Yes, Pairing arrangements are possible.
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
If there are n cysteines, then there are n sulfur atoms that can form disulfide bonds. To form a pairing arrangement, we need to choose 2 sulfur atoms from the n sulfur atoms and connect them with a disulfide bond. We repeat this process until all sulfur atoms are paired up.
The number of ways to choose 2 sulfur atoms from n sulfur atoms is given by the binomial coefficient
[tex]$\binom{n}{2}$[/tex]
Once two sulfur atoms are paired up, we can remove them from the pool of sulfur atoms and continue pairing the remaining sulfur atoms in the same way.
Therefore, the total number of pairing arrangements is given by:
[tex]$\binom{n}{2} \cdot \binom{n-2}{2} \cdot \binom{n-4}{2} \cdots \binom{4}{2} \cdot \binom{2}{2}$[/tex]
which can be simplified as:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
Since we are choosing pairs, we divide by 2 for each pair and the order of the pairs doesn't matter. Also, we divide by (n/2)! to account for the fact that the pairs can be arranged in any order.
Note- that n must be even for this formula to hold.
Therefore, the general formula for the number of different pairing arrangements when there are n cysteines (and n is even) is:
[tex]$\frac{n!}{2^n (n/2)!}$[/tex]
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Is this relationship a direct variation X -3 2 1 y -4 6 4
the relationship between x and y given by the values (-3, -4), (2, 6), and (1, 4) is not a direct variation.
To determine whether the relationship between x and y is a direct variation, we need to check if y is directly proportional to x. In other words, we need to check if there is a constant of proportionality that relates the two variables.
To do this, we can calculate the ratio of y to x for each pair of corresponding values:
y/x = (-4)/(-3) = 4/2 = 2
y/x = 6/2 = 3
y/x = 4/1 = 4
If y is directly proportional to x, then the ratio of y to x should be the same for all pairs of corresponding values. However, in this case, the ratios are not equal. Therefore, the relationship between x and y is not a direct variation.
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Please help I do not understand this .
2. A boat traveling at 30 miles per hour with a tow line of 400 feet will give a parasail rider a height of 300 feet.
a) Draw and label a diagram to represent this situation. (2 points)
b) What is the angle of elevation from the boat to the parasail rider? (5 points)
c) What is the horizontal distance from the parasail rider to the boat? (5 points)
d) What do you notice about the angle of elevation of this flight compared to the. anale of elevation of the flight described in Exercise 1? Use trigonometric functions to explain wny this is true. (10 points)
e) What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed? (10 points)2. A boat traveling at 30 miles per hour with a tow line of 400 feet will give a parasail rider a height of 300 feet.
a) Draw and label a diagram to represent this situation. (2 points)
b) What is the angle of elevation from the boat to the parasail rider? (5 points)
c) What is the horizontal distance from the parasail rider to the boat? (5 points)
d) What do you notice about the angle of elevation of this flight compared to the. anale of elevation of the flight described in Exercise 1? Use trigonometric functions to explain wny this is true. (10 points)
e) What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed? (10 points)
The angle of elevation is approximately 36.87 degrees and the horizontal distance is 264.6 feet
What is the angle of elevation from the boat to the parasail ridera.
The diagram is attached below;
b. We can use the tangent function to find the angle of elevation:
tan(θ) = opposite / adjacent
tan(θ) = 300 / 400
tan(θ) = 0.75
θ = tan^(-1)(0.75)
θ ≈ 36.87 degrees
So the angle of elevation from the boat to the parasail rider is approximately 36.87 degrees.
c. We can use the Pythagorean theorem to find the horizontal distance from the parasail rider to the boat:
d = √(400^2 - 300^2)
d ≈ 264.6 feet
So the horizontal distance from the parasail rider to the boat is approximately 265 feet.
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In a school of 145 students, each was asked to choose one or more activities from sport, music and drama. 76 students choosr sport, 64 chose music and 40 students chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. How many students chose all three activities?
7 number of students chose all three activities.
To find out how many students chose all three activities, we need to subtract the number of students who chose two activities from the total number of students. There are 76 students who chose sport, 64 students who chose music, and 40 students who chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. We can subtract these two-activity choosers from the total number of students to find out how many chose all three activities: 145 - (12 + 7 + 21) = 105. Therefore, 7 students chose all three activities.
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Given:
AC‾ \overline{AC}
AC
and
BD‾\overline{BD}
BD
bisect each other.
Prove:
△BEC≅△DEA\triangle BEC \cong \triangle DEA
△BEC≅△DEA.
As a result of angle-angle-side (AAS) alignment, we have ABO, DBO, and AEO, CEO.
To prove △BEC≅△DEA:
First, we can see that segment AC and segment BD intersect at point O, which is the point of intersection of the angle bisectors of △BED.
Since AC and BD are angle bisectors, they are perpendicular bisectors of each other, so they divide the angles of △BED into congruent angles.
This means that angle ABO is congruent to angle DBO, and angle AEO is congruent to angle CEO.
Since angle ABO and angle AEO are vertical angles, they are congruent.
Similarly, angle DBO and angle CEO are vertical angles, so they are congruent.
Therefore, we have △ABO≅△DBO and △AEO≅△CEO by angle-angle-side (AAS) congruence.
Since BE is common to both triangles, we can conclude that △BEC≅△DEA by side-angle-side (SAS) congruence.
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Work out the volume of the cone radius is 3. 5 and length is 12
To work out the volume of the cone, we can use the formula V = (1/3) * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone. The volume of the cone is approximately 171.55 cubic units.
The formula for calculating the volume of a cone is given as V = (1/3) * π * r² * h. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height of the cone. By substituting the given values, the volume of the cone is calculated to be approximately 171.55 cubic units. This formula is widely used in various fields, such as architecture, engineering, and manufacturing. Calculating the volume of a cone is useful in determining the amount of material required to construct or fill a cone-shaped object, such as a cone-shaped container or a cone-shaped structure. The formula is also used in solving real-life problems related to cones, such as calculating the volume of ice cream in a cone-shaped ice cream cone or the volume of a cone-shaped tank used for storing liquids.
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(7.2 x 1017) x (7.5 x 10-9 X (3.6 x 10-8) x (2.5 x 1010) X
Answer:
Step-by-step explanation:
483278.4
Write a standard form quadratic equation with -2 and 3 as solutions
x² - x - 6 = 0 is the standard form quadratic equation with solutions of -2 and 3.
A quadratic equation with two solutions is what?There are two roots—or solutions—to a quadratic equation with real or complex coefficients. These two possibilities may or may not be distinct, and they may or may not be true. The standard quadratic equation, Y=x2x6, can be solved using the set of solutions 2, 3, which are given.
The elements of a quadratic equation whose solutions are -2 and 3 are (x + 2) and (3, respectively) (x - 3).
The total value of the quadratic equation is 0.
We can add the two elements together to obtain the quadratic equation in standard form:
(x + 2) (x - 3) = x²-3x+2x-6
Simplifying this expression, we get:
x²- x - 6 = 0
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Ava spent 3 hours yesterday practicing the piano. She is going to spend at least 3 hours practicing today which number line shows
this
The number line that models the total amount of time Ava will practice piano in all is shown in the figure and Ava will practice piano for a total of 6 hours.
We can model the total amount of time Ava will practice piano in all using a number line. Since she practiced for 3 hours yesterday and is going to practice for another 3 hours today, we can represent this on a number line as follows:
The number line above represents the total amount of time Ava will practice piano in all. The first mark (0) represents the starting point, which is when she has not started practicing yet. The second mark (3) represents the time she spent practicing yesterday, and the third mark (6) represents the time she will spend practicing today. The distance between the first mark and the third mark (0 to 6) is the total amount of time Ava will practice piano in all, which is 6 hours.
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Please helppp!!!!!!!!!!!!
The length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.
What is angle ?
An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are often referred to as the sides of the angle. Angles are typically measured in degrees or radians and are used to describe the amount of turn between two lines or surfaces.
In a circle, the measure of the arc of a sector is proportional to the measure of the central angle that it subtends. Therefore, to find the length of the arc of the sector in this problem, we need to first find the measure of the central angle that corresponds to the inscribed angle of 312 degrees.
The measure of the central angle is equal to twice the measure of the inscribed angle, which is 312/2 = 156 degrees. This is because the inscribed angle subtends an arc that is half as long as the arc subtended by the central angle.
The length of the arc of the sector can be calculated using the formula:
arc length = (central angle / 360 degrees) x (2 x pi x radius)
Plugging in the values we have:
arc length = (156/360) x (2 x pi x 4mm)
arc length = (13/30) x (8pi)
arc length = (104/30) x pi
arc length ≈ 34.557mm
Therefore, the length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.
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Error Analysis Adding and subtracting fractions
In addition of fractions together student added the denominators together, which is the error in solution. You must have like denominators in order to add fractions together is the strategy for solution. Haley bought 7/8 pound of cheese.
We have a incorrect solution of problem consists addition and subtraction fractions. We have to identify error and solve problem correctly and also share a strategy for solution. Now the problem is defined as : Quantity of mozzarella cheese bought by Haley = [tex] \frac{3}{8} [/tex] pound
Quantity of parmesan cheese bought by Haley = [tex] \frac{1}{2} [/tex] pound
Total pound of cheese that she did bought = sum of parmesan cheese and mozzarella cheese
= [tex] \frac{3}{8} + \frac{1}{2} [/tex]
Incorrect work:
[tex] \frac{3}{8} + \frac{1}{2} = \frac{4}{10}[/tex] [tex]= \frac{2}{5} [/tex]
Identification and Explain the Error :
In the problem student correctly identified that this was addition of fractions however he was incorrect in solving. When adding fractions together you do not add denominators together.
He also forgot that you must have "like" denominators.
Correct Solution:
[tex] \frac{3}{8} + \frac{1}{2} [/tex]
For addition of fractions, make the same denominator in both of fractions. So, multiply the denominator and numentor in fraction 1/2 by 4.
[tex] = \frac{3}{8} + \frac{1 \times 4}{2\times 4} = \frac{3}{8} + \frac{4}{8} [/tex][tex] =\frac{7}{8} [/tex], which is the required solution.
Strategy: We do not add denominator together ever. You must have like denominators in order to add them together. Hence, Haley bought 7/8 pound of cheese.
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Complete question:
Error Analysis Adding and subtracting fractions :
Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then share a strategy this student could use to prevent the same error in the future. Haley bought 3/8 pound of mozzarella cheese and 1/2 pound of parmesan cheese. How many pound of cheese did she buy?
Incorrect work or solution : 3/8 + 1/2
= 4/10 = 2/5
Haley bought 2/5 pound of cheese.
Select all equations that are equivalent to x2+6x=16.
The equivalent equation of x^2 + 6x = 16 are (x + 3)^2 = 25 and x^2 + 6x + 9 = 25
How to determine the equivalent equationFrom the question, we have the following parameters that can be used in our computation:
x2+6x=16
Express properly
So, we have the following representation
x^2 + 6x = 16
Add 9 to both sides of the equation
x^2 + 6x + 9 = 25 --- this represents option (c)
Expand
x^2 + 3x + 3x + 9 = 25
When the expression is factorized, we have
(x + 3)^2 = 25
Hence, the equivalent equation is (x + 3)^2 = 25
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Complete question
Select all equations that are equivalent to x2+6x=16.
The options are added as an attachment
If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, what will be P(A|B)?
If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, then the probability of P(AIB) = 3/5.
Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with absolute certainty. We can only predict the probability of an event by using it, i.e. the probability of it occurring.
The probability can range from 0 to 1, where 0 means the event is unlikely to happen and 1 means it will definitely happen. All events in the sample space have a probability of 1. For example, when we flip a coin, heads or tails, there are only two possible outcomes (H, T). But when you toss two coins, there are four possible outcomes, namely {(H, H), (H, T), (T, H), (T, T)}.
According to the Question:
Given that:
P(A) = 7/13
P(B) = 5/13
P(A∩B) = 3/13
We know that :
P(A|B) = P(A∩B) / P(B).
(By formula for conditional probability)
P(AIB) = (3/13)÷ (5/13)
= 3/5
Hence, the value of P(A|B) = 3/5.
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PLEASE HELP!! I NEED HELP
Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for the trip are given as follows:
Distance of 230 miles.Time of 7 hours.Hence the velocity is obtained as follows:
230/7 = 32.86 miles per hour.
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I need to know how to find the x,y, and z
Answer:
x =~ 31.2
y =~ 18
z =~ 9
Step-by-step explanation:
cos 30º = 27 / x
0.8660 = 27 / x
x = 27 / 0.8660
x =~ 31.18
w = height (smaller trinagle w, y, z)
tg 30º = w / 27
0.5774 = w / 27
w = 27 * 0.5774
w = 15.5898
tg 30º = z / 15.5898
0.5774 = z / 15.5898
z = 0.5774 * 15.5898
z = 9.00155052
cos 30º = 15.5898 / y
0.8660 = 15.5898 / y
y = 15.5898 / 0.8660
y =~ 18
Nuhome movers charges $95 per
hour for loading/unloading
Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. His total moving cost including tax charges equals to the $2,053.8375.
We have to calculate Jay's moving cost if the service also charges 7.25% tax on the total. Here, Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. Now, first we determine the NuHome Movers charges,
Rate of NuHome Movers charges for loading/unloading services = $95 per hour and NuHome Movers charges for 9 hours of loading/unloading services = Multiplication of number of hours by rate of service = 9× $95 = $855 --(1)
Rate of NuHome Movers charges for packing/unpacking services = $80 per hour land NuHome Movers charges for 7 hours of packing/unpacking services = Multiplication of number of hours by rate of service = 7× $80 = $560--(2)
Now, determine charge for truck rental,
Rate of NuHome Movers charges for truck rental = $2.50 per mile
and NuHome Movers charges for 200 miles truck rental = number of miles × rate of each mile = $2.50 × 200
= $500--(3)
Thus, total cost of charges which Jay will pay = charges cost for packing/unpacking services + charges cost for loading/unloading services + charges for truck rental
= $855 + $560 + $500 ( from (1), (2),(3))
= $1,915
Tax charges on total = 7.25%
Determine the Jay's total moving cost including taxes = $1,915 + $1915(7.25/100)
= $1,915 + $1915( 0.0725)
= $1,915 + $138.8375
= $2,053.8375
Hence, required cost value is $2,053.8375.
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Complete question :
NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
On a scale drawing of a dock for a marina, 1 inch equals 18 feet. The dock is 250 feet long. What is the length of the dock on the scale drawing?
The length of the dock on the scale drawing would be 13.89 inches (250/18 = 13.89).
On a scale drawing of a dock for a marina, 1 inch equals 18 feet. This means that for every inch on the scale drawing, it represents 18 feet in reality. The dock is 250 feet long. To calculate the length of the dock on the scale drawing, divide 250 by 18. This gives the result of 13.89. This means that the length of the dock on the scale drawing is 13.89 inches. This is because for every inch on the scale drawing, it represents 18 feet in reality. Therefore, the length of the dock on the scale drawing is 13.89 inches (250/18 = 13.89). To ensure accuracy, the calculation should be double checked. This can be done by multiplying 13.89 by 18 which should give the result of 250. This confirms that the length of the dock on the scale drawing is 13.89 inches.
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if anyone could help, would be much appreciated
[tex]g( \sqrt{55} ) = ( \sqrt{55} ) {}^{2} + 11 = 55 + 11 = 66[/tex]
[tex]f(g(55)) = f(66) = \sqrt{66 - 2} = \sqrt{64} = 8[/tex]
The value of the function f(g(√55)) is 3√7.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
We have the function:
f(x) = √ (x - 2)
and, g(x) = x² + 11.
As, g(√55)
= (√55)² + 11
= 55 + 11
= 66
So, f(g(√55))
= √ (65 - 2)
= √63
= 3√7
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face A
2cm
20%
face B
2cm
Both watch faces are circular with radius 2cm.
The materials used to make both watch faces have the same thickness.
A is made entirely of plastic.
B has a 20° sector of metal and à 340° sector of plastic.
The ratio of the cost per cm² of the metal to the cost per cm² of the plastic is 3:2
Work out the ratio of the cost of the materials for A to the cost of the materials for B.
Give your answer in its simplest form.
You must show all your working.
Therefore , the solution of the given problem of ratio comes out to be 8:17 .
Describe ratio.The simple formula "a / b," where "b" may be greater than zero, can be used to determine a group of integers "a" and "b" that appear to be equal. Two ratios are combined to form a ratio. If there were only one man and three ladies, the fraction would be 1:1. In the group, there are 3/4 women and 1/4 males. Parts can be a division between things, a figure, or a particular percentage of a component's volume.
Here,
Let x be the price of plastic per square centimetre used to create visage A.
Consequently, the price of the components for aspect A is:
=> 4πx
The metal sector's size on face B is:
=> (20/360)π(2cm)² = (1/9)π cm²
The plastic sector's size on face B is:
=> (340/360)π(2cm)² = (17/9)π cm²
Face B's entire surface size is:
=> (1/9)π + (17/9)π = 2π cm²
Let y be the plastic's expense per square centimetre used to create face B.
Consequently, the price per cm2 of the metal used to create face B is three and a half times the price per cm2 of the plastic, leading to:
=> (3/2)y = (3/2)(2x) = 3x
The material cost for the metal section on face B is inversely correlated with its area, so:
=> (1/9)π(3x)
The price of the plastic used in the section on face B is inversely proportional to its area, so:
=> (17/9)πy
=> 8πx : 17πy = 8 : 17
The response is 8:17,
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lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 825 meters from the base of the cliff. The angle of elevation from sea level to the base of
he lighthouse is 37.2". The angle of elevation from sea level to the top of the lighthouse is 38.3°. Find the height of the lighthouse from the top of the cliff.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.
The height of the lighthouse from the top of the cliff is given as 25.3 cm
How to solve for the heighttan 37.2 = h / 825
h = 825 * 0.7590
h = 626.209
tan 38.3 = 626.209 + a / 825
825 tan 38.3 = 626.209 + a
651.55 = 626.209 + a
a = 651.55 - 626.209
a = 25 . 33 meters
Hence we can say that the height of the lighthouse from the top of the cliff is given as 25 . 33 meters
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Ms. Brown's class has 7 boys and 8 girls. Mrs. Ball's class has 4 boys and 10 girls. If one student is randomly selected from each class, what is the probability they are both girls? Answer as simplified fraction.
Considering the probability of independent events, if one student is randomly selected from each class, the probability they are both girls is 8/21.
Definition of probabilityProbability establishes a relationship between the number of favorable events and the total number of possible events.
Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:
Probability= number of favorable cases÷ number of possible cases
Probability of Independent EventsTwo events A and B are said to be independent if and only if the probability of event B is not influenced by the occurrence of event A or vice versa.
For any number of independent events, the probability that all the events will occur is the product of the probabilities that the individual events will occur. That is, if A and B are independent events, P(A and B) = P(A)×P(B).
Probability in this caseYou know:
Ms. Brown's class= 8 girls and 7 boys= 15 studentsMrs. Ball's class= 10 girls and 4 boys= 14 studentsIf one student is randomly selected from each class, the probability that a girl is selected in each class is calculated as:
Probability in Ms. Brown's class= 8÷ 15= 8/15Probability in Mrs. Ball's class= 10÷ 14= 10/14Now, the probability that both students selected for the classes are girls, considering that these are independent events, is calculated as:
Probability of both students selected for the classes are girls = Probability in Ms. Brown's class× Probability in Mrs. Ball's class
Probability of both students selected for the classes are girls = 8/15× 10/14
Probability of both students selected for the classes are girls = 8/21
Finally, the probability they are both girls is 8/21.
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4x+3y=21 and 4x+2y=16
Solve the simentaneous equations
the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.
We can solve this system of equations using either substitution or elimination method.
Using substitution method:
From the second equation, we can solve for x in terms of y:
4x + 2y = 16
4x = 16 - 2y
x = 4 - (1/2)y
Substitute this expression for x into the first equation:
4x + 3y = 21
4(4 - (1/2)y) + 3y = 21
16 - 2y + 3y = 21
y = 5
Now, substitute y = 5 into either of the original equations to solve for x:
4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 6
x = 3/2
Therefore, the solution to is x = 3/2 and y = 5.
We can check this solution by substituting x = 3/2 and y = 5 into both equations:
4x + 3y = 21
4(3/2) + 3(5) = 6 + 15 = 21
and 4x + 2y = 16
4(3/2) + 2(5) = 6 + 10 = 16
So the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.
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Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1).
Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.)
questions to answer:
What is Miguel’s expected value from playing the game?
Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays?
What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
On average, Miguel loses half a dollar every time he plays.
How to solve
To check all the events (6), we label the chips.
Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices.
Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one.
The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$.
In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on.
On average, Miguel loses half a dollar every time he plays.
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Painters painted half of a wall yellow, their boss told them it was supposed to be painted red, they waited for it to dry and then started covering the yellow with red. At the end of the day, 5/6 of the yellow was painted red, how much of the whole wall had been painted red.
Answer: 1/6
Step-by-step explanation:
1/1 - 5/6
2 6-5/6
2 1/6
HELP. Turn the equation into y=mx+b if not already. Figure out whether it has one solution, no solution or infinite solutions. Use graphing, substitution or elimination.
-3x+3y=4
-x+y=3
(same slope or different slop?)
(same y-intercept or different y-intercept?)
Answer:
Starting with the given system of equations:
-3x + 3y = 4
-x + y = 3
To solve for y in terms of x, we can rearrange each equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, we can add 3x to both sides and divide by 3 to obtain:
3y = 3x + 4
y = x + 4/3
So the slope of the first equation is 1 and the y-intercept is 4/3.
For the second equation, we can add x to both sides to obtain:
y = x + 3
So the slope of the second equation is also 1, but the y-intercept is different at 3.
To determine the number of solutions, we can use either substitution or elimination.
Using substitution, we can solve for x in the second equation:
x = y - 3
Then substitute this expression for x in the first equation:
-3(y - 3) + 3y = 4
Simplifying, we get:
-3y + 9 + 3y = 4
9 = 4
This is a contradiction, so the system has no solution.
Alternatively, we can use elimination to solve for y:
-3x + 3y = 4
-x + y = 3
Multiplying the second equation by 3, we get:
-3x + 3y = 4
-3x + 3y = 9
Subtracting the second equation from the first, we get:
0x + 0y = -5
This is a contradiction, so the system has no solution.
In summary, the given system of equations has no solution. The two equations have the same slope but different y-intercepts.
Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]
Answer:
Equation 1: y = x + 4/3
Equation 2: y = x +3
No solution, same slope, different y-intercepts.
Step-by-step explanation:
The two equations have been converted to y=mx+b or slope-intercept form. The slope is the same (1), but the intercepts are different. Equation 1 crosses the y-axis at (0, 4/3), Equation 2 crosses the y-axis at (0,3). Both equations represent parallel lines, so there is no solution because they will never intersect each other.
Sarah invested £12 000 in a unit trust five years ago.
The value of the unit trust has increased by 7% per annum for each of the last 3 years.
Before this, the price had decreased by 3% per annum.
Calculate the current price of the unit trust.
Give your answer to the nearest whole number of pounds.
Answer:efefef
Step-by-step explanation:
efregtythth
what is solved 5x+6=3l
Helen is about to ride a straight water slide. The launching platform is at the top of a tower that is 21 feet tall. The splash pool at the end of the slide is 72 feet from the base of the tower. How long is the water slide itself?
feet=
The length of the slide itself in feet would be = 75 ft.
How to calculate the length of the water slide?To calculate the length of the water slide the Pythagorean formula should be used which is written as follows;
C² = a² + b²
a = length of the tower = 21 ft
b = distance from the base of the tower = 72ft
C = length of the water slide = ?
c² = 21²+72²
C² = 441 + 5184
c² = 5625
C = √5625
C = 75 ft
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A lake near Susan's house is predicted to lose water every day because of a drought. The table shows the estimated water depth in feet, y, after x days of drought. 0 100 1 99.5 2 99 3 98.5 4 98 5 97.5 Choose the function that represents the data. O y = -0,5x + 100 O y=-x05 + 100 O y=-0.5x² + 100 Oy= - +100 X 0.5
As the table shows the estimated water depth in feet, y, after x days of drought. The function that represents the data is y = -0,5x + 100. The Option A is correct.
What does a function means?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.
Based on the given table, it appears that the water depth is decreasing by 0.5 feet every day due to the drought. Additionally, the initial depth of the lake was 100 feet.
Therefore, the function that represents the data is y = -0.5x + 100 where y represents the water depth in feet and x represents the number of days of drought.
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The lateral area of the smaller cylinder is 25pi and the lateral area of the larger cylinder is 64pi. If the volume of the smaller cylinder is 150pi, what is the volume of the larger cylinder?
The volume of the larger cylinder is (25/8)πR³.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in units of cubic meters, cubic centimeters, cubic feet.
According to question:Let's denote the radius and height of the smaller cylinder as r and h, respectively, and the radius and height of the larger cylinder as R and H, respectively.
We know that the lateral area of a cylinder is given by the formula:
Lateral area = 2πrh
Using this formula for the smaller and larger cylinders, we get:
25π = 2πrh
64π = 2πRH
Dividing both sides of the first equation by 2π, we get:
rh = 25/2π
We also know that the following formula determines a cylinder's volume:
Volume = πr²h
Using this formula for the smaller cylinder, we get:
150π = πr²h
Substituting rh = 25/2π from above, we get:
150π = πr²(25/2π)
r² = 12
Taking the square root of both sides, we get:
r = √12 = 2√3
Substituting this value into rh = 25/2π, we get:
h = 25/(2πr) = 25/(4π√3)
Now, we can use the ratio of the lateral areas to find the ratio of the heights:
25π/64π = (2πrh)/(2πRH)
25/64 = rh/RH
25/64 = (2√3)(25)/(4πR)(H)
H = 2hR/r
Finally, we can use the formula for the volume of the larger cylinder to find its volume:
Volume = πR²H
Volume = πR²(2hR/r)
Volume = 2πR³h/r
Substituting the values we found for r, h, and H, we get:
Volume = 2π(R³)(25/(4π√3))/(2√3)
Volume = (25/8)πR³
Therefore, the volume of the larger cylinder is (25/8)πR³.
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