Answers
Answer:
Question 4
a) 0.667
b) 0.833
c) 0.833
d) 0
Question 5
a) 32 yards
b) $312
Step-by-step explanation:
Probability question 4
The best way to solve these probability questions is to enumerate and count the total set of outcomes and then enumerate and count the specific set of outcomes they are looking for in each part .
Since the experiment consists of rolling a fair single 6-sided die we can enumerate the set of possible outcomes as
{1, 2, 3, 4, 5, 6}. This is also referred to in probability as sample space.
There are 6 possible outcomes
The probability of getting any one number is 1/6 whether it be a 1, a 2 or 3, 4, 5 or 6.
In general P(a specific outcome) = Number of ways of getting that outcome ÷ total number of all possible outcomes
part a)
Rolling an even==> Set of outcomes = {2, 4, 6}
Rolling a 3 => {3}
Rolling a 3 or even = {2, 3, 4, 6}; 4 elements
P(even or 3 ) = 4/6 = 2/3 = 0.667
Part b)
Number > 2 ==> { 3, 4, 5, 6}
Even: {2, 4, 6}
Even or greater than 2 = {2, 3, 4, 5, 6}; 5 elements - we do not duplicate
P(Even or greater than 2 ) = 5/6 = 0.833
part c)
Odd number: {1, 3, 5}
Number less than 6: {1, 2, 3, 4, 5}
Combining the two we get: {1, 2, 3, 4, 5} for a total of 5 outcomes
P(odd or less-than 6 ) = 5/6 = 0.833
part(d)
Rolling a 2 and a 4
You cannot roll a 2 and a 4 in one toss so the probability is 0
Question 5
I think you have overly complicated the working of this problem. There is no need to use right triangle, hypotenuse etc
If you have a rectangle with length = L and width = W, the perimeter is just
P = 2( L + W)
Here we can choose any dimension for L and the other for W
Let's choose L = 11 (greater number)
W = 5
Perimeter P = 2 (11 + 5) = 2(16) = 32 yards
b) It costs $3.25 per foot for the fencing..
Careful! The only tricky part here is the units. It is given in $ per square foot whereas the dimensions of the plot are given in yards and the perimeter is also in yards. Watch out for these tricks in other questions
Convert perimeter from yards to feet
32 yards = 32 x 3 = 96 feet (there are 3 feet to a yard)
Cost of 96 feet of fencing at $3.25 per foot
= 96 x 3.25 = $312
Related Questions
Which equation represents the situation below?
After a 20% discount, the cost of a pair of headphones was $260. How much did the headphones cost before the discount?
Let h = original cost of headphones
Answers
Answer:
Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:
Precio original = Precio después del descuento / (1 - Porcentaje de descuento)
Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.
Sustituyendo los valores conocidos, obtenemos:
Precio original = 260 / (1 - 0.2)
Precio original = 260 / 0.8
Precio original = 325
Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:
Answer:
The answer is D. (1-0.2)h=260
Step-by-step explanation:
The differential equations depicting the dynamics of four Single-Input-Single-Output (SISO) systems are given below. (iii) \( \dddot{y}(t)+0.25 \dot{y}(t)+1.25 y(t)=u^{2}(t) \)
Answers
Therefore, the transfer function of the system is:
G(s) = Y(s) / U(s) = U(s) / (s^3 + 0.25s + 1.25)
In summary, the differential equation depicting the dynamics of a fourth Single-Input-Single-Output (SISO) system is y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t), and the transfer function of the system is G(s) = U(s) / (s^3 + 0.25s + 1.25).
The differential equation describing the dynamics of a single-input-single-output (SISO) system is given by ddy(t) + ay'(t) + by(t) = cdu(t), where y(t) is the output of the system, u(t) is the input of the system, and d, a, b, and c are constant coefficients representing the system dynamics.
For the given differential equation, which is the dynamics of four Single-Input-Single-Output (SISO) systems, we have:
[tex]y(t) + ay'(t) + by''(t) + cy'''(t) = u(t)[/tex]
Here, we have the third-order differential equatior : [tex]y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t)[/tex]
The given equation is a third-order, linear, time-invariant (LTI) differential equation. In control theory, a differential equation that relates the input u(t) to the output y(t) of a system is known as the transfer function.
The transfer function of the given system can be found by applying the Laplace transform to the differential equation:
s^3Y(s) + 0.25sY(s) + 1.25Y(s) = U^2(s)
where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.
Solving for Y(s), we get:
Y(s) = U^2(s) / (s^3 + 0.25s + 1.25)
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Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. i About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If x and y are even integers, then x + y is an even integer. (b) If x + y is an even integer, then x and y are both even integers.
(c) If x2 = y?, then x = y. (d) If x and y are real numbers and x < y, then x2 < y?. (e) If x and y are positive real numbers and x < y, then x2 < y?.
Answers
The given statements are True , False, False, True and True.
They are elaborated in points below:
(a) True:
Let x and y be even integers.
Then, by definition, x = 2a and y = 2b for some integers a and b.
Adding these equations, we get x + y = 2a + 2b = 2(a + b), which is an even integer. Therefore, the statement is true.
(b) False:
A counterexample is x = 1 and y = 3. Then x + y = 4, which is even, but neither x nor y is even.
Therefore, the statement is false.
(c) False:
A counterexample is x = -2 and y = 4. Then x² = (-2)²= 4 and y = 4² = 16, but x ≠ y. Therefore, the statement is false.
(d) True:
Since x < y, we have y - x > 0. Multiplying both sides by y + x, we get y² - x² > 0.
Rearranging the terms, we have x² < y².
Since x and y are both non-negative, we can take the square root of both sides to get x < y.
Therefore, the statement is true.
(e) True:
Since x and y are positive, we can take the square root of both sides of the inequality x < y to get √x < √y.
Then, multiplying both sides by √x + √y, we get x + 2√xy + y > x + y.
Since x + y is positive, we can divide both sides by x + y to get 1 + 2√(xy)/(x+y) > 1.
Rearranging the terms, we get √(xy) < (x + y)/2. Squaring both sides, we get xy < (x + y)²/4.
Simplifying, we get x²/4 - xy + y²/4 > 0. Rearranging the terms, we get (x - y/2)² > 0, which is always true since the square of any non-zero number is positive. Therefore, the statement is true.
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three cards are drawn without replacement from an ordinary deck of 52 playing cards. what is the probability that the 3rd card is a heart if the first card was a heart and the second card was a club?
Answers
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152. It is the product of the probabilities.
What is the probability?The probability that the 3rd card is a heart if the first card was a heart and the second card was a club when three cards are drawn without replacement from an ordinary deck of 52 playing cards.
There are 13 hearts in a deck of 52 cards.
Therefore, P(1st card is a heart) = 13/52 = 1/4
There are 13 clubs in a deck of 52 cards. Since one heart is already drawn in the first card, there are only 51 cards left in the deck.
Therefore, P(2nd card is a club) = 13/51
There are only 12 hearts remaining in the deck since one heart is already drawn in the first card. There are only 50 cards left in the deck since two cards are already drawn.
Therefore, P(3rd card is a heart) = 12/50 = 6/25
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is:
P(3rd card is a heart | 1st card is a heart and 2nd card is a club) = P(1st card is a heart) × P(2nd card is a club) × P(3rd card is a heart) = (1/4) × (13/51) × (6/25) = 39/5,775 = 0.0152 (rounded to 5 decimal places)
Therefore, the probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152.
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what is the solution to the equality shown?
3m+5>2(m-7)
Answers
Hello,
3m + 5 > 2(m - 7) =
3m + 5 > 2m - 14
3m - 2m > - 14 - 15
x > - 29
Step-by-step explanation:
3m±2m>-14-5
5m>-19
m>-19/5
m>3.8
every year educational services (ets) selects readers for the advanced placement exams. recently the ap* statistics exam has been graded in lincoln, nebraska. one objective of ets is to achieve equity in grading by inviting teachers to be readers from all parts of the nation. however budgets are a consideration also. the accountants at ets wonder if the flights from cities west of lincoln are the same as flight costs from cities east of lincoln. a random sample of the expense vouchers from last year was reviewed for the cost of airline tickets. costs (in dollars) are shown in the table. indicate what inference procedure you would use to see if there is a significant difference in the costs of airline flights between the west and east coasts to lincoln, nebraska, then decide if it is okay to actually perform that inference procedure. (check the appropriate assumptions and conditions and indicate whether you could or could not proceed. you do not have to do the actual test.)
Answers
To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.
Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.
Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.
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A poll agency reports that 38% of teenagers aged 12-17 own smartphones. A random sample of 120 teenagers is drawn. Round your answers to at least four decimal places as needed.a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?
Answers
The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.
a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?a)Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45We know that the proportion of teenagers aged 12-17 who own smartphones is 0.38. Now, we need to find the probability that the proportion of sampled teenagers who own smartphones is between 0.35 and 0.45.The sample size is 120.Let P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z scores for both sides, i.e. for 0.35 and 0.45.z1 = (0.35 - 0.38) /0.048 = -0.625z2 = (0.45 - 0.38) /0.048 = 1.458Hence, P(0.35 < p < 0.45) is equal to P(-0.625 < z < 1.458).The probability can be calculated using standard normal tables, which gives 0.5763. Therefore, the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is 0.5763.b) Find the probability that less than 45% of sampled teenagers own smartphonesLet P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z score as follows:z = (0.45 - 0.38) /0.048 = 1.458We must find the probability that a randomly selected teenager from the sample has less than 0.45 probability of owning a smartphone. This probability can be calculated using a standard normal table. P(z < 1.458) = 0.9265, thus, the probability that less than 45% of sampled teenagers own smartphones is 0.9265.c) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?For this, we need to find the Z-score of 0.30.z = (0.30 - 0.38) /0.048 = -1.667The probability is obtained using a standard normal table. The probability is 0.0475. The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.
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consider a european put option on a non-dividend paying stock with a current stock price of $100 and 4 years until expiration. the strike price of the option is unknown you are given that: ape(s,t) as -05 determine a numerical value for: ape(s,t) da please round your numerical answer to the nearest integer.
Answers
The strike price of the option is $101.5, rounded to the nearest integer, whicch is given as the APE(s,t)= -0.5.
What is asset price elasticity?The asset price elasticity (APE) of a European Put Option at time 't' is the ratio of the change in the option price to the change in the stock price, given that all other factors remain constant.
The APE(s,t) of a European put option is calculated using the formula APE(s,t) = -S+Ke-rτ.
In this case, the current stock price is $100 and the time until expiration is 4 years.
We can solve for K, the strike price of the option, given the APE(s,t) is -0.5.
K = S + APE(s,t) + reτ
K = 100 - 0.5 + (0.5 x 4)
K = 101.5
The strike price of the option is $101.5, rounded to the nearest integer.
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/c and /d are vertical angles.if /c is 140, what is the measure of/d?
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Problem 4: Find the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort). Solution. Given that the population is governed by a Gompertz model IN = r Nlog(K)
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In the following question, among the conditions given, It can be given by Ymax = H(N*)So the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) can be calculated using the above formula.
To find the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) we will start with the formula of the Gompertz model that is, IN = r Nlog(K)Solution: Given that the population is governed by a Gompertz model = r Nlog(K)We know that the harvesting term that is responsible for the overexploitation of the resources, hence we can write the Gompertz model as dN/dt = rN[1 - N/K] - H(x)WhereH(x) can be a constant yield or constant effort in the harvesting term.
To find the maximum sustainable yield, we will use the concept of steady-state or equilibrium population level. Steady-state condition:dN/dt = 0Solving this equation gives us the steady-state population level, say N*.Now we need to calculate the maximum amount of resources that can be harvested sustainably. This maximum amount of resources harvested sustainably is called the maximum sustainable yield (MSY). It can be given by Ymax = H(N*)So the maximum sustainable yield for a population governed by a Gompertz model and subjected to harvesting (either constant yield or constant effort) can be calculated using the above formula.
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A tin of nuts contains 36 cashews, 14 pecans, 27 peanuts, and 13 pistachios. Find the probability of reaching in and selecting a pecan and then a cashew. Assume the nuts are chosen without replacement. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer:28/445 or 6.2921 %
Step-by-step explanation:
There are 90 nuts all together. There are 14 pecans so it would be a 14/90 chance. Then since you are not replacing the nut there are 89 nuts. There are 36 cashews which would be a 36/89 chance. Because in the problem it says to find the probability of the selecting a pecan and then a cashew we know it is an and situation. Since it is an and situation you would multiply. You would do 14/90 times 36/89. This gives you 504/8010 which reduced is 28/445 or 6.2921%. Do you have and questions?
The price of a new car is £12500
It is reduced by £11625
Work out the percentage reduction
Answers
To work out the percentage reduction, we need to find the difference between the original price and the reduced price, and express that difference as a percentage of the original price:
Original price = £12500
Reduced price = £11625
Difference = £12500 - £11625 = £875
Percentage reduction = (Difference / Original price) x 100%
= (£875 / £12500) x 100%
= 7%
Therefore, the percentage reduction in the price of the car is 7%.
Answer:
Step-by-step explanation:
Discount [tex]= \pounds12,500 -\pounds11625= \pounds875[/tex]
Percentage reduction [tex]=\frac{875}{12500} \times 100 = 7[/tex]
The price of a new car was reduced by 7%.
Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money
into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously
Part 1: Describe the type of equation that models Jerry’s situation. Create that equation of Jerry’s situation. Using the equation you created, how much money will be in Jerry’s account after 3 years? 10 years?
Think: What do I know and what does it mean? What plan am I going to try?
PLEASE HELP!!!!!
Answers
Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.
What is simple interest?Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.
The given situation can be modeled as a linear equation given by:
y = mx + c
For Jerry we have:
y = 50x + 125
For 3 years = 36 months we can substitute x = 36:
y = 50(36) + 125
y = 1825
For x = 10:
y = 50(120) + 125
y = 6125
Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.
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A triangle has one side that measures 1 1/2 inches and another side that measures 2 1/4 inches. The angle between these sides measures 60°. Draw the triangle in the space below. Label the given side lengths and angle measure on the figure. Is it possible to draw a different triangle with those measurements
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the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
What is triangle?A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees, and the longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle. Triangles can be classified according to their side lengths and angles. For example, an equilateral triangle has three equal sides and three equal angles of 60 degrees each, while an isosceles triangle has two equal sides and two equal angles. A scalene triangle has no equal sides or angles. Triangles are important in geometry and have many applications in mathematics and other fields, such as architecture, engineering, physics, and computer graphics.
by the question.
Draw a straight-line segment and label it as the given side that measures 1 1/2 inches.
From one endpoint of the first line segment, draw another line segment that forms a 60° angle with the first line segment. Label this second line segment as the given side that measures 2 1/4 inches.
Draw a third line segment that connects the endpoints of the first two-line segments. This will complete the triangle.
To label the triangle, label the given side that measures 1 1/2 inches with the corresponding length measurement, and label the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
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Find the unknown lengths of these isosceles right triangles. (Leave radicals in simplest radical form.) (ASAP!!!!) (it’s urgent!)
Answers
The required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
What is Right angled triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question:19) Using Pythagoras theorem
[tex]c^2=a^2+a^2[/tex]
[tex]c^2=\sqrt{a^2+a^2}[/tex]
[tex]c=\sqrt{8^2+8^2}[/tex]
c = 8√2 units
20) It is isosceles triangle,So a = b
Now
[tex]$Sin(45) =\frac{a}{\frac{\sqrt{5}}{7} }[/tex]
a = [tex]\frac{\sqrt{10} }{14}[/tex]
Thus, required answers are 19) c = 8√2 units 20) a = b =a = [tex]\frac{\sqrt{10} }{14}[/tex].
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_____ is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal
Answers
Decibel is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal.
What is a decibel?
Decibel, also known as dB, is a logarithmic unit that measures the intensity of a sound or the strength of an electrical or electromagnetic signal. A decibel measures the relative amplitude of a sound or signal, rather than its absolute magnitude. Because decibels are logarithmic, they are used to express both large and small differences in amplitude. A difference of 1 decibel corresponds to a power ratio of approximately 1.26 to 1.
Logarithmic measure: A logarithmic scale is a scale that has a constant ratio between successive values. Decibels, for example, are a logarithmic scale. The decibel scale is used to measure the amplitude of sound waves and electrical or electromagnetic signals. Because decibels are logarithmic, they can be used to express a wide range of signal levels, from very weak to very strong.
Relative measure: Relative measure is a measure that compares one value to another. It is used in a variety of fields, including statistics, physics, and engineering. Decibels are a relative measure because they compare one signal to another. They are used to express the relative gain or loss of a signal, rather than its absolute magnitude.
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
B'( , )
Answers
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, 2).
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis is represented and modeled by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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This is the Challenge:
There is a race consisting of 10 individual races in a row. You are able to bet on the racecars for a chance to multiply your money. The potential payout and chances of winning per racer are listed below.
Blue
- 30% Chance of winning
- 2x Payout on winning bids
Red
- 25% Chance of winning
- 2.5x Payout on winning bids
Purple
- 18% Chance of winning
- 3x Payout on winning bids
Yellow
- 10% Chance of winning
- 5x Payout on winning bids
Black
- 8% Chance of winning
- 7x Payout on winning bids
Green
- 5% Chance of winning
- 10x Payout on winning bids
Orange
- 3% Chance of winning
- 15x Payout on winning bids
Pink
- 1% Chance of winning
- 50x Payout on winning bids
At the end of the race, bets placed on the top 3 winning racecars will be paid back to the player depending on the sheep's placement
1st Place: 100% Bet Payout
2nd Place: 40% Bet Payout
3rd Place: 10% Bet Payout
All other bets placed on non top 3 place racecar will be lost
You can safely assume that if one is likely to win but doesn't win then they are statistically most likely to come second and so on
During the 10 rounds, what is the most efficient bets to increase your money?
Answers
Calculating the expected value of payout using the probabilities given, we can bet on blue for all 10 races, bet on red for all 10 races and bet on purple for all 10 races
What is the most efficient bets to increase the return?To determine the most efficient bets to increase your money during the 10 rounds, we need to consider the probability and potential payout for each racecar. We can start by calculating the expected value of each racecar's payout:
Blue: 0.3 x 2 = 0.6
Red: 0.25 x 2.5 = 0.625
Purple: 0.18 x 3 = 0.54
Yellow: 0.1 x 5 = 0.5
Black: 0.08 x 7 = 0.56
Green: 0.05 x 10 = 0.5
Orange: 0.03 x 15 = 0.45
Pink: 0.01 x 50 = 0.5
Based on the expected value of payout, the most efficient bets would be on the racecars with the highest expected value. However, we also need to consider the probability of each racecar winning or placing in the top 3.
To maximize our chances of winning, we should bet on the racecars with the highest probability of winning or placing in the top 3, even if their expected payout is not the highest.
Assuming that if one racecar is likely to win but doesn't win, they are statistically most likely to come second, and so on, we can rank the racecars in terms of their probability of winning or placing in the top 3:
1. Blue - 30% chance of winning
2. Red - 25% chance of winning
3. Purple - 18% chance of winning
4. Black - 8% chance of winning
5. Yellow - 10% chance of winning
6. Green - 5% chance of winning
7. Orange - 3% chance of winning
8. Pink - 1% chance of winning
Based on this ranking, the most efficient bets would be as follows:
1. Bet on Blue for all 10 races. The expected payout is not the highest, but the probability of winning is the highest at 30%.
2. Bet on Red for all 10 races. The probability of winning is the second-highest at 25%.
3. Bet on Purple for all 10 races. The probability of winning is the third-highest at 18%.
Betting on these three racecars will give you the highest chance of winning or placing in the top 3, and therefore, the most efficient bets to increase your money. However, keep in mind that gambling always carries risks, and there is no guarantee of winning.
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A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
++++
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea level.
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
O C. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
SUBMIT
Answers
To solve the question asked, you can say: So the dolphin's new location expressions is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer.
what is expression ?In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems.
Move 3 units to the right on the outer diameter number line. Exit with -3. The dolphin was 3 feet below sea level.
To find the dolphin's new location, we need to determine the dolphin's direction of movement and distance traveled. In this case the dolphin swam to the bottom. This means it has moved in the negative direction on the number line. Then she swam three feet. This means she has moved 3 units to the right (or positive side) on the number line.
So we need to start at the dolphin's original position of -6 and move it 3 units to the right to -3. So the dolphin's new location is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer.
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Can someone pass help!!:(
Answers
Answer:
proofs attached to answer
Step-by-step explanation:
proofs attached to answer
Fatoumata is working two summer jobs, making $15 per hour lifeguarding and making $10 per hour tutoring. In a given week, she can work at most 12 total hours and must earn a minimum of $140. Also, she must work at least 8 hours lifeguarding. If � x represents the number of hours lifeguarding and � y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer:
not sure if this sign � was important did it the best way I could
Step-by-step explanation:
To solve this problem graphically, we will first set up a system of inequalities based on the given information:
x ≥ 8 (Fatoumata must work at least 8 hours lifeguarding)
y ≤ 12 - x (Fatoumata can work at most 12 total hours)
15x + 10y ≥ 140 (Fatoumata must earn a minimum of $140)
To graph these inequalities, we can plot the points (8,0), (12,0), and (0,14) on a coordinate plane and draw lines connecting them. The line between (8,0) and (12,0) represents the constraint on the number of hours Fatoumata can work, while the line between (8,0) and (0,14) represents the constraint on the amount of money she must earn. The shaded region that satisfies all three inequalities is the feasible region.
To find one possible solution, we can pick any point within the feasible region. One such point is (8,6), which represents working 8 hours lifeguarding and 6 hours tutoring. This point satisfies all three inequalities:
x ≥ 8 is true since x = 8
y ≤ 12 - x is true since y = 6 ≤ 12 - 8
15x + 10y ≥ 140 is true since 15(8) + 10(6) = 180 ≥ 140
Therefore, one possible solution is for Fatoumata to work 8 hours lifeguarding and 6 hours tutoring to earn at least $140 while not exceeding 12 total hours worked.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is
| ____ | = ____
The minimum possible diameter of a soccer ball is ____,
and the maximum possible diameter is ____
Answers
The equation that can be used to find d, the diameter of a new soccer ball, is: |d - 8.65| = 0.05
What is diameter ?
Diameter is the distance across a circle passing through its center, and it is defined as the length of a straight line passing through the center of a circle and connecting two points on the circumference of the circle. In the case of a soccer ball, the diameter is the distance between two opposite points on the surface of the ball, passing through its center.
Radius is a term used in geometry to refer to the distance from the center of a circle to any point on its circumference. It is defined as half of the diameter of a circle. In the case of a soccer ball, the radius is the distance from the center of the ball to its surface. The radius is related to the diameter by the formula:
radius = diameter / 2
The minimum possible diameter of a soccer ball is:
d = 8.65 - 0.05 = 8.60 inches
The maximum possible diameter is:
d = 8.65 + 0.05 = 8.70 inches
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Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Answers
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b
where m is the slope, and b is the y-intercept.
Comparing this to the given equation, we see that m=3 for the given line.
Perpendicular linesThe slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...
desired slope = -1/m = -1/3
Y-interceptThe slope-intercept equation above can be solved for b to give ...
b = y -mx
Then the y-intercept for the line we want is ...
b = 5 -(-1/3)(3) = 5 +1 = 6
The equation of the desired line is y = -1/3x +6.
__
Additional comment
Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.
Given slope = 3; perpendicular slope = -1/3
Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m
y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3
The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.
Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?
Answers
Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.
We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.
Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.
32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.
Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.
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Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Answers
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
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Find the magnitude and direction of the vector <2,7>. Round angles to the nearest degree and other values to the nearest tenth. 7.3; 73°7.3; 74°7.4; 73°7.4; 74
Answers
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
We have,
To find the magnitude and direction of the vector <2, 7>, we can use trigonometric concepts. Let's break down the steps:
Magnitude (Length) of the Vector:
The magnitude of a vector <x, y> is given by the formula:
Magnitude = √(x² + y²)
For the given vector <2, 7>:
Magnitude = √(2² + 7²) = √(4 + 49) = √53 ≈ 7.3 (rounded to the nearest tenth)
Direction (Angle) of the Vector:
The angle θ that the vector makes with the positive x-axis can be found using trigonometric functions:
θ = arctan(y / x)
For the given vector <2, 7>:
θ = arctan(7 / 2) ≈ 74° (rounded to the nearest degree)
Thus,
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
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Suppose a random sample of size 45 is selected from a population with σ = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
a. The population size is infinite.
b. The population size is N = 50,000.
c. The population size is N = 5000.
d. The population size is N = 500.
Answers
The value of the standard error of the mean in each of the following cases:
a. The population size is infinite = 1.4142
b. The population size is N = 50,000 = 1.4135
c. The population size is N = 5000 = 1.4073
d. The population size is N = 500 = 1.343
The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.
Standard error calculation:
σ = 10
n = 50
A) when size is infinite, the standard deviation of the sample mean is given by the formula;
σ_x' = σ/√n
Thus,
σ_x' = 10/√50
σ_x' = 1.4142
B) size is given, thus, the standard deviation of the sample mean is given by the formula;
σ_x' = (σ/√n)√((N - n)/(N - 1))
Thus, with size of N = 50,000, we have;
σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))
σ_x' = 1.4142 x 0.9995
σ_x' = 1.4135
C) at N = 5000;
σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))
σ_x' = 1.4073
D) at N = 500;
σ_x' = 1.4142 x √((500 - 50)/(500 - 1))
σ_x' = 1.343
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Determine whether the function is concave upwards and downwards
x^4 - 2x^3 + 5
Answers
The function f(x) = x⁴ - 2x³ + 5 is concave downwards on the interval (0,1) and concave upwards everywhere else.
What is concavity of the function?
To determine the concavity of the function f(x) = x⁴ - 2x³ + 5, we need to find its second derivative f''(x).
f(x) = x⁴ - 2x³ + 5
f'(x) = 4x³ - 6x²
f''(x) = 12x² - 12x
The concavity of the function is determined by the sign of its second derivative.
If f''(x) > 0 for all x, the function is concave upwards.
If f''(x) < 0 for all x, the function is concave downwards.
Let's solve for f''(x) = 12x² - 12x:
12x² - 12x = 0
12x(x - 1) = 0
x = 0 or x = 1
When x < 0, f''(x) > 0, so the function is concave upwards.
When 0 < x < 1, f''(x) < 0, so the function is concave downwards.
When x > 1, f''(x) > 0, so the function is concave upwards.
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A farmer sells cows for $350 each and chickens for $75 apiece. At market, he sold 11 animals for a total of $2475. How many of each animal were sold?
Answers
Answer:
Let's use algebra to solve this problem.
Let's start by defining some variables to represent the number of cows and chickens the farmer sold. Let c be the number of cows and h be the number of chickens. We know that the farmer sold a total of 11 animals, so:
c + h = 11 (Equation 1)
We also know that the total amount of money the farmer received was $2475. The amount he received from selling cows was $350 times the number of cows, or 350c. The amount he received from selling chickens was $75 times the number of chickens, or 75h. So:
350c + 75h = 2475 (Equation 2)
Now we have two equations with two unknowns. We can solve for one variable in terms of the other in the first equation:
c + h = 11
c = 11 - h
We can substitute this expression for c into the second equation:
350c + 75h = 2475
350(11 - h) + 75h = 2475
Simplifying and solving for h:
3850 - 350h + 75h = 2475
-275h = -1375
h = 5
So the farmer sold 5 chickens. We can substitute this value of h back into the first equation to find c:
c + h = 11
c + 5 = 11
c = 6
Therefore, the farmer sold 6 cows and 5 chickens.
Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for every $0. 50 she raised the price, she sold 8 fewer bracelets. What price should she charge in order to make the highest possible gross income?
Answers
$17.5 price should she charge in order to make the highest possible gross income.
Given two points are (400, 10) and (392, 10.5)
slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625
Equation is
p -10 = -0.0625(x-400)
p-10 = -0.0625x + 25
p = -0.0625x + 35
find revenue as
R=x*p
-0.0625x² + 35x
To maximize,
R'(x) =0
-0.125x + 35 = 0
35/0.125 = x
280 = x
when x is equal to 280, find
p= -0.0625(280) + 35
p= -17.5 +35
p= 17.5
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