Answer:
a) W'(t) = 1.51 -0.0138t + 0.000762t² pounds/day
Step-by-step explanation:
The median weight of a boy with age between 0 and 36 months is given by:
[tex]W(t) = 8.38+1.51t-0.0069t^2 + 0.000254t^3[/tex]
To find the rate of change of weight with respect to time, that is, the change in weight measured in pounds caused by a unit change in time, measured in days, simply derivate the weight function over time:
[tex]\frac{d(W(t)}{dt}= W'(t) = 1.51-0.0138t + 0.000762t^2[/tex]
The rate of change is 1.51 -0.0138t + 0.000762t² pounds/day.
Whats an explicit rule for this? 14, 20, 26, 32, etc. Write an explicit formula for the nth term an.
Answer:
a(n)=14+6(n-1)
Step-by-step explanation:
The first term is 14. This would be an arithmetic sequence, so you will add 6 to every term: the common difference is 6.
14+6= 20
20+6=26
You have the formula a(n)= a(1)+d(n-1)
a(n)= 14+6(n-1)
14 for the first term, 6 for the common difference.
Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)
(a) The set of natural numbers x that satisfy x + 4 = 1.
(b) Use set-builder notation to write the following set.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Answer:
a) Empty set
b) [tex]\{x : x \in N \text{ and } x < 13\}[/tex]
Step-by-step explanation:
Roster form is a comma separated list form of set.
a) The set of natural numbers x that satisfy x + 4 = 1.
[tex]x + 4 = 1\\x = -3 \notin N[/tex]
Thus, x is an empty set.
b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
We use x to represent this set. Now x belongs to natural number and is less than equal to 12.
Thus, it can be written as:
[tex]\{x : x \in N \text{ and } x < 13\}[/tex]
the average age of men who had walked on the moon was 39 years, 11months, 15days. Is the value aparameter or a statistic?
Answer:
Parameter
Step-by-step explanation:
We are given the following in the question:
The average age of men who had walked on the moon was 39 years, 11 months, 15 days.
Population and sample:
Population is the collection of all observation for variable of interest or individual of interest.Sample is a subset for population.Parameter and statistic:
Any variable or value describing a population is known as parameter.Any value describing a sample is known as statistic.Population of interest:
men who had walked on the moon
Value:
average age of men who had walked on the moon
Thus, the give value describes a population and hence, it is a parameter.
A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90 degrees.What depth will provide maximum cross-sectional area and hence allow the most water to flow?
Answer:
18 in^2
Step-by-step explanation:
1 )The three sides of the gutter add up to 12
2x+ y = 12
2) Subtract 2x from both sides.
y = 12 — 2x
3 )Find the area of the rectangle in terms of x and simplify.
Area = xy = x(12 — 2x) = -2x^2+12x = f(x)
4 ) x=-b/2a
x co-ordinate of the vertex= -12/2(-2)=3
5 )Plug in 3 for x into they equation.
y co-ordinate of the vertex= 12 — 2(3) = 6
6 ) Plug in 3 for x and 6 for y.
Area= xy = 3(6) = 18
RESULT
18 in^2
Kristina walks 7 1/2 miles in 5 hours. At this rate, how many miles can Kristina walk in 9 hours
Answer:
13.5
Step-by-step explanation:
7 1/2=7.5
7.5/5*9=13.5
How to find the area of a square ABC D
Answer:
The answer to your question is 13 u²
Step-by-step explanation:
We know that the small triangle is surrounded by right triangles so we can use the Pythagorean theorem to find the lengths of the small triangle
AD² = 3² + 2²
Simplify
AD² = 9 + 4
AD² = 13
AD = [tex]\sqrt{13}[/tex]
Find the area of the square
Area = side x side
Area = AD x AD
Area = [tex]\sqrt{13} x \sqrt{13}[/tex]
Area = 13 u²
Binomial Distribution. Research shows that in the U.S. federal courts, about 90% of defendants are found guilty in criminal trials. Suppose we take a random sample of 25 trials. (For this problem it is best to use the Binomial Tables).Based on a proportion of .90, what is the variance of this distribution?
Answer:
The variance of this distribution is 0.0036.
Step-by-step explanation:
The variance of n binomial distribution trials with p proportion is given by the following formula:
[tex]Var(X) = \frac{p(1-p)}{n}[/tex]
In this problem, we have that:
About 90% of defendants are found guilty in criminal trials. This means that [tex]p = 0.9[/tex]
Suppose we take a random sample of 25 trials. This means that [tex]n = 25[/tex]
Based on a proportion of .90, what is the variance of this distribution?
[tex]Var(X) = \frac{p(1-p)}{n}[/tex]
[tex]Var(X) = \frac{0.9*0.1}{25} = 0.0036[/tex]
The variance of this distribution is 0.0036.
Suppose that operators A^ and B^ are both Hermitian, i.e, A^` = A^ and B^` = B^.
Answer the following and show your work:
(a) Is A^² Hermitian?
(b) Is A^B^ Hermitian?
(c) Is A^B^+ B^A^ Hermitian?
(d) Is it possible for A^ to have complex eigenvalues, or must they be real?
Answer:
a) A^² is a Hermitian operator
b) A^B^ is not a Hermitian operator
c) A^B^+ B^A^ is a Hermitian operator
d) It is not possible to be complex it must be a real number
Step-by-step explanation:
In order to understand this solution we need to define the concept Hermitian
HERMITIAN
This can be defined as a matrix whose elements are real and symmetrical i.e. it a square matrix that is equal to its own conjugate, or we can simply put that its a matrix in which those pairs of element that are symmetrically placed with respect to the principal diagonal are complex conjugates.i.e the diagonal elements( Hermitian operators) are real numbers while others are complex numbers.
The solution to the question above are on the first and second uploaded image.
Suppose that you are hiking on a terrain modeled by z=xy+y^3−x^2. You are at the point (2,1,−1).
(a) Determine the slope you would encounter if you headed due West from your position. What angle of inclination does this correspond to?
(b) Determine the slope you would encounter if you headed due North-West from your position. What angle of inclination does this correspond to?
(c) Determine the slope you would encounter if you headed due South-West from your position. What angle of inclination does this correspond to?
(d) Determine the steepest slope you could encounter from your position and the direction of that slope (as a unit vector).
Answer:
a) D_u . ∀ f ( 2 , 1 ) = 3 , Q = 72 degrees
b) D_u . ∀ f ( 2 , 1 ) = 4*sqrt(2) , Q = 80 degrees
c) D_u . ∀ f ( 2 , 1 ) = - sqrt(2) , Q = -54.74 degrees
d) u = 1 / sqrt(34) *(-3i +5j) , D_u . ∀ f ( 2 , 1 ) = +/- sqrt (34) , Q = 80.27 degrees
Step-by-step explanation:
Given:
- The terrain is modeled as a surface:
f(x , y) = x*y + y^3 - x^2
At point P( 2 , 1 , -1 ) is the current position:
Find:
(a) Determine the slope you would encounter if you headed due West from your position. What angle of inclination does this correspond to?
(b) Determine the slope you would encounter if you headed due North-West from your position. What angle of inclination does this correspond to?
(c) Determine the slope you would encounter if you headed due South-West from your position. What angle of inclination does this correspond to?
(d) Determine the steepest slope you could encounter from your position and the direction of that slope (as a unit vector).
Solution:
- We will compute the gradient of the vector ∀ f @ point P( 2 , 1 , -1 ) as follows:
∀ f ( x , y ) = (y - 2x ) i + ( x + 3y^2) j
- Evaluate at point P ( 2 , 1 ):
∀ f ( 2 , 1 ) = (1 - 2*2 ) i + ( 2 + 3*1^2) j
∀ f ( 2 , 1 ) = -3 i + 5 j
- We will use the result of ∀ f @ point P( 2 , 1 , -1 ) for the all the parts.
a)
- The direction due west can be written as a unit vector u_w = - i .
- Now compute the directional derivative in the direction of u_w = - i
D_u . ∀ f ( 2 , 1 ) =-3 i + 5 j . - i
D_u . ∀ f ( 2 , 1 ) = 3
- Now compute the angle of inclination Q for the following direction:
Q = arctan(3) = 71.57 = 72 degrees
Hence, along the direction due west from position we ascend with an inclination of approximately 72 degrees.
b)
- The direction due north-west can be written as a unit vector u_w = - i + j .
- Now compute the directional derivative in the direction of u_w = - i + j
D_u . ∀ f ( 2 , 1 ) =-3 i + 5 j . (- i + j) / sqrt(2)
D_u . ∀ f ( 2 , 1 ) = 8 / sqrt(2) = 4*sqrt(2)
- Now compute the angle of inclination Q for the following direction:
Q = arctan(4*sqrt(2)) = 79.98 = 80 degrees
Hence, along the direction due north-west from position we ascend with an inclination of approximately 80 degrees.
c)
- The direction due south-west can be written as a unit vector u_w = - i - j .
- Now compute the directional derivative in the direction of u_w = - i - j
D_u . ∀ f ( 2 , 1 ) =-3 i + 5 j . (- i - j) / sqrt(2)
D_u . ∀ f ( 2 , 1 ) = -2 / sqrt(2) = - sqrt(2)
- Now compute the angle of inclination Q for the following direction:
Q = arctan(-sqrt(2)) = -54.74 degrees
Hence, along the direction due south-west from position we descend with an inclination of approximately 55 degrees.
d)
- We know that ∀ f ( 2 , 1 ) gradient points in the direction greatest increase, hence, So from P the direction of greatest increase is ∇f(P) = -3i +5j. The unit vector pointing in this direction is:
u = 1 / sqrt(34) *(-3i +5j)
- so we have:
D_u . ∀ f ( 2 , 1 ) = u . ∀ f ( 2 , 1 ) = (-3i +5j) . (-3i +5j) / sqrt(34)
= +/- sqrt (34)
- Hence, the steepest ascent or decent is of :
Q = arctan ( sqrt(34)) = 80.27 degrees
If an angle of 96 degrees is rotated 90 degrees clockwise. what the measure?
Answer:
The measure is 6°.
Step-by-step explanation:
If an angle of 96 degrees is rotated 90 degrees clockwise then the measure of the new angle will be given by
= 96° - 90° = 6°
If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.137 nm, calculate the volume of its unit cell.
Answer:
[tex]5.796\times 10^{-29}m^3[/tex]
Step-by-step explanation:
Atomic radius of metal=0.137nm=[tex]0.137\times 10^{-9}[/tex]m
[tex]1nm=10^{-9}m[/tex]
Structure is FCC
We know that
The relation between edge length and radius in FCC structure
[tex]a=2\sqrt 2r[/tex]
Where a=Edge length=Side
r=Radius
Using the relation
[tex]a=2\sqrt 2\times 0.137\times 10^{-9}=0.387\times 10^{-9}m[/tex]
We know that
Volume of cube=[tex](side)^3[/tex]
Using the formula
Volume of unit cell=[tex](0.387\times 10^{-9})^3=5.796\times 10^{-29} m^3[/tex]
The volume of a unit cell is approximately 0.0580 nm³.
To find the volume of the unit cell for a metal with a face-centered cubic (FCC) crystal structure given an atomic radius of 0.137 nm, follow these steps:
Atomic Radius Interpretation: In a face-centered cubic unit cell, the atomic radius (r) is related to the edge length (a) of the unit cell by the equation:Thus, the volume of the unit cell is approximately 0.0580 nm³.
Someone please help me!
Answer:
The answer to your question is below
Step-by-step explanation:
43.-
x = [tex]\sqrt{27^{2} + 22^{2}- 2(27)(22)cos 73}[/tex]
x = [tex]\sqrt{865.66}[/tex]
x = 29.42
44.-
x = [tex]\sqrt{10^{2} + 14^{2} -2(10)(14)cos 66}[/tex]
x = [tex]\sqrt{182.11}[/tex]
x = 13.49
45.-
cos x = [tex]\frac{11^{2} - 17^{2} - 10^{2}}{-2(11)(17)}[/tex]
cos x = 0.7166
x = 44.22°
46.-
x = [tex]\sqrt{16^{2} + 12^{2} -2(16)(12)cos75}[/tex]
x = [tex]\sqrt{300.61}[/tex]
x = 17.34
47.-
cos P = [tex]\frac{6^{2} - 13^{2} -11^{2}}{-2(13)(11)}[/tex]
cos P = 0.888
P = 27.36°
sinR/13 = sinP/6
sin R = 13sin27.36/6
sinR = 0.996
R = 84.71°
Q = 180 - 84.71 - 27.36
Q = 67.93°
48.-
D = 180 - 25 - 113
D = 42°
CD = 9Sin113/sin42
CD = 12.38
ED = 9sin25/sin42
ED = 5.68
2.82 For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife will not vote?
The probability that at least one member of a married couple will vote is 0.34 or 34%. The probability of a wife voting given that her husband will vote is approximately 0.7143 or 71.43%. The probability of a husband voting given his wife will not vote is 0.06 or 6%.
Explanation:The subject of this question is probability within the realm of mathematics. To find the probability of at least one member of a married couple voting, we can use the formula P(A or B) = P(A) + P(B) - P(A and B).
Therefore, the probability is 0.21 (husband voting) + 0.28 (wife voting) - 0.15 (both voting), which equals 0.34.
For (b), the probability that the wife will vote, given that her husband will vote, is P(Wife|Husband) = P(Wife and Husband)/P(Husband).
So, this probability is 0.15/0.21, which equals approximately 0.7143.
For (c), the probability that the husband will vote, given that his wife will not vote, is P(Husband|Wife not voting) = P(Husband) - P(Husband and Wife).
So, this probability is 0.21 - 0.15, which yields 0.06 or 6%.
If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit card. Thirty percent of customers use coupons and 35% of customers pay with debit cards. Given that a customer does not pay with a debit card, the probability that the same customer does not use coupons is ________. A) 0.52 B) 0.60 C) 0.77 D) 0.85
Answer:
A. 0.52
Step-by-step explanation:
Let D be the event that person used Debit card and C b the event that person used coupon.
We have to find the probability of customer does not use coupons given that a customer does not pay with a debit card,
P(C'/D')=P(C')P(D'/C')/[P(C')P(D'/C')+P(D')P(D'/C')]
We are given that P(D)=0.35, P(C)=0.30 and P(D/C)=0.5.
P(D')=1-0.35=0.65
P(C')=1-0.3=0.7
P(D'/C')=0.5.
P(C'/D')=0.7(0.5)/[0.7(0.5)+0.65(0.5)]
P(C'/D')=0.35/[0.35+0.325]
P(C'/D')=0.35/[0.35+0.325]
P(C'/D')=0.35/0.675
P(C'/D')=0.5185=0.52
Thus, the probability of customer does not use coupons given that a customer does not pay with a debit card is 0.52.
A person takes a trip, driving with a constant peed of 89.5 km/h, except for a 22.0-min rest stop. If the peron's average speed is 77.8 km/h, (a) how much time is spent on the trip and (b) how far does the person travel?
Answer:
a) The person traveled 2.83 hours.
b) The person travels 220.17 kilometers.
Step-by-step explanation:
We have that the speed is the distance divided by the time. Mathematically, that is
[tex]s = \frac{d}{t}[/tex]
(a) how much time is spent on the trip and
The peron's average speed is 77.8 km/h, which means that [tex]s = 77.8[/tex]
The person distance traveled is:
22 min is 22/60 = 0.37h.
So for the time t1, the person traveled at a speed of 89.5 km/h. Which has a distance of 89.5*t1.
For 0.37h, the person was at a stop, so she did not travel. This means that the total distance is
[tex]d = 89.5t1 + 0 = 89.5t1[/tex]
The total time is the time traveling t and the stoppage time 0.37. So
[tex]t = t1 + 0.37[/tex]
We want to find t1, which is the time that the person was driving.
So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{89.5t1}{t1 + 0.37}[/tex]
[tex]77.8t1 + 77.8*0.37 = 89.5t1[/tex]
[tex]11.7t1 = 28.786[/tex]
[tex]t1 = \frac{28.786}{11.7}[/tex]
[tex]t1 = 2.46[/tex]
The total time is
[tex]t = t1 + 0.37 = 2.46 + 0.37 = 2.83[/tex]
The person traveled for 2.83 hours.
(b) how far does the person travel?
The person traveled 2.46 hours at an average speed of 77.8 km/h. So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{d}{2.83}[/tex]
[tex]d = 77.8*2.83 = 220.17[/tex]
The person travels 220.17 kilometers.
For the next two questions, let the null and alternative hypotheses be LaTeX: H_0H 0: LaTeX: \mu=\:8μ = 8 and LaTeX: H_aH a : LaTeX: \mu>8μ > 8. Assume that the population standard deviation LaTeX: \sigmaσ is not known. Becca collects a sample of size LaTeX: n=9n = 9 and computes LaTeX: \overline{x}=11x ¯ = 11 and LaTeX: s=6s = 6. Is LaTeX: \sigmaσ known?
Answer:
[tex]t=\frac{11-8}{\frac{6}{\sqrt{9}}}=1.5[/tex]
[tex]p_v =P(t_{(8)}>1.5)=0.086[/tex]
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, we can conclude that the mean is higher than 8 at 5% of signficance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=11[/tex] represent the mean height for the sample
[tex]s=6[/tex] represent the sample standard deviation for the sample
[tex]n=9[/tex] sample size
[tex]\mu_o =8[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test. (assumed)
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 8, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 8[/tex]
Alternative hypothesis:[tex]\mu > 8[/tex]
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{11-8}{\frac{6}{\sqrt{9}}}=1.5[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=9-1=8[/tex]
Since is a one side upper test the p value would be:
[tex]p_v =P(t_{(8)}>1.5)=0.086[/tex]
Conclusion
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, we can conclude that the mean is higher than 8 at 5% of signficance.
To determine if the population standard deviation is known, we can use the formula for the standard error of the mean (SEM) and use the t-distribution for a sample size of 9.
Explanation:To determine if the population standard deviation LaTeX: \sigma\sigma is known, we can use the formula for the standard error of the mean (SEM):
SE = \frac{s}{\sqrt{n}}
If the sample size is less than or equal to 30, we can use the t-distribution to find the critical value for a given level of significance. If the sample size is greater than 30, we can use the z-distribution. In this case, since the sample size is 9, the t-distribution should be used.
Thus, with a sample size of 9 and the population standard deviation not known, \sigma\sigma is not known.
Learn more about Standard Error of the Mean here:https://brainly.com/question/14524236
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what is the solution to the equation A/2= -5
Answer:
A = -10
Step-by-step explanation:
A/2 = -5
Multiply both sides by the denominator of the fraction
We have A/2 x2 = -5 x 2
A = -10
Answer:
-10
Step-by-step explanation:
It is the easiest equation.
A/2= -5
At first, we have to multiply both the sides by 2. Therefore, we can get,
[tex]\frac{A*2}{2}[/tex] = (-5 × 2)
or, A = -10
Therefore, the value of A is -10. It remains negative because we cannot multiply both the sides by -1. If we do that, we cannot determine the constant.
Answer: A = -10
Fred wants to buy a video game that costs $54. There was a markdown of 20%. How much is the discount?
Mar 10, 2012 - Markups and Markdowns Word Problems - Independent Practice Worksheet. $6640. $3.201 ... 2) Fred buys a video game disk for $4. There was a discount of 20%.What is the sales price? 20% of 1 pay 8090 ... 5) Timmy wants to buy.a scooter and the price was $50. When ... at a simple interest rate of 54%.
A researcher wants to determine if socioeconomic status (low, moderate, high) is related to smoking (yes or no). The Chi-Square null hypothesis for this study is that socioeconomic status is related to smoking behavior.A. TrueB. False
Answer:
The chi-square null hypothesis for the study that "socioeconomic status is related to smoking behavior" is False
Step-by-step explanation:
The chi-square null hypothesis is false because the chi-square null hypothesis states that no relationship exists on the categorical variables in a population, they are all independent of each other.
A punch recipe requires 2/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?
Answer:
The unit rate is 6 1/4 cups of soda per cup of pineapple juice
Step-by-step explanation:
we know that
To find out the unit rate of soda to pineapple juice in the punch, divide the cups of soda by the cups of pineapple juice
so
[tex]2\frac{1}{2} :\frac{2}{5}[/tex]
Convert mixed number to an improper fraction
[tex]2\frac{1}{2}=2+\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]
substitute
[tex]\frac{5}{2} :\frac{2}{5}[/tex]
Multiply in cross
[tex]\frac{25}{4}= 6.25[/tex]
Convert to mixed number
[tex]6.25=6+0.25=6+\frac{1}{4}= 6\frac{1}{4}[/tex]
That means
The unit rate is 6 1/4 cups of soda per cup of pineapple juice
Answer:
6 1/4
Step-by-step explanation:
A player of a video game is confronted with a series of 3 opponents and a(n) 77% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends).
Round your answers to 4 decimal places.
a. What is the probability that a player defeats all 3 opponents in a game?
b. What is the probability that a player defeats at least two opponents in a game?
c. If the game is played 2 times, what is the probability that the player defeats all 3 opponents at least once?
Answer:
a.) 0.4565
b.) 0.8656
c.) 0.4615
Step-by-step explanation:
We solve this using the probability distribution formula of combination.
nCr * p^r * q^n-r
Where
n = number of trials
r = successful trials
probability of success = p = 77% =0.77
Probability of failure= q = 1-0.77 = 0.23
a.) When exactly 3 opponents are defeated, When n = 3 and r = 3, probability becomes:
= 3C3 * 0.77³ * 0.23^0
= 1 * 0.456533 * 1
= 0.456533 = 0.4565 (4.d.p)
b.) When at least 2 opponents are defeated, that is when r = 2 and when r = 3,
When r = 2, probability becomes:
= 3C2 * 0.77² * 0.23¹
= 3 * 0.5929 * 0.23
= 0.409101
When 3 opponents are defeated, we calculated it earlier to be 0.456533
Hence, probability that at least 2 opponents are defeated
= 0.409101 + 0.456533
= 0.865634 = 0.8656(2.d.p)
c.) If 2 games are played, probability he defeat all 3 at least once in the game will be the sum (probability of defeating all 3 opponents in the first game and not defeating all 3 in the second game) + (probability of defeating all three opponents in both games)
Probability of defeating all three opponents in the first game = 0.456533
Probability of not defeating all three opponents in the second game = 1 - 0.456533 = 0.543467
Hence ,
probability of defeating all 3 opponents in the first game and not defeating all 3 in the second game = 0.465633 * 0.543467 = 0.253056
probability of defeating all three opponents in both games
= 0.456533 * 0.456533
=0.208422
Probability he defeats all three opponents at least once in 2games
= 0.253056 + 0.208422
=0.461478 = 0.4615(4.d.p)
A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When an emergency situation does not exist, the alarm sounds with probability 0.02. A real emergency situation is a rare event, with probability 0.004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists?
Answer:
6.56% probability that a real emergency situation exists.
Step-by-step explanation:
We have these following probabilities:
A 0.4% probability that a real emergency situation exists.
A 99.6% probability that a real emergency situation does not exist.
If an emergency situation exists, a 95% probability that the alarm sounds.
If an emergency situation does not exist, a 2% probability that the alarm sounds.
The problem can be formulated as the following question:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In this problem:
What is the probability of a real emergency situation existing, given that the alarm has sounded.
P(B) is the probability of there being a real emergency situation. So [tex]P(B) = 0.004[/tex].
P(A/B) is the probability of the alarm sounding when there is a real emergency situation. So P(A/B) = 0.95.
P(A) is the probability of the alarm sounding. This is 95% of 0.4%(real emergency situation) and 2% of 99.6%(no real emergency situation). So
P(A) = 0.95*0.04 + 0.02*0.996 = 0.05792
Given that the alarm has just sounded, what is the probability that a real emergency situation exists?
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.004*0.95}{0.05792} = 0.0656[/tex]
6.56% probability that a real emergency situation exists.
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find c1 and c2 given the following initial conditions. (Your answers will not contain a variable.) y(1) = 0, y'(1) = e c1 = Incorrect: Your answer is incorrect. c2 = Incorrect: Your answer is incorrect. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y = Incorrect: Your answer is incorrect.
Answer:
c₁ = 1/2
c₂ = - e²/2
y = (1/2)*(eˣ - e²⁻ˣ)
Step-by-step explanation:
Given
y = c₁eˣ + c₂e⁻ˣ
y(1) = 0
y'(1) = e
We get y' :
y' = (c₁eˣ + c₂e⁻ˣ)' ⇒ y' = c₁eˣ - c₂e⁻ˣ
then we find y(1) :
y(1) = c₁e¹ + c₂e⁻¹ = 0
⇒ c₁ = - c₂/e² (I)
then we obtain y'(1):
y'(1) = c₁e¹ - c₂e⁻¹ = e (II)
⇒ (- c₂/e²)*e - c₂e⁻¹ = e
⇒ - c₂e⁻¹ - c₂e⁻¹ = - 2c₂e⁻¹ = e
⇒ c₂ = - e²/2
and
c₁ = - c₂/e² = - (- e²/2) / e²
⇒ c₁ = 1/2
Finally, the equation will be
y = (1/2)*eˣ - (e²/2)*e⁻ˣ = (1/2)*(eˣ - e²⁻ˣ)
Applying the initial conditions, it is found that the solution is:
[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]
------------------------
The solution for the PVI is given by:
[tex]y = c_1e^{x} + c_2e^{-x}[/tex]
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The condition [tex]y(1) = 0[/tex] means that when [tex]x = 0, y = 1[/tex], and thus, we get:
[tex]c_1e + c_2e^{-1} = 0[/tex]
[tex]c_1e+ \frac{c_2}{e} = 0[/tex]
[tex]c_1e^{2} + c_2 = 0[/tex]
[tex]c_2 = -c_1e^{2}[/tex]
------------------------
The derivative is:
[tex]y^{\prime}(x) = c_1e^{x} - c_2e^{-x}[/tex]
Applying the condition [tex]y^{\prime}(1) = e[/tex], we get:
[tex]c_1e - \frac{c_2}{e} = e[/tex]
Considering [tex]c_2 = -c_1e^{2}[/tex]:
[tex]c_1e + c_1\frac{e^2}{e} = e[/tex]
[tex]c_1e + c_1e = e[/tex]
[tex]2c_1e = e[/tex]
[tex]2c_1 = 1[/tex]
[tex]c_1 = \frac{1}{2}[/tex]
------------------------
The second constant is:
[tex]c_2 = -c_1e^{2} = -\frac{e^2}{2}[/tex]
And the solution is:
[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]
A similar problem is given at https://brainly.com/question/13244107
An education researcher collects data on how many hours students study at various local colleges. The researcher calculates an average to summarize the data. The researcher is using ______.A)measure of central tendency
B) descriptive statistical method
C) intuitive statistical method
D) inferential statistical method
Answer:
Correct option is (B) descriptive statistical method
Step-by-step explanation:
Descriptive statistics branch in statistics deals with the representation of the data using distinct brief coefficients. These coefficients are used as either the representative of the sample or the population.
The descriptive statistics branch is divided into two sub branches:
Measure of central tendencyMeasure of dispersion.The three measures of central tendency are:
Mean (or Average)MedianMode.The measures of dispersion are:
VarianceStandard deviationRangeKurtosisSkewnessThe education researcher computes the average number of hours student study at various local colleges.
The average of a data is the mean value which is the measure of central tendency.
Thus, the researcher is using descriptive statistical method to summarize the data.
Final answer:
The education researcher is using descriptive statistical methods by calculating an average of study hours, which is a measure of central tendency, a fundamental aspect of descriptive statistics.
Explanation:
An education researcher who collects data on how many hours students study at various local colleges and then calculates an average to summarize this data is using descriptive statistical methods. Descriptive statistics involve organizing and summarizing data to provide a clear overview of its characteristics. Examples of descriptive statistics include measures of central tendency (mean, median, mode), which indicate the typical value within a data set, and measures of variability (range, variance, standard deviation), which show how spread out the data points are. The calculation of an average, or mean, falls under the measure of central tendency, making it a key component of descriptive statistics.
A quantum object whose state is given by is sent through a Stern-Gerlach device with the magnetic field oriented in the y-direction. What is the probability that this object will emerge from the + side of this device?
Answer:
The probability that the object will emerge from the + side of this device is 1/2
Step-by-step explanation:
Orienting the magnetic field in a Stern-Gerlach device in some direction(y - direction) perpendicular to the direction of motion of the atoms in the beam, the atoms will emerge in two possible beams, corresponding to ±(1/2)h. The positive sign is usually referred to as spin up in the direction, the negative sign as spin down in the explanation, the separation has always been in the y direction. There can be some other cases where magnetic field may be orientated in x-direction or z-direction.
How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Infinitely many F. None of the above
Hello, you haven't provided the system of equations, therefore I will show you how to do it for a particular system and you can follow the same procedure for yours.
Answer:
For E1 -> Exactly one
For E2 -> None
For E3 -> Infinitely many
Step-by-step explanation:
Consider the system of equations E1: y = -6x + 8 and 3x + y = 4, replacing equation one in two 3x -6x +8 = 4, solving x = 4/3 and replacing x in equation one y = 0. This system of equations have just one solution -> (4/3, 0)
Consider the system of equations E2: y = -3x + 9 and y = -3x -7, replacing equation one in two -3x + 9 = -3x -7, solving 9 = -3. This system of equations have no solution because the result is a fallacy.
Consider the system of equations E3: 2 = -6x + 4y and -1 = -3x -2y, taking equation one and solving y = 1/2 + 3/2x, replacing equation one in two -1 = -3x -1 +3x, solving -1 = -1. This system of equations have infinitely many solution because we find a true equation when solving .
List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places)P(x=0) P(x=6)
P(x=1) P(x=7)
P(x=2) P(x=8)
P(x=3) P(x=9)
P(x=4) P(x=10)
P(x=5)
Answer:
a. P(X = 0)= 0.001
b. P(X = 1)= 0.001
c. P(X=2)= 0.044
d. P(X=3)= 0.117
e. P(X=4)= 0.205
f. P(X=5)= 0.246
g. P(X=6)= 0.205
h. P(X=7)= 0.117
i. P(X=8)= 0.044
j. P(X=9)= 0.001
k. P(X=10)= 0.001
Step-by-step explanation:
Hello!
You have the variable X with binomial distribution, the probability of success is 0.5 and the sample size is n= 10 (I suppose)
If the probability of success p=0.5 then the probability of failure is q= 1 - p= 1 - 0.5 ⇒ q= 0.5
You are asked to calculate the probabilities for each observed value of the variable. In this case is a discrete variable with definition between 0 and 10.
You have two ways of solving this excersice
1) Using the formula
[tex]P(X)= \frac{n!}{(n-X)!X!} * (p)^X * (q)^{n-X}[/tex]
2) Using a table of cummulative probabilities of the binomial distribution.
a. P(X = 0)
Formula:
[tex]P(X=0)= \frac{10!}{(10-0)!0!} * (0.5)^0 * (0.5)^{10-0}[/tex]
P(X = 0) = 0.00097 ≅ 0.001
Using the table:
P(X = 0) = P(X ≤ 0) = 0.0010
b. P(X = 1)
Formula
[tex]P(X=1)= \frac{10!}{(10-1)!1!} * (0.5)^1 * (0.5)^{10-1}[/tex]
P(X = 1) = 0.0097 ≅ 0.001
Using table:
P(X = 1) = P(X ≤ 1) - P(X ≤ 0) = 0.0107-0.0010= 0.0097 ≅ 0.001
c. P(X=2)
Formula
[tex]P(X=2)= \frac{10!}{(10-2)!2!} * (0.5)^2 * (0.5)^{10-2}[/tex]
P(X = 2) = 0.0439 ≅ 0.044
Using table:
P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.0547 - 0.0107= 0.044
d. P(X = 3)
Formula
[tex]P(X = 3)= \frac{10!}{(10-3)!3!} * (0.5)^3 * (0.5)^{10-3}[/tex]
P(X = 3)= 0.11718 ≅ 0.1172
Using table:
P(X = 3) = P(X ≤ 3) - P(X ≤ 2) = 0.1719 - 0.0547= 0.1172
e. P(X = 4)
Formula
[tex]P(X = 4)= \frac{10!}{(10-4)!4!} * (0.5)^4 * (0.5)^{10-4}[/tex]
P(X = 4)= 0.2051
Using table:
P(X = 4) = P(X ≤ 4) - P(X ≤ 3) = 0.3770 - 0.1719= 0.2051
f. P(X = 5)
Formula
[tex]P(X = 5)= \frac{10!}{(10-5)!5!} * (0.5)^5 * (0.5)^{10-5}[/tex]
P(X = 5)= 0.2461 ≅ 0.246
Using table:
P(X = 5) = P(X ≤ 5) - P(X ≤ 4) = 0.6230 - 0.3770= 0.246
g. P(X = 6)
Formula
[tex]P(X = 6)= \frac{10!}{(10-6)!6!} * (0.5)^6 * (0.5)^{10-6}[/tex]
P(X = 6)= 0.2051
Using table:
P(X = 6) = P(X ≤ 6) - P(X ≤ 5) = 0.8281 - 0.6230 = 0.2051
h. P(X = 7)
Formula
[tex]P(X = 7)= \frac{10!}{(10-7)!7!} * (0.5)^7 * (0.5)^{10-7}[/tex]
P(X = 7)= 0.11718 ≅ 0.1172
Using table:
P(X = 7) = P(X ≤ 7) - P(X ≤ 6) = 0.9453 - 0.8281= 0.1172
i. P(X = 8)
Formula
[tex]P(X = 8)= \frac{10!}{(10-8)!8!} * (0.5)^8 * (0.5)^{10-8}[/tex]
P(X = 8)= 0.0437 ≅ 0.044
Using table:
P(X = 8) = P(X ≤ 8) - P(X ≤ 7) = 0.9893 - 0.9453= 0.044
j. P(X = 9)
Formula
[tex]P(X = 9)= \frac{10!}{(10-9)!9!} * (0.5)^9 * (0.5)^{10-9}[/tex]
P(X = 9)=0.0097 ≅ 0.001
Using table:
P(X = 9) = P(X ≤ 9) - P(X ≤ 8) = 0.999 - 0.9893= 0.001
k. P(X = 10)
Formula
[tex]P(X = 10)= \frac{10!}{(10-10)!10!} * (0.5)^{10} * (0.5)^{10-10}[/tex]
P(X = 10)= 0.00097 ≅ 0.001
Using table:
P(X = 10) = P(X ≤ 10) - P(X ≤ 9) = 1 - 0.9990= 0.001
Note: since 10 is the max number this variable can take, the cummulated probability until it is 1.
I hope it helps!
Match each shape on the left to every name that describes it on the right. Some answer options on the right will be used more than once.
The student is undertaking an English language assignment designed to strengthen their understanding of vocabulary, word formation, and spelling through a variety of exercises including word scrambles, pattern recognition, spelling reviews, and word categorization.
Explanation:The student appears to be working on a language arts activity related to vocabulary and word structure. The question likely requires them to engage with various linguistic exercises such as word scrambles, identifying patterns in spelling or pronunciation, reviewing correct spellings, and categorizing words. Such tasks are designed to help students learn about word formation, synonyms, antonyms, and the nuances of English spelling.
Word Scrambles and Patterns
For word scrambles, students are expected to rearrange the letters to form meaningful words. In doing this, they might uncover a hidden word that pertains to the lesson's focus. Identifying patterns in words might involve recognizing prefixes, suffixes, or roots that appear consistently across different words.
Reviewing Spelling
The student is also asked to choose the word with the correct spelling. This likely involves comparing similar words and identifying the correctly spelled one, perhaps with the aid of a dictionary for verification.
Categorizing Words
In the task of sorting words into groups, students might have to classify words based on different criteria such as part of speech, phonetic features, or spelling patterns. This reinforces their understanding of language structure and proper spelling conventions.
A. Find n so that the number sentence below is true. 2^-6*2^n=2^9.
N=_____________
B. Use the laws of exponents to demonstrate why 2^3•4^3=2^9 is true and explain.
This is true because
n = 15
Step-by-step explanation:
Step 1: Calculate n by using the law of exponents that a^m × a^n = a^m+nFor 2^-6*2^n=2^9, a = 2, m = -6 and m + n = 9
⇒ -6 + n = 9
⇒ n = 15
Step 2: Given 2³ × 4³=2^9. Use law of exponents to prove it.⇒ 2³ × 4³ can also be written as 2³ × (2²)³ = 2³ × 2^6 [This is based on the law of exponents (a^m)^n = (a)^m×n]
⇒ 2³ × 2^6 = 2^ (3 + 6) = 2^9 [Using the law of exponents a^m × a^n = a^m+n]
When analyzing data on the number of employees in small companies in one town, a researcher took square roots of the counts. Some of the resulting values, which are reasonably symmetric, were 4, 5, 5, 7, 7, 8, and 11.
What were the original values, and how are they distributed?
Answer:
The original values are : 16, 25, 25, 49, 49, 64, 121.
Step-by-step explanation:
We know that a researcher took square roots of the counts. Some of the resulting values, which are reasonably symmetric, were 4, 5, 5, 7, 7, 8, and 11. We calculate the original values:
[tex]4^2=16\\5^2=25\\5^2=25\\7^2=49\\7^2=49\\8^2=64\\11^2=121\\[/tex]
The original values are : 16, 25, 25, 49, 49, 64, 121.
We conclude that the original data is not simmetric.
The original values obtained by reversing the square root transformation are 16, 25, 25, 49, 49, 64, and 121. These values show variability in the number of employees across different small companies in the town. The transformed dataset was made more symmetrical for statistical analysis.
When a researcher applies a square root transformation to a dataset, the purpose is often to make the data more symmetrical and easier to analyze using certain statistical methods.
Given the transformed values 4, 5, 5, 7, 7, 8, and 11, we can reverse the transformation to find the original values.
The square of each transformed value yields the original data points:
4² = 165² = 255² = 257² = 497² = 498² = 6411² = 121Thus, the original values are 16, 25, 25, 49, 49, 64, and 121. These values are distributed with some repeated data points and a range from 16 to 121.
This distribution indicates variability in the number of employees across the small companies studied.