Two 5-year old girls, Alyse and Jocelyn, have been training to run a 1 mile race. Alyse’s 1 mile time A is approximately Normally distributed with a mean of 13. 5 minutes and a standard deviation of 2. 5 minutes.
Jocelyn’s 1 mile time J is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 1. 5 minutes.
Assuming A and J are independent random variables, what is the probability that
Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day?
I'm more so looking for an explanation on how to find the answer, thanks :)
Answers
The probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day is approximately 0.2676
To find the probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day, we need to compare the distribution of their running times.
Let X be the running time of Alyse and Y be the running time of Jocelyn. Then, we have
X ~ N(13.5, 2.5^2)
Y ~ N(12, 1.5^2)
We want to find P(X < Y). We can start by standardizing the variables:
Zx = (X - 13.5) / 2.5
Zy = (Y - 12) / 1.5
Then, we have
P(X < Y) = P(X - Y < 0)
Substituting the standardized variables, we get
P(X - Y < 0) = P((Zx - Zy) < (0 - (13.5-12)/sqrt(2.5^2 + 1.5^2)))
Using the standard Normal distribution table or calculator, we find that the probability of Zx - Zy being less than -0.624 is approximately 0.2676.
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Related Questions
3 feet
1 foot
2 feet
A package is shaped like a right rectangular prism. Use the dimensions shown to find the surface area of this package.
A)
6 square feet
B)
12 square feet
20 square feet
D)
22 square feet
Answers
Answer:
its B) 22
Step-by-step explanation:
:) ........bbbbbb
Newton-Cotes formulas for evaluating ∫abf(x)dx were based on polynomial approximations of f(x). Show that if y=f(x) is approximated by a natural cubic spline with evenly spaced knots at x0,x1,…,xn, the quadrature formula becomes I=2h(y0+2y1+2y2+⋯+2yn−1+yn)−24h3(k0+2k1+k2+⋯+2kn−1+kn) where h is the distance between the knots and ki=yi′′. Note that the first part is the composite trapezoidal rule; the second part may be viewed as a "correction" for curvature.
Answers
The quadrature formula for the natural cubic spline with evenly spaced knots becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + k1 + k2 + ⋯ + kn-1 + kn), where h is the distance between the knots and ki = yi''.
To show that if y = f(x) is approximated by a natural cubic spline with evenly spaced knots, the quadrature formula becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + 2k1 + k2 + ⋯ + 2kn-1 + kn), where h is the distance between the knots and ki = yi''.
The natural cubic spline interpolates the function f(x) using piecewise cubic polynomials between each pair of adjacent knots. Let's denote the spline functions as Si(x) for i = 0 to n-1, where Si(x) is defined on the interval [xi, xi+1].
The composite trapezoidal rule is used to approximate the integral of f(x) over each interval [xi, xi+1]. It is given by the formula:
Ti = h/2 * (yi + yi+1)
where Ti represents the approximation of the integral over the interval [xi, xi+1].
Summing up the trapezoidal approximations over all intervals, we get:
I = T0 + T1 + T2 + ⋯ + Tn-1
= (h/2) * (y0 + y1) + (h/2) * (y1 + y2) + ⋯ + (h/2) * (yn-1 + yn)
= h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn)
Now, let's consider the correction term for curvature. The curvature term measures the second derivative of the spline functions at each knot. Using the notation ki = yi'', we have:
C = (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)
Adding the curvature correction term to the trapezoidal approximation, we obtain the final quadrature formula:
I = h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)
This formula represents the integration approximation using the natural cubic spline with evenly spaced knots. The first part corresponds to the composite trapezoidal rule, and the second part provides a correction for the curvature of the spline.
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Can someone show me how to work this problem?
Answers
The correct statement regarding the similarity of the triangles in this problem is given as follows:
similar; RYL by SAS similarity.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
In this problem, we have that the angle R is equals for both triangles, and the two sides between the angle R in each triangle form a proportional relationship.
Hence the SAS theorem holds true for the triangle in this problem.
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I set z=t=0(x,y,z,t)
and I got a partial solution (0,1,0,0).
I solved two homogeneous matrices once for z=1
and t=0
, then for z=0
and t=1
and I got two solutions (1,1,1,0)
and (1,1,0,1).
Then, I got (0,1,0,0)+a∗(1,1,1,0)+b∗(1,1,0,1
)
Therefore, all possible results are (0,1,0,0),(1,0,1,0),(1,0,0,1),(0,1,1,1)
Would this be correct?
Answers
The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).
Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.
Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).
Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).
Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).
To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.
(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)
Expanding this expression, you get:
(0+a+b, 1+a+b, 0+a, 0+b)
Simplifying, you obtain the following set of solutions:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Therefore, the correct set of possible results would be:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.
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yeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Evaluate the expression.
(5+9÷3)2
Answers
Answer:
The answer to the equation is 16
Answer:
16
Step-by-step explanation:
Simplify 9\div 39÷3 to 33.
(5+3)\times 2(5+3)×2
2 Simplify 5+35+3 to 88.
8\times 28×2
3 Simplify.
1616
Use the diagram below to answer questions 4 and 5.
4. Name an angle vertical to ZTPQ.
1.)TPU
2.)ZOPU
3.)ZUPR
4.)none of these
———————————————
5. If ZUPT = 48°, what is the measure of ZRPU?
1.)48°
2.)132
3.)180°
4.)228°
Answers
Answer:
b
Step-by-step explanation:
bUse the diagram below to answer questions 4 and 5.
4. Name an angle vertical to ZTPQ.
1.)TPU
2.)ZOPU
3.)ZUPR
4.)none of these
———————————————
5. If ZUPT = 48°, what is the measure of ZRPU?
1.)48°
2.)132
3.)180°
b4.)228°
A fair die is tossed 180 times .A one refers to the face with one dot. Thou, P(one = 1/6. computer the approximate probability of obtaining at least 37. ones
Answers
The approximate probability of obtaining at least 37 ones is -0.000005.
Given that, a fair die is tossed 180 times. A one refers to the face with one dot.
Thus, P(one) = 1/6.The probability of obtaining at least 37 ones can be approximated using the normal distribution.
Using the central limit theorem, we have,μ = n * P = 180 * (1/6) = 30 andσ² = n * P * (1 - P) = 180 * (1/6) * (1 - 1/6) = 25/6
Since we cannot use a normal distribution directly since we need to find the probability of at least 37 ones, we use a continuity correction by considering the range from 36.5 to 37.5 ones.
Now, using the standard normal distribution, we have, z = (37.5 - 30) / √(25/6) = 5.40 and z = (36.5 - 30) / √(25/6) = 4.87
Using a table of standard normal distribution, the probability corresponding to z = 5.40 and z = 4.87 are 0.0000034 and 0.0000084, respectively.Using continuity correction, the approximate probability of obtaining at least 37 ones is given by,P(X ≥ 37) ≈ P(36.5 ≤ X ≤ 37.5) = P( z ≤ 5.40) - P(z ≤ 4.87)= 0.0000034 - 0.0000084= -0.000005
Therefore, the approximate probability of obtaining at least 37 ones is -0.000005.
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The approximate probability of obtaining at least 37 ones is 0.8051.
Given that a fair die is tossed 180 times where the probability of getting a one is 1/6.
We need to find the approximate probability of obtaining at least 37 ones.
Using the binomial probability distribution, the probability of getting r successes in n independent trials can be given by:
\(P(r) = nCr x (p^r) x (1-p)^(n-r)\)
Where n = 180, p = 1/6, q = 1- p = 5/6
We want to find the probability of getting at least 37 ones.
Therefore, we can subtract the probability of getting less than 37 ones from 1.
\(P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)So, P(X≤36) = P(X=0) + P(X=1) + P(X=2) + .....+ P(X=36)P(X= r) = nCr x (p^r) x (q)^(n-r)\)
On substituting the given values, we get:
P(X≤36) = ∑P(X = r)
n = 180
r = 0 to 36
p = 1/6, q = 5/6
\(P(X≤36) = ∑(nCr) × (p^r) × (q)^(n-r)\)
n = 180, p = 1/6, q = 5/6= 0.1949
On subtracting it from 1, we get:
\(P(X≥37) = 1 - P(X<37) = 1 - P(X≤36)≈ 1 - 0.1949≈ 0.8051\)
Therefore, the approximate probability of obtaining at least 37 ones is 0.8051.
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monica has a goal to complete a triathlon. the race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run. in training, monica can swim at an average pace of 2.1mph. she rides her bike at an average of 18.8mph and runs at 5.1mph. estimate how long it will take her to complete the triathlon.
Answers
3.31 it will take her to complete the triathlon.
To find this, we can apply the equation distance = rate x time.
We are aware of the length and pace of each triathlon leg. Let's name them, respectively, d and r. We must locate the time, which we shall designate as t.
d = r x t or
t = d/r
The distance is 0.93, or 93/100, and the rate is 1.2, or 12/10 when swimming. As a result of our formula, we have:
12/10 divided by 93/100 yields the same result as
93/100 * 10/12
time to swim = 93/120 = 31/40
We have a distance of 24.8 miles, or 248/10, and a speed of 18.8 miles, or 188/10, for biking. Using the same formula, we obtain:
248/10 divided by 188/10 or
248/10 * 10/188 = 248/188 = 62/47 = time to bike
Finally, for the run, the distance is 6.2 = 62/10 and the rate is 5.1 or 51/10. Plugging this into the formula gives:
62/10 divided by 51/10 or
62/10 * 10/51 = 62/51 = time to run
= 31/40 + 62/47 + 62/51
=3.31
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which of the following hypotheses can be tested with the data that was collected? group of answer choices the average number of consumers that prefer catalogs in spanish is large the average number of consumers that prefer catalogs in english is large the percent of hispanics that are likely to buy from an l.l. bean catalog is higher than 30% the percent of hispanics that prefer to read catalogs in spanish is equal or higher than 30%
Answers
The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%
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Problems Group A Learning objective 3 P3-33A Journalizing adjusting entries and subsequent journal entries 1. b. DR Insurance Expense, \$4,500 Laughter Landscaping has collected the following data for the December 31 adjusting entries: a. Each Friday, Laughter pays employees for the current weck's work, The amount of the weekly payroll is $7,000 for a five-day workweek. This year December 31 falls on a Wednesday. Laughter will pay its employees on January 2. b. On January 1 of the current year, Laughter purchases an insurance policy that covers two years, $9,000. c. The beginning balance of Office Supplies was $4,000. During the year, Laughter purchased office supplies for $5,200, and at December 31 the office supplies on hand total $2,400. d. During December, Laughter designed a landscape plan and the client prepaid $7,000. Laughter recorded this amount as Unearned Revenue. The job will take several months to complete, and Laughter estimates that the company has carned 40% of the total revenue during the current year. c. At December 31, Laughter had carned $3,$00 for landscape services completed for Turnkey Appliances. Turnkey has scared that they will pay Laughter on January 10. f. Depreciation for the current year includes Equipment, $3,700; and Trucks, $1,300. g. Laughter has incurred $300 of interest expense on a $450 interest payment due on January 15. Requirements 1. Journalize the adjusting encry needed on December 31 , for each of the previous items affecting Laughter Landscaping. Assume Laughter records adjusting entrics only at the end of the year. Requirement 1 only
Answers
The journaliztion of the the adjusting entries needed for the previous items affecting Laughter Landscaping on December 31 is made.
To journalize the adjusting entries needed on December 31 for the previous items affecting Laughter Landscaping, you would make the following entries:
b. DR Insurance Expense, $4,500
CR Prepaid Insurance, $4,500
c. DR Office Supplies Expense, $6,800
CR Office Supplies, $6,800
d. DR Unearned Revenue, $4,200
CR Service Revenue, $4,200
c. DR Accounts Receivable, $3,000
CR Service Revenue, $3,000
f. DR Depreciation Expense - Equipment, $3,700
CR Accumulated Depreciation - Equipment, $3,700
DR Depreciation Expense - Trucks, $1,300
CR Accumulated Depreciation - Trucks, $1,300
g. DR Interest Expense, $300
CR Interest Payable, $300
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2. Determine if the expressions are equivalent by comparing the models.
Answers
Answer:
answer 4 y +rdcmeint or 67456
Step-by-step explanation:
how do you do factors of 5 grade
Answers
Answer:
If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.
Step-by-step explanation:
Solve for x.190°АBDC70°x =degrees
Answers
Let's determine the value of x.
\(\text{ x = }\frac{1}{2}(\text{ Arc AB + Arc CD)}\)\(\text{ = }\frac{1}{2}(190^{\circ}+70^{\circ})\)\(\text{ = }\frac{260^{\circ}}{2}\)\(\text{ x = 130}^{\circ}\)Therefore, the measure of x = 130 degrees.
What is similar denominator?
Answers
Similar denominators are fractions with same value of denominator.
What is denominator and similar denominator?
A denominator is a number that appears below the fraction's horizontal line. The fraction's bottom number indicates the total number of equally-sized pieces into which an object has been divided.
Similar denominators are two or more fractions whose denominators are same. For example \(\frac{5}{12}\) and \(\frac{7}{12}\) are similar denominators.
By calculating the LCM of the denominators and then multiplying the fractions by a suitable number, we can make the denominators of two fractions similar or equal.
To compare similar denominators fractions we need check numerator only.
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A furnace operates at 2,300°F. Before it
can be used to extract metal from an ore,
the temperature must be raised to
3,600°F. This takes place at a rate of
250°F per quarter hour. Which equation
gives the furnace temperature T after q
quarter hours?
A T= 2509 + 2300
B T = 250q + 3600
C T = 2300q + 250
DT= 3600q + 250
Answers
Multiply the rate per quarter hour by quarter hours: 250g. This then gets added to the starting temperature of 2300
The answer would be : A. T = 250g + 2300
What are four consecutive even integers if the first integer is −4?
Responses
−4, −3, −2, −1
negative 4 , negative 3 , negative 2 , negative 1,
−4, −5, −6, −7
negative 4 , negative 5 , negative 6 , negative 7,
−4, −2, 0, 2
negative 4 , negative 2 , 0, 2,
−4, −6, −8, −10
Answers
Negative 4 , negative 6 , negative 8 , negative 10.
What is integer?An integer is a whole number that can be either positive, negative, or zero. It is not a fraction, decimal, or a percentage. Integers are the basic building blocks of mathematics and are used to represent whole numbers in equations. They are also used in computer programming languages to represent whole numbers.
negative 4 , negative 3 , negative 2 , negative 1,
−4, −5, −6, −7
negative 4 , negative 5 , negative 6 , negative 7,
−4, −2, 0, 2
negative 4 , negative 2 , 0, 2,
−4, −6, −8, −10
negative 4 , negative 6 , negative 8 , negative 10.
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I need help with this please! Thanks :)
Which of these is the result of completing the square for the expression x^2 + 8x – 30?
Answers
Answer:
Option 2. That is the best option for this problem
4.There are many cylinders with radius 6 meters. Let h represent the height in meters and Vrepresent the volume in cubic meters.a.Write an equation that represents the volume V as a function of the height h.b.Sketch the graph of the function, using 3.14 as an approximation for π.C.If you double the height of a cylinder, what happens to the volume? Explain this using the equationd.If you multiply the height of a cylinder by 1/3, what happens to the volume? Explain this using the graph.
Answers
Answer:
(a)V=36πh
Explanation:
• Radius = 6 meters
\(\text{Volume of a cylinder}=\pi r^2h\)Part A
An equation that represents the volume V as a function of the height h is:
\(\begin{gathered} V=\pi\times6^2\times h \\ V=36\pi h \end{gathered}\)Part B
Using 3.14 as an approximation for π
\(\begin{gathered} V=36\times3.14\times h \\ V=113.04h \end{gathered}\)The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).
Part C
The initial equation for volume is:
\(V=113.04h\)When h=1
\(V=113.04\times1=113.04m^3\)If you double the height of a cylinder, h=2:
\(V=113.04\times2=226.08m^3\)We observe that when the height is doubled, the volume of the cylinder is also doubled.
Part D
The initial equation for volume is:
\(V=113.04h\)If the height of the cylinder is multiplied by 1/3, we have:
\(\begin{gathered} V=\frac{113.04h}{3} \\ V=37.68h \end{gathered}\)The volume of the cylinder will be divided by 3.
Using the graph, we observe a horizontal stretch of the graph by 1/3.
Paul was thinking of a number. Paul doubles it and adds 8.7 to get an answer of 23.4. Form an
Answers
2x +8.7 = 23.4
In that case he was thinking of the number 7.35
Ramon and Hector ride their bikes at constant rates during a race. Ramon rides 45 miles in 3 hours. The distance, y, in miles, Hector rides in x hours is given by the equation y = 18x. Which statement is true?
No answer text provided.
No answer text provided.
Ramon rides his bike 3 miles per hour faster than Hector rides his bike.
Ramon rides his bike 27 miles per hour faster than Hector rides his bike.
Ramon rides his bike 3 miles per hour slower than Hector rides his bike.
Ramon rides his bike 27 miles per hour slower than Hector rides his bike.
Answers
We will find the speeds of both persons, the correct option is:
"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."
Which statement is correct?First, we know that Ramon rides 45 miles in 3 hours, then its speed is:
S = 45mi/3h = 15mi/h
And we know that Hector position is given by:
y = 18x
Where x is time in hours, so his velocity is 18mi/h.
Then we can see that:
Ramon's speed = 15mi/hHector's speed = 18mi/hSo the correct statement is:
"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."
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Test tomorrow and I need this to make sense please
Answers
x=-4
Step-by-step explanation:
see the picture for full solution
How many numbers from 1 through 400 have a 2 in the units place (ones place) and are divisible by 4?
Answers
Answer:
2 6 9 7 4 7 66 46 66 74 89 84 653 88
If A = {1, 2, 3, 4} and B = {4, 5, 6}, find A ∪ B.
Answers
Answer:
{ 1,2,3,4,5,6}
Step-by-step explanation:
A bike shop charges x dollars to rent a bike for half a day and 2x dollars to rent a bike for a full day.write an algebric equation for the cost of renting five bikes for half a day and three bikes for a full day if the total cost is dollar 330.how much does it cost to rent a bike for a full day?
Answers
The cost of renting a bike for a full day is $110.
To write an algebraic equation for the cost of renting five bikes for half a day and three bikes for a full day, we can use the following expression: C = 5x/2 + 3(2x)where C is the total cost of renting the bikes.
Given that the total cost is $330, we can substitute it into the equation and solve for x.330 = 5x/2 + 6xMultiplying both sides by 2 to eliminate the fraction:660 = 5x + 12xSimplifying:17x = 660Dividing both sides by 17:x = 38.82
Therefore, the cost of renting a bike for a half day is $38.82 and the cost of renting a bike for a full day is $2x = $2(38.82) = $<<2*38.82=77.64>>77.64.
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the correlation between variable x and variable y is represented by which of the following? group of answer choices r(xy)2 rxy rx(y) rx/y previousnext
Answers
Given statement solution is :- The correlation between variable x and variable y is represented by "rxy".
Correlation is Positive when the values increase together, and; Correlation is Negative when one value decreases as the other increases.
There are three basic types of correlation: positive correlation: the two variables change in the same direction. negative correlation: the two variables change in opposite directions. no correlation: there is no association or relevant relationship between the two variables.
A basic example of positive correlation is height and weight—taller people tend to be heavier, and vice versa. In some cases, positive correlation exists because one variable influences the other. In other cases, the two variables are independent from one another and are influenced by a third variable.
The correlation between variable x and variable y is represented by "rxy".
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What is the weight (in grams) of a liquid that exactly fills a 465. 0 milliliter container if the density of the liquid is 0. 982 grams over milliliter? Round to the nearest hundredth when necessary and only enter numerical values, which can include a decimal point. (6 points)
Answers
Answer:
456.63
Step-by-step explanation:
Expand The expression -1/4(8r+12y) to write an equivalent expression. Use as few terms as possible.
Answers
you start a game with $60 in your wallet. you keep flipping a fair coin. if heads, you make $1 dollar, if tails, you loose 1$. you stop the game when you either have no money or you reach $100. what is the probability of being broke at the end of the game?
Answers
the probability of being broke at the end of the game is essentially 100%.
we can consider each coin flip as a separate event, with a probability of 0.5 for heads and 0.5 for tails. Let's calculate the probability of being broke at the end of the game.
First, we need to consider how many flips it would take to go from $60 to $0. If we keep losing $1 per flip, we would need to lose 60 times to reach $0. The probability of losing 60 times in a row is (0.5)^60, which is an extremely small number.
Secondly, we need to consider how many flips it would take to reach $100. If we keep winning $1 per flip, we would need to win 40 times to reach $100. The probability of winning 40 times in a row is (0.5)^40, which is also an extremely small number.
It is highly unlikely that someone would lose 60 times in a row, but it is still a possibility. As the number of flips increases, the probability of being broke becomes more and more certain.
In conclusion, while the probability of being broke at the end of the game is not exactly 100%, it is extremely close to that value.
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what is our goal when solving a system of equations?
Answers
Answer:
Look below.
Step-by-step explanation:
Our goal when solving a system of equations is to reduce two equations that have two variables, down to a single equation with one variable.