A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high.
(a) How much work is done in pulling the rope to the top of the building?
(b) How much work is done in pulling half the rope to the top of the building?
Answers
(a) To pull the entire rope to the top of the building, we need to overcome the weight of the rope and lift it 120 feet against gravity. The weight of the rope is:
0.5 lb/ft * 50 ft = 25 lb
The work done in lifting the rope is given by:
W = Fd
where W is the work done, F is the force applied, and d is the distance moved in the direction of the force. In this case, the force applied is the weight of the rope, which is 25 lb, and the distance moved is 120 feet. Therefore:
W = 25 lb * 120 ft = 3000 ft-lb
So the work done in pulling the rope to the top of the building is 3000 ft-lb.
(b) To pull half of the rope to the top of the building, we need to overcome the weight of half of the rope and lift it 120 feet against gravity. The weight of half of the rope is:
0.5 lb/ft * 25 ft = 12.5 lb
The work done in lifting half of the rope is:
W = Fd = 12.5 lb * 120 ft = 1500 ft-lb
So the work done in pulling half of the rope to the top of the building is 1500 ft-lb.
Related Questions
Triangle XYZ is rotated to create the image triangle X'Y'Z'.
On a coordinate plane, 2 triangles are shown. The first triangle has points X (negative 2, 2), Y (1, 2), Z (0, 4). The second triangle has points X prime (2, negative 2), Y prime (negative 1, negative 1), Z prime (0, negative 4).
Which rules could describe the rotation? Select two options.
R0, 90°
R0, 180°
R0, 270°
(x, y) → (–y, x)
(x, y) → (–x, –y)
Answers
Answer:
The correct option is;
R0, 180°
Step-by-step explanation:
The coordinates of ΔXYZ are given as follows;
X(-2, 2), Y(1, 2), Z(0, 4)
The coordinates of ΔX'Y'Z' are given as follows;
X'(2, -2), Y'(-1, -1), Z'(0, -4)
Whereby, the coordinates of the point Y' is (-1, -2), we have the rule that describe the transformation of ΔXYZ to ΔX'Y'Z', given as follows
Coordinates of the preimage = (x, y)
Coordinates of the image = (-x, -y)
Which is in accordance with the transformation by rotation 180° about the origin.
Answer:
b,e
Step-by-step explanation:
if two tables have a one-to-many relationship, which of the following do you typically need to add to the table on the "many" side?
Answers
When two tables have a one-to-many relationship, you typically need to add a foreign key to the table on the "many" side to link the records to the corresponding record in the "one" table.
In a one-to-many relationship, the table on the "one" side is usually the primary key table, and the table on the "many" side is usually the foreign key table. The foreign key is used to link the records in the "many" table to the corresponding record in the "one" table. This is done by adding a column to the "many" table that contains the primary key value from the "one" table.
When designing a database, it is important to establish relationships between tables to ensure data integrity and avoid redundant data. In a one-to-many relationship, one record in the primary key table can be associated with many records in the foreign key table. To establish a one-to-many relationship, you need to create a primary key in the "one" table and a foreign key in the "many" table. The foreign key is a column that contains the primary key value from the "one" table. For example, if you have a "customers" table and an "orders" table, the "customers" table would be the primary key table and the "orders" table would be the foreign key table. Each record in the "orders" table would have a foreign key column that contains the customer ID from the "customers" table.
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In the triangle shown below AB=BC=10
and AC=12.
To
A) 0.4
B) 0.6
C) 0.8
D) 1.2
10
B
12
What is the value of sin ?
10
#
0
point
Answers
The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.
What is Pythagorean theorem?
The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.
The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.
The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.
The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.
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A specific breed of dog is well known for how long they can live for. On average, they live for 162 months, with a standard deviation of 30 months. What percentage of dogs live for less than 144 months?
Answers
Answer: 27.43%
Explanation:
Let x be a random variable representing the age of the specific breed of dogs. Since the age is normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula;
z = (x - μ)/σ
where
x is the sample mean
μ is the population mean
σ is the population standard deviation
From the information given,
μ = 162
σ = 30
x = 144
By substituting these values into the formula, we have
z = (144 - 162)/30
z = - 0.6
We want to find P(x < 144). This is the area under the curve to the left of z = - 0.6 on the standard normal distribution table. By looking at z = - 0.6 on the table,
P(x < 144) = 0.2743
Thus, the probability that a dog will live for less than 144 months is 0.2743
We would convert it to percentage by multiplying by 100. We have
0.2743 x 100 = 27.43%
4. Charlene is reading a book that has a volume of 120 in ³ and cover
dimensions of 8 in. by 10 in.
The front and back covers are each 0.5 cm thick, and each page is 0.05
mm thick.
Charlene can read 20 pages per hour.
Determine how many hours it will take for Charlene to read the entire book.
Answers
The number of hours required by Charlene to read the complete book will be 37.1 hours.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
Given that:-
Charlene is reading a book that has a volume of 120 in ³ and covers dimensions of 8 in. by 10 in.The front and back covers are each 0.5 cm thick, and each page is 0.05 mm thick.Charlene can read 20 pages per hour.First, we will calculate the total thickness of the book:-
V = 120 cubic inches
V = A x t
120 = 8 x 10 x t
t = ( 120 )/( 80) = 1.5 inches.
t = 1.5 x 2.54 = 3.81 cm
Now we have a cover thickness of 0.5 cm so the total cover thickness will be 0.1 cm and the thickness of the page will be 0.05 mm or 0.005 cm.
The volume of the pages is:-
Vp = 3.81 - 0.1 = 3.71 cubic cm
The number of the pages will be calculated as:-
Number of the pages = \(\dfrac{3.71}{0.005}\) = 742 pages.
We have 20 pages 1 hour so 742 pages will be readable in:-
Reading time = 742 / 20 = 37.1 hours.
Therefore the number of hours required by Charlene to read the complete book will be 37.1 hours.
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please help:
What is an equation in slope-intercept form for the line given?
Answers
The equation of the line passing through points (-1, 2) and (1, -1) is y = -1.5x + 0.5
How to solve an equationAn equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the slope of the line and b is the y intercept
The line given passes through the point (-1, 2) and (1, -1). The equation is:
y - 2 = [(-1-2)/(1 - (-1)](x - (-1)]
y - 2 = -(3/2)(x + 1)
y = -(3/2)x - (3/2)
y = -1.5x + 0.5
The equation of the line is y = -1.5x + 0.5
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Times Interest Earned - Data Analysis a) The following information is from the Income Statements of the Einstein Corporation:
Current year Prior Year Income before Interest and Taxes $ 700,000 $ 650,000 Interest Expense $ 200,000 $ 150,000 Income before Taxes $ 500,000 $ 500,000 Tax Expense $ 100,000 $ 100,000
Net Income $ 400,000S 400,000 1) Calculate the number of times interest is earned for the current year? 2) Calculate the number of times interest is earned for the prior year? b) What conclusions can you draw?
Answers
Therefore,TIE = EBIT / Interest expenseCurrent Year TIE= 700,000 / 200,000 = 3.5 times prior Year TIE = 650,000 / 150,000 = 4.3 times) The Einstein Corporation's TIE in the current year is less than the prior year. The corporation's debt service costs have grown as the TIE has decreased.
a) The Times Interest Earned (TIE) is calculated by dividing income before interest and taxes (EBIT) by interest expense. Therefore,TIE = EBIT / Interest expenseCurrent Year TIE= 700,000 / 200,000 = 3.5 times prior Year TIE = 650,000 / 150,000 = 4.3 times) The Einstein Corporation's TIE in the current year is less than the prior year. The corporation's debt service costs have grown as the TIE has decreased. Therefore, it may be in trouble if it continues to increase its debt service expenditures at the current rate. In addition, the company must take steps to increase its earnings before interest and taxes (EBIT) to increase the TIE ratio, indicating that it can meet its debt obligations more easily.
Therefore,TIE = EBIT / Interest expenseCurrent Year TIE= 700,000 / 200,000 = 3.5 times prior Year TIE = 650,000 / 150,000 = 4.3 times) The Einstein Corporation's TIE in the current year is less than the prior year. The corporation's debt service costs have grown as the TIE has decreased.
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What is the percent increase from 87 to 157? *PLEASE HELP ME*
Answers
Answer:
It should be an 80.45% increase.
Tim explained a function in words and Paul wrote an equation. Tim The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. Paul yâÂ’1,400=56(x 26) Whose function has the smaller y-intercept? Tim’s with a y-intercept of $2,700 Paul’s with a y-intercept of $2,856 Paul’s with a y-intercept of $2,800 Tim’s with a y-intercept of $2,780.
Answers
Option D: Tim's with a y-intercept of $2,780.
Given that:
Equation given by Paul:
\(y - 1400 = 56(x + 26)\\or\\y = 56x + 2856\)
Data given by Tim:
Total amount at the end of 8 months = $4,500
Interest per month = $225
Thus principal amount can be calculated by: \(4580 - 8 \times 225 = 2780\) in dollars.
Thus the equation for Tim will be:
\(y = 2780 + 225x\)
Thus it is visible that the y-s intercept for Tim's equation is smaller ( since 2780 < 2856).
Thus Option D is correct.
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This program specification provides a sample of the pseudocode drafted to outline the algorithmic solution for solving a problem. The program attempts to average two test scores for each student in the class.
Prompt user to enter the first name of the student.
Test whether the user enters a character 'Q' or 'q' to quit the program.
If the user hasn't quit the program, prompt the user to enter the first score.
Validate the score entered.
Add this score to the student's total score.
Prompt the user to enter the second score.
Determine the average score of both values.
Although the program compiles, links, and runs, several logic errors will provide unwarranted results.
Identify the necessary variables needed to collect and calculate data.
Identify the errors that you noticed and explain why they are errors.
Identify when you are using decision or looping structures and explain how this helps your program.
Provide complete and adequate pseudocode instructions.
Answers
In order to collect and calculate data, you need several variables.
There are several errors in this code, which include: The program does not take into account that the user can enter lower or higher numbers than expected. This is resolved by using loops that validate the scores entered.
In order to collect and calculate data, you need several variables. For example: first name, score 1, score 2, total score and the average score of both values. Here is the pseudocode that includes all of the requirements mentioned above:```
Begin
Declare character studentName
Declare number score1, score2, totalScore, averageScore
Display "Enter Q to quit or the first name of the student"
Input studentName
While (studentName != 'Q' and studentName != 'q')
Display "Enter the first score"
Input score1
While (score1 < 0 or score1 > 100)
Display "Invalid input. Please enter a score between 0 and 100"
Input score1
End While
Display "Enter the second score"
Input score2
While (score2 < 0 or score2 > 100)
Display "Invalid input. Please enter a score between 0 and 100"
Input score2
End While
totalScore = score1 + score2
averageScore = totalScore / 2
Display studentName, "has an average score of", averageScore
Display "Enter Q to quit or the first name of the student"
Input student Name
End While
End
```
There are several errors in this code, which include:
1. The program does not take into account that the user can enter lower or higher numbers than expected. This is resolved by using loops that validate the scores entered.
2. There is no total score calculated to provide an average score. The solution is to add the scores together and calculate the average.
3. The program did not specify that the scores must be between 0 and 100. This is remedied by using decision-making structures in the form of "while" loops that repeat the prompt for a score until it is between 0 and 100.
4. The variable that holds the name of the student is declared as a character, which means it can only hold one character. This is resolved by declaring it as a string.
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How do you write an equation for a parabola with the vertex and Y intercept?
Answers
To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Consider an example where vertex is (2,1) and y-intercept is (0,-3).
The equation of parabola needs to be deduced using these points.
The equation of a parabola in vertex form is -
y=a(x-h)^2+k
Here, a is a constant and (h ,k) are the coordinates of the vertex.
So, (h,k)=(2,1)
⇒y=a(x−2)^2+1
To obtain the value of a, substitute (0,−3) into the equation -
-3=4a+1
4a=-4
a=-1
⇒y=-1(x−2)^2+1
Now, distribute and simplify -
y=-1(x−2)^2+1
y=-(x^2-4x+4)+1
y=-x^2+4x-4+1
y=-x^2+4x-3
On, graphing this equation a parabola is obtained.
Therefore, to write an equation of parabola vertex form is used.
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Picture below has question/answer choices!!
Answers
The statements that is true about the similarity of the two triangles the option D
D. ΔMNO and ΔJKL are not similar triangles
What are similar triangles?Similar triangles are triangles which have proportional corresponding sides
The parameters in the question are;
The length of segment MN = 20
Length of segment NO = 12
Length of segment OM = 25
Measure of angle ∠O = 56°
Length of segment LJ =- 15
Length of segment JK = 12
Length of segment KL = 9
Measure of angle ∠L = 56°
Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included angle between the two sides are congruent
The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL
However, the ratio of the sides LK to ON and JL to MO are;
9/12 ≠ 15/25
Therefore, the triangles are not similar
The correct option is option D
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What is the area of this rectangle?
A rectangle with the length labeled 3 and two-sixths meters and the width labeled 2 and three-fourths meters.
five and five-twelfths m2
six and six twenty-fourths m2
six and five-tenths m2
nine and four twenty-fourths m2
Answers
The area of the rectangle is:
length x width
We need to first convert the length and width to the same units. We can convert them to twelfths of a meter, since both 6 and 4 are factors of 12.
Length = 3 and 2/6 meters = 3 x 12/6 + 2/6 = 18/6 + 2/6 = 20/6 = 10/3 twelfths of a meter
Width = 2 and 3/4 meters = 2 x 12/4 + 3/4 = 24/4 + 3/4 = 27/4 twelfths of a meter
Now we can find the area:
Area = length x width = (10/3) x (27/4) = 90/12 = 15/2 = 7.5 square meters
Therefore, the answer is option C) six and five-tenths m² (rounded to one decimal place).
The top of building A is 418 feet high. This is about 3 times as high as the top of building B.
About how high is the top of building B?
Select the numbers that correctly complete the sentence.
The top of building B is between
Choose...
feet high.
Answers
Answer:139.33 or 139 ft high
Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139
Simplify \(6x^{2} -\frac{16}{2} +\sqrt[n]{25}\)
Answers
Answer:
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME!!!!!
Answers
9514 1404 393
Answer:
$7.00 per week
Step-by-step explanation:
The balance at the end of week 1 is $39-32 = $7.00 higher than at the start. The rate of change is $7.00 per week.
Answer:
$ 7.00 per weekStep-by-step explanation:
#CarryOnLearningplease help me no links pls im giving my finals points away for this dont let me down!
Answers
Answer:
D, purple line.
Hope this helps!
Good luck with your finals!
Answer:
Gregor Mendel knew how to keep things simple. In Mendel's work on pea plants, each gene came in just two different versions, or alleles, and these alleles had a nice, clear-cut dominance relationship (with the dominant allele fully overriding the recessive allele to determine the plant's appearance
Step-by-step explanation:
ok intro dear new sis
Select the correct hypotheses to investigate our research question: Has the distribution of beliefs changed since 2009?
a. H0: There is no association between beliefs and year. | HA: There is some association between beliefs and year.
b. H0: p1 = 0.32, p2 = 0.15, p3 = 0.46, p4 = 0.07 | HA: At least one pi differs from the proportions in 2009.
Answers
The correct hypothesis to investigate our research question: Has the distribution of beliefs changed since 2009 is
b. H0: p1 = 0.32, p2 = 0.15, p3 = 0.46, p4 = 0.07 | HA: At least one pi differs from the proportions in 2009. So the correct option is option b.
To investigate the about the correct hypotheses to investigate our research question and has the distribution of beliefs changed since 2009 select the following hypotheses:
H0: p1 = 0.32, p2 = 0.15, p3 = 0.46, p4 = 0.07 (There is no change in the distribution of beliefs since 2009.)
HA: At least one pi differs from the proportions in 2009 (There is some change in the distribution of beliefs since 2009.)
This is option (b) in your given choices. These hypotheses will allow you to test whether the distribution of beliefs has changed since 2009 by comparing the proportions of each belief in your sample to the proportions in 2009.
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Consider the diagram.
Which equations are true? Select all true equations.
Answers
Answer:
Sum of angles of a triangle is 180, so x + y + w = 180
Straight angle is 180 , so y + z = 180
From the first 2 conditions :
=>x + y +w = y + z
=> x + w = z
Option 1, 2, 5
The equations which are true are given by,
w + x + y = 180w + x + y = 180y + z = w + x + yw + x + y = 180y + z = w + x + yw + x = z What is an Equation?Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.
From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.
Here all interrior angles of triangle are x,y,w
So, x+y+w = 180
Hence first option is correct.
Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.
here exterrior angle is z and opposite two interrior of z are x,w
So, w+x = z
Hence last option is correct.
Again y+z = y+w+x
so second option is also true.
Hence correct options or equations are given by:
w + x + y = 180w + x + y = 180y + z = w + x + yw + x + y = 180y + z = w + x + yw + x = zLearn more about Equation here -
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Evaluate x+y when x=1/3 and y=−7/4. Write your answer in a fraction in simplest form.
Answers
Answer:
-17/12
Step-by-step explanation:
We have x+y
If x=1/3 and y=-7/4,
we can substitute them in and get:
1/3+(-7/4)
=1/3-7/4
=4/12-21/12
=-17/12
Answer:
1/3 + -7/4 =
4/12 + -21/12=
-17/12=
-1 5/12 this is what i got i dont know how the hail i got this 0_o
Step-by-step explanation:
which functions can generate all the values in table 2
Answers
Answer:
animania-1.12.2-1.6.2.jar
A company makes fish tanks in the shape of right rectangular prisms. The company has an order for a fish tank that must be exactly 4 feet long and hold at least 35 cubic feet of water. The company wants to save money on materials and will make the tank with the smallest surface area possible. The dimensions of the tank must be in whole foot increments and a top is included in the construction What dimensions for the width and height of the fish tank will satisfy the requirements
Answers
The dimensions for the width and height of the fish tank will be 4 feet and 2 feet .
What is dimension?Dimension is the measurable extent of a particular kind, such as length, breadth, depth, or height.
According to the given problem,
let , b = is the width of the fish tank
h = is the height of the fish tank given that , hold at least 35 cubic feet of water .
so ,
4×b×h ≥ 35
⇒ h ≥ 35/4b
now , surface area of the fish tank
⇒ 4b + 2× 4h + 2× bh
now substitute the value of h
here
⇒ ≥ 4b +70/b + 35/2
⇒ ≥ 40(70)^1/2 + 35/2 (if and only if b= (70)^1/2 / 2 , the equal sign holds )
therefore ,
= (70)^1/2 / 2 b ≈ 4.18 so b is 4 . when b = 4 ,
h = 35 / 4 × 4 = 2.1875 round off h = 2
so , the minimum surface area of fish tank is
⇒ 4×4+ 2× 4×2 + 2× 4×2⇒ 48
hence , the height and the width of the fish tank is 2 and 4 .
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If r is the position vector (with components x1, x2, x3) and v is any vector, show that
Answers
The position vector r (with components x1, x2, x3) and any vector v can be expressed as r = x1*i + x2*j + x3*k and v = a*i + b*j + c*k, respectively.
How can we show that the dot product of the position vector r and the vector v is equal to the sum of the products of their corresponding components?The dot product of two vectors is defined as the sum of the products of their corresponding components. Therefore, the dot product of r and v can be calculated as:
r · v = (x1*i + x2*j + x3*k) · (a*i + b*j + c*k)
= (x1*a) + (x2*b) + (x3*c)
Here, we multiplied the corresponding components and summed them up. The dot product represents the scalar projection of one vector onto the other, which indicates the magnitude of one vector in the direction of the other.
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wind energy in the u.s. generated about 74 million megawatt hours of electricity in 2009. this quantity increased at an approximately constant rate and reached about 254 million megawatt hours by 2017. estimate how many more megawatt hours were generated from wind in 2020 than in 2016.
Answers
We can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.
What is Division?
Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse operation of multiplication and is represented using the division symbol ÷ or the forward slash /.
Solution:
To estimate how many more megawatt hours were generated from wind in 2020 than in 2016, we need to make some assumptions and approximations since the problem only provides data for 2009 and 2017.
Assuming that the wind energy generation continued to increase at the same constant rate between 2017 and 2020, we can estimate the amount of wind energy generated in 2020 as follows:
1. From 2009 to 2017, the wind energy generation increased by 254 million - 74 million = 180 million megawatt hours.
2. The time period between 2009 and 2017 is 8 years, so the average annual increase in wind energy generation is 180 million / 8 years = 22.5 million megawatt hours per year.
3. Therefore, we can estimate the wind energy generation in 2020 as 254 million + 3 years x 22.5 million = 322.5 million megawatt hours.
4. Similarly, we can estimate the wind energy generation in 2016 as 74 million + 7 years x 22.5 million = 224.5 million megawatt hours.
5. The difference in wind energy generation between 2020 and 2016 is then:
322.5 million - 224.5 million = 98 million megawatt hours.
Therefore, we can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.
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. A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a committee. How many different committees are possible if:
Answers
There are 364 different committees of 3 people. There are 436 different committees of 4 people.
How to find possibilities of different committees?There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:
Different committees of 3 people can be formed from this groupTo calculate the number of different committees of 3 people, we can use the combination formula, which is:
\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)
where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:
\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)
Therefore, there are 364 different committees of 3 people that can be formed from this group.
Different committees of 4 people can be formed, with at least one person from each grade levelTo solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:
\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)
Next, we calculate the number of committees that do not include a freshman, which is:
\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)
Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:
\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)
\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)
\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)
Now we can apply the principle of inclusion-exclusion, which is:
Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.
Plugging in the values, we get:
$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$
Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.
Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.
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How to convert 160 cm to inches?
Answers
Answer:
62.9921
Step-by-step explanation:
1 cm is equal to 0.393701, so 160 cm = 160 × 0.393701 = 62.9921 inches, in unit of measurement.
What is unit of measurement?A unit of measurement is a specific magnitude of a quantity that has been established in advance, is recognised by law or custom, and is used as a benchmark for measuring other quantities of the same kind. Any extra quantity of that type can be expressed as a multiple of the measurement unit.
Length is an example of a physical quantity. The letter "m" stands for the unit of measurement known as the metre, which designates a specific, predetermined length. For instance, when the term "10 metres" (or 10 m) is used, it refers to a length that is 10 times the precise, predetermined length known as "metre."
From ancient times to the present, human endeavour has depended on the definition, acceptance, and practical application of units of measurement.
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Eli is following this recipe to bake bread rolls.
He uses 600 mL of water.
How much of the other ingredients does he use?
Recipe: Makes 10 bread rolls
600 g flour
9 g salt
12 g yeast
30 mL oil
500 mL water
(Proportion)
Answers
10.8 g salt
14.4 g yeast
36 mL oil
Carmen is planning rail lines for a new train station. Help her find
. Explain how you found that solution.
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The angle based on the information given about the rail is 163°.
How to illustrate the information?From the information given, the value of angle 2 will be:
17° + x = 180° (angle on a straight line)
Collect like terms
x = 180° - 17°
x = 163°
In this case, it should be noted that angle 1 and 2 are alternate angles. Therefore, angle 1 will be 163°.
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Factor the polynomial x2 2x – 3x – 6 by double grouping. Group terms with common factors: (x2 2x) (– 3x – 6) Factor the GCF from each group: x(x 2) – 3(x 2) Write the polynomial as a product of binomials:.
Answers
Polynomial are expressions. The factored form of the polynomial x²-x-6 is (x-3)(x+2).
What are polynomial?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
In order to find the factored form of the given quadratic equation, we will break constant b(-1) into two parts such that the sum of the parts is -1, while their product is equal to the product of the constant a(1) and c(-6).
Therefore, the solution of the polynomial is,
\(x^2-x-6\\\\=x^2+2x-3x-6\\\\=x(x+2)-3(x+2)\\\\=(x-3)(x+2)\\\)
Hence, the factored form of the polynomial x²-x-6 is (x-3)(x+2).
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Please help!!!
Doctor storz sees 84 patients in 7 days while Doctor Odes sees 60 patients in 5 days. Are these patients per day rates proportional?
Answers
Answer:
Yes they are proportional
Step-by-step explanation:
84/7 = 12
60/5 = 12
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