By using the concept of expectation, it can be calculated that
a) Probability distribution of Y
P(Y = 0) = 0.63
P(Y = 1) = 0.25
P(Y = 2) = 0.12
b) Mean of Y = 0.49
Standard deviation of Y = 0.6999
c) Mean of selling price = $4.4
Standard deviation of selling price = $0.99
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
[tex]x_1, x_2, ...., x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1, p_2,...., p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula
[tex]E(x) = p_1x_1 + p_2x_2 + ... + p_nx_n[/tex]
a)If a fat quarter has more than 2 defects, it cannot be sold and is discarded.
The table for the probability distribution of X is given
P(X [tex]\leq[/tex] 2) = 0.58 + 0.23 + 0.11 = 0.92
For probability distribution of Y
P(Y = 0) = P(X= 0 | X [tex]\leq[/tex] 2) = [tex]\frac{0.58}{0.92}[/tex] = 0.63
P(Y = 1) = P(X= 1 | X [tex]\leq[/tex] 2) = [tex]\frac{0.23}{0.92}[/tex] = 0.25
P(Y = 2) = P(X= 2 | X [tex]\leq[/tex] 2) = [tex]\frac{0.11}{0.92}[/tex] = 0.12
Mean of Y = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0,25 + 2 [tex]\times[/tex] 0.12 = 0.49
E([tex]Y^2[/tex]) = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0.25 + 4 [tex]\times[/tex] 0.12 = 0.73
Variance = [tex]0.73 - 0.49^2[/tex] = 0.4899
Standard deviation = [tex]\sqrt{0.4899} = 0.6999[/tex]
b) Here, E(G) = 0.40, V(G) = [tex]0.66^2[/tex]
The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
Selling price = 5 -1.5G
Mean of selling price = 5 - 1.5[tex]\times[/tex] 0.4 = 5 - 0.6 = $4.4
Variance of selling price = [tex]5 - 1.5^2 \times 0.66^2\\[/tex] = $0.9801
Standard deviation of selling price = [tex]\sqrt{0.9801}[/tex] = $0.99
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Complete Question
Company f sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable x represent the number of defects on a fat quarter created by company f. The following table shows the probability distribution of x.
x 0 1 2 3 4 or more
probability 0.58 0.23 0.11 0.05 0.03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
(a) Construct the probability distribution of the random variable Y.
(b) Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company
a rectangular prism with dimensions of (x-3),(x-1), and (x-8) has a volume of 33x cubic units. what are the dimensions of the prism?
The dimensions of the rectangular prism with the volume 33x cubic units are 11units, 9units, 4 units.
As given in the question,
Dimension of the rectangular prism in form of x are :
( x - 3 ) , ( x - 1 ) , and ( x - 8 )
Volume of the rectangular prism = 33x cubic units
⇒ ( x - 3 )( x - 1 )( x - 8 ) = 33x
⇒ ( x² -4x + 3 )( x - 8) = 33x
⇒ x³ -12x² + 35x -24 = 33x
⇒ x³ -12x² + 2x -24 = 0
⇒ x² ( x - 12 ) + 2 ( x - 12 ) = 0
⇒ ( x - 12 )( x² + 2 ) = 0
⇒ x = 12 or x = √ -2
Dimensions cannot be square root of negative.
⇒ x = 12
x - 3 = 9 units
x -1 = 11 units
x - 8 = 4 units
Therefore, the dimensions of the rectangular prism are 9 units, 11unitsm and 4 units.
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sam discovered that the pool in his backyard is leaking slowly. the pool holds 15,684 gallons of water, and is leaking at a rate of 8 gallons per day. after how many days will the pool be empty
Answer:
It will take the pool 1,960.5 days for the pool to become empty.
Step-by-step explanation:
We can find this answer by simply dividing the two numbers together:
15,684 ÷ 8 = 1,960.5 days.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
1960.5 days
Step-by-step explanation:
[tex]\boxed{\textsf{Rate (gallons per day)} = \sf \dfrac{Volume\;(gallons)}{Number\; of\; days}}[/tex]
Given:
Volume = 15,684 gallonsRate = 8 gallons per daySubstitute the given values into the formula:
[tex]\implies 8=\dfrac{15684}{\sf Number\;of\;days}[/tex]
[tex]\implies \sf Number\;of\;days=\dfrac{15684}{8}[/tex]
[tex]\implies \sf Number\;of\;days=1960.5[/tex]
Therefore, if the pool is leaking at a rate of 8 gallons per day, the pool will be empty after 1960.5 days.
(10,0) and (-2, 4)
Find the slope
The slope is -1/3.
The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.
Slope = m = tan θ = (y2 - y1)/(x2 - x1)
Slope = 2−1 / 2−1
= 4-0 / -2-10
= 4 /-12
= −1/3.
The slope is -1/3.
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Which statement can be concluded using the true statements shown?
If two angles in a triangle measure and x degrees, then the third angle measures (90 − x) degrees.
In triangle ABC, angle A measures 90 degrees and angle B measures .
Angle C must measure 50 degrees.
Angle C must measure 40 degrees.
Angle C must measure (90 − 40) degrees.
Angle C must measure (90 − 30) degrees.
The correct measure of the third angle in the triangle as we can see is 40 degrees.
What is a right angled triangle?We know that a right angle triangle is one in which one of the angles of the triangle is 90 degrees. If we know that one of the angles of the triangle has been given as 90 degrees, it then follows that the other two angles would have to be complementary.
Let us remind ourselves here and now that the angles that we say that they are complementary are the angles that do add up to about an angle of ninety degrees.
Having said this, we can see that the third angle is the angle A measures 90 degrees and angle B measures 50 degrees, it then follows that the third angle must have to measure 40 degrees. This would now give the correct balance of all the angles in the triangle.
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Missing parts;
Which statement can be concluded using the true statements shown? If two angles in a triangle measure 90° and x degrees, then the third angle In triangle ABC, angle A measures 90 degrees and angle B measures 50°. A.Angle C must measure 50 degrees B.Angle C must measure 40 degrees C.Angle C must measure (90 - 40) degrees D.Angle C must measure (90 - 30) degrees
Answer:
Angle C must measure 40 degrees.
Step-by-step explanation:
took it
solve for the variable c in this equation: a(c + b) = d question 2 options: or c = d/a - b or c = d/a + b or c = b - d/a or c = d/b - a
Solving the equation a(c + b) = d for variable c, the variable c = (d/a) – b. (Option A)
Equation refers to a statement that represents an equality of values of two mathematical expressions and is indicated by the sign =.
In the given equation a(c + b) = d, in order to solve for the variable c, we must isolate the c variable at one side and collect other variables on the other side of the equation.
Given equation is:
a(c + b) = d
Divide both sides by a:
(1/a)*a(c + b) = d/a
c + b = d/a
Subtract b from both sides:
c + b – b = (d/a) - b
c = (d/a) – b
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Solve 4x³ 40x2 +96x = 0 by factoring. List the answers
from least to greatest separated by commas with no spaces.
-
Answer:
x=0,4,6
Step-by-step explanation:
Sonya is thinking of a mystery number (m). She says it can be represented with the function rule: m = 4f +7, where f is her favorite number.
If Sonya's favorite number is 12, what is the mystery number?
The mystery number by Sonya is 55
How to determine the mystery number?From the question, we have the following equation that can be used in our computation:
m = 4f + 7
Where
f = favorite number = 12
So, we have
m = 4 * 12 + 7
Evaluate the products
This gives
m = 48 + 7
Evaluate the sum
m = 55
Hence, the number is 55
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which congruence theorem can be used to prove △bda ≅ △bdc?ahlbssacaasdsss
To prove △BDA ≅ △BDC, SSS congruence theorem should be used.
What is the Side-Side-Side congruence theorem of triangles?
If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by the SSS rule.
Given that ΔBDA is similar to ΔBDC and:
AD ≡ DC
AB ≡ BC
BD ≡ BD (shared side)
△BDA ≅ △BDC
The best postulate to use is the side-side-side (SSS) postulate.
Hence, to prove △BDA ≅ △BDC, the SSS congruence theorem should be used.
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on a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. if 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
The percent of the ship's passengers held round-trip tickets is 50/100 = 50%.
Since the number of passengers on the ship is immaterial, let the number of passengers on the ship be 100 for convenience.
Let x be the number of passengers that held round-trip tickets.
Then, since 20 percent of the passengers held a round-trip ticket and took their cars aboard the ship, 0.20(100) = 20 passengers held round-trip tickets and took their cars aboard the ship.
The remaining passengers with round-trip tickets did not take their cars aboard, and they represent 0.6x (that is, 60 percent of the passengers with round-trip tickets).
Thus, 0.6x + 20 = x, from which it follows that 20 = 0.4x, and so x = 50.
The percent of passengers with round-trip tickets is, then, 50/100 = 50%
A roundtrip flight is a flight itinerary that includes one flight to a vacation spot and some other flight lower back from that destination, which include flying from NYC to Paris after which Paris lowers back to NYC. The direction might also include layovers or connections, however, the beginning and endpoint are equal.
Ask the enterprise to alter the round-trip ticket for one-way usage. although airways exercise a varying degree of flexibility, many airlines will regulate a round-ride fare to permit one-manner use, though a few airlines might also charge a penalty or charge for this provider.
also known as “return air tickets,” round-journey tickets are flights from and again to the equal place beginning. A one-manner price tag, then again, simplest lets you to fly your destination, now not back from it.
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urgenttt sorryyy thankss tooo
Answer:
7/10
Step-by-step explanation:
30 : 5 = 6 to Sali
10 : 100 = x : 30
x = 30 * 10 / 100
x = 3 * 1 = 3 to Jane
30 - (6+3) = 30 - 9 = 21
21/30
(21 : 3)/(30:3)
7/10
Use partial quotients to find the quotient for 590 divided by 6
Answer:98.3333333333 (98)
The number 590 is called the numerator or dividend, and the number 6 is called the denominator or divisor.
The quotient of 590 and 6, the ratio of 590 and 6, as well as the fraction of 590 and 6 all mean (almost) the same:
590 divided by 6, often written as 590/6. The answer is actually 98 but if I am wrong sorry.
The temperature went from -16°F to 7°F. What was the change in temperature?
-9°F
23°F
-23°F
9°F
Answer:
23°F
Step-by-step explanation:
because its from a negative temp to a positive the inc is positive and -16-+7 is 16+7 = 23
PLEASE HELP
For this graph, determine whether x and y are proportional.
If x and y are proportional, fill in the blank with a number in simplest form.
Answer:
Proportional
y is 0.4 times x
or
y is 2/5 times x
Both numbers are the same, I don't know which form the computer expects you to enter
Step-by-step explanation:
x and y are proportional since there is a linear relationship between y and x.
Let's verify this
When x = 5, y = 2. So y/x = 2/5 = 0.4
So y = 0.4x
When x = 10, y = 4
So y/x = 4/10 = 2/5 = 0.4
Again y = 0.4x
So the answer is 0.4, same as 2/5
Answer:
Step-by-step explanation:
the x and y are proportional because the number increases by the same number each time. so y =2 and x=5 then on the next one, if it's proportional, y will = 4 and x will = 10. another way you can be sure that it is proportional is that every time you add the first number you can divide it and get the first number. for example if you divide 4 by 2 you will get 2. if you divide 10 by 2 you get 10. so in a short answer yes it is proportional
amc 12a 2014] let a < b < c be three integers such that a, b, c is an arithmetic progression and a, c, b is a geometric progression. what is the smallest possible value of c?
The smallest possible value of c is 1 in this case.
If the integer a, b and c are in arithmetic progression.
Then we can write,
b = (a+c)/2
If the integer a, b and c are in geometric progression,
Then, we can write,
b = √(ac)
Now, we can write,
a+b = 2√(ac)
Squaring both sides,
a²+c²+2ac = 4ac
(a-c)² = 0
So,
a = c.
If a = c.
Then,
b = (a+a)/2
b = a
So, a = b = c.
Smallest possible positive integer is 1.
So, the smallest possible value of c is 1.
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If 15 baseballs weigh 75 ounces, how many baseballs weigh 15 ounces?
1: 5 baseballs
2:10 baseballs
3: 3 baseballs
4:75 baseballs
If 15 baseballs weigh 75 ounces, how many baseballs weigh 15 ounces?
1: 5 baseballs
2:10 baseballs
3: 3 baseballs
4:75 baseballs
75oz / 15 baseballs = 5 oz each
15 oz / 5 oz = 3 baseballs
9) John and Sarah are each saving money for a car. The total amount of money John will
save is given by the function J = 28 + 4x.
The total amount Sarah will save is given
by the function S = x2 + 2x + 20. After
how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.
To find out how many weeks it will take for John and Sarah to save the same amount of money, we must set their respective functions equal to each other and solve for x.
J = S
28 + 4x = x2 + 2x + 20
x2 + 2x - 4x - 8 = 0
x2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = -2
Since x must be a positive value, the answer is that it will take John and Sarah 4 weeks to have the same amount of money saved.
What is the solution to the equation below? 2(x-3)= 2x+5
A.) X=2 3/4 C.) There is no solution
B) x= 3 3/4 D.) There are infinitely many solution
The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.
Given that,
To determine the solution to the equation 2(x-3)= 2x+5.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given equation,
2(x-3)= 2x+5
2x - 6 = 2x + 5
-6 ≠ 5
Thus, The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.
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Which of the fractions below are less than 3/4? Select four. A)3/5 B)5/8 C')5/6 D)1/2 E)7/12
1+1 = ??????????????????
Answer:
2
Step-by-step explanation:
one apple and another equals to 2.
Answer: 11
Step-by-step explanation: you put one and one together lol
a satellite in a circular orbit 1250 kilometers above earth makes one complete revolution every 110 minutes. find its linear speed, round your answer to 2 decimal places. assume that earth is a sphere of radius 6400 kilometers.
Its linear speed would be 1637.75 miles/hour
Vt = 435,49 Km/min
Vt = 26129 Km/hour
Vt = 16630, 35 miles/hour
The distance from the earth center up to the satellite position is:
Earth radius + distance above the earth
radius of satellite 6400 + 1250 = 7650 Km
linear speed = Vt = 2π*r/T
where
r is the radius of the satellite and T period = 110 min
Then
Vt = 6,28* 7650 / 110
Vt = 4804/110
Vt = 43,674.54 Km/min
To get it in Km/h we must multiply by 60
Vt = 26204m/hour
And finally, to get it in miles per hour we divide it by 16
Vt = 1637.75 miles/hour
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V+6>5
how do you solve this equation?
Answer:
v > -1
Step-by-step explanation:
v + 6 > 5
We want to work backwards to solve this, therefore we must subtract 6 on both sides to isolate v.
v + 6 > 5
(- 6) (-6)
v > -1
3. Can you find the ratio of AB to AC and the ratio of DE to EF?
Its a written response type answer, so yes, no. And why or why not
Answer: Yes
Step-by-step explanation:
If you were to be given the numbers for the corresponding coefficient you can solve this question just like as if they were real numbers. Even if you weren't given values, The coefficients unknown value is usually presumed as 1.
if a= 10 b=5 c=6 d=50 e=100 f=1
ab= 10:5
ac= 10:6
de= 50:100
ef= 100:1
if they were all one then they would just be 1:1
Tell whether the following is or is not a polygon and justify your answer
Answer: A. yes, closed and lines are straight B. No, curved lines C. no, curved lines D. yes, closed have lines are straight E. yes, closed have lines are straight E. yes, closed and lines are straight F. No, curved lines G. yes, closed and lines are straight H. yes, closed and lines are straight
Step-by-step explanation:
TRUE/FALSE. inferential statistics allows a researcher to make inferences about a specific population based on data taken from a sample.
A researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.
Explain the term inferential statistics?Inferential statistics use data from the experiment's sample of subjects to compare the different treatments and draw conclusions about the subject population as a whole.
Inferential statistics come in a wide variety, and each form is suitable for a particular research methodology and set of sample characteristics. A statistical field known as inferential statistics is one that employs analytical tools to make inferences about the larger population by analyzing samples taken at random. Generalizations about than a population are what inferential statistics are intended to do.Thus, a researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.
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Eleanor and billie make 752 brownies this give them to their 9 friends to share. what impact did the remainder have on this answer
Answer:
Step-by-step explanation:
This impact shows the Eleanor and Billie will have some leftover brownies.
Lets see.
752/9
752=720+27+5
720/9=80, 27/9=3, and 5/9 has a Remainder of 5.
80+3=83 R 5
Under her cell phone plan, Jocelyn pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $55 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes she can use while staying within her budget.
if the classroom supplies, outdoor games, toys for the playground and paint for all three classrooms are represented by 3x2, xy3, 2x3y, and 4xy respectively, multiply the polynomial expressions. write your answer in descending order according to the x variable. please use the palette below to enter your answer.
To represent outside games, playground equipment, and paint for all three classrooms, multiply the polynomial expressions by 3x2, xy3, 2x3y, and 4xy, accordingly.
This polynomial's formula is 12x^5y^3 + 24x^4y^3 + 18x^3y^3
Numerous branches of mathematics and science use polynomials. used to approximate other functions in calculus and numerical analysis to approximate other functions in calculus and numerical analysis. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics.Algebraic varieties and polynomial rings, two core concepts in algebra and algebraic geometry, are constructed using polynomials in higher mathematics.
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Rami's grandfather paid $67.83 for a length of rope that cost $0.95 per foot. He then cut the rope into pieces that were each 3 feet long. How many 3-foot pieces of rope did Rami's grandfather make? Enter your answer in the box.
The number of 3-foot pieces of rope that Rami's grandfather could make would be = 23.8 pieces.
What is rope?Rope is a thick cord that is material up of synthetic or organic materials that are interwoven together which can be used to support a structure.
The amount of money paid by Rami's grandfather for the rope = $67.83
The amount that the rope is sold per foot = $0.95/ft
To calculate the number of ft he bought;
= 67.83/0.95
= 71.4ft of rope
The number of 3-foot piece that he can cut
= 71.4/3
= 23.8 pieces.
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A theme park sells adult tickets (a) for $159.50 and child tickets (c) for $109.00. The theme park needs to make at least 5.49 million dollars to make a profit each day. Which inequality could the theme park use to determine how many of each ticket must be sold in a day to make a profit?
A. 159.50a + 109c ≤5,490,000
B. 159.50a + 109c ≥5,490,000
C. 159.50a + 109c <5,490,000
D. 159.50a + 109c >5,490,000
Answer:A
Step-by-step explanation:
Inequality could the theme park use to determine the Total number of tickets that must be sold in a day to make a profit is 159.50a + 109c ≥5,490,000.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given, Tickets for an amusement park are available for adults (a) for $159.50 and for kids (c) for $109.00. The theme park requires daily revenue of at least $5.49 million to turn a profit.
total earning per day = 159.50a + 109c
this should be greater than (>) or at least equal to 5.49 million.
Therefore, The total number of tickets that must be sold in a day to generate a profit is 159.50a + 109c ≥ 5,490,000. Inequality might be used by the theme park to calculate this amount.
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consider the following binomial experiment: the probability that a fuse produced by a certain company will be defective is 37⁄100 . if 500 fuses are produced each day, how many can we expect to find each day that are defective ? a) 189 b) 187 c) 185 d) 183 e) 188 f) none of the above.
We can expect to find 185 defective fuses each day.
The correct answer is c) 185.
At first we have to find the expected number of defective fuses each day, we can use the formula for the expected value of a binomial distribution:
Expected Value (μ) = n * p
where:
n = number of trials (in this case, the number of fuses produced each day) = 500
p = probability of success (in this case, the probability that a fuse is defective) = 37/100 = 0.37
Expected Value (μ) = 500 * 0.37 = 185
So, we can expect to find 185 defective fuses each day.
The correct answer is c) 185.
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