R) are given by ...
C = 36x +200R = 76xProfitProfit is the difference between revenue and cost. The break-even point is the point at which profit is zero:
P = R -C
0 = 76x -(36x +200)
0 = 40x -200 . . . . simplify
0 = x -5 . . . . . . . . . divide by 40
x = 5 . . . . . . . . . add 5
The break-even point is at x=5. Revenue and cost are both 380 at that point.
TableIf you prefer to look at these values in a table, you can consider ...
[tex]\displaystyle \begin{array}{ccc}x&C&R\\\cline{1-3}\vphantom{\^B}3&308&228\\4&344&304\\5&380&380\\6&416&456\end{array}[/tex]
We notice that cost and revenue are the same for x=5. They are both 380 for that value of x.
GraphAnother way to find the break-even point is to use a graph to plot cost and revenue on the same vertical axis. The point at which the lines cross is the break-even point. The break-even point coordinates are (5, 380).
Which government tax policy is most likely to result in an increase in consumer demand? A - an increase in personal income tax B - a decrease in corporate tax C - a decrease in personal income tax D - an increase in corporate tax
The correct answer is "C" - a decrease in personal income tax is most likely to result in an increase in consumer demand.
Define Tax.Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.
What is VAT?A value-added tax, often referred to as a goods and services tax in some nations, is a kind of tax that is imposed gradually. At every stage of manufacture, distribution, or sale to the final customer, it is added to the cost of a good or service.
There is an increase in consumer demand when personal income taxes are cut because people have more money that they can spend on products and services.
On the other hand, a rise in personal income taxes would reduce the amount of disposable money that consumers have, which will result in a drop in demand from consumers.
In a similar vein, a rise in company tax would result in higher business costs and lower profits, both of which would reduce consumer demand. Conversely, a drop in corporate tax would not directly influence consumer spending.
So the correct answer is C.
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What is the equation for the linear relationship in slope intercept form?
Answer:
y=1/2x-3
Step-by-step explanation:
y=mx+b
y=1/2x-3
Solve for x.
3 1/2 ≥ 1.4x
A. x ≥ 2 1/2
B. x ≤ 2 1/2
C. x ≥ 4 9/10
D. x ≤ 4 9/10
To solve for x, we need to get x by itself on one side of the equation. To do this, we can start by subtracting 1.4x from both sides of the equation. This gives us:
3 1/2 - 1.4x ≥ 0
Next, we can simplify the left side of the equation to get:
7/2 - 7/5x ≥ 0
Now we can divide both sides of the equation by -7/5 to get:
-5/2x ≤ -7/2
Finally, we can multiply both sides of the equation by -2/5 to get:
x ≥ 4 9/10
Therefore, the solution is x ≥ 4 9/10, which corresponds to answer choice C.
Answer:
x ≥ 4 9/10 C:)
Step-by-step explanation:
F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8
Answer:
gfifhdrtjttt9668ztjt*
Graph the system.
What is the estimated solution of the system?
Enter your answer in the blanks. Round each coordinate to the nearest integer.
The lines intersect closest to the integer coordinates
The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.
What is Graph of System of Linear EquationsA graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.
In the given problem, we have two linear equations which are
y = 3x - 6 ...eq(i)
y = 2/5x + 5 ...eq(ii)
Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.
The coordinates to the nearest integer are (x, y) 4 and 7
The value of x is 4 and y is 7
Kindly find attached graph below.
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how do i do this qustion
The slope of the line is 20.
The slope represents the rate of change in the price per hour is $20.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Two coordinates from the graph.
(1, 60) and (3, 100)
Slope.
= (100 - 60) / (3 - 1)
= 40 / 2
= 20
The slope represents the rate of change in the price per hour.
Thus,
The value of the slope is 20.
The slope denotes that the rate of charge per hour is $20.
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Jeremy made nine out of twelve basketball shots in P.E. class. What decimal and percent represents the number of shots he made?
Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=x³-6; translation 3 units left, followed by a reflection in the y-axis.
The function obtained after transformation is given as -x³ + 9x²- 27x + 21.
How to transform a graph of the function?The graph of a function can be transformed by either shifting it in the right, left, up or down.
When the transformation is rightwards, the function becomes as f(x - a).
For left shifting it is f(x + a).
The function is given as f(x) = x³- 6.
The translation of 3 units towards left can be written as,
f(x + 3) = (x + 3)³ - 6
⇒ x³ + 9x² + 27x + 21
For reflection across y axis replace -x with x as below,
⇒ (-x)³ + 9(-x)² + 27 × -x + 21
⇒ -x³ + 9x²- 27x + 21
Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.
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one leg of a right triangle is 8 cm what could the other length be justify your answer
Answer:
6-L2
10-hypotenuse
Step-by-step explanation:
Pythagorean theorem
What is dual expression?
The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .
What is a Boolean Expression ?
The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.
Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .
If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .
The given question is incomplete , the complete question is
What is Dual Boolean Expression ?
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At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be
Probability measures how probable something is to occur.
What the probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.
Probability is a measure of how likely something is to happen.
18 Marines, 10 Navy personnel, and 3 Coast Guard troops received their wings at a recent naval aviation school graduation.
Total: 18 + 10 + 3 = 31
a. 1 of each. P = C 18 * C 10 * C 3 / C 3 31
= (18 * 10 * 3) / 4495 = 0.120
b: 0 members of the navy = (C_{21} ^ 3)/(C_{21} ^ 3) = 1330/4495 = 0.296
c: 3 Marines.
p = (G ^ 3)/(C_{31} ^ 3) = (8 + 6)/4495 = 0.182
The complete question is
At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be
a.1 of each 0.120 b. members of the Navy 0.296 c. Marines 0.182.
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what is x if 2/6+x=11/18
Answer:
multiply top and bottom of 2/6 to get 6/18, then subtract the answer by 6/18 , you get 5/18
Step-by-step explanation:
Answer:
x = 5/18
Step-by-step explanation:
what is x if 2/6+x=11/18
2/6 + x = 11/18
x = 11/18 - 2/6
x = 5/18
----------------------------
check2/6 + 5/18 = 11/18
11/18 = 11/18
The answer is good
Perform the calculation then round to the appropriate number of significant digits
Answer:
315
Step-by-step explanation:
88.2 × 3.5742 = 315.24444
Answer: 315
Please hurry it's timed i need help
The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given the function as;
cosx - √(3 - 3cos³x) = 0
cosx = √(3 - 3cos³x)
Taking square root on both sides.
cos ²x = √(3 - 3cos³x) ²
cos ²x = (3 - 3cos³x)
For solving for x in
cos ²x = (3 - 3cos³x)
cos ²x = 3 (1 - cos³x)
(1 - cos³x) = cos ²x/3
x= π/6 + 2πn
or
x=11π/6 + 2πn
where n is an integer.
30° + 360° n, 330° + 360°n
The correct answer is C.
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If $x$ is a positive multiple of 8 and $x^2>100$, but $x<20$, what is $x$?
Answer:
16
Step-by-step explanation:
16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.
Answer:
[tex]$x=\boxed{16}$[/tex]
Step-by-step explanation:
Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.
To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.
Therefore, $x=\boxed{16}$.
The length and the breadth of a rectangular room is in 3:2 and its area is 96m². Find the length and breadth of the room. [Ans: 12m, 8m]
Answer:12m,8m
Step-by-step explanation:BREAADTH
What critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 15 observations
A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).
The critical t-value is what?The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.
How do we determine the appropriate value of T *?Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.
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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).
The critical t-value is what?The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.
How do we determine the appropriate value of T?Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.
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how do i solve -2.4>b/-2.5 step by step
Step-by-step explanation:
hope this helps....see above for answer
A recipe for 3 people uses 150 g of flour. How much flour is needed to
make the same recipe for 6 people? Give your answer in grams (g).
600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.
Given that a recipe for 3 people uses 150 g of flour.
We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.
So if the number of people will increase so the quantity of flour will be needed more.
The flour needed to make the recipe for 1 people is = 150/3 = 50 g.
The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.
Hence 600 g flour is needed to make the same recipe for 6 people.
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OMG PLEASE HELP FAST, Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in the attached graph in slope intercept form is written as
y = -6x + 2How to write the equation of the lineThe slope, m of the linear function is calculated using the points on the graph (1, -4) and (2, -10)
m = (y₀ - y₁) / (x₀ - x₁)
plugging in the values and evaluating
m = (-10 + 4) / (2 - 1)
m = (-6) / (1)
m = -6
equation passing through point (2, -10), using the point slope formula
(y - y₁) = m (x - x₁)
y - (-10) = -6(x - 2)
y + 10 = -6x + 12
rearranging the equation
y = -6x + 12 - 10
y = -6x + 2
The equation of the line in slope intercept form is written as y = -6x + 2
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Awatch which loses a half a minute was set to read the correct time at 0445h on Monday. determine the time in 12 hour clock system,the watch will show on the following Friday at 1845h
The Correct answer is 5.50 p.m
ExplanationTime between Monday 0445h and Friday 1845h
= 4 x 24 + 14 = 110h
Time lost = 0.5 x 110
= 55min
Time shown in 12 hour system
1845 – 55 = 1750 h
= 5.50 p.m
What is a 12-hour Clock system?On an analogue clock, the 12-hour clock is most frequently displayed as the digits 1 through 12; on a digital clock, it is typically followed by either a.m. (ante meridiem, Latin for "before noon") or p.m. (post meridiem, Latin for "after noon").
What is a 24-hour Clock system?Digital clocks are more frequently used to display the 24-hour clock, which is printed in a 4-digit format with the first two numbers denoting the hour and the final two denoting the minutes.
No need for a.m. or p.m. is necessary because each time represents one of the 24 hours in a day. For instance, 0300 is the third hour of the day, or 3am; 1400 is the fourteenth hour of the day, or 2pm; and 1830 is the thirty-minute mark after the eighteenth hour of the day, or 6.30pm.
How can we change 12-hour time format into a 24-hour clock format?Children can be taught to add 12 to the hours after noon in order to change a 12-hour clock to a 24-hour one. For instance, 3pm becomes 15:00 since 3 + 12 = 15.
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The time shown on 19:45h Fridays is 06: 55 pm Friday.
What is meant by clock system?A collection of synchronized clocks that can communicate with one another and display the exact same time every single time is known as a clock network or clock system. A constant pulse known as a system clock or system timer aids the computer clock in maintaining accurate time. It keeps track of how many seconds have passed since the epoch and utilizes that information to determine the current date and time.
A piece of electronic equipment inside a computer that continuously emits a high-frequency signal to keep everything in sync. electrical gadget type. a piece of equipment that operates electronically. a computerized time-of-day clock.
Given: Watch loses = 1/2 minute every hour
Time difference = 19: 45 h Friday - US:45 h Monday
=4 days 14 hours
=24 × 4+14 hours
=96+14
=110 hours
Time lost [tex]$= & 144^{55} \times \frac{1}{2} \mathrm{~min} \\[/tex]
= 55 min
Time shown on 19:45h Fridays
= 19: 45 - 0: 55
= 18: 55 h Friday
= 06: 55 pm Friday
Hence, 06: 55 pm Friday
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