Answer:
180 Feet Per Minute
Step-by-step explanation:
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An airplane has an air speed of 700 kilometers per hour at a bearing of 30 degrees The wind velocity is 40 kilometers per hour from the west Use vectors to find the art speed of the plane Round to the nearest hundredth
Answer:
The red arrow shows the resultant vector. We have a Side Angle Side triangle ABC so can use The Cosine Rule:
a2=b2+c2−2bccosA
This becomes:
R2=7002+402−(2×700×40×cos45)
R2=491,600−39,597.9
R=672.3xkm/hr
This is the groundspeed of the aircraft.
To find θ we can use The Sine Rule:
sinCc=sinAa
This becomes:
sinθ40=sin45672.3
sinθ=0.04207
θ=2.41∘
This is known as the drift angle and is the correction the pilot should apply to remain on course.
The heading is the direction the aircraft's nose is pointing which is 000∘.
The track is the actual direction over the ground which is 357.6∘
An alternative method to this would be to separate each vector into vertical and horizontal components and add.
The resultant can be found using Pythagoras.
Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
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Which table has a constant of proportionality between 7 and x of 1/4? Choices are in the image
Answer:
A. has a constant proportion of 1/4.
If you have a piece of glass that is 12in X 12in - how many square feet is it?
Answer:
1 square foot is the answer
Answer:
1 ft^2
Step-by-step explanation:
We know 12 inches = 1 ft
12 inches by 12 inches
1 ft by 1 ft
The area is 1 * 1 = 1 ft^2
The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
A.
2
B.
-
C.
-2
D.
Explanation: Parallel lines have the same slopes, but different y intercepts.
Answer:
the slope of the red line is also -1/2
Step-by-step explanation:
If 6x + 5y = 10, what is y in terms of x?
Please include an explanation!
what you're trying to do is form an equation for y
6x + 5y = 10
5y = -6x + 10 we need y to be singular so divide by numeral before y
y = - 6x/5 + 10/5
y = - 6x/5 + 2
Algebra Review
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n^3 +9.
Answer:
Step-by-step explanation:
1. The sum of one-third of a number and 27
= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]
2. The product of a number squared and 4
[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]
3.Write a verbal expression for 5n^3 +9.
The sum of the product and of 5 and a cubed number and 9
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
21, 14, 13, 24, 17, 22, 25, 12
Required:
a. Calculate the sample mean and the sample standard deviation.
b. Construct the 90% confidence interval for the population mean.
c. Construct the 95% confidence interval for the population mean
Answer:
a
[tex]\= x = 18.5[/tex] , [tex]\sigma = 5.15[/tex]
b
[tex]15.505 < \mu < 21.495[/tex]
c
[tex]14.93 < \mu < 22.069[/tex]
Step-by-step explanation:
From the question we are are told that
The sample data is 21, 14, 13, 24, 17, 22, 25, 12
The sample size is n = 8
Generally the ample mean is evaluated as
[tex]\= x = \frac{\sum x }{n}[/tex]
[tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]
[tex]\= x = 18.5[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]
[tex]\sigma = 5.15[/tex]
considering part b
Given that the confidence level is 90% then the significance level is evaluated as
[tex]\alpha = 100-90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 2.995[/tex]
The 90% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]
[tex]15.505 < \mu < 21.495[/tex]
considering part c
Given that the confidence level is 95% then the significance level is evaluated as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]
=> [tex]E = 3.569[/tex]
The 95% confidence interval is evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]
[tex]14.93 < \mu < 22.069[/tex]
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)
(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
Answer:
a
[tex]df = 24.32[/tex]
b
[tex]df = 30.10[/tex]
c
[tex]df = 30.7[/tex]
d
[tex]df = 25.5[/tex]
Step-by-step explanation:
Generally degree of freedom is mathematically represented as
[tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]
Considering a
a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]
[tex]df = 24.32[/tex]
Considering b
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.10[/tex]
Considering c
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.7[/tex]
Considering c
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]
[tex]df = 25.5[/tex]
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
Perimeter =68 Length (L) is 4 less than twice the width (W)
Answer:
Length = 21.3333333333; Width: 12.6666666667
Step-by-step explanation:
Perimeter = 68
Perimeter of a rectangle:
2 (L +W)
Length (L) = 2W - 4
Width = W
2 ( 2W -4 +W) = 68
=> 2 (3W - 4) = 68
=> 6w -8 = 68
=> 6w = 76
=> w = 12.6666666667
Length = (12.6666666667 X 2) - 4
=> 21.3333333333
An apartment building is infested with 6.2 X 10 ratsOn average, each of these rats
produces 5.5 X 10' offspring each year. Assuming no rats leave or die, how many additional
rats will live in this building one year from now? Write your answer in standard form.
Answer: 3.41x10^3
Step-by-step explanation:
At the beginning of the year, we have:
R = 6.2x10 rats.
And we know that, in one year, each rat produces:
O = 5.5x10 offsprins.
Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:
(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2
and we can write:
34.1 = 3.41x10
then: 34.1x10^2 = 3.41x10^3
So after one year, the average number of rats is: 3.41x10^3
70 points! Please answer fast!
Answer:
slope = 2
Step-by-step explanation:
will make it so simple and short
slope = rise / run
slope = 6 / 3
slope = 2
Answer:
B
Step-by-step explanation:
The formula for slope is (y2-y1)/(x2-x1)
In this case it is (1+5)/(3-0)
6/3
2
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor.
What is the recommended investment portfolio for this client?
What is the annual return for the portfolio?
a) The Investment portfolio consisting of the internet fund and Blue chip fund would be the recommended Portfolio for a moderate risk investor
b) The annual return for the portfolio is = $5100 ( Calculated using the excel formula sheet attached below )
The best/recommended investment portfolio for this client is the Investment portfolio consisting of the internet fund and Blue chip Fund because the Portfolio consists of a lower risk rating of 4 for every thousand which is conservative, and also an Internet fund which has a risk rating of 6 for every thousand ( aggressive ). The combination of a high and low risk investment fund in a portfolio results to an average/moderate risk portfolio.
Calculating the Annual return for the portfolio ( using the excel sheet below)
Model Internet fund Blue chip fund
Amount to invest 20 30
Total amount invested = 20 + 30 = 50
Total risk rating = 240
Total return = 5.1
hence: The recommended investment portfolio for this client is the Blue chip fund and the total return on the portfolio = $5100 applying the excel formulae attached below
Internet Fund = $20,000
Blue chip fund = $30,000
Learn more : https://brainly.com/question/7589262
Which value is a solution to w∕18 ≥ –1?
Answer:
w ≥ -18
Step-by-step explanation:
Answer:
w is greater than or equal to-18
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?
Answer:
Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
After 11 hours of burning, a candle has a height of 23.4 centimeters.
After 30 hours of burning, its height is 12 centimeters.
What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29
m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = -11.4%2F19(x - 11)
y - 23.4 = -11.4%2F19x + 125.4%2F19
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19
y = -11.4%2F19x + 570%2F19
y = -11.4%2F19x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = -11.4%2F19(13) + 30
y = -148.2%2F19 + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs
what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:
Step-by-step explanation:
Lets, turn this into words and use order of operations, First, we look for multiplication and division.
the sum of one fourth of 5 times of 8 and 10 gets you 1/4(5*8) + 10 = 20
what is the number if 4 is subtracted from the sum
20 - 4 = 16
Describe in words how you would solve the linear system y = 3x + 1 and y = - 2x + 3.
Please help! Stuck on this question!!
Answer:
The 2 Gallon Tank is Enough
Step-by-step explanation:
A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.
There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.
[tex]8 * 2 = 16[/tex]
So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.
Answer:
2 gallon tank
Step-by-step explanation:
16 pints is the same as 2 US gallons
Will Give Brainliest Please Answer Quick
Answer:
Option (2)
Step-by-step explanation:
If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.
By using this property,
Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.
By applying Pythagoras theorem in right triangle KNJ,
(KJ)² = (KN)² + (NJ)²
(33)² = (6√10)² + (NJ)²
NJ = [tex]\sqrt{1089-360}[/tex]
NJ = [tex]\sqrt{729}[/tex]
= 27 units
Since, GJ = 2(NJ)
GJ = 2 × 27
GJ = 54 units
Option (2) will be the answer.
Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
The train on the course of moving to the side track has to be moving faster so the trains don't hit eachother.
Step-by-step explanation:
Laws of physics....
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches? 28 1/4" and 20"
Answer:
282.5 inches squared
Step-by-step explanation:
A triangle is half the area of a square.
So we will solve the area as if we were finding the area for a square, and then we halve the result.
Length multiply by height to get the area:
28.25 × 20 = 565 inches squared
Now, half the answer to get the area of the triangle:
565/2=282.5 inches squared
A researcher measures daily driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?
Answer:
There is a positive correlation between these two variables.
Step-by-step explanation:
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.
Thus, there is a positive correlation between these two variables.
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99 using the cumulative standard normal distribution table
Answer:
6.642
Step-by-step explanation:
Given that mean = 2
standard deviation = 2
Let X be the random Variable
Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])
X [tex]\sim[/tex] N(2,2)
By Central limit theorem;
[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]
[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]
P(X<x) = 0.09
[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]
[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]
P(X < x) = 0.99
[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]
[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]
[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]
[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]
[tex]( \dfrac{X-2}{2})= 2.321[/tex]
X -2 = 2.321 × 2
X -2 = 4.642
X = 4.642 +2
X = 6.642
Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.
Answer:
side st.Step-by-step explanation:
st corresponds to kj since a it has five sides.What is the smallest number that has both 6 and 9 as a
factor?
A 54
B 12
C 36
D 18
Answer:
yep it's D
Step-by-step explanation:
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
8192
Step-by-step explanation:
2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192
Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in different pacemakers randomly selected from this batch of and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Complete question is;
Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Answer:
P(All three are not caused by firmware) = 83.84%
Probability that the entire batch will be accepted = 0.8384
Step-by-step explanation:
We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.
Thus,
Cases not caused by firmware = 8834 - 504 = 8330
So, probability of the first case not being affected by firmware is;
P(first case not caused by firmware) = 8330/8834
Also,
Probability of second case not being affected by firmware is given as;
P(second case not caused by firmware|first case not affected by firmware) = 8329/8833
Similarly,
Probability of third case not being affected by firmware is given as;
P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832
Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.
Thus, we will make use of the general multiplication rule which is;
P(A & B) = P(B) × P(A|B)
Thus;
P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)
Plugging in the relevant values, we have;
P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)
P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%
Find the slope of the line through the points (-4, 6) and (8,4).
I need help on this
Start with the slope formula.
m = y2-y1/x2 - x1
We take the second y minus the first y
over the second x minus the first x.
So we have 4 - 6/8 - -4.
This simplifies to -2/12 which reduces to -1/6.