Answer:
The maximum number of people that can be invited is 65.
Step-by-step explanation:
Based on the information given in the question, the equation to solve the question will be:
80 + 37x = 2500
80+37x=2500
Step 1: Simplify both sides of the equation.
37x+80=2500
Step 2: Subtract 80 from both sides.
37x+80−80=2500−80
37x=2420
Step 3: Divide both sides by 37.
37x/37 = 2420/37
x= 2420/37
x = 65.4
x ≈ 65
The school store sells headbands for $2 each and T-shirts for $8 each. write ordered pairs to compare the cost of headbands to T-shirts for 0,1,2,3,4,: and 5 of each of them.
Use a table to show the two numerical patterns.
The cost of headbands follows the rule "add 2."0,2,4,6,8,10
The cost of T-shirts follows the rule "add 8." 0,8,16,32,40.
Then write the corresponding terms as ordered pairs.
Corresponding terms are those that appear in identical places in two similar situations.
Generate two numerical patterns given their rules. Understand that a term is a number in a pattern and corresponding terms are numbers in two patterns that show up in the same place in each pattern (e.g., the second term of each pattern are corresponding terms
.1) use the rule add 8 to find the cost of 6 t-shirts
cost of 5 t-shirts to get the cost of 6 t-shirts.
the cost of 5 t-shirts plus $8 is $40+$8= $48
2) the second number is 4 times the first number.
one pattern starts at 0 and follows the rule add 2.
another pattern starts at 0 and follows the rule add5.
corresponding terms as ordered pairs
0,0
2,8
4,16
6,24
8.32
10,40
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During final 172 students visited the math lab in total .if 4 out of were male is the percentage of female students who visited the math lab ? ( Round to the nearest tenant)
110% percent of female students visited the math lab.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages.
During the final exam, the number of students that visited the math lab is 172 in total.
Of the total number of students, 4 out of 11 were male.
Therefore, the total number of females that visited the math lab is:
no. of females = 11 - 4 = 7.
Therefore, the percentage of female students who visited the math lab is :
[tex]F=\frac{7}{11} \times 172\\\\F=109.4\\F=110[/tex]
Therefore, the percentage of female students who visited the math lab is 110%.
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endpoint of the
segment LN if
N(-8,2) and the
midpoint is
M(2,-4).
The final endpoint values are: (12,-6)
What is the midpoint?
The midway point of a line or segment is referred to as the midpoint. It creates an evenly spaced division in the line. In essence, it divides the lines into two.
According to the question, the coordinates of a line LN is given as: N (-8,2) and Midpoint M M(2,-4).
To calculate the midpoint, use the standard midpoint formula which is represented as below:
Midpoint =[tex]\frac{x1 + x2 }{2}[/tex] and [tex]\frac{y1 + y2 }{2}[/tex]
From the given data, the values are:
X1 = -8; Y1 = 2; X = 2; Y = -4
Therefore, the calculated midpoint is:
2 = -8 + [tex]\frac{x2}{2}[/tex] = 12
4 = 2 + [tex]\frac{y2}{2}[/tex] = -6
Hence, the final endpoint values are (12,-6)
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Translate into a variable expression. Then simplify.
1. a number n minus the difference between the number and seven
2. a number n increased by two-thirds of the number
3.twelve more than the square of a number n added to the difference between the number and fifteen
4.the sum of two times a number n and fourteen added to the product of fourteen and the number
5.The sum of two numbers is twenty-six. Using x to represent the smaller of the two numbers, translate "the difference between two more than the larger number and twice the smaller number" into a variable expression. Then simplify.
6.A financial advisor has invested $14,000 in two accounts. If one account contains x dollars, express the amount in the second account in terms of x.
7. A 9-foot board is cut into two pieces of different lengths. Express the length of the longer piece in terms of the length L of the shorter piece.
Find the midpoint of points A(-5, 3) and B(5, -1) graphically.
Plot the line segment AB by clicking twice on the graph.
s
Start over
-109-8 7 6 543
2 4
y
S
3 4
5
6
7
8
9 10
Mid point of the points A(-5, 3) and B(5, -1) is point C(0,1)
Mid point is a point that lies at the center of any measured distanced.
The points are written in the coordinate forms having first term as 'x' coordinate value called as abscissa and second term as 'y' coordinate value called as ordinate.
A = (x₁ , y₁) = (-5 , 3)
B = (x₂ , y₂) = (5 , -1)
Mid point formula [tex]( \frac{x1 +x2}{2} , \frac{y1+y2}{2} )[/tex], is used to find the midpoint of a line.
Mid point of the points A(-5, 3) and B(5, -1) ,
x₁ = -5
x₂ = 5
y₁ = 3
y₂ = -1
So, mid point C = [tex]( \frac{(-5)+5}{2} , \frac{3+(-1)}{2} )[/tex]
C = [tex]( \frac{0}{2} , \frac{2}{2} )[/tex]
C = (0 , 1) = (x , y)
The mid point of the points A(-5, 3) and B(5, -1) is point C(0 , -1)
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البلاغcdddffffdsaawefbjjhhg
Answer:
x=37
Step-by-step explanation:
If you stare at the picture long enough you can tell that you have six straight angles, which add up to [tex]180\°\times 6 = 1080\°[/tex]. You now need to take away the internal angles, that add up to [tex]180\° \times 6-360\° = 720\°[/tex]*
What you have left is two expression of the same quantity - the sum of the external angles. In one case is [tex]360\°[/tex] (the difference between the two values) and in the other is the sum of the various expressions containing x.[tex]2x +(x+10)+(x+18)+3x+(x-1)+x = 360\\9x = 360 - 27 \rightarrow 9x = 333\rightarrow x=37[/tex]
*Pick any point inside the polygon, and join it to the corners. You will create as many triangles as you have sides - in our case 6. Sum of angles will be 180 times the number of sides, minus a whole round angle - the one in the center.
A certain population demographic may be defined as someone older than 26, but les than 30 years of age. Express this statement using inequalities.
Answer:
26 < d < 30
Step-by-step explanation:
D is greater than 26 but less than 30.
Someone older than 26, but less than 30 years of age will be written as 26 < x < 30.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A certain population demographic may be defined as someone older than 26, but less than 30 years of age.
Let 'x' be the age of someone.
If the age of someone is greater than 26, then the inequality is written as,
26 < x ...1
If the age of someone is smaller than 30, then the inequality is written as,
x < 30 ...2
Combine both inequalities, then we have
26 < x < 30
Someone older than 26, but less than 30 years of age will be written as 26 < x < 30.
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LESSON 7.3 HELPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
THERE ARE 4 DIFFERENT QUESTIONS PLEASE ANSWER ALL 4 TO GET THE POINTS THANKS YOU
Find the missing side lengths. Leave your answers as radicals in simplest form.
Using relations in a right triangle, the missing side lengths are given as follows:
1. D. [tex]x = 7\sqrt{2}, y = 7[/tex]
2. B. [tex]x = 3\sqrt{2}, y = 2[/tex].
3. C. x = 6, y = 3.
4. C. [tex]x = 2\sqrt{5}, y = \frac{2\sqrt{15}}{3}[/tex]
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For the first triangle, we have that:
tan(45º) = 7/y
1 = 7/y
y = 7.
Applying the Pythagorean Theorem:
x² = 7² + 7²
x = sqrt(2 x 49)
[tex]x = 7\sqrt{2}[/tex]
Hence the correct option is:
D. [tex]x = 7\sqrt{2}, y = 7[/tex]
For the second triangle, we have that:
tan(45º) = y/3
1 = y/3
y = 3.
Applying the Pythagorean Theorem:
x² = 3² + 3²
x = sqrt(2 x 9)
[tex]x = 3\sqrt{2}[/tex]
Hence the correct option is:
B. [tex]x = 3\sqrt{2}, y = 2[/tex].
For the third triangle, we have that:
[tex]\tan{30^\circ} = \frac{y}{3\sqrt{3}}[/tex]
[tex]\frac{\sqrt{3}}{3} = \frac{y}{3\sqrt{3}}[/tex]
y = 3 x 3/3
y = 3.
Then:
[tex]\sin{30^\circ} = \frac{y}{x}[/tex]
0.5 = 3/x
x = 6.
Hence the correct option is:
C. x = 6, y = 3.
For the fourth triangle, we have that:
[tex]\sin{30^\circ} = \frac{y}{\frac{4\sqrt{15}}{3}}[/tex]
[tex]0.5 = \frac{y}{\frac{4\sqrt{15}}{3}}[/tex]
[tex]y = \frac{2\sqrt{15}}{3}[/tex]
[tex]\cos{30^\circ} = \frac{x}{\frac{4\sqrt{15}}{3}}[/tex]
[tex]\frac{\sqrt{3}}{{2}} = \frac{x}{\frac{4\sqrt{15}}{3}}[/tex]
[tex]x = 2\sqrt{5}[/tex]
Hence the correct option is:
C. [tex]x = 2\sqrt{5}, y = \frac{2\sqrt{15}}{3}[/tex]
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Please help with this !
Answer:
1. 26, cuz 17+9=26
2. 50, cuz 60-10=50
3. 19, cuz 33-14=19
Hope these will help you as you can't just ask for answers.
help please get it right and explain how to calculate it for brainliest
Alex invests $1,000 in his company's stock. After a year, the value of Alex's stock has increased to $1,250. What rate of return has Alex received?
Alex has received a rate of return of 0.25, or 25%, on his investment.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate the rate of return that Alex has received, we can use the formula:
rate of return = (final value - initial value) / initial value
where the final value is the value of the investment after the period of time in question, and the initial value is the value of the investment at the beginning of that period.
In this case, the final value is $1,250 and the initial value is $1,000, so we have:
rate of return = (1250 - 1000) / 1000 = 0.25
Therefore, Alex has received a rate of return of 0.25, or 25%, on his investment.
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PLEASE ANSWER QUICKLY!
power series interval of convergence (x+3)^n/(n) n is equal to 1
Interval of convergence of the power series [tex]\frac{(x+3)^{n} }{n}[/tex] ; n = 1 is -5 < x < -1.
A power series is a special type of infinite series representing a mathematical function in the form of an infinite series that either converges or diverges.
[tex]\lim_{n \to \infty} |\frac{an+1}{an}|[/tex] is the formula used to calculate the intervals for convergence or divergenceThe series is aₙ = [tex]\frac{(x+3)^{n} }{n}[/tex]
To generate aₙ₊₁ term replace 'n' with 'n + 1'
aₙ₊₁ = [tex]\frac{(x+3)^{n+1} }{n+1}[/tex]
Now plugging aₙ and aₙ₊₁ in the formula L = [tex]\lim_{n \to \infty} |\frac{an+1}{an}|[/tex]
L = [tex]\lim_{n \to \infty} |\frac{\frac{(x+3)^{n+1} }{n+1} }{\frac{(x+3)^{n} }{n} }|[/tex]
L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }/{\frac{(x+3)^{n} }{n} }|[/tex]
L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }*{\frac{n }{(x+3)^{n} }|[/tex]
L = [tex]\lim_{n \to \infty} |{\frac{(x+3) }{n+1} }*{n}|[/tex]
L = [tex](x+3)\lim_{n \to \infty} |{\frac{n}{n+1} }|[/tex]
L = [tex](x+3)\lim_{n \to \infty} |{\frac{n*(\frac{1}{n}) }{(n+1)*(\frac{1}{n}) } }|[/tex]
Since n = 1
L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{1+1} |[/tex]
L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{2} |[/tex]
L = [tex]\frac{1}{2} * |x+3|[/tex]
The ratio tells us that if L < 1 then the series will converge
[tex]\frac{1}{2}*(x+3) < 1[/tex]
[tex](x+3) < 2[/tex]
The interval of convergence will be
-2 < (x + 3) < 2
-5 < x < -1
The interval of convergence for the power series [tex]\frac{(x+3)^{n} }{n}[/tex] is -5 < x < -1
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find the solution set the this inequality 2x -3 > 2x-5/2
Answer:
0> 1/2
Step-by-step explanation:
You are building a shelf that fits in a corner in the figure the entire shelf is EGH. each unit in the coordinate plane represents one inch. Find the area A of the shelf. E is (25,20) G is (15,10) H is (25,10)
Answer:
Step-by-step explanation:
Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.
Answer:
112.5 units²
Step-by-step explanation:
Area of the shelf = ½*base*height.
The base is the distance between Z(0, 5) and Y(15, 5)
The height is the distance between X(15, 20) and Y(15, 5).
Therefore area of the shelf = ½*ZY*XY
Use the distance formula to find ZY and XY.
Distance between Z(0, 5) and Y(15, 5):
Let,
Distance between X(15, 20) and Y(15, 5):
Let,
Area of shelf = ½*15*15 = ½*225 = 112.5 units²
#10
Mr. Oliveros buys tickets to take theater
students to a play. Mr. Oliveros spends $45.00
in all. He spends $10 for his ticket and spends
the rest on student tickets. Each student ticket
is $2.50. How many student tickets does Mr.
Oliveros buy?
Answer:
14.
Step-by-step explanation:
1) if mr. Oliveros spent 10$ for his ticket, then the rest sum of his money is 45-10=35$;
2) according to the condition mr. Oliveros spends 35$ for unknown number tickets for students, where 2.5$ for each student. Using this conditiion it is possible to calculate the number of student tickets:
35/2.5=14.
Multiply the number 4 by . Add 6 to the product. Divide this sum by 2. Subtract 3 from the quotient.
1st number is 1 the result is
The original number is represented by x So, the result is the multiplier of 2.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
Dividend ÷ Divisor = Quotients
It is given that Multiply the number 4. Add 6 to the product. Divide this sum by 2. Subtract 3 from the quotient.
Let x = original number
(4x + 6)/2 - 2
= (4x /2 + 6/2) - 2
= 2x + 3 -2
= 2x+1
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The complete question is;
Write a conjecture that relates the result of the process to the original number selected. Represent the original number as x. What is the result?
a father is 4 times as old as his son. in 20 years the father will be twice as old as his son. find the present age of each.
Answer:
2(s+20)
Step-by-step explanation:
hope this helps
Answer: son is 10 years old and father is 40 years old
Step-by-step explanation:
Let the present age of son is x years
Then the present age of father is 4x years
4x+20=2(x+20)
4x+20=2x+40
4x+20-20=2x+40-20
4x=2x+20
4x-2x=2x+20-2x
2x=20
Divide both parts of the equation by 2:
x=10 years
4x=4(10)
4x=40 years
help me in economics please see the picture
Answer:
12
Step-by-step explanation:
Given a table of supply and demand at each price point, you are asked for the equilibrium price if the demand numbers are decreased by 0.5 million.
Equilibrium priceThe equilibrium price is the price at which the quantity demanded is equal to the quantity supplied.
For the given table, we see that a price of $14 thousands will result in both demand and supply being 2.00 millions per year. That is the equilibrium price before any adjustment to the table is made.
The problem statement is telling you to use a table that has all of the demand values decreased by 0.5 million. That makes the demand column read ...
2.25, 2.00, 1.75, 1.50, 1.25, 1.00, 0.75
This new column of reduced demand values matches the numbers in the supply column when they are both 1.75 million per year. That match occurs on the line with price $12 thousand.
The new equilibrium price is $12 thousand.
3
For the equation, y=x-1, determine the slope of the line (a) parallel to the given line and (b) perpendicular to the given line.
(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The slope of the line parallel to the given line is
(Type an integer or a fraction.)
OB. The slope of the line parallel to the given line is not defined.
(b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line perpendicular to the given line is
(Type an integer or a fraction.)
...
OB. The slope of the line perpendicular to the given line is not defined.
h
This question: point(s) P
a. The slope of the line parallel to y = 3/4x - 1 is: 3/4.
b. The slope of the line perpendicular to y = 3/4x - 1 is: -4/3.
What is the Slope of Lines that are Perpendicular and Lines that are Parallel?If two lines are parallel to each other, they will have the same slope value. On the other hand, if the two lines are perpendicular to each other, they will have slopes that are negative reciprocals of each other.
Thus, given the equation, y = 3/4x - 1, the slope of this line is 3/4.
The negative reciprocal of 3/4 is -4/3.
Therefore, we can conclude that:
a. The slope of the line parallel to y = 3/4x - 1 is: 3/4.
b. The slope of the line perpendicular to y = 3/4x - 1 is: -4/3.
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A circle has a radius of 7 inches. Find the arc length intercepted by a central angle of 280˚.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =280 \end{cases}\implies s=\cfrac{(280)\pi (7)}{180}\implies s=\cfrac{98\pi }{9}\implies s\approx 34.21[/tex]
HELP ME OUT PLEASE!!!!!
What is the rate of change of y with respect to x for this function? Record your answer in the boxes below.
The rate of change of y with respect to x for given function is -0.2
We know that, the slope of a function is nothing but the rate of change of y with respect to x of a function.
In this question, we have been given a linear function passing through points (-3, 3.6) and (5, 2)
We need to find the slope of the line passing through points (-3, 3.6) and (5, 2)
Let m be the slope.
By using the formula of the slope,
m = (2 - 3.6) / (5 - (-3))
m = -1.6 / 8
m = -0.2
Therefore, the rate of change of y with respect to x for given function is -0.2
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verbal expression for 2n + 7
Answer
Two times a number plus seven
Step-by-step explanation:
Hope this helps!!!
On a quiz, a student factored 25x² - 15x + 2 by grouping as follows.
25x² - 15x + 2 = 25x²5x - 10x + 2
= 5x(5x − 1)− 2(5x − 1) This is the student's answer.
He thought his answer was correct since it checked by multiplying. What went wrong? What is the correct factored form?
Select the correct choice below and fill in the answer box(es) to complete your choice.
A. The student did not factor the groups correctly. The correct factored form is □
B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is □
C. The pair of integers to write the middle term is not correct. The correct factored form is □
D. The sign between the two terms is not correct. The correct factored form is □
The correct answer regarding the factoring of the expression 25x² - 15x + 2 is:
B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).
How to factor an expression?An expression is factored placing the common terms in evidence, and then simplifying the entire expression according to these terms.
For this problem, the expression is:
25x² - 15x + 2.
After the first step, he found the following factorization:
5x(5x - 1) - 2(5x - 1).
However, this procedure is incomplete, as (5x - 1) is common to both terms of the subtraction. Thus the completely simplified expression is:
(5x - 1)(5x - 2).
As:
The correct option is:
B. The expression is the sum of two terms. He needs to factor out the common factor. The correct factored form is (5x - 1)(5x - 2).
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Find a in degrees.
Round to the nearest hundredth.
[tex]\large \bf \implies{53.1 \degree}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow \: sin \: α = \frac{8}{10} = 0.8 \\ \\\bf \longrightarrow \: α = arc \: sin (0.8)= 53.1°[/tex]
Students are raising money by selling wristbands. They buy 500 wristbands for just $0.90 each. They want to make at least $250.How much money should they charge for each wristband?
The amount that the students should charge for the wristbands will be at least $1.40.
How to illustrate the information?From the information, the students want to buy 500 wristbands for just $0.90 each and they want to make at least $250.
Therefore, the amount that they should charge for each will be:
Total cost = 500 × $0.90 = $450
Therefore, the amount charged be:
500x - 450 >= 250
Collect like terms
500x >= 250 + 450
500x >= 700
x >= 700/500
x>= $1.4
They should charge at least $1.40.
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A scale drawing of a rectangular park is 8 inches wide
and 11 inches long.
The actual park is 330 yards long. What is its area?
Use paper to help you with your thinking.
79200 square yards
240 square yards
88 square yards
2640 square yards
The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.
What is area of rectangle?Area of rectangle=Length * width.
Given:
scale length of rectangular park = 11 inch =
scale width of rectangular park = 8 inch
scale length / actual length of park = scale width/ actual width of park
11/330= 8/ actual width of park
1/30 = 8/ actual width of park
actual width of park = 240
So,
Area = length* width
=330*240
= 79200 square yards
Hence, the area of the actual parking is 79200 square yards.
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The steps to solve the equation 7(x + 3) = 9x - 4x − 35 are listed below. Put the justifications for the steps in the correct order to correspond with the steps.
7(x + 3) = 9x - 4x + 37
Step 1: 7x + 21 = 9x - 4x + 37
Step 2: 7x+ 21 - 21 = 9x - 4x +37 - 21
Step 3: 7x = 5x +16
Step 4: 7x - 5x = 5x - 5x +16
Step 5: 2x = 16
Step 6: 2x ÷ 2 = 16 ÷ 2
Step 7: x = 54
-Reorder Answers-
Subtraction Property of Equality
Simplification
Distributive Property
Subtraction Property of Equality
Combine like terms
Combine like terms
Division Property of Equality
The answer include the following:
Step 1: 7x + 21 = 9x - 4x + 37 - distributive property.
Step 2: 7x+ 21 - 21 = 9x - 4x +37 - 21 - subtraction property
Step 3: 7x = 5x +16 - combine like terms.
Step 4: 7x - 5x = 5x - 5x +16 - subtraction property.
Step 5: 2x = 16 - combine like terms
Step 6: 2x ÷ 2 = 16 ÷ 2 - division property.
Step 7: x = 54 - simplification.
What is Simplification?This is referred to as process in which a mathematical expression is replaced by another so as to ensure that it is simpler and shorter in other solve the problem and for better understanding.
In the case of 7(x + 3) = 9x - 4x − 35, distributive property is used to expand the bracket and collecting of like terms are also used for easier subtraction and addition process
This employs the use of different arithmetic operations such as division, etc and the steps above shoes the most appropriate justifications in this type of scenario.
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HL - Segment Proofs
6 of 86 of 8 Items
Question
Write the letter of the property, definition, or postulate that justifies each statement.
If 2XY = YZ, then YZ = 12YZ
Addition Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Multiplication Property of Equality
Division Property of Equality
Division Property of Equality
Substitution Property
Substitution Property
Reflexive Property
Reflexive Property
Symmetric Property
Symmetric Property
Transitive Property
Transitive Property
Definition of Congruence
Definition of Congruence
Definition of Midpoint
Definition of Midpoint
Segment Addition Postulate
If 2XY = YZ then XY = 1/2YZ this is division property of equality.
What are some properties of equality ?Division property of equality, multiplication property of equality, subtraction property of equality and addition property of equality.
According to the given question we have to define each property that we used to solve or interpret if 2XY = YZ, then XY = 1/2YZ.
This is division property of equality.
2XY = YZ
Now if we divide both sides of the equality by 2 we'll get
XY = 1/2 YZ and we know diving by a same constant on both sides of the inequality doesn't change the equality relation.
If 2XY = YZ, then YZ = 12YZ is not the correct question,The correct question is If 2XY = YZ then XY = 1/2YZ.
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Bill Murray has 16 3/4 days of vacation per year. To date, he has taken 1 3/4 days in January, 4 2/3 days in February, and 2 1/6 days in March. How much more vacation time is Bill entitled to?
Bill Murray has 16 3/4 days in total of vacation per year. Bill entitled to 8 1/6 days more vacation time.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bill Murray has 16 3/4 days in total.
(16×4 + 3)/4 = 67/4 days.
Then;
1 3/4 = (1×4 + 3)/4 = 7/4 days
4 2/3 = (4×3 + 2)/3 = 14/3 days
2 1/6 = (2×6 + 1) = 13/6 days
To add and then subtract them directly, we need to bring all fractions to the same denominator.
we have to multiply each fraction by a fitting n/n factor to bring the denominators to 12
67/4 = 67/4 × 3/3 = 201/12
7/4 = 7/4 × 3/3 = 21/12
14/3 = 14/3 × 4/4 = 56/12
13/6 = 13/6 × 2/2 = 26/12
Thus the remaining vacation time will be
201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6
49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days
Hence, Bill Murray has 16 3/4 days in total of vacation per year. Bill entitled to 8 1/6 days more vacation time.
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