Answer:
The resultant of the given vectors by component method is [tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex].
Step-by-step explanation:
First we define each vector by applying using rectangular form:
1) [tex]\|\vec E\| = 23\,km[/tex], 11º north of east.
[tex]\vec E = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})[/tex] (Eq. 1)
2) [tex]\|\vec N\| = 25\,km[/tex], 24º east of north.
[tex]\vec N = 25\,km\cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})[/tex] (Eq. 2)
3) [tex]\|\vec G\| = 19\,km[/tex], 18º south of west.
[tex]\vec G = 19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})[/tex] (Eq. 3)
4) [tex]\|\vec R\| = 27\,km[/tex], 58º west of north.
[tex]\vec R = 27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})[/tex] (Eq. 4)
The resultant of given vectors is determined by vector sum, that is:
[tex]\vec U = \vec E + \vec N + \vec G + \vec R[/tex] (Eq. 5)
[tex]\vec U = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})+25\,km \cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})+19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})+27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})[/tex]
[tex]\vec U = (23\,km\cdot \cos 11^{\circ}+25\,km\cdot \sin 24^{\circ}-19\,km\cdot \cos 18^{\circ}-27\,km\cdot \sin 58^{\circ})\,\hat{i}+(23\,km\cdot \sin 11^{\circ}+25\,km\cdot \cos 24^{\circ}-19\,km\cdot \sin 18^{\circ}+27\,km\cdot \cos 58^{\circ})\,\hat{j}[/tex]
[tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex]
The resultant of the given vectors by component method is [tex]\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km][/tex].
Can someone help me find the area of the triangle
please!!!
Answer:
18
Step-by-step explanation:
If December 6 falls on a Saturday, then January 19 of the next year falls on which day of the week?
January 19 would fall on a Tuesday
A random sample of 5 homes in Newberry, Florida had a mean of $169,900 and a standard deviation of $21,756. Construct a 95% confidence interval for the average home of this size in Newberry.
A. (144885.25, 194914.75).
B. (150440.842, 189359.16).
C. (150830, 188969.98).
D. (142886, 196914).
Answer:
D. (142886, 196914).
Step-by-step explanation:
To solve for this question, we would use t score instead of z score. The reason is because, our sample size is small.
The formula for Confidence Interval =
C.I = Mean ± t score × standard deviation/√n
n = 5 samples
Degrees of freedom = n - 1 = 5 - 1 = 4
The t score for a 95% confidence interval with degrees of freedom 5 is : 2.776
Hence,
Confidence Interval =
169,900 ± 2.776 × 21,756/√5
169,900 ± 2.776 × 9.7295789837
169, 900 ± 27009.311259
Confidence Interval
169,900 - 27009
= 142886
169, 900 + 27009.311259
= 196914
Hence, the confidence interval = (142886, 196914)
Option D is the correct answer
Using the t-distribution, it is found that the 95% confidence interval for the average price of a home of this size in Newberry is of (142886, 196914), given by option D.
In this problem, we have the standard deviation for the sample, thus, the t-distribution is used to solve this question.
The sample mean is [tex]\overline{x} = 169900[/tex].The sample standard deviation is [tex]s = 21756[/tex].The sample size is [tex]n = 5[/tex]First, we find the number of degrees of freedom, which is the sample size subtracted by 1, so df = 5 - 1 = 4.
Then, we find the critical value for the 95% confidence interval with 4 df, which looking at the t-table or using a calculator is given by t = 2.7765.
The margin of error is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In this case:
[tex]M = 2.7765\frac{21756}{\sqrt{5}} = 27014[/tex]
The confidence interval is:
[tex]\overline{x} \pm M[/tex]
Then
[tex]\overline{x} - M = 169900 - 27014 = 142,886[/tex].
[tex]\overline{x} + M = 169900 + 27014 = 196,914[/tex].
Thus, the correct option is D. (142886, 196914).
A similar problem is given at https://brainly.com/question/15180581
kelly flies a distance of 2,100 miles. The trip takes 4 2/3 hours.
What is the airplane's unit rate of speed in miles per hour?
Answer:
450 miles per hour
Step-by-step explanation:
Kelly flies at a distance of 2,100 miles
The time taken for the trip is 4 2/3 hours
Therefore the rate of speed can be calculated as follows
= 2,100 ÷ 4 2/3
= 2,100 ÷ 14/3
= 2100 × 3/14
= 150 × 3
= 450 miles per hour
Answer:
450
Step-by-step explanation:
10 raise to power2 - 11 raise to power 2 + 4raise to power2
Answer:
-5
Step-by-step explanation:
100 - 121 + 16
Power of 2 just means to multiply the number by iteself. So 10×10, 11×11, 4×4.
What is the slope of the line that passes through the points (−10,0) and (-13, 3)?
Answer:
-1
Step-by-step explanation:
To find slope
m=y2-y1
--------
x2-x1
m= 3-0
-----
-13-(-10)
m= 3
---
-3
m=-1
9
The rate shown represents the number of residents for each police officer in a city.
400 residents
1 police officer
Which rate is equivalent?
10,000 residents
25 police officers
O
4,000 residents
100 police officers
2 residents
800 police officers
500 residents
101 police officers
chart below
Answer:
A: 10,000 residents to 25 police officers
Step-by-step explanation:
400*25=10,000
Yoooo who’s smart I need help in this ASAP
Answer:
3[tex]\sqrt[9]{Z}[/tex]²
Step-by-step explanation:
Expression -
(27[tex]\sqrt[3]{Z}[/tex]²) ^1/3
Transform the expression -
³[tex]\sqrt[3]{27}[/tex][tex]\sqrt[3]{Z}[/tex]²
Simplify - //Note: ignore the ' * '//
3[tex]\sqrt[3]{*}[/tex][tex]\sqrt[3]{z}[/tex]²
Simplify (Again) -
3[tex]\sqrt[9]{Z}[/tex]²
PLSSS HELPPPPP MEEEE III WILLL GIVVVEEE BRAINLIESTTTT!!!!!!
Answer:
it should be 4.5
Step-by-step explanation:
7. What is the equation of the line that passes through (-1, -4) and (0,5)?
A.) y = 9x + 5 B.) y = 5x + 9 C.) y = -9x + 5 D.) y = -5x + 9 E.) none of these
1
Answer:
A)y=9x+5
Step-by-step explanation:
If x=-1, y=-4,
y=9*-1+5=(-9)+5=-4
If x=0, y=5,
y=9*0+5=5
Write an expression in simplest form that represents the area of the banner
Answer:
Can I have a picture so I can give you one
Step-by-step explanation:
thank you
Amani is calculating the slope of the trend line in the scatterplot below. On a graph, a trend line goes through points (3, 60) and (8, 41). How can Amani use the trend line to check the reasonableness of her answer? She should expect the slope to be negative because the line tilts down moving from left to right on the graph. She should expect the slope to be negative because more points are below the line than above the line. She should expect the slope to be positive because the line has a positive y-intercept. She should expect the slope to be positive because all the plotted points have positive coordinates.
Answer:
amani has to use the positive line
What was Madame de Soto’s motive for intervening?
Answer:
On May 21, 1541, the Spaniards saw for the first time the Mississippi River, the “Father of the Water” south of Memphis, Tennessee. They crossed the river and made their way through Arkansas and Louisiana. Then, early in 1542, de Soto turned back to the Mississippi River
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Which of the following correctly represents the given data in the problem?
a = 24, g = 48, h = 22, i = 80
a = 22, c = 80, d = 24, i = 48
a = 24, b = 48, c = 22, i = 48
a = 24, c = 48, e = 22, i = 80
Answer:
D
Step-by-step explanation:
100% true
Answer:
It is D
Step-by-step explanation:
Find the slope of the line that passes through the points (5,2) and (6,10). *
Answer:
8
Step-by-step explanation:
[tex] \frac{10 - 2}{6 - 5} = 8[/tex]
Answer:
The slope of the line is 8
Step-by-step explanation:
Use this formula for calculating the slope with two points:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
(5,2) = ([tex]x_{1}[/tex],[tex]y_{1}[/tex])
(6,10) = ([tex]x_{2}, y_{2}[/tex])
Substitute the points into the equation
10 - 2 = 8
-------- --- = 8
6 - 5 = 1
So the slope would be 8.
In a certain assembly plant, three machines, B1, B2, B3, make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective.
A. Suppose that a finished product is randomly selected. What is the probability that it is defective?
B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.
Answer:
a. The probability that the finished product selected is defective is 2.45%.
b. The probability that product chosen randomly was defective and made by machine B3 is 20.41%.
Step-by-step explanation:
Let A represents the defective product.
We also have the following from the question:
P(B1) = Probability or percentage of the made by machine B1 = 30%, or 0.30
P(B2) = Probability or percentage of the made by machine B2 = 45%, or 0,45
P(B3) = Probability or percentage of the made by machine B3 = 25%, or 0.25
P(A/B1) = Probability or percentage of product B1 that is defective = 2%, or 0.02
P(A/B2) = Probability or percentage of product B2 that is defective = 3%, or 0.03
P(A/B3) = Probability or percentage of product B3 that is defective = 2%, or 0.02
We can therefore proceed as follows:
A. Suppose that a finished product is randomly selected. What is the probability that it is defective?
To determine this, the rules of elimination is applied and we have:
P(A) = (P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3)) ………… (1)
Where;
P(A) = Probability that the selected product is defective = ?
Substitutes the values defined above into equation (1), we have:
P(A) = (0.30 * 0.02) + (0.45 * 0.03) + (0.25 * 0.02)
P(A) = 0.006 + 0.0135 + 0.005
P(A) = 0.0245, or 2.45%
Therefore, the probability that the finished product selected is defective is 2.45%.
B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.
To calculate this, the Bayes’ rule is employed as follows:
P(B3/A) = (P(B3) * P(A/B3)) / [(P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3))] = (P(B3) * P(A/B3)) / P(A) ………….... (2)
Where;
P(B3/A) = The probability that product chosen randomly was defective and made by machine B3 = ?
Also, from the values already defined and obtained in part A, we have:
P(B3) = 0.25
P(A/B3) = 0.002
P(A) = 0.0245
Substituting the values into equation (2), we have:
P(B3/A) = (0.25 * 0.02) / 0.0245
P(B3/A) = 0.005 / 0.0245
P(B3/A) = 0.2041, or 20.41%
Therefore, the probability that product chosen randomly was defective and made by machine B3 is 20.41%.
Problems 4 (a and b), 6 (a,b, and c), 7 (a,b, and c), 8, and 9 (a,b, and c) Thank you so much!
For real help on this, people will receive more points to prevent point stealing.
Answer:
no problem glad to help
please help with all of them
Answer:
1 - D
2 - D
3 - B
Answer:
D. Quadrant 4
D. 1,2
B. A and B
Step-by-step explanation:
brainlest pls
Add preposition ...The plane landed ____the ranway.
Answer:
On
The plane landed ON the runway.
Step-by-step explanation:
A preposition is a word that shows the relationship of a noun or pronoun with another word.
For example, in this sentence the noun is plane and we need to connect it with runway.
And on is the answer that makes the most sense.
3y+6 divided by 2a:let y=4 and x=3
Answer:
3
Step-by-step explanation:
You first plug in the values for x and y into the equation
3(4)+6÷ 2(3)
Then Simplify each side
12+6÷6
18÷6
=3
There are 720 dishes that need to be rinsed. Brian can rinse them in 72 minutes by himself. It will take his friend Boris 144 minutes to rinse these dishes. How
long will it take them itthey rinse these 720 dishes together?
minutes
Answer:
It will take both of them 48 minutes to rinse all the dishes.
Step-by-step explanation:
Brian can do 720/72 = 10 dishes per minute.
Boris can do 720/144 = 5 dishes per minute
Together, they do 15 dishes per minute
720/15 = 48 minutes
imagine you have to hunt find food to eat what kind of food will you find
Answer:
deer
Step-by-step explanation:
Answer:
hmm...wild dear and plants
Shonda painted 3 walls in her home. She used 34 of her paint. She used the same amount of paint on each wall.
How much of her paint was used on each wall?
Answer:
1/4
Step-by-step explanation:
please help need assistance
Answer:
18
Step-by-step explanation:
Keep in mind that anything with a subscript of 0 always comes out as a 1
16(1)+2(2)²(4⁻¹)
= 16+8(4⁻¹)
=16 + 8(1/4)
=16+2
=18
Hope this helps! :)
Find the hypotenuse of a right triangle with a side of 6 and a side of 8.
(ONLY put the number of your answer.) *
Answer:
10 (can't just write a number bcs i couldn't send yoy if i won't write something else)
The sum of two numbers is 8 and
their difference is 2.
Answer:
The numbers are 3 and 5.
Step-by-step explanation:
Hope that helped.
Also can I please have Brainliest?
Only if I'm right of course
The modified expression x^3(2x+5)-4(2x+5) has two terms with a common factor of
Answer:
( 2 x +5) ( x ^3 − 4 )
Step-by-step explanation:
I dont think this the answer your looking for, however, if you work backwards from here by expanding, you might get what you want. :)
please
help i’ve been stuck on
this all day
Answer:
CPB
Step-by-step explanation:
acute is less than 90 degrees and right is 90 degrees and obtuse is over 90 degrees
Answer: The answer is CPB
Suppose X has a continuous uniform distribution over the interval [1.3, 6.2]. Round your answers to 3 decimal places.
Required:
a. Determine the mean of X.
b. Determine the variance of X
c. What is P(X < 3.7)?
Answer:
(a) 3.75
(b) 2.00083
(c) 0.4898
Step-by-step explanation:
It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].
(a)
Compute the mean of X as follows:
[tex]\mu_{X}=\frac{a+b}{2}=\frac{1.3+6.2}{2}=3.75[/tex]
(b)
Compute the variance of X as follows:
[tex]\sigm^{2}_{X}=\frac{(b-a)^{2}}{12}=\frac{(6.2-1.3)^{2}}{12}=2.00083[/tex]
(c)
Compute the value of P(X < 3.7) as follows:
[tex]P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898[/tex]
Thus, the value of P(X < 3.7) is 0.4898.
Marty worked 19.5 hours last week. He earns $8.50 per hour. What were Marty’s earnings last week?
Answer:
Step-by-step explanation:
Marty's earnings = 8.50 x 19.5 = 165.75
