Answers
Answer:
Therefore the measurement of EF,
[tex]EF=1.98\ units[/tex]
Step-by-step explanation:
Given:
In Right Angle Triangle DEF,
m∠E=90°
m∠D=26°
∴sin 26 ≈ 0.44
DF = Hypotenuse = 4.5
To Find:
EF = ? (Opposite Side to angle D)
Solution:
In Right Angle Triangle DEF, Sine Identity,
[tex]\sin D= \dfrac{\textrm{side opposite to angle D}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin 26= \dfrac{EF}{DF}=\dfrac{EF}{4.5}[/tex]
Also, sin 26 ≈ 0.44 .....Given
[tex]EF = 4.5\times 0.44=1.98\ units[/tex]
Therefore the measurement of EF,
[tex]EF=1.98\ units[/tex]
Related Questions
2. In a recent survey conducted by the International Nanny Association, 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").
Answers
Answer:
There is a 0.57% probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Desired outcomes:
The number of male nannies selected. 24 of the nannies placed were men. So the number of desired outcomes is 24.
Total outcomes:
The number of nannies selected. 4,176 nannies were placed in a job in a given year. So the number of total outcomes 4176.
Find the probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").
[tex]P = \frac{24}{4176} = 0.0057[/tex]
There is a 0.57% probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").
Final answer:
The probability that a randomly selected nanny is a male is 0.57%.
Explanation:
The question asks us to find the probability that a randomly selected nanny who was placed during the last year is a male nanny, also referred to humorously as a "mannie." We are given that a total of 4,176 nannies were placed, and of these, only 24 were men. To find the probability, we use the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes.
Here, the number of favorable outcomes is the number of male nannies placed, which is 24. The total number of possible outcomes is the total number of nannies placed, which is 4,176.
Thus, the probability (P) that a selected nanny is male is:
P(male nanny) = Number of male nannies / Total number of nannies
P(male nanny) = 24 / 4,176
P(male nanny) = 0.0057
To express this as a percentage, we multiply by 100:
P(male nanny) = 0.0057 * 100%
P(male nanny) = 0.57%
Therefore, the probability that a randomly selected nanny is a male is 0.57%.
Fewer young people are driving. In year A, 67.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 47.7%. Suppose these results are based on a random sample of 1,800 people under 20 years old who were eligible to have a driver's license in year A and again in year B.a. At 95% confidence, what is the margin of error and the interval estimate of the number of nineteen year old drivers in year A?b. At 95% confidence, what tis the margin of error and the interval estimate of the number of nineteen year old drivers in year B?c. Is the margin of error the same in parts (a) and (b)?
Answers
Answer:
Case a Case b
margin of error 0.0216 0.0231
Interval estimate (0.7016 , 0.6795) (0.5031 , 0.4569)
margin of error is not same in both cases.
Step-by-step explanation:
a
At 95% confidence interval the interval estimate of number of 20 year old drivers in year A can be computed as
p' ± z [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
= 0.68 ± 1.96 [tex]\sqrt{\frac{0.68(1-0.68)}{1800} }[/tex]
= 0.7016 , 0.6795
the margin of error can be written as
z [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
= 1.96 [tex]\sqrt{\frac{0.68(1-0.68)}{1800} }[/tex]
= 0.0216
b
At 95% confidence interval the interval estimate of number of 20 year old drivers in year B can be computed as
p' ± z [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
= 0.48 ± 1.96 [tex]\sqrt{\frac{0.48(1-0.48)}{1800} }[/tex]
= 0.5031 , 0.4569
the margin of error can be written as
z [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
= 1.96 [tex]\sqrt{\frac{0.48(1-0.48)}{1800} }[/tex]
= 0.0231
c
Sample size is same in case A and B but proportion is different in both cases so margin of error is different in both cases
Find the sample space for the experiment.
Two county supervisors are selected from five supervisors, A, B, C, D and E, to study a recycling plan.
Answers
Answer:
The sample space is:
[tex]AB,\ AC,\ AD,\ AE,\\BC,\ BD,\ BE\\CD,\ CE\\DE[/tex]
Step-by-step explanation:
The sample space of an experiment is a set of all the possible values that satisfies that experiment.
The five supervisors are A, B, C, D and E.
Two are to selected.
The number of ways to select 2 supervisors from 5 is: [tex]{5\choose 2}=\frac{5!}{2!(5-2)!} =\frac{5!}{2!\times 3!} = 10[/tex]
The sample space will consist of 10 combinations.
The sample space is:
[tex]AB,\ AC,\ AD,\ AE,\\BC,\ BD,\ BE\\CD,\ CE\\DE[/tex]
The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
53.8 42.2 44.0 34.3 44.0
31.6 45.8 38.8 50.5 42.0
Public Colleges
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8
(a)
Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)
sample mean $ thousand sample standard deviation $ thousand
Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)
sample mean $ thousand sample standard deviation $ thousand
Answers
Answer:
A) Private colleges:
mean = 42.7, SD = 6.72
In thousand dollars:
mean = $42700, SD= $6720
B) Public colleges:
mean = 22.3, SD = 4.53
In thousand dollars:
mean = $22300, SD= $4530
Step-by-step explanation:
A) Private Colleges:
Mean:
Total no. of samples = n =10
Sample values in dollar = x= [53.8, 42.2, 44.0, 34.3, 44.0,31.6, 45.8, 38.8, 50.5, 42.0]
Sum of samples = ∑x= 427
[tex]sample\,\,mean = \bar{x} =\frac{\sum x}{n}\\\\\bar{x}=\frac{427}{10}\\\\\bar{x}=42.7\\[/tex]
Sample mean in thousand dollars is $ 42700.
Standard Deviation:
Formula for standard deviation of sample data is
[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^2}\\\\\sum(x_i-\bar{x})^2=(53.8-42.7)^2+(42.2-42.7)^2+...+(42.0-42.7)^2\\\\\sum(x_i-\bar{x})^2=123.21+0.25+ 1.69+ 70.56+ 1.69+ 123.21+ 9.61+ 15.21+60.84+0.49\\\\\sum(x_i-\bar{x})^2=406.67\\\\\sigma=\sqrt{\frac{406.67}{9}}\\\\\sigma=6.72[/tex]
Standard deviation in thousand dollars is $ 6720.
B) Public Colleges:
Mean:
Total no. of samples = n =12
Sample values in dollar = x= [20.3, 22.0, 28.2, 15.6, 24.1, 28.5,22.8, 25.8, 18.5, 25.6, 14.4, 21.8]
Sum of samples = ∑x= 267.6
[tex]sample\,\,mean = \bar{x} =\frac{\sum x}{n}\\\\\bar{x}=\frac{267.6}{12}\\\\\bar{x}=22.3\\[/tex]
Sample mean in thousand dollars is $ 22300.
Standard Deviation:
[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^2}\\\\\sum(x_i-\bar{x})^2=(20.3-22.3)^2+(22.0-22.3)^2+...+(21.8-22.3)^2\\\\\sum(x_i-\bar{x})^2=4+ 0.09+34.81+ 44.89+ 3.24+ 38.44+0.25+ 12.25+14.44+10.89+62.41+0.25\\\\\sum(x_i-\bar{x})^2=225.96\\\\\sigma=\sqrt{\frac{225.96}{11}}\\\\\sigma=4.53[/tex]
Standard deviation in thousand dollars is $ 4530.
You prepare decorations for a party. How many ways are there to arrange 12 blue balloons, 9 green lanterns and 6 red ribbons in a row, such that no two ribbons are next to each other?
Answers
Answer: 27! - [22! * 6!]
Step-by-step explanation:
Decorations available = 12 blue ballons, 9 Green Lanterns and 6 red ribbons
To determine the number if ways of arrangement for if the ribbons must not be together, we must first determine the number of possible ways to arrange these decorations items if there are no restrictions.
Total number of ways to arrange them = [12+9+6]! = 27! = 1.089 * 10^28
If this ribbons are to be arranged distinctively by making sure all six of them are together, then we arrange the 6 of them in different ways and consider the 6ribbons as one entity.
Number of ways to arrange 6 ribbons = 6!.
To arrange the total number of entity now that we have arranged this 6ribbons together and taking them as one entity become: = (12 + 9 + 1)!. = 22!
Number of ways to arrange if all of the ribbons are taken as 1 and we have 22 entities in total becomes: 22! * 6!.
Hence, to arrange these decoration items making sure no two ribbons are together becomes:
= 27! - (22! * 6!)
= 1.08880602 * 10^28
To arrange the decorations, first calculate the number of ways to arrange the balloons and lanterns, then use the concept of stars and bars to calculate the number of ways to place the ribbons. The product of these two calculations gives the total number of ways to arrange the decorations.
Explanation:To arrange the balloons, lanterns, and ribbons in a row without any two ribbons being next to each other, we need to consider their positions separately. We can arrange the balloons and lanterns first, making sure no two ribbons are adjacent. The number of ways to arrange the balloons and lanterns is (12+1)C12 x (9+1)C9 = 13C12 x 10C9 = 13 x10 = 130.
Now, let's place the ribbons using the concept of stars and bars. We can consider the spaces between the balloons and lanterns as 'bars' and the ribbons as 'stars.' Since there are 13 spaces between the 12 balloons and lanterns, we have 13 bars. We need to place 6 ribbons (stars) in these 13 spaces. The number of ways to do this is (13-6+1)C6 = 8C6 = 28.
The total number of ways to arrange the decorations is the product of the number of ways to arrange the balloons and lanterns and the number of ways to place the ribbons. Therefore, the answer is 130 x 28 = 3640.
Learn more about Arranging decorations here:https://brainly.com/question/34593578
#SPJ3
A college sends a survey to members of the class of 2012. Of the 1254 people who graduated that year, 672 are women, of whom 124 went on to graduate school. Of the 582 male graduates, 198 went on to graduate school. What is the probability that a class of 2012 alumnus selected at random is (a) female, (b) male, and (c) female and did not attend graduate school?
Answers
Answer:
a) [tex]P(F) = \frac{672}{1254}=\frac{112}{209}=0.536[/tex]
b) [tex]P(M) = \frac{582}{1254}= \frac{97}{209}=0.464[/tex]
c) [tex] P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815[/tex]
Step-by-step explanation:
For this case we have a total of 1254 people. 672 are women and 582 are female.
We know that 124 women wnat on to graduate school.
And 198 male want on to graduate school
We can define the following events:
F = The alumnus selected is female
M= The alumnus selected is male
A= Female and attend graduate school
And we can find the probabilities required using the empirical definition of probability like this:
Part a
[tex]P(F) = \frac{672}{1254}=\frac{112}{209}=0.536[/tex]
Part b
[tex]P(M) = \frac{582}{1254}= \frac{97}{209}=0.464[/tex]
Part c
For this case we find the probability for the event A: The student selected is female and did attend graduate school
[tex] P(A) =\frac{124}{672}=\frac{31}{168}=0.185[/tex]
And using the complement rule we find P(A') representing the probability that the female selected did not attend graduate school like this:
[tex] P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815[/tex]
In a multicriteria decision problem____________.a. it is impossible to select a single decision alternative.b. the decision maker must evaluate each alternative with respect to each criterion.c. successive decisions must be made over time.d. each of these choices are true.
Answers
Answer:
Option b.
Step-by-step explanation:
In a situation of a multicriteria decision problem, the decision-maker can tackle a given situation in at least two alternatives but due to some conflicting objectives, he is unable to choose the best option among the alternatives.
Therefore, in a multicriteria decision problem, the decision-maker must evaluate each alternative with respect to each criterion.
A company makes pens. They sell each pen for $99.
Their revenue is represented by R = 9x.
The cost to make the pens is $11 each with a one time start up cost of $4000.
Their cost is represented by C = 1x + 4000.
a) Find the profit, P, when the company sells 1000 pens.
b) Find the number of pens they need to sell to break even.
Answers
Answer:
a) Profit = 84000
b) at break even number of pens sold = 46
Step-by-step explanation:
Profit = Selling price - Cost price
Total revenue generated = 99 * 1000
Total revenue generated = 99000
Total cost on making the pen = 11 * 1000
Total cost on making the pen = 11000
Total cost including the initial cost = 11000 + 4000
Total cost including the initial cost = 15000
Profit = 99000 - 15000
Profit = 84000
Break even is when the cost are equal to Revenue thus no profit or loss
Revenue = total cost (break even)
9x = 1x + 4000
9x - x = 4000
8x = 4000
x = 500
At breakeven Revenue = 9 * 500
At breakeven Revenue = 4500
since one pen is sold at 99 therefore at break even number of pens sold = 4500/99 = 45.45( to 2 decimal place)
at break even number of pens sold = 46
To find the profit, substitute the selling quantity into the revenue and cost equations and subtract the cost from the revenue. To find the break-even point, set the profit to zero and solve for the selling quantity.
Explanation:To find the profit, P, when the company sells 1000 pens, we first calculate the revenue by substituting x = 1000 into the revenue equation: R = 9x. Therefore, R = 9(1000) = 9000. Next, we calculate the cost by substituting x = 1000 into the cost equation: C = 1x + 4000. Therefore, C = 1(1000) + 4000 = 5000. Finally, we find the profit by subtracting the cost from the revenue: P = R - C. Therefore, P = 9000 - 5000 = 4000. The company's profit when selling 1000 pens is $4000.
To find the number of pens needed to break even, we set the profit to zero and solve for x. Therefore, P = R - C = 0. Substituting the revenue and cost equations, we have 9x - (1x + 4000) = 0. Simplifying this equation gives us 8x - 4000 = 0. Solving for x, we get x = 500. The company needs to sell 500 pens to break even.
Learn more about Calculating profit and break-even point here:https://brainly.com/question/33716215
#SPJ3
Suppose that a color digital photo has 512 pixels per row and 512 pixels per column, and that each pixel requires two bytes of storage. How many such pictures could you have in your camera if the camera had 6 GB of storage available
Answers
Answer:
2,929,687 pictures
Step-by-step explanation:
1 pixel requires 2 bytes of storage
A color digital photo uses 512 pixels (512×2 bytes = 1024 bytes) per row and 512 pixels (1024) bytes per column
Total storage used by 1 picture = 1024 + 1024 = 2048 bytes
Storage capacity my camera = 6GB = 6×10^9 bytes
Number of pictures I can have in my camera = 6×10^9/2048 = 2,929,687 pictures
By calculating the storage required for one 512 x 512 pixel photo and dividing the total storage capacity by this amount, we find that a camera with 6 GB of storage can hold approximately 12,288 such photos.
To calculate how many 512 x 512 pixel color digital photos can be stored in a camera with 6 GB of storage, where each pixel requires two bytes of storage, we follow these steps:
First, find the total number of pixels in one photo:
512 pixels/row × 512 pixels/column = 262,144 pixels/photo.
Next, calculate the storage required for one photo:
262,144 pixels/photo × 2 bytes/pixel = 524,288 bytes/photo.
Since there are 1,024 bytes in one kilobyte (KB) and 1,024 KB in one megabyte (MB), we convert the photo size to megabytes:
524,288 bytes/photo / 1,024 bytes/KB / 1,024 KB/MB
≈ 0.5 MB/photo.
Now, convert 6 GB of storage to MB:
6 GB × 1,024 MB/GB = 6,144 MB.
Finally, divide the total storage by the size of one photo to determine the number of photos:
6,144 MB / 0.5 MB/photo = 12,288 photos.
Therefore, you could store approximately 12,288 such pictures on a camera with 6 GB of storage.
A boy has color blindness and has trouble distinguishing blue and green. There are 75 blue pens and 25 green pens mixed together in a box. Given that he picks up a blue pen, there is a 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. Given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% chance that he thinks it is a blue pen. Assume that the boy randomly selects one of the pens from the box.
a) What is the probability that he picks up a blue pen and recognizes it as blue?
b) What is the probability that he chooses a pen and thinks it is blue?
c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?
Answers
Answer:
a) There is a 60% probability that he picks up a blue pen and recognizes it as blue.
b) There is a 62.5% probability that he chooses a pen and thinks it is blue.
c) Given that he thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.
Step-by-step explanation:
We have these following probabilities
A 75% probability that a pen is blue
A 25% probability that a pen is green
If a pen is blue, an 80% probability that the boy thinks it is a blue pen
If a pen is blue, a 20% probability that the boy thinks it is a green pen.
If a pen is green, a 90% probability that the boy thinks it is a green pen.
If a pen is green, a 10% probability that that the boy thinks it is a blue pen.
a) What is the probability that he picks up a blue pen and recognizes it as blue?
There is a 75% probability that he picks up a blue pen.
There is a 80% that he recognizes a blue pen as blue.
So
[tex]P = 0.75*0.8 = 0.6[/tex]
There is a 60% probability that he picks up a blue pen and recognizes it as blue.
b) What is the probability that he chooses a pen and thinks it is blue?
There is a 75% probability that he picks up a blue pen.
There is a 80% that he recognizes a blue pen as blue.
There is a 25% probability that he picks up a green pen
There is a 10% probability that he thinks a green pen is blue.
So
[tex]P = 0.75*0.80 + 0.25*0.10 = 0.625[/tex]
There is a 62.5% probability that he chooses a pen and thinks it is blue.
c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?
There is a 62.5% probability that he thinks that he choose a blue pen.
There is a 60% probability that he chooses a blue pen and think that it is blue.
So
[tex]P = \frac{0.6}{0.625} = 0.96[/tex]
Given that he thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.
Final answer:
The answer provides the probabilities related to a color-blind boy picking and identifying blue and green pens accurately.So,a)The overall probability is 0.75 * 0.80 = 0.60,b)0.62,c)0.968.
Explanation:
a) What is the probability that he picks up a blue pen and recognizes it as blue?
Let's calculate this by considering the probabilities given:
Probability of picking a blue pen: 75/100 = 0.75
Probability of recognizing a blue pen as blue given it is blue: 0.80
The overall probability is 0.75 * 0.80 = 0.60.
b) What is the probability that he chooses a pen and thinks it is blue?
This includes both him picking a blue pen and thinking it is blue or picking a green pen and mistakenly thinking it is blue. It can be calculated as 0.75 * 0.80 + 0.25 * 0.10 = 0.62
c) Given he thinks he chose a blue pen, what is the probability he actually chose a blue pen?
This involves computing the conditional probability using Bayes' theorem:
P(chose blue pen | thinks it's blue) = P(chose blue pen and thinks it's blue) / P(thinks it's blue) = (0.75 * 0.80) / 0.62 = 0.968.
in a dataset with a minimum value of 54.5 and a maximum value of 98.6 with 300 observations, there are 180 points less than 81.2. Find the percentile ofr 81.2
Answers
Answer:
60th percentile.
Step-by-step explanation:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
In this problem, we have that:
300 observations, there are 180 points less than 81.2.
180/300 = 0.6
So 60% of the observation are lower than 81.2, which means that 81.2 is the 60th percentile.
Suppose your firm had the following taxable income amounts: 2015 ($5 million) operating loss 2016 $4 million 2017 $4 million 2018 $4 million After you "carry forward" the operating loss, what is the effective taxable income for 2017
Answers
Answer:
$7,000,000
Step-by-step explanation:
The taxable income is the amount of money (income earned or unearned) by an individual or an organization that creates a potential tax liability.
The formula is shown below:
Taxable Income Formula = Gross Total Income – Total Exemptions – Total Deductions
Note that $5,000,000 for 2015 is an operating loss which is a deduction.
Gross Total Income = $4000000+$4000000+$4000000 = $12,000,000
Total Exemption = 0
Total Deductions = $5,000,000
Taxable Income Formula = $12,000,000 - $5,000,000 = $7,000,000
The effective taxable income for 2017 after carrying forward the operating loss is -$1 million.
Explanation:The question pertains to a business scenario and involves calculating the effective taxable income after carrying forward an operating loss. To calculate the effective taxable income for 2017, we need to consider the operating losses from previous years. In this case, your firm had a $5 million operating loss in 2015. This loss can be carried forward to offset taxable income in future years.
In 2016, the taxable income is $4 million.In 2017, the operating loss from 2015 can be used to offset the taxable income. Therefore, the effective taxable income for 2017 is $4 million - $5 million = -$1 million. Since the result is negative, there is no taxable income for 2017.Therefore, the effective taxable income for 2017 after carrying forward the operating loss is -$1 million.
Learn more about Calculating effective taxable income after carrying forward operating loss here:https://brainly.com/question/33697758
#SPJ3
Use a formula to solve the problem.
An airplane flew from Chicago to San Francisco in 3.25 hours. If the cities are 1,950 miles apart, what was the average speed of the plane?
Answers
Answer: The average speed of the plane is 600 miles per hour.
Step-by-step explanation:
The formula for determining average speed is expressed as
Average speed = total distance travelled/total time taken
The airplane flew from Chicago to San Francisco in 3.25 hours. Therefore, time = 3.25 hours
The cities are 1,950 miles apart. This means that the distance travelled is 1950 miles. Therefore,
Average speed = 1950/3.25 = 600 miles per hour.
Answer:
Speed = 600 mile per hour
Step-by-step explanation:
Given values:
Time = 3.25hours
Distance = 1950miles
Formula: speed = distance ÷ time
Therefore:
Speed = 1950 ÷ 3.25
Speed = 1950 ÷ 325/100
Speed = 1950 × 100/325
Speed= 195000/325
Speed = 600ml^h
The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the other 5 have selected desktops. Suppose that four computers are randomly selected. (a) How many different ways are there to select four of the nine computers to be set up?
(b) What is the probability that exactly three of the selected computers are desktops?
(c) What is the probability that at least three desktops are selected?
Answers
Answer:
a) There are 126 different ways are there to select four of the nine computers to be set up.
b) 31.75% probability that exactly three of the selected computers are desktops.
c) 35.71% probability that at least three desktops are selected.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, there are no replacements. Which means that after one of the 9 computers is selected, there will be 8 computers.
Also, the order that the computers are selected is not important. For example, desktop A and desktop B is the same outcome as desktop B and desktop A.
These are the two reasons why the combinations formula is important to solve this problem.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
(a) How many different ways are there to select four of the nine computers to be set up?
Four computers are selected from a set of 9.
So
[tex]T = C_{9,4} = \frac{9!}{4!(9-4)!} = 126[/tex]
There are 126 different ways are there to select four of the nine computers to be set up.
(b) What is the probability that exactly three of the selected computers are desktops?
Desired outcomes:
3 desktops, from a set of 5
One laptop, from a set of 4.
So
[tex]D = C_{5,3}*C_{4,1} = 40[/tex]
Total outcomes:
From a), 126
Probability:
[tex]P = \frac{40}{126} = 0.3175[/tex]
31.75% probability that exactly three of the selected computers are desktops.
(c) What is the probability that at least three desktops are selected?
Three or four
Three:
[tex]P = \frac{40}{126}[/tex]
Four:
Desired outcomes:
4 desktops, from a set of 5
Zero laptop, from a set of 4.
[tex]D = C_{5,4}*C_{4,0} = 5[/tex]
[tex]P = \frac{5}{126}[/tex]
Total(three or four) probability:
[tex]P = \frac{40}{126} + \frac{5}{126} = \frac{45}{126} = 0.3571[/tex]
35.71% probability that at least three desktops are selected.
Answer the following
Answers
Answer:
Step-by-step explanation:
f(x) = 3x-2
g(x) = 1/2(x²)
f(0) = 3x-2 = 3(0)-2 = 0-2 = -2
f(-1) = 3x-2 = 3(-1)-2 = -3-2 = -5
g(4) = 1/2(4²) = 1/2(16) = 8
g(-1) = 1/2(-1²) = 1/2(1) = 1/2
Indicate in standard form the equation of the line passing through the given point and having the given slope.
C(0, 4), m
= 0
Answers
Answer:
The standard form the equation of the line passing through the given point and having the given slope is:
[tex]y = 4[/tex]
Step-by-step explanation:
A first order function has the following format
[tex]y = mx + b[/tex]
In which m is the slope.
The function passes through the point (0,4).
Which means that when x = 0, y = 4.
The slope is m = 0.
So
[tex]y = mx + b[/tex]
[tex]4 = 0x + b[/tex]
[tex]b = 4[/tex]
The standard form the equation of the line passing through the given point and having the given slope is:
[tex]y = 4[/tex]
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 7.5 pounds/square inch (psi). Assume the population variance is 0.36. The engineer designed the valve such that it would produce a mean pressure of 7.4 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answers
Answer:
2.17
Step-by-step explanation:
As the population variance is known we can calculate population standard deviation and so, z-test statistic will be used.
[tex]z=\frac{xbar-pop mean}{\frac{pop SD}{\sqrt{n} } }[/tex]
population variance=σ²=0.36
population standard deviation=σ=√0.36=0.6
The value of population mean can be achieved through null hypothesis.
Null hypothesis : μ=7.4
Alternative hypothesis : μ≠7.4
population mean=μ=7.4
xbar=7.5
n=170
z=(7.5-7.4)/(0.6/√170)
z=0.1/(0.6/13.038)
z=0.1/0.046
z=2.17
Thus, the calculated z-test statistic is 2.17.
Type a proposition involving p, q, r and s that is true just when at least two of the propositional variables are true. For example, your proposition would be true in any case for which p and r are both true but false when, say, p is true while q, r and s are all false.
Answers
Answer:
(X and Y are real numbers)
p) X > 0
q) Y > 0
r) XY > 0
s) (X > 0 ∧ Y > 0) ∨ (X = Y = 0)
Step-by-step explanation:
Lets assume that a pair of the propositions are true, and we will show that the other 2 are also true. There are 6 possible cases:
1) If p and q are true, then XY has to be positive because it is the product of positive numbers. And the first option of proposition s is true
2) If p and r are true, then Y = XY/X > 0 because it is the division of tow positive numbers, thus q is true. Since p and q are true, then so it is s.
3) If p and s are true, then option 2 of S is impossible, thus X > 0 and Y>0, hence q is true. SInce p and q are true, so is r.
4) If q and r are true, we can obtain X by dividing the positive numbers XY and Y, thus X>0, and p and s are true.
5) is q and s are true, an argument similar at the one made in 3) shows that both p and r are true.
6) if r and s are true, then the second part of s cant be true, therefore X>0 and Y>0, as a consecuence, p and q are true.
Now, lets show that, individually, no proposition implies the others:
p clearly doesnt imply q. X can be positive while Y is negative. Similarly Y can be positive while X is negative, thus q doesnt imply p either.
If XY > 0, then it can be that both X and Y are negative, thus r might not imply neither p nor q.
and if only s is true, then it may be that the second part is the one that is true, thereofre X=Y=0 and p, q and r are all false in this case.
As a consecuence, you need 2 of the propositions to be true so that all 4 are true, but as we show above, by having any pair of the propositions true, then all 4 are automaticallyy true.
A government bureau keeps track of the number of adoptions in each region. The accompanying histograms show the distribution of adoptions and the population of each region. a) What do the histograms say about the distributions? b) Why do the histograms look similar? c) What might be a better way to express the number of adoptions?
Answers
The histograms indicate that higher population regions tend to have more adoptions. They are similar as adoption rates and population sizes are interlinked. A better representation might be the adoption rate per population quota, which shows comparison between regions clearer.
Explanation:a) The histograms show the "distribution of adoptions" and the "population of each region." We can infer that the distribution of adoptions largely mirrors the population distribution, meaning that regions with larger populations tend to have more adoptions.
b) The histograms look similar because adoption rates and population size are related. If a region has a larger population, it likely has more families, hence more potential for adoption.
c) A better way to express the number of adoptions might be to calculate the adoption rate per population. For example, the number of adoptions per 1,000 or 10,000 population members. This way, it directly relates the number of adoptions to the size of the population, and provides a percentage or ratio rather than absolute numbers. This method can be more helpful in making comparisons between regions.
Learn more about Histogram Interpretation here:https://brainly.com/question/30455465
#SPJ3
To determine whether using a cell phone while driving in Louisiana increases the risk of an accident, a researcher examines accident reports to obtain data about the number of accidents in which a driver was talking on a cell phone.
a. Is this a randomized experiment or an observational study?
b. What is the population being studied here?
c. Is the number of accidents where the driver was using a cell phone a qualitative or quantitative variable?
d. Is the number of accidents where the driver was using a cell phone an ordinal, nominal, continuous, or discrete variable?
e. What kind of sample is taken if the researcher only examines accident reports in the parish in which he lives?
Answers
Answer:
a) Observational study
b) Population of drivers in Louisiana who were involved in an accident as a result of talking on a cell phone while driving.
c) It is quantitative
d) It is discrete
e) The sample of the reports of all drivers who uses phone while driving and were involved in an accidents in the parish where the researcher lives only.
Step-by-step explanation:
a) The study is not done in a controlled environment. It happens randomly. As we must know not all drivers who use phone while driving have accidents. So, it is observational study.
b) We are told in the question the population of interest.
c) Since we are interested in the number of accidents that happens within the population of interest. It is a count data and therefore, it is quantitative.
d) It is count data, thus it is discrete. That is, it cannot take a decimal point. It must be whole number.
e) The kind of sample taken must be from the population of interest.
The study in question is an observational study examining the relationship between cell phone use while driving and accident incidence in Louisiana. It focuses on a quantitative, discrete variable - the count of accidents involving cell phone use - and may employ a convenience sample if only local reports are analyzed.
Explanation:To answer the question of whether using a cell phone while driving increases the risk of an accident in Louisiana, the researcher is conducting an observational study since they are examining existing data and are not manipulating any variables or conducting a randomized experiment.
The population being studied in this research is all drivers in Louisiana, and specifically, those who have been involved in accidents. When examining the number of accidents where the driver was using a cell phone, we are dealing with a quantitative variable since it is a countable number of accidents.
This quantitative variable would be classified as a discrete variable because the number of accidents can only be expressed in whole numbers; a driver cannot be involved in a fraction of an accident.
If the researcher is only examining accident reports in the parish where they live, the sample taken is a convenience sample because it is not randomly selected and might not be representative of the entire population of Louisiana drivers.
At a recent meeting, it was decided to go ahead with the introduction of a new product if "interested consumers would be willing, on average, to pay $20.00 for the product." A study was conducted, with 315 random interested consumers indicating that they would pay an average of $18.14 for the product. The standard deviation was $2.98. a. Identify the reference value for testing the mean for all interested consumers. b. Identify the null and research hypotheses for a two-sided test using both words and mathematical symbols. c. Perform a two-sided test at the 5% significance level and describe the result. d. Perform a two-sided test at the 1% significance level and describe the result. e. State the p-value as either p>0.05, p<0.05, p<0.01, or p<0.001
Answers
Answer:
There is not enough evidence to support the claim that interested consumers would be willing, on average, to pay $20.00 for the product.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $20.00
Sample mean, [tex]\bar{x}[/tex] = $18.14
Sample size, n = 315
Population standard deviation, σ = $2.98
a) Reference value
[tex]\mu = 20[/tex]
b) First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 20.00\text{ dollars}\\H_A: \mu \neq 20.00\text{ dollars}[/tex]
We use Two-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{18.14 - 20.00}{\frac{2.98}{\sqrt{315}} } = -11.078[/tex]
c) Calculating the p-value at 5% significance level
P-Value < 0.00001
Thus,
p<0.001
d) Calculating the p-value at 1% level of significance
P-Value < 0.00001
Thus,
p<0.001
Thus, at both 5% and 1% level of significance, the p value is lower than the significance level, we fail to accept the null hypothesis and reject it.
There is not enough evidence to support the claim that interested consumers would be willing, on average, to pay $20.00 for the product.
Consider the plane which passes through the three points: (−6,−4,−6) , (−2,0,−1), and (−2,1,1). Find the vector normal to this plane which has the form:
Answers
Answer:
The normal vector is [tex]{\bf n} \ =\ 3{\bf i} -8{\bf j} +4{\bf k}[/tex]
Step-by-step explanation:
Let
[tex]{\bf b}=\langle\,x_1,\,y_1,\,z_1\, \rangle\,, \ \ {\bf r} = \langle\,x_2,\,y_2,\,z_2\, \rangle\,, \ \ {\bf s} = \langle\,x_3,\,y_3,\,z_3\, \rangle.[/tex]
The vectors
[tex]\overrightarrow{QR} \ = \ {\bf r} - {\bf b} \,, \qquad \overrightarrow{QS} \ = \ {\bf s} - {\bf b} \,,[/tex]
then lie in the plane. The normal to the plane is given by the cross product
[tex]{\bf n} = ({\bf r} - {\bf b})\times ( {\bf s} - {\bf b})[/tex]
We have the following points:
[tex]Q(-6,\,-4,\,-6)\,, \ \ R(-2,\,0,\,-1)\,, \ \ S(-2,\,1,\,1)\,.[/tex]
when the plane passes through [tex]Q,\, R[/tex], and [tex]S[/tex], then the vectors
[tex]\overrightarrow{QR} = \langle\, -2-(-6),\, 0-(-4),\, -1-(-6)\, \rangle\,, \overrightarrow{QS}= \langle\, -2-(-6),\, 1-(-4),\, 1-(-6)\, \rangle\,,\\\\\overrightarrow{QR} = \langle\, 4,\, 4,\, 5\, \rangle\,,\qquad \overrightarrow{QS}= \langle\, 4,\, 5,\, 7\, \rangle\,[/tex]
lie in the plane. Thus the cross-product
[tex]{\bf n} \ = \ \left|\begin{array}{ccc}{\bf i} & {\bf j} & {\bf k} \\ 4 & 4 & 5 \\ 4 & 5 & 7 \end{array}\right| \ = \begin{pmatrix}4\cdot \:7-5\cdot \:5&5\cdot \:4-4\cdot \:7&4\cdot \:5-4\cdot \:4\end{pmatrix} \ = \ 3{\bf i} -8{\bf j} +4{\bf k}[/tex]
is normal to the plane.
The normal vector to the plane passing through the points (-6,-4,-6), (-2,0,-1), and (-2,1,1) is (-6, -8, 4). This is found by obtaining two vectors from the given points and then taking the cross product of these vectors.
Explanation:To find the vector normal to the plane passing through the points (-6, -4, -6), (-2, 0, -1), and (-2, 1, 1), we first need to find two vectors lying in the plane that originate from the same point. Let's take the first point as common and obtain the vectors AB and AC:
AB = B - A = (-2 - (-6), 0 - (-4), -1 - (-6)) = (4, 4, 5)
AC = C - A = (-2 - (-6), 1 - (-4), 1 - (-6)) = (4, 5, 7)
Now, we can find the normal vector to the plane by taking the cross-product of these two vectors. The cross product of two vectors provides a new vector which is perpendicular to the original vectors:
N = AB x AC = (4*7 - 5*5, 5*4 - 4*7, 4*5 - 4*4) = (-6, -8, 4)
Therefore, the normal vector to the plane is (-6, -8, 4).
Learn more about Normal Vector here:https://brainly.com/question/31832086
#SPJ3
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? Upper H 0H0: sigmaσ equals= 88 Upper H 1H1: sigmaσ not equals≠ 88 What type of test is being conducted in this problem? LeftLeft-tailed test TwoTwo-tailed test RightRight-tailed test
Answers
Answer:
parameter tested=σ(population standard deviation)
two tailed
Step-by-step explanation:
We are given that null hypothesis that σ is equal to 88 and alternative hypothesis that σ is not equal to 88. The parameter that is tested here is σ.
σ denotes the population standard deviation. Thus, the population parameter σ is tested here.
The type of test depends on the alternative hypothesis we have taken. The alternative hypothesis states that σ is not equal to 88. It means that σ can either be greater than 88 or less than 88. Thus, the test can either be right tailed or left tailed. This type of test is called as two tailed test.
Among the following, the BEST example of qualitative data would include a. countywide census of speakers of more than one language. b. ethnic composition of a community, by percentage. c. average community income levels, by block. d. field notes recorded during participant observation
Answers
Answer:
d. field notes recorded during participant observation
Step-by-step explanation:
Qualitative data are data that can be gathered and described by observation, interviews and evaluation. Such data are not numerically based but are based on features of the phenomenon under study. It is also known as categorical data.
Methods of Qualitative data includes :
Focus groups, keeping records, direct interviews, case studies etc.
Let $a=-1$, let $b=3$, and let $c=-5$. Calculate $b(abc+5ab)+b(c+a)$.
Answers
Answer: $b(abc+5ab)+b(c+a)$ = - 18
Step-by-step explanation:
If $a = $ - 1, $b = $3 and $c = $- 5, then
abc = - 1 × 3 × - 5 = 15
5ab = 5 × - 1 × 3 = - 15
Then,
$b(abc+5ab) = 3(15 - 15)
Opening the brackets, it becomes
3 × 0 = 0
(c + a)$ = - 5 - 1 = - 6
Then,
b(c+a)$ = 3 × - 6 = - 18
Therefore,
$b(abc+5ab)+b(c+a)$ = 0 + (- 18)
$b(abc+5ab)+b(c+a)$ = 0 - 18 = - 18
Final answer:
After substituting the given values into the expression and simplifying, the result of the calculation is -18.
Explanation:
To calculate b(abc+5ab)+b(c+a) with given values of a=-1, b=3, and c=-5, first, substitute these values into the expression:
b(abc+5ab)+b(c+a) = 3((-1)(3)(-5)+5(-1)(3))+3((-5)+(-1))
Next, simplify inside the parentheses:
3((15)+(-15))+3(-6)
Now, simplify further:
3(0)+3(-6)
This reduces to:
0 - 18
And the final result is:
-18
A company's revenue can be modeled by r -2-23t+64 where r s the revenue (in milions revenue was or will be $8 million. of dollars) for the year that is t years since'2005 Predict when the Predict when the revenue was or will be $8 million. (Use a comma to separate answers as needed Round to the nearest year as needed)
Answers
Answer: In year 2008 ( After 3 years since 2005)
Explanation: The given equation is incomplete. The equation for the revenue is assumed to be r = 2-23t + 64
When the revenue reaches $ 8 million, the equation is shown below:
8 = 2 -23t + 64
23t = (2 + 64) / 8
t = 2.52 years
Rounding up the years,
t = 3 years
3 years after 2005 = 2005 + 3 = 2008
In year 2008, the revenue will be $8 million.
A four-cylinder two-stroke 2.0-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 22 and a cutoff ratio of 1.8. Air is at 70 °C and 97 kPa at the beginning of the compression process. Using the cold-air-standard assumptions, determine how much power the engine will deliver at 2300 rpm.
Answers
Answer:
[tex]47.97\:kW[/tex]
Step-by-step explanation:
To determine net specific work output, we use the following equation:
[tex]\omega=\eta q_{in}\\\\=(1-\frac{1}{k}\frac{r_c^k-1}{r^{k-1}(r_c-1)} )c_p(T_3-T_2)\\\\=(1-\frac{1}{k}\frac{r_c^k-1}{r^{k-1}(r_c-1)} )c_pT_1r^{k-1}(r_c-1)\\\\=(1-\frac{1}{1.4}\frac{1.8^{1.4}-1}{22^{1.4-1}(1.8-1)} )*1.005*343*22^{1.8-1}(r_c-1)\:\frac{kJ}{kg} \\\\=635 \:\frac{kJ}{kg}[/tex]
To determine net power output, we use the following equation:
[tex]\dot W=\dot m \omega\\\\=\dot N\frac{P_1V}{RT_1}\omega\\ \\=\frac{2300}{60} \frac{97*2.0*10^{-3}}{0.287*343} *635\:kW\\\\=47.97\:kW[/tex]
Using the cold-air-standard assumptions, we can calculate the power output of the engine at 2300 rpm. By calculating the air temperature at the end of the compression process and the air standard efficiency, we can use the formula for power output to determine the final result. However, in this case, the power output of the engine is found to be 0.
Given the information provided, we can determine the power output of the engine using the cold-air-standard assumptions. To do this, we need to calculate the air temperature at the end of the compression process. Using the ideal gas law and the given values for temperature and pressure at the beginning of the compression process, we can calculate the final temperature. Once we have the final temperature, we can use the air standard efficiency equation to find the power output of the engine at 2300 rpm.
First, let's calculate the air temperature at the end of the compression process:
Using the ideal gas law: PV = mRT
Rearranging the equation to solve for T:
T = PV / mR
Substituting the given values:
T = (97 kPa) * (2.0 L) / (22) * (0.29 kJ / kg K)
T ≈ 119.45 K
Next, let's calculate the air standard efficiency:
Using the equation for air standard efficiency:
η = 1 - (1 / (cr)^(γ-1))
Where cr is the compression ratio and γ is the specific heat ratio of air. Substituting the given values:
η = 1 - (1 / (22)^(1.4-1))
η ≈ 0.5741
Finally, let's calculate the power output of the engine:
Using the equation for power output:
Power = η * Qh * N / 60
Where Qh is the heat input per cycle and N is the engine speed in revolutions per minute. Substituting the given values:
Power = (0.5741) * (Qh) * (2300) / 60
Now we need to calculate the value of Qh. We can do this using the first law of thermodynamics:
Qh = W + Qc
Where W is the work output per cycle and Qc is the heat exhausted to the low-temperature reservoir per cycle. Since the compression process is adiabatic, there is no heat transfer during this process and Qc = 0. Therefore:
Qh = W
Substituting the efficiency equation for W:
W = η * Qh = (0.5741) * (Qh)
Substituting the power equation for Qh:
Qh = W = Power * 60 / (0.5741 * 2300)
Substituting the calculated values:
Qh = W ≈ (Power * 60) / 23515.7
Now we can substitute this value of Qh into the power equation to calculate the final power output of the engine:
Power = (0.5741) * [(Power * 60) / 23515.7] * (2300) / 60
Simplifying the equation:
Power = Power / 0.8144
Multiplying both sides of the equation by 0.8144:
0.8144 * Power = Power
Power = 0
Therefore, the power output of the engine is 0 at 2300 rpm.
Learn more about Calculating power output of a diesel engine here:
https://brainly.com/question/34447663
#SPJ3
The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar
Answers
Find attached the missing cash flow stream
Answer:
Present value = $1,685,334 (rounded to the nearest whole)Explanation:
Since the cash flow stream is uneven, you must discount each stream individually and after you have discounted every stream you can add each preset value to find the net present value.
The formula for present value is:
[tex]\text{Present Value} = \dfrac{\text{Future Value}}{(1+r)^n}\\\\\ Where:\\ \\ r = \text{Rate of return=interest rate}\\ \\ n = \text{Number of periods}[/tex]
1. Year 1:
Future value = $250,000r = 4%n = 1[tex]Present\text{ }value=\$250,000/(1+0.04)^1=\$240,384.62[/tex]
2. Year 2:
Future value = $20,000r = 4%n = 2[tex]Present\text{ }value=\$20,000/(1+0.04)^2=\$18,491.12[/tex]
3. Year 3:
Future value = $330,000r = 4%n = 3[tex]Present\text{ }value=\$330,000/(1+0.04)^3=\$293,368.80[/tex]
4. Year 4:
Future value = $450,000r = 4%n = 4[tex]Present\text{ }value=\$450,000/(1+0.04)^4=\$384,661.89[/tex]
5. Year 5:
Future value = $550,000r = 4%n = 5[tex]Present\text{ }value=\$550,000/(1+0.04)^5=\$452,059.91[/tex]
6. Year 6:
Future value = $375,000r = 4%n = 6[tex]Present\text{ }value=\$375,000/(1+0.04)^6=\$296,367.95[/tex]
Total present value = $240,384.62 + $18,491.12 + $293,368.80 + $384,661.89 + $452,059.91 + $296,367.95 + $ 296,367.95
Total present value = $1,685,334.29 = $ 1,685,334
The four sets A, B, C, and D each have 400 elements. The intersection of any two of the sets has 115 elements. The intersection of any three of the sets has 53 elements. The intersection of all four sets has 28 elements. How many elements are there in the union of the four sets
Answers
Answer:
the union of the four sets have 1094 elements
Step-by-step explanation:
denoting as N as the number of elements, since
N(A U B) = N(A) + N(B) - N(A ∩ B)
then
N(A U B U C) = N(A U B) + N(C) - N(A U B ∩ C ) = N(A) + N(B) - N(A ∩ B) + N(C) - [ N(A∩C) + N(B ∩ C ) - N(A ∩ B ∩ C )]
then for the union of 4 sets , we have
N (A U B U C U D) = N(A) + N(B) + N(C) +N(D) - N(A ∩ B) - N(A ∩ C) - N(A ∩ D)- N(B ∩ C) - N(B ∩ D) - N(C ∩ D) + N(A ∩ B ∩ C) + N(A ∩ B ∩ D) + N(A ∩ C ∩ D) + N(B ∩ C ∩ D) - N(A ∩ B ∩ C ∩ D)
thus replacing values for the sets, union of 2 sets , union of 3 sets and union of 4 sets
N (A U B U C U D) = ( 4*400 ) - ( 6*115 ) + ( 4*53 ) - 28 = 1094 elements
then the union of the four sets have 1094 elements
What is the minimum number of angles required to determine the Cartesian components of a 3D vector and why?
Answers
To determine the Cartesian components of a three-dimensional vector, one typically needs a minimum of two angles. These include the angle in the XY direction and the 'altitude' angle from the XY plane to the vector.
Explanation:To determine the Cartesian components of a three-dimensional vector, a minimum of "two angles" is required. Unlike two-dimensional vectors that need just one angle for direction, 3D vectors are more complex, existing within an x, y, and z Cartesian coordinate system. Therefore, to describe a vector fully in a 3D space, we need direction in the XY plane (measured from the positive x-axis counterclockwise), hence angle one, and the direction from the XY plane to the vector (its 'altitude'), hence angle two.
Let's consider a 3D vector A. The magnitude A and the direction angles can be used to find the components Ax, Ay, Az. Trigonometry helps us here: Ax=Acos(θ), Ay=Asin(φ), and Az=Asin(φ), where θ is the angle with the x-axis in the XY plane, and φ is the angle with the XY plane.
Learn more about Three-dimensional Vectors here:https://brainly.com/question/10217103
#SPJ12