Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.
When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:
WWx (two women and one of either gender)
WMx (one woman, one man, and one of either gender)
MWx (one man, one woman, and one of either gender)
MMx (two men and one of either gender)
In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.
In outcome 1 (WWx), a woman is selected twice, so x = 2.
In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.
In outcome 4 (MMx), no women are selected, so x = 0.
Therefore, the possible values of x are 0, 1, 2, and 3.
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−4x+7=2y−3 how do i solve for x
get rid of y. that's all you have to do.
magic the gathering is a popular card game. cards can be land cards, or other cards. we consider a game with two players. each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand. (a) assume that player one has 10 land cards in their deck and player two has 20. with what probability will each player have four lands in their hand? (b) assume that player one has 10 land cards in their deck and player two has 20.with what probability will player one have two lands and player two have three lands in hand? (c) assume that player one has 10 land cards in their deck and player two has 20. with what probability will player two have more lands in hand than player one?
Probability the player two have more lands in hand than player one is:
A) 0.0135
B) 0.102
What is probability?
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
Here, we have
Given: each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand.
A ) probability of each player having four lands in their hand
Given data:
player 1 has 10 land cards
player two(2) having 20 land cards
Hence, the probability can be calculated as
= 0.0135
B) probability of player one having two lands and player two having three lands in hand
Given data:
player one (1) has 10 land cards
player two has 20
Hence, the probability of player one having two lands and player two having three lands in hand can be calculated as attached below
= 0.102
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classify each peptide chain as part of a parallel β sheet, part of an antiparallel β sheet, either type of β sheet, or not part of a β sheet.
The first figure represents Antiparallel β sheet. Second figure is parallel β sheet. Third figure represents neither of the two types. The fourth figure is also parallel β sheet and the fifth figure represents both types.
Antiparallel and parallel β-sheets are two different arrangements of the β-strands in a protein structure.
In an antiparallel β-sheet, the direction of the peptide bonds in the individual β-strands is opposed to each other, meaning that the N-terminal end of one strand points in the opposite direction from the N-terminal end of the neighboring strand. The hydrogen bonds between the strands run perpendicular to the direction of the peptide bonds and hold the strands together.
In a parallel β-sheet, the direction of the peptide bonds in the individual β-strands is the same, meaning that the N-terminal end of one strand points in the same direction as the N-terminal end of the neighboring strand. The hydrogen bonds between the strands run parallel to the direction of the peptide bonds and hold the strands together.
Both antiparallel and parallel β-sheets play important roles in the structure and function of proteins, and are found in many different types of proteins, including enzymes, transport proteins, and structural proteins.
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Complete question:
classify each peptide chain as part of a parallel β sheet, part of an antiparallel β sheet, either type of β sheet, or not part of a β sheet. options in document attached below.
suzy borrows $4500 and agrees to repay it all in equal monthly instalments over 3 years. Simple interest at 7.2% p.a is charged on a loan. find the amount of each instalment
The amount of Suzy's instalment every month if it is agreed to repay equal amount monthly is $152
What is the amount of each instalment?Simple interest = principal × rate × time
= 4500 × 0.072 × 3
= $972
Total amount to repay = $4500 + $972
= $5472
Repayment time = 3 years
Suzy will repay every month
3 years= 12 months × 3
= 36 months
Since,
the repayment is equal every month
Amount of instalment every month= $5472 / 36
= $152
Therefore, Suzy will repay $152 each month instalmentally.
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a bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep. a) compute the work required to lift the bucket from the bottom of the well to the top. (5pts) b) oops, we forgot to tell you! the chain that is being used to lift the bucket weighs 0.55 lbs per foot. now find the correct amount of work required to lift the bucket from the bottom of the well all the way to the top. (5pts) c) oh no! where is our head at today? we completely forgot to mention that the bucket has a hole in the bottom. it only weighs 35lb when it reaches the top, due to the water leaking out at a constant rate. now compute the real work required to lift the bucket from the bottom of the well to the top of the well. (recall that the bucket is being lifted at a constant rate, as well.) (5pts)
If the weight of the bucket is 70 lb , then the work required to lift the bucket from bottom is 135240 foot-pounds .
We use the formula : Work = Force × Distance to calculate the work done
where "Force" is weight of bucket filled with water and "Distance" is height it is lifted.
The weight of bucket filled with water is = 70 pounds.
We convert this to a force in pounds force, by using g = 32.2 feet per second squared ;
So , Force = Weight × Gravity
⇒ 70 lb × 32.2 ft/s² = 2254 lb-ft/s²
The distance that the bucket is lifted is = 60 feet ;
So , work required to lift bucket from bottom of well to top is :
⇒ Work = Force × Distance = 2254 lb-ft/s² × 60 ft
⇒ 135240 foot-pounds
Therefore , it will require 135240 foot-pounds of work to lift the bucket filled with water from the bottom of the well to the top.
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The given question is incomplete , the complete question is
A bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep.
Compute the work required to lift the bucket from the bottom of the well to the top .
Evaluate the expression.
[2³x (225+9)]-33
[2³ x (225 +9)] - 33 =
(Simplify your answer.)
This question has two parts. First, answer Part A. Then, answer Part B.
The distance that Makayla travels on her skates varies directly with time as shown in the table.
Write a direct variation equation in the form y = kx to represent this relationship. Express the constant of variation as a decimal.
A linear clear variation is represented by the equation y = kx, in which k is the area under the curve y = mx + b and b is the zero-valued y-intercept.
Y KX Y is what kind of variation?The polynomial y = mx (commonly stylized y = kx), which seems referred to as a direct variation, can be obtained from the theory y = mx + b if m is a sufficiently small factor and b = 0. In other words, you may claim that y directly depends on x or that y is proportionate to x.
K in Y KX: What does it mean?The standard format for presenting a direct variation is y=kx. The letters "y" and "x" are variables, and the letter "k" is a constant. Making a table will allow you to identify those ordered pairs that statisfy the example of y=2x.
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The volume of a cube of side 2A is
Answer:
8a3
Step-by-step explanation:
volume of cube = Lcube
one side=length of cube
so
volume of cube= L3
=2a3
= 2A × 2A × 2A
= 8A3Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Answer:
Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Step-by-step explanation:
Find the total wingspan
Answer:
9.9 cm
Step-by-step explanation:
The right triangle has one-half the wing span as a leg.
The hypotenuse is 5.8cm and the other leg is 3cm
If we let the unknown leg of the triangle be x, by the Pythagorean theorem we know the sum of the squares of the two legs must be equal to the square of the hypotenuse .
So
x² + 3² = 5.8²
x² = 5.8² - 3²
= 33.64-9
= 24.64
x = √24.64
= 4.96
Total wingspan = 4.96 × 2 = 9.9 cm
Two sides of a triangle measure 15 inches and 18 inches, respectively. Which of these is NOT a possible length for the third side of the triangle? Responses A 24 inches24 inches B 18 inches18 inches C 4 inches4 inches D 32 inches32 inches E 36 inches
Answer:
e
Step-by-step explanation:
The rule of the sides of a triangle is that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This rule is also known as the triangle inequality theorem.
0.22, 21%,0.21, 0.22 from least to greatest
0.21, 0.21, 0.22, 0.22 is the sequence from least to greatest.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
0.22, 21%, 0.21, 0.22
Now,
21% = 21/100 = 0.21
So,
0.22, 0.21, 0.21, 0.22
Arranging from least to greatest.
0.21, 0.21, 0.22, 0.22
Thus,
0.21, 0.21, 0.22, 0.22 is the sequence from least to greatest.
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HELP!!
A plane left Kennedy Airport on Tuesday morning for a 730-mile, 6-hour trip. For the first part of the trip, the average speed was 115 mph. For the remainder of the trip, the average speed was 125 mph. How long did the plane fly at each speed?
A. First part of trip: __ h
B. Second part of trip: __ h
The first part of the trip took approximately 6.39 hours and the second part of the trip took approximately 5.84 hours.
Solving for Time and Average Speed in a Two-Part Plane TripIn this problem, we are given the distance, total time, and average speeds for two parts of a plane trip.
Using the formula for average speed
Distance = average speed x time,
We can set up two equations and solve for the times spent flying at each speed.
We define t₁ as the time spent flying at 115 mph and t₂ as the time spent flying at 125 mph.
From the equation
730 miles = 115 mph x t₁,
we solve for t₁ and get
t₁ = 6.391304347826087 hours.
Similarly, from the equation
730 miles = 125 mph x t₂,
we solve for t₂ and get
t₂ = 5.84 hours.
Therefore, the plane flew at an average speed of 115 mph for approximately 6.39 hours and at an average speed of 125 mph for approximately 5.84 hours.
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There are hundred students in a class who took an examination in Math and Science. 68 of them passed in Science, 32 passed in both Mathematics and Science, 12 students did not pass in any of the subjects
(i) How many students passed in Mathematics?
The number of student that pass mathematics is 52.
How to solve set theory?There are hundred students in a class who took an examination in Math and Science. 68 of them passed in Science, 32 passed in both Mathematics and Science, 12 students did not pass in any of the subjects. Therefore, the number of student that passes maths can be solved as follows:
U = 100
n(S) = 68
n(M n S) = 32
n(M U S)' = 12
Let
x = number of student that pass maths
Therefore,
100 = 68 + x - 32 + 12
100 - 68 + 32 - 12 = x
x = 52
Therefore,
number of student that pass maths = 52
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a vendor at the basket ball game go to 405 bottles of water on Saturday she sold 127 fewer bottles on Sunday she sold 178 bottles on Sunday
The correct answer is 178 bottles of water sold on Sunday.
What is vendor ?Vendor is a person or a company that sells goods or services. The term is commonly used to refer to individuals who sell items at events, markets, or street stalls. Vendors may sell a variety of products, including food, drinks, clothing, accessories, and more
If the vendor sold 405 bottles of water on Saturday, and sold 127 fewer bottles on Sunday, then on Sunday she sold 405 - 127 = 278 bottles of water.
However, the question states that she actually sold 178 bottles of water on Sunday, so the number of bottles she sold on Sunday was incorrect.
The correct answer is 178 bottles of water sold on Sunday.
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how many pattern block trapezoids would create 3 hexagons
18 pattern block trapezoids would be needed to create 3 hexagons.
Pattern block trapezoids are geometric shapes used for pattern block activities.
Each hexagon is typically made up of 6 pattern block trapezoids.
To determine the number of pattern block trapezoids required to create 3 hexagons, multiply the number of hexagons by the number of trapezoids in each hexagon.
Number of trapezoids = Number of hexagons × Number of trapezoids in each hexagon
= 3 × 6
= 18
Therefore, 18 pattern block trapezoids would be needed to create 3 hexagons.
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12 - 1 / 5r = 2r + 1
Answer: r = 5
Step-by-step explanation:
Bob buys a big bag of beans for $2. 37. Find x, the number of dollars he gave the cashier if he received $17. 63 in change
Bob gave the cashier $15.26 for the bag of beans.
To find the value of x, we need to subtract the cost of the beans from the total amount given to the cashier. The cost of the beans is $2.37, and the change received is $17.63.
Therefore, the value of x can be calculated as:
x = Total amount given to the cashier - Cost of the beans
x = $17.63 - $2.37
x = $15.26
A cashier is an employee who works in a retail or service industry, responsible for handling cash, credit card payments, and providing customer service. They are often the first and last point of contact for customers in a business. Cashiers use a cash register or computer system to record transactions, and must be able to accurately count money, make change, and reconcile the cash drawer at the end of their shift.
They also need to be proficient in using technology, such as scanners and card readers, to process transactions. In addition, cashiers must have good communication skills to interact with customers, answer questions, and resolve any issues. Other responsibilities may include stocking shelves, maintaining a clean and organized workspace, and ensuring that customers receive accurate pricing and promotional discounts.
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Ivy invested GH¢1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?
The total value of the investment of $1000.00 at 5% simple interest for 5 years equals $1,250.
Total principal 'P' amount invested by Ivy is equal to $1,000.
Time period of investment 't' = 5 years
Rate of simple interest 'r' = 5%
Simple interest = ( Principal × rate of interest × time ) / 100
⇒ Simple interest = ( 1000 × 5 × 5 ) / 100
⇒ Simple interest = $250
Total value of the invested principal amount is equal to
= Principal amount + simple interest
= $1,000 + $250
= $1,250
Therefore, the total investment value of the principal amount at simple interest rate for 5 years is equal to $1,250.
The above question is incomplete, the complete question is:
Ivy invested $1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?
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what’s wrong with the question
The graph is wrong because of less than or equal to sign. the correct inequality for the given graph would be y ≥ 3x - 2.
What is inequality?
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
The given graph is wrong for the given inequality y ≤ 3x - 2
The correct graph for the given inequality is shown below.
The given graph would be correct for the inequality
y ≥ 3x - 2.
Hence, the graph is wrong because of less than or equal to sign. the correct inequality for the given graph would be y ≥ 3x - 2.
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Need step-by-step explanation. Will mark the brainliest. Basically explained this equation as if i am a 5 year old child. (with step of course)
attached is solution. please excuse handwriting.
break up summation into two smaller summation,
then use summation formula for E (x)
9) An 8.2 km section of highway increases 870 m in elevation. The horizontal distance of the road is 8154m.
a) Calculate the slope to three decimal places
b) Calculate the angle of elevation to one decimal place. Tan x= opposite/adjacent
c) Calculate the percent grade to one decimal place. Percent Grade slope X 100
How to figure out the area of a right angle triangle
The area of a right triangle can be found by multiplying half of the length of the base by the height.
The formula for the area of a right triangle is:
Area = (1/2) * base * height
It is important to note that the base and height must be perpendicular to each other, forming a right angle in the triangle. If the triangle is not a right triangle, then the area cannot be found using this formula.
To use this formula, simply measure the length of the base and height and plug these values into the formula. The result will be the area of the triangle, expressed in square units.
It is also worth noting that the height and base of a right triangle can be any two sides that form a right angle, not just the sides that are labeled as the base and height.
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One number is 3 less than 4 times a second number. The difference of the
first number and twice the second number is 7. What are the two numbers?
Show your work.
Answer:
atq= let no.be x and y
x= 4y-3.......(1)
x-2y=7....(2)
subtracting both eqn
x-x+2y=4y-3-7
2y=4y-10
-2y= -10
y=5 ........second no.
first no...x=7+2y=7+10=17.......first no.
Step-by-step explanation:
g is most data likely to be skewed or symmetric? there is no right or wrong here but discuss and take a side on the issue.
Most data is likely to be skewed following a particular trait because when considering real life data, it is likely that it may concentrate on one end of the values on the real line as there is high uncertainty that exists with real life.
There is very little confidence that the population would behave in expected ways.
The skewed distribution implies the distribution that is not symmetrical. If a distribution is skewed it can be skewed to the left i.e. mean lies to the left of the center or skewed to the right i.e. mean lies to the right of the center of the distribution.
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Vocabulary Explain how to isolate the variable in the eqaution -2/3n = 7 + 15
The variable n in the original equation -2/3n = 7 + 15 is equal to -12.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.
In order to isolate the variable in the equation -2/3n = 7 + 15, the first step is to subtract 7 from each side of the equation. This results in -2/3n = 8. Next, multiply each side of the equation by 3 to cancel out the 3 in the denominator. This leaves -2n = 24. Finally, divide each side of the equation by -2 to isolate the variable n. This results in the equation n = -12. Therefore, the variable n in the original equation -2/3n = 7 + 15 is equal to -12.
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Question 4 of 10
Given the inequalities y> 3x-1 and y<-2x+ 1 graphed on the same
coordinate grid, which of the following statements are true? Check all that
apply.
A. The line for y=-2x+1 will be solid.
B. Shading will be below the y=-2x+ 1 line and below the y= 3x - 1
line.
C. Shading will be above the y=-2x+1 line but below the y= 3x-1
line.
D. None of the above
SUBMIT
Answer:
Step-by-step explanation:
The correct answer is C. Shading will be above the y=-2x+1 line but below the y= 3x-1 line.
The line y=-2x+1 is a line with a slope of -2 and a y-intercept of 1. It represents the solutions that are greater than -2x+1.
The line y=3x-1 is a line with a slope of 3 and a y-intercept of -1. It represents the solutions that are less than 3x-1.
So, when you graph both of these lines on the same coordinate plane, the solutions that satisfy both inequalities will be the region that is above the line y=-2x+1 but below the line y=3x-1, and this is the region that will be shaded.
on a certain hot summers day, 613 people used the public swimming pool
The number of children and adults in swimming pool is 398 and 224.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form;
Ax + B = 0.
We are given that;
Number of people swimming=613
Price of children=$1.75
Price of adults= $2.25
Total= $1184.75
Let, number of children be x
Number of adults be y
Now, the equations will be
x+y=613....1
1.75x+2.25y=1184.75....2
On solving both the equations
X=389, y=224
Therefore, the solution of linear equation will be 389 and 224.
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The complete question is;
on a certain hot Summer's Day 613 people use the public swimming pool the daily prices are $1.75 for children $2.25 for adults the receipts for admission totaled $1184.75 how many children and how many adults when I am at the public for that day
scores on a certain test are normally distributed with a variance of . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than units.
A sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units.
To find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, we can use the formula:
n = [ (z * σ) / E ]^2
where n is the required sample size, z is the critical value for the desired confidence level (95% confidence level corresponds to a z-value of 1.96), σ is the population standard deviation (given as the square root of the variance, which is √(70) ≈ 8.37), and E is the maximum error, or the maximum difference between the sample mean and population mean that we are willing to tolerate (which is given as 2.5 units).
Substituting the given values into the formula, we get:
n = [ (1.96 * 8.37) / 2.5 ]^2
n ≈ 43.48
Rounding up to the nearest whole number, we get a required sample size of n = 44.
Therefore, a sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, assuming a normal distribution with a population variance of 70.
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scores on a certain test are normally distributed with a variance of 70 . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2.5 units.
Find the distance travelled by rahul, if he takes 6 rounds of a square field of side=120m
The distance travelled by Rahul, if he takes 6 rounds of a square field of side = 120m is 2880 meters.
We are given that Rahul takes 6 rounds of a square field of side length 120m. To find the total distance he travels, we need to calculate the perimeter of the square field and multiply it by the number of rounds.
The perimeter of a square is the sum of the lengths of its four sides. Since the side length of the square field is 120m, the perimeter is:
4 * 120m = 480m
This is the distance Rahul covers in one round around the square field.
To find the total distance he covers in 6 rounds, we multiply the distance covered in one round by the number of rounds:
480m * 6 = 2880m
So, Rahul covers a total distance of 2880 meters.
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