Answer:
The following system is not linear.
The following system is time-invariant
Step-by-step explanation:
To determine whether a system is linear, the following condition must be satisfied:
[tex]f(a) + f(b) = f(a+b)[/tex]
For [tex]y(t) = cos(3t)[/tex], we have
[tex]y(a) = cos(3at)[/tex]
[tex]y(b) = cos(3bt)[/tex]
[tex]y(a+b) = cos(3(a+b)t) = cos(3at + 3bt)[/tex]
In trigonometry, we have that:
[tex]cos(a+b) = cos(a)cos(b) - sin(a)sin(b)[/tex]
So
[tex]cos(3at + 3bt) = cos(3at)cos(3bt) - sin(3at)sin(3bt)[/tex]
[tex]y(a) + y(b) = cos(3at) + cos(3bt)[/tex]
[tex]y(a+b) = cos(3(a+b)t) = cos(3at + 3bt) = cos(3at)cos(3bt) - sin(3at)sin(3bt)[/tex]
Since [tex]y(a) + y(b) \neq y(a+b)[/tex], the system [tex]y(t) = cos(3t)[/tex] is not linear.
If the signal is not multiplied by time, it is time-invariant. So [tex]y(t) = cos(3t)[/tex]. Now, for example, if we had [tex]y(t) = t*cos(3t)[/tex] it would not be time invariant.
Can Someone please explain how to solve this. The directions say, "Solve the system by graphing. Then check your solution."
Try this suggested solution (see the attached picture, the answer is [-2;1]).
1 step to drow the graph required in the condition;
2 step to find intersection point (this is the A point);
3 step, check stage, to solve the system of two equations.
4 to compare the results in step 2 and step 3.
In 2004, 34.2 million accountants e-filed income tax returns. That was 114% of the number who e-filed in 2003. Find the number of accountants who e-filed income tax returns in 2003.
Answer:
30 million.
Step-by-step explanation:
Let x be the number of accountants who e-filed income tax returns in 2003.
We have been given that in 2004, 34.2 million accountants e-filed income tax returns. That was 114% of the number who e-filed in 2003.
We can represent our given information in an equation as:
[tex]\frac{114}{100}\cdot x=34.2[/tex]
[tex]1.14x=34.2[/tex]
[tex]\frac{1.14x}{1.14}=\frac{34.2}{1.14}[/tex]
[tex]x=30[/tex]
Since the number is given in millions, therefore, 30 million accountants e-filed income tax returns in 2003.
A team of 4 golfers scored 69,73,70, and 74 on the first round on a
par 72 course. They reduced their team score by 3 on the second
round.
a) How many strokes above or below par was the team score on the
first round?
Answer: There are 2 strokes below par that the team has scored in the first round.
Step-by-step explanation:
Since we have given that
Scores of a team
69, 73, 70 and 74
on the first round on a part 72 course.
Now, we need to find the number of strokes above or below the par.
So, we will compare all the scores with 72.
So,
69-72 = -3(below par)
73-72 = 1 (above par)
70-72= - 2 (below par)
74-72 = 2 ( above par)
So, Number of strokes above or below par is given by
[tex]-3+1-2+2\\\\=-2[/tex]
Hence, there are 2 strokes below par that the team has scored in the first round.
Social Sciences Alcohol Abstinence The Harvard School of Public Health completed a study on alcohol consumption on college campuses. They concluded that 20.7% of women attending all-women colleges abstained from alcohol, compared to e6% of women attending coeducational colleges. Approximately 4.7% of women college students attend all-women schools. Source: Harvard School of Public Health. (a) What is the probability that a randomly selected female student abstains from alcohol? (b) If a randomly selected female student abstains from alcohol, what is the probability she attends a coedücational colege?
Answer:
a) There is a 6.69% probability that a randomly selected female student abstains from alcohol.
b) If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.
Step-by-step explanation:
This is a probability problem:
We have these following probabilities:
-20.7% of a woman attending an all-women college abstaining from alcohol.
-6% of a woman attending a coeducational college abstaining from alcohol.
-4.7% of a woman attending an all-women college
- 100%-4.7% = 95.3% of a woman attending a coeducational college.
(a) What is the probability that a randomly selected female student abstains from alcohol?
[tex]P = P_{1} + P_{2}[/tex]
[tex]P_{1}[/tex] is the probability of a woman attending an all-women college being chosen and abstaining from alcohol. There is a 0.047 probability of a woman attending an all-women college being chosen and a 0.207 probability that she abstain from alcohol. So:
[tex]P_{1} = 0.047*0.207 = 0.009729[/tex]
[tex]P_{2}[/tex] is the probability of a woman attending a coeducational college being chosen and abstaining from alcohol. There is a 0.953 probability of a woman attending a coeducational college being chosen and a 0.06 probability that she abstain from alcohol. So:
[tex]P_{2} = 0.953*0.06 = 0.05718[/tex]
So, the probability of a randomly selected female student abstaining from alcohol is:
[tex]P = P_{1} + P_{2} = 0.009729 + 0.05718 = 0.0669[/tex]
There is a 6.69% probability that a randomly selected female student abstains from alcohol.
(b) If a randomly selected female student abstains from alcohol, what is the probability she attends a coedücational colege?
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
Here:
What is the probability of a woman attending a coeducational college, knowing that she abstains from alcohol.
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.
We have the following probabilities:
[tex]P(B)[/tex] is the probability of a woman from a coeducational college being chosen. So [tex]P(B) = 0.953[/tex]
[tex]P(A/B)[/tex] is the probability of a woman abstaining from alcohol, given that she attends a coeducational college. So [tex]P(A/B) = 0.06[/tex]
[tex]P(A)[/tex] is the probability of a woman abstaining from alcohol. From a), [tex]P(A) = 0.0669[/tex]
So, the probability that a randomly selected female student attends a coeducational college, given that she abstains from alcohol is:
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{(0.953)*(0.06)}{(0.0669)} = 0.8287[/tex]
If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.
Write the following as a ratio: 304 calories burned in 56 minutes
Answer:
The required ratio is 38 : 7
Step-by-step explanation:
Given,
304 calories burned in 56 minutes,
That is, the number of calories burnt in 56 minutes = 304
So, the ratio of the calories burnt and time in minutes = [tex]\frac{304}{56}[/tex]
∵ HCF(304, 56) = 8,
Thus, the ratio of price of photos and number of photos = [tex]\frac{304\div 8}{56\div 8}[/tex]
= [tex]\frac{38}{7}[/tex]
Nori placed an order for 10 chairs that cost d dollars each and 2 tables that cost D dollars each. Write an expression for the total cost of the chairs and tables. 20d 10d + 2D 200 10D + 2d
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Cost of each chair be d dollar
Cost of each table be D dollar
Number of chairs = 10
Number of tables = 2
cost of 10 chairs become [tex]10\times d=10d[/tex]
cost of 2 tables become [tex]2\times D=2D[/tex]
So, the total cost of chairs and tables would be
[tex]10d+2D=Total\ cost[/tex]
Hence, Second option is correct.
State whether each pair of sets is equal, equivalent, or neither.
{d,o,g}: {c,a,t}
{run} : {{r,u,n}
{t,o,p} :{p,o,t}
Answer:
The set {d,o,g}: {c,a,t} is equivalent but not equal.
The set {run} : {r,u,n} is neither equivalent nor equal.
The set {t,o,p} :{p,o,t} is equal.
Step-by-step explanation:
Consider the provided sets.
Two sets are equal if they have the exact same elements.
Two sets are equivalent if they have the same number of elements.
Now consider the provided sets:
{d,o,g}: {c,a,t}
The number of elements in set {d,o,g} is 3.
The number of elements in set {c,a,t} is 3.
Thus, the sets are equivalent, but they have different elements, so the sets are not equal.
{run} : {r,u,n}
The number of elements in set {run} is 1.
The number of elements in set {r,u,n} is 3.
Thus, the sets are not equivalent, also they have different elements, so the sets are not equal.
{t,o,p} :{p,o,t}
The number of elements in set {t,o,p} is 3.
The number of elements in set {p,o,t} is 3.
Also they have same elements i.e (o, p and t),
Hence, the sets are equal.
Sets {d,o,g} and {c,a,t} are equivalent, {run} and {{r,u,n}} are neither, and {t,o,p} and {p,o,t} are equal. Equality refers to having identical elements, while equivalence means having the same number of elements.
Explanation:We are asked to determine if each pair of sets is equal, equivalent, or neither. Let's consider each pair:
Equal sets have exactly the same elements. For instance, {1, 2, 3} is equal to {3, 2, 1}.Equivalent sets have the same number of elements, but not necessarily the same elements. For example, {1, 2, 3} is equivalent to {a, b, c} because both have three elements.Two sets are neither equal nor equivalent if they do not have the same elements and their sizes are different.So for the given sets:
The sets {d,o,g} and {c,a,t} are equivalent because they both contain three elements, but they are not equal because the elements are different.The sets {run} and {{r,u,n}} are neither equal nor equivalent. The first set has one element, 'run', and the second set has one element as well, but it is the set {r,u,n}, which has three distinct elements inside it.The sets {t,o,p} and {p,o,t} are equal because they contain exactly the same elements, just in a different order.Jacob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out how many of each (quarters and dimes) Jacob has. What do the unknowns in this system represent and what are the two equations that that need to be solved? Finally, solve the system of equations.
Answer: The required number of quarters is 23 and that of dimes is 37.
Step-by-step explanation: Given that Jacob has 60 coins consisting of quarters and dimes and the combined value of the coins is $9.45.
We are to find the number of quarters and dimes.
Let x and y represents the number of quarters and dimes respectively.
Then, according to the given information, we have
[tex]x+y=60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.25x+0.10y=9.45\\\\\Rightarrow 25x+10y=945\\\\\Rightarrow 5x+2y=189~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 2, we have
[tex]2(x+y)=2\times60\\\\\Rightarrow 2x+2y=120~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (iii) from equation (ii), we get
[tex](5x+2y)-(2x+2y)=189-120\\\\\Rightarrow 3x=69\\\\\Rightarrow x=\dfrac{69}{3}\\\\\Rightarrow x=23.[/tex]
And, from equation (i), we get
[tex]23+y=60\\\\\Rightarrow y=60-23\\\\\Rightarrow y=37.[/tex]
Thus, the required number of quarters is 23 and that of dimes is 37.
Final answer:
Jacob has 23 quarters and 37 dimes. We use a system of linear equations with two unknowns representing the number of quarters (q) and dimes (d) to determine the quantities by solving for q and d.
Explanation:
To solve the question of how many quarters and dimes Jacob has, we need to use a system of linear equations. The unknowns in this system represent the number of quarters and dimes. Let's define q as the number of quarters and d as the number of dimes Jacob has. Therefore, we have two equations:
The total number of coins: q + d = 60
The total value of coins: 0.25q + 0.10d = 9.45
Solving the system of equations, we begin by multiplying the second equation by 100 to get rid of decimals, resulting in 25q + 10d = 945. We can use either substitution or elimination to solve for q and d. Let's use the elimination method:
Multiply the first equation by -10 and add it to the second equation to eliminate d.
-10q - 10d = -600
(25q + 10d) + (-10q - 10d) = 945 + (-600)
15q = 345
q = 345 / 15
q = 23
Now that we have the number of quarters, we can find the number of dimes:
Substitute q = 23 in the first equation.
23 + d = 60
d = 60 - 23
d = 37
Hence, Jacob has 23 quarters and 37 dimes.
Prove that the curve a(t) = (cost, sin 2t, cos 2t) is regular on R and that it self-intersects at (1,0,1). Check the self-intersection part by using algebra and also by using Geofte
Answer:
The function a (t) is a vector function composed of the component functions [tex]a_ {1} (t) = cost, a_ {2} (t) = sin2t[/tex] and [tex]a_ {3} (t) = cos2t[/tex]. How [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are infinitely derivable functions in R, so they are regular functions in R.
Now, for[tex]t = 0[/tex], you have to [tex]a (0) = (cos (0), sin2 (0), cos2 (0)) = (1, 0, 1)[/tex]. How the functions [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are periodic functions with period [tex]2 \pi,[/tex] the vector function [tex]a (t)[/tex] will take the same point [tex](1, 0 , 1)[/tex] at [tex]t = 2n\pi, n = 0, 1, 2, 3, ...[/tex] then the vector function is auto-intercepted
Step-by-step explanation:
In a certain city of several million people, 7.7% of the adults are unemployed. If a random sample of 300 adults in this city is selected, approximate the probability that at least 26 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal place
Answer: 0.2643
Step-by-step explanation:
Given : The proportion of adults are unemployed : p=0.077
The sample size = 300
By suing normal approximation to the binomial , we have
[tex]\mu=np=300\times0.077=23.1[/tex]
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{300\times0.077(1-0.077)}\\\\=4.61749932323\approx4.62[/tex]
Now, using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponding to 26 will be :-
[tex]z=\dfrac{26-23.1}{4.62}\approx0.63[/tex]
Using standard distribution table for z , we have
P-value=[tex]P(z\geq0.63)=1-P(z<0.63)[/tex]
[tex]=1-0.7356527=0.2643473\approx0.2643[/tex]
Hence, the probability that at least 26 in the sample are unemployed =0.2643
The Order of Magnitude for the total length of 6 cars, which average 8 feet
each, is ______
Answer:
The Order of Magnitude is 1
Step-by-step explanation:
If
N=a*10^{b}
b is the order of magnitude
Total length = 6 * 8 feet= 48 feet=4.8*10^1 feet
Answer:
The order of magnitude of length is 2.
Step-by-step explanation:
Since we are given the total number of cars is 6 and the length of each car is 8 feet hence the length of 6 cars equals
[tex]Length=6\times 8=48[/tex]
Now by definition of order of magnitude we know it is the smallest power of 10 by which a number can be represented.
Mathematically order of magnitude of 'N' is given by 'b'
[tex]N=a\times 10^{b}\\\\with\\\\\frac{\sqrt{10}}{10}\leq a<\sqrt{10}[/tex]
Hence we can write
[tex]48=0.48\times 10^{2}[/tex]
Since the power of 10 is 2 hence the order of magnitude of 48 feet is 2.
Calculate:
(Round two decimal places for final answer)
3gallons (gal) =_____liters (L)
Answer:
13.64 litres
Explanation
Since 1 gallon = 4.546 litres
Therefore...3 gal
; 3 × 4.546 = 13.64 litres
How do you find the slope intercept form of an equation?
Answer:
The equation of line can be written as,
y = mx + c
where, m is slope
and c is intercept of line.
Now, Suppose we have equation: ax + by + c = 0
So, transforming the given equation in above standard equation.
⇒ by = -ax - c
⇒ [tex]y = \frac{-a}{b}x +\frac{-c}{a}[/tex]
Now comparing this equation with standard equation. We get,
[tex]m =\frac{-a}{b}[/tex]
and [tex]c = \frac{-c}{a}[/tex]
Hence, Intercept = [tex]c =\frac{-c}{a}[/tex] for line ax + by + c = 0.
A sample of households in a community is selected at random from the telephone directory. In this community, 2% of households have no telephone, 14% have only cell phones, and another 25% have unlisted telephone numbers. The sample will certainly suffer from
A. nonresponse.
B. false responses.
C. undercoverage.
D. None of the above.
Answer:
under coverage
Step-by-step explanation:
From the given information we can say that 2% of households have no telephone, 14% have only cell phones, and another 25% have unlisted telephone numbers. Since, the facility is available some part of population and not available to the whole population so, clearly its an examples under coverage.
Which of the following statements is biconditional?
I am sleeping if and only if I am snoring.
Mary will eat pudding today if and only if it is custard.
It is raining if and only if it is cloudy.
None of the above.
Why is the answer none of the above?
Answer with Step-by-step explanation:
We are given some statements
We have to find that which statements is bi-conditional
We know that
Bi-Conditional statement:It is combination of conditional statement and its converse written as if and only if .Bi- conditional statement is true if and only both the conditions are true.
1.I am sleeping if and only if I am snoring.
If I am sleeping then I am snoring .Then,it may be true or may not be true.
If I am snoring then I am sleeping .It is true.
Its one side true result.So, it is not bi conditional true statement.
2.Mary will eat pudding today if and only if is custard.
If Mary will eat pudding today then it is custard.It may or may not be true because pudding can be any soft sweet desserts.It is not necessary that it is custard only.
If it is custard then Mary will east pudding today.It is true, because it is soft sweet dessert.
Hence, it is one side true. Therefore, It is not bi- conditional true.
3.It is raining if and only if it is cloudy.
If it is raining then it is cloudy .It is true.
But if it is cloudy then it is raining. It may be true or may not be true.
Hence, it is one side true result.Therefore, it is not bi conditional true.
Therefore, any given statement is not both side true.
So, the answer is none of the above because bi conditional statement is true if and only if both the conditions are true.
The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. A random sample of 19 houses is taken and results in a sample mean of 1350 square feet. Find the margin of error for a 80% confidence interval for the population mean.
Final answer:
To find an 80% confidence interval's margin of error for a population mean with a known standard deviation of 137 square feet and a sample mean of 1350 square feet from 19 houses, we use a Z-score of 1.28 and find the margin of error to be approximately 40.24 square feet.
Explanation:
To find the margin of error for a 80% confidence interval for the population mean, we need to use the formula for the margin of error (EM) which incorporates the Z-score corresponding to the confidence level, the population standard deviation (σ), and the sample size (n). Since the population standard deviation is known (137 square feet), we use the Z-distribution for our calculations.
The Z-score for an 80% confidence level is approximately 1.28, since an 80% confidence level corresponds to 40% in each tail of the normal distribution, and looking up 0.40 in the Z-table gives us 1.28. We can now calculate EM using the following formula:
EM = Z * (σ/√n)
Plugging in the values we obtain:
EM = 1.28 * (137/√19)
This results in an EM of:
EM = 1.28 * (137/4.3589) ≈ 1.28 * 31.4396 ≈ 40.2427
Therefore, the margin of error for the population mean at an 80% confidence level is approximately 40.24 square feet.
Prove that for all n ≥ 4 the inequality 2n < n! holds.
Answer:
For all n ≥ 4, 2n < n!
Step-by-step explanation:
Let's use the induction method to prove this statement.
In the induction method, first we prove the statement for n=4
1) If n = 4 ⇒2(4) < 4! ⇒2(4) < 24 ⇒8 < 24.
Therefore the statement holds for n=4
2) Now we assume that the statement is valid for n = k
⇒2k < k!
3) Now we will prove the statement holds for n = k +1
We will prove that 2(k + 1) < (k +1)!
(k + 1)! = (k+1) (k) (k-1) .... (3) (2) (1)
If the statement is valid for k + 1, then it would mean that
2 (k + 1) < (k+1) (k) (k-1) ... (3) (2) (1)
2 < (k) (k-1).... (3) (2) (1)
which is clearly true since k ≥4
Therefore the statement n ≥4, 2n < n! is true.
Using proof by induction, we establish the base case for n = 4 and then assume 2k < k! to show 2(k+1) < (k+1)! holding true for k ≥ 4, which proves the inequality for all n ≥ 4.
Explanation:To prove that 2n < n! for all n ≥ 4, we will use proof by induction.
We start by establishing the base case for n = 4, where we compute 2^4 = 16 and 4! = 24 which confirms that 16 < 24.
Now, assume the inequality 2k < k! is true for some k ≥ 4.
For our inductive step, we need to show that if 2k < k! then 2(k+1) < (k+1)!.
Multiplying both sides of our assumption by 2 gives us 2*2k < 2*k!, and since k ≥ 4, we know that 2 < k + 1.
Multiplying our original inductive assumption by (k + 1) gives us (k+1)*2k < (k+1)*k!, which simplifies to 2(k+1) < (k+1)! as required.
Are the rational numbers closed under multiplication?
Answer:
Yes, The rational numbers are closed under multiplication.
Step-by-step explanation:
A rational number is a number which can be expressed in the form of a fraction [tex]\frac{x}{y}[/tex], where x and y are integers and y ≠ 0.
Now, closure property of multiplication states that if two rational numbers are multiplied then the product is also a rational number. Thus, if r and t are rational numbers, then
r×t = s, where s is the product of r and t
s is also a rational number.
Hence, the rational numbers are closed under multiplication.
This can be better explained with the help of an example [tex]\frac{3}{4} \times \frac{2}{5} = \frac{6}{20}[/tex],
It is clear that [tex]\frac{6}{20}[/tex] is a rational number.
In a study of stress levels in U.S. army recruits stationed in Iraq, researchers obtained a complete list of the names of recruits in Iraq at the time of the study. They listed the recruits alphabetically and then numbered them consecutively. One hundred random numbers between one and the total number of recruits were then generated using a random-number generator on a computer. The 100 recruits whose numbers corresponded to those generated by the computer were interviewed for the study. What is the population of interest in this study?
Answer:
The population in a statistical study is determined by all the individuals that could be part of the study, that is, all the individuals that have common characteristics that make them individuals of interest to the researcher.
In the study of the previous statement, the population is made up of all recruits from the US Army. UU. in Iraq at the time of the study.
Step-by-step explanation:
Final answer:
The population of interest in the study of stress levels among U.S. army recruits stationed in Iraq is all U.S. army recruits stationed in Iraq at the time of the study.
Explanation:
The question asks about the population of interest in a study of stress levels among U.S. army recruits stationed in Iraq. In this context, the population of interest refers to the entire group of individuals that the researchers aim to understand or make inferences about based on their study. Given the details of the study, the population of interest in this case includes all U.S. army recruits stationed in Iraq at the time of the study.
The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.
1. What is probability demand will exceed 900 units in a month?
2. What is probability demand will be less than 392 units in a month?
Answer: a) 0.1587 b) 0.0618
Step-by-step explanation:
Let x be the random variable that represents the monthly demand for a product.
Given : The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.
i.e. [tex]\mu=700[/tex] and [tex]\sigma=200[/tex]
a) Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponds to x= 900 will be :
[tex]z=\dfrac{900-700}{200}=1[/tex]
Now, by using the standard normal z-table , the probability demand will exceed 900 units in a month :-
[tex]P(z>1)=1-P(z\leq1)=1-0.8413=0.1587[/tex]
Hence, the probability demand will exceed 900 units in a month=0.1587
a) Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponds to x= 392 will be :
[tex]z=\dfrac{ 392-700}{200}=-1.54[/tex]
Now, by using the standard normal z-table , the probability demand will be less than 392 units in a month :-
[tex]P(z<-1.54)=1-P(z<1.54)=1-0.9382=0.0618[/tex]
Hence, the probability demand will be less than 392 units in a month = 0.0618
The probabilities requested can be found by calculating the z-scores for the given values and then using a standard normal distribution table to locate the associated probability.
Explanation:To find the probability that the monthly demand for a product will exceed 900 units when the mean demand is 700 units and the standard deviation is 200 units, we need to calculate the z-score and then use the standard normal distribution table.
The z-score is calculated by the formula:
Z = (X - μ) / σ
Where:
X is the value of interest (900 units in this case).μ (mu) is the mean of the distribution (700 units).σ (sigma) is the standard deviation of the distribution (200 units).Thus, the z-score for 900 units is:
Z = (900 - 700) / 200 = 1
Using standard normal distribution tables or software, we find the probability associated with a z-score of 1.
For the second question, the z-score for 392 units is calculated in the same way:
Z = (392 - 700) / 200 = -1.54
Again, using standard normal distribution tables or software, we find the probability associated with a z-score of -1.54.
It is important to understand that these probabilities represent the area under the curve of the normal distribution from the z-score to the end of one tail.
Let S = {a, b, c). Find the following:
a) the number of reflexive relations on S
b)the number of reflexive and symmetric relations on S
Answer:
The number of reflexive relations on S is 64.
The number of reflexive and symmetric relations on S is 8.
Step-by-step explanation:
Consider the provided set S = {a, b, c}.
The number of elements in the provided set is 3.
Part (a) the number of reflexive relations on S
To calculate the number of reflexive relation on S we can use the formula as shown:
Total number of Reflexive Relations on a set: [tex]2^{n(n-1)}[/tex].
Where, n is the number of elements.
In the provided set we have 3 elements, so substitute the value of n in the above formula:
[tex]2^{3(3-1)}[/tex]
[tex]2^{3(2)}[/tex]
[tex]2^{6}[/tex]
[tex]64[/tex]
Hence, the number of reflexive relations on S is 64.
Part(b) The number of reflexive and symmetric relations on S.
To calculate the number of reflexive and symmetric relation on S we can use the formula as shown:
Total number of Reflexive and symmetric Relations on a set: [tex]2^{\frac{n(n-1)}{2}}[/tex].
Where, n is the number of elements.
In the provided set we have 3 elements, so substitute the value of n in the above formula:
[tex]2^{\frac{3(3-1)}{2}}[/tex]
[tex]2^{\frac{3(2)}{2}}[/tex]
[tex]2^{\frac{6}{2}}[/tex]
[tex]2^{3}[/tex]
[tex]8[/tex]
Hence, the number of reflexive and symmetric relations on S is 8.
Write down all elements of the set {XER: X3 -x = 0).
Answer:
The elements of given set are -1, 0 and 1.
Step-by-step explanation:
The given set is
[tex]\{x\in R:x^3-x=0\}[/tex]
We need to find all the elements of given set.
The given equation is
[tex]x^3-x=0[/tex] .... (1)
Solve this equation o find the value of x.
Taking out common factors.
[tex]x(x^2-1)=0[/tex]
Using zero product property,
[tex]x=0[/tex]
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm 1[/tex]
All rational and irrational numbers are real numbers.
On solving equation (1) we get x = -1, 0, 1. All these numbers are real number. So, the elements of given set are -1, 0 and 1. The set is defined as
{ -1, 0, 1}
Therefore, the elements of given set are -1, 0 and 1.
For the given pair of events A and B, complete parts (a) and (b) below. A: When a page is randomly selected and ripped from a 2424-page document and destroyed, it is page 2020. B: When a different page is randomly selected and ripped from the document, it is page 1616. a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.) b. Find P(A and B), the probability that events A and B both occur. a. Choose the correct answer below.
Answer:
The two events are dependent.
the probability that events A and B both occur is:
[tex]\frac{1}{2424}\times \frac{1}{2423}=1.7026052585\times 10^{-7}\ or\ 0.00000017[/tex]
Step-by-step explanation:
Consider the provided information.
Event A: When a page is randomly selected and ripped from a 2424-page document and destroyed, it is page 2020.
Event B: When a different page is randomly selected and ripped from the document, it is page 1616.
Part(A)
The occurring of one event affects the probability of the other event.
Because if we ripped one page then the probability of ripping second page will going to change as the size of sample space will decrease.
For example: The document has 2424 page, that means size of sample space is 2424. If we ripped another page, the sample size will be 2423. That means event B is depending on event A.
Thus, the two events are dependent.
Part(B)
The probability that events A and B both occur.
If we select a page randomly from 2424-page document, the probability will be: 1/2424
Now we have 2423 pages left in the document as one page is destroyed.
The probability of selecting another page is: 1/2423.
Thus, the probability that events A and B both occur is:
[tex]\frac{1}{2424}\times \frac{1}{2423}=1.7026052585\times 10^{-7}\ or\ 0.00000017[/tex]
Solve for b.
b +3(3 - 2b) = 1 - 2(b + 1)
Answer:
b+3(3-2b)=1-2(b+1)
One solution was found :
b = 10/3 = 3.333
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
b+3*(3-2*b)-(1-2*(b+1))=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(b+(3•(3-2b)))-(1-2•(b+1)) = 0
Step 2 :
Equation at the end of step 2 :
(b + 3 • (3 - 2b)) - (-2b - 1) = 0
Step 3 :
Equation at the end of step 3 :
10 - 3b = 0
Step 4 :
Solving a Single Variable Equation :
4.1 Solve : -3b+10 = 0
Subtract 10 from both sides of the equation :
-3b = -10
Multiply both sides of the equation by (-1) : 3b = 10
Divide both sides of the equation by 3:
b = 10/3 = 3.333
One solution was found :
b = 10/3 = 3.333
Step-by-step explanation:
Use the method of your choice to determine the probability below. Being dealt three sixes off the top of a standard deck of well-shuffled cards. The probability is . (Type an integer or a simplified fraction.)
Answer:
1/5525
Step-by-step explanation:
We now that a standard deck has 52 different cards. Also we know that a standard deck has four different suits, i.e., Spades, Hearts, Diamonds and Clubs. We can find the following cards for each suit: Ace, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King.
Now, the probability of getting any of these cards off the top of a standard deck of well-shuffled cards is 1/52. As we have 4 different sixes, we have that the probability of getting a six is 4/52. When we get a six, in the deck only remains 3 sixes and 51 cards, so, the probability of getting another six later is 3/51. When we get the second six, in the deck only remains 2 sixes and 50 cards, so, the probability of getting the third six is 2/50. As we have independet events, we should have that the probability of getting 3 sixes off the top of a standard deck of well-shuffled cards is
(4/52)(3/51)(2/50)=
24/132600=
12/66300=
6/33150=
3/16575=
1/5525
The probability of being dealt three sixes off the top of a standard deck of well-shuffled cards is approximately 1/5513 or 0.00018 when rounded to five significant digits.
Explanation:The subject of this question is probability in mathematics. In a standard deck of 52 playing cards, there are four sixes: one each of hearts, diamonds, clubs, and spades. When looking at the probability of being dealt three sixes off the top of a well-shuffled deck, looking at drawing one card at a time in succession grants us the solution.
For the first card, the probability of drawing a six is 4/52. If you draw a six, there are now three sixes left in a 51-card deck. So, the probability of drawing a six on the second draw is 3/51. Using the same logic, the probability of drawing a six on the third draw is 2/50.
The probability of these three events happening in succession is the product of their individual probabilities, which is calculated as follows: (4/52) * (3/51) * (2/50) = 24/132600 = 0.00018 when rounded to 5 significant digits, or simplified, this is approximately 1/5513.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
Let P(x,y) be a propositional function if ꓯyꓱxP(x,y) is true does it necessarily follow that ꓱxꓯyP(x,y) is true? Justify your answer or give a counter-example
Answer: Ok, we know that ꓯ y ꓱ x P(x,y) is true, and suppose we are working with integers.
Lets create a counter-example
if P(x,y) : x = y, then for all integer y you can find another integer x such the proposition is true, and ꓯ y ꓱ x P(x,y) is true.
now the second part; ꓱ x ꓯyP(x,y) is true? this means that exist an x, such that p(x,y) is true for all the y in the domain. Now, is also easy to se that, for each x, there is only one y that keeps the proposition true, and is y = x.
So ꓱx ꓯy P(x,y) is not true
Imagine that Amy counted 60 numbers per minute and continued to count nonstop until she reached 19,000. Determine a reasonable estimate of the number of hours it would take Amy to complete the counting. It will take Amy approximately (Type a whole number.) hours to count to 19,000.
At a rate of 60 numbers per minute, Amy would need approximately 5.28 hours to count to 19,000. Rounding to the nearest whole number gives a final estimate of 6 hours.
Explanation:To answer the question, we'll need to estimate the time Amy would take to count to 19,000. She is counting at a frequency of 60 numbers per minute. This rate is constant throughout her counting.
Therefore, we need to divide the total number of numbers she is counting, which is 19,000, by the rate at which she is counting, which is 60 numbers per minute. The result is approximately 316.67 minutes. To convert this to hours, we divide by 60 (as there are 60 minutes in an hour). That gives us approximately 5.28 hours. Because the question asks for a reasonable whole number estimate, we can round this number up to give us a final answer of 6 hours.
Learn more about Time Estimation here:https://brainly.com/question/28579204
#SPJ2
You may already use algebra in your daily life for several things. How do you imagine that you will use basic algebraic equations in your healthcare career? Explain...
Please gave me an idea guys
Answer:
Depending on the path that we decide to take, the algebra can help us in many forms.
As an example in the pharmaceutical/medical area, the nurses and doctors use basic algebra formulas to calculate dosages on different drugs depending on variables such as the weigh of each patient (commonly expressed as X or Y).
They used to have some paper sheets with formulas for different drug preparations (liquid ones particularly) within hospitals to avoid errors in medication.
Algebra is an area of mathematics that deals with the study of symbols and the rules for manipulating these symbols. Elementary algebra is used in virtually every field and occupation there is. Algebra is also employed in healthcare.
As a healthcare provider, it is important to be able to read vital signs. Many of these are expressed as algebraic equations. Such equations can also be important when it comes to administering the right doses of medicine or converting different units of measurement.
Consider a survey involving the cookie preferences of a sample of 1,214 adults. If 9% answered "sugar/shortbread," find the decimal and reduced fraction of that percentage.
decimal :
reduced fraction :
Final answer:
To convert 9% to both a decimal and a reduced fraction: as a decimal, 9% is 0.09; as a reduced fraction, it is 9/100, which cannot be further reduced.
Explanation:
The question is about converting a percentage to a decimal and a reduced fraction. To find the decimal equivalent of 9%, you divide 9 by 100, which gives 0.09. For the reduced fraction, since 9% is equivalent to 9/100, you look for the greatest common divisor of 9 and 100, which is 1. Therefore, the fraction 9/100 is already in its reduced form since no number other than 1 divides both 9 and 100 evenly.
In summary:
Decimal: 0.09
Reduced fraction: 9/100
For most answers, you will simply enter your numeric answer directly into the space provided to the right of the equal sign. Answer the following question by typing the numeric answer into the answer box. If you have a gross of items, you have 144 items. If you buy a gross of eggs, how many dozen eggs do you have? Express your answer in dozens. Do not enter the units; they are provided to the right of the answer box.
Answer:
12
Step-by-step explanation:
144 = 12×12 = 12×(1 dozen) = 12 dozen
A gross is equal to 144 items. So, if you have a gross of eggs, you would have 12 dozen eggs.
A gross is equal to 144 items. Since there are 12 items in a dozen, to find how many dozen eggs you have in a gross, you divide 144 by 12. This gives you a total of 12 dozen eggs.
Learn more about Gross to Dozen Conversion here:https://brainly.com/question/34269230
#SPJ2