Answer:
[tex]v \cdot w = 8.0[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]|v| = |w| = 4[/tex] --- the side lengths
Required
[tex]v \cdot w[/tex]
[tex]v \cdot w = |v| \cdot |w| \cdot (cos\theta)[/tex]
From the question, we understand that v and w are sides of an equilateral triangle.
This means that:
[tex]\theta = 60^o[/tex] --- angles in an equilateral triangle
So:
[tex]v \cdot w = |v| \cdot |w| \cdot (\cos 60)[/tex]
So, we have:
[tex]v \cdot w = 4 * 4 * 0.5[/tex]
[tex]v \cdot w = 8.0[/tex]
The probability that a patient recovers from a disease is 0.3.
If 6 people are known to have contacted the disease, what is the probability that at least 4 survive?
Answer:
0.07047
Step-by-step explanation:
at least 4 people survive is
4 people survive and 2 don't +
5 people survive and 1 doesn't +
all 6 people survive
the probability of 4 people to survive is the product of the individual probabilities :
0.3×0.3×0.3×0.3 = 0.3⁴ = 0.0081
times the probability 2 don't survive
0.7×0.7 = 0.49
0.0081×0.49 = 0.003969
now, the chance that 4 out of 6 survive is that probabilty times how many times we can select 4 out of 6.
to select 4 out of 6 is
[tex] \binom{6}{4} [/tex]
= 6! / (4! × (6-4)!) = 6! / (4! × 2!) = 6×5/2 = 30/2 = 15
so, the probability of having 4 survivors is
15×0.003969 = 0.059535
the probability of 5 people surviving is 0.3⁵ times one not
0.3⁵×0.7 = 0.001701
we have 6 over 5 combinations to pick 5 out of 6 = 6.
so, in total for 5 survivors we get
6×0.001701 = 0.010206
and the probabilty of all 6 surviving is
0.3⁶ = 0.000729
so, the probability of at least 4 out of 6 surviving is
0.059535 +
0.010206 +
0.000729
---------------
0.070470
Question 14(Multiple Choice Worth 5 points)
Find all polar coordinates of point P where P = negative pi divided by 6.
(1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
(1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
(1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
(1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
Answer:
Find all polar coordinates of point P where P = (5 , -pi+%2F6 ).
There are two sets of possibilities.
(1) Same (positive) magnitude and an angle that is the same as the given angle, or differs from the given angle by an even multiple of pi:
P = (5, -pi%2F6%2B2n%2Api )
(2) Opposite (negative) magnitude and an angle that differs from the given angle by an odd multiple of pi:
(-5, -pi%2F6%2B%282n%2B1%29pi)
answer is: (5,-pi%2F6+%2B+2n%2Api) or (-5, -pi%2F6%2B%282n%2B1%29pi)
Answer:
negative pi divided by 6 + (2n + 1)π) or (-1, negative
-3x=6x + 2 solve for x
Answer:
Step-by-step explanation:
6x+3x= -2
9x= -2
x= -2/9
Answer:
-3x=6x+2
⇒-9x=2
⇒x=-2/9
Step-by-step explanation:
Identify the X intercept and the yIntercept of the line 4x-2y=-12
Answer:
X-intercept = -3 and y-intercept = 6
Step-by-step explanation:
We can start off by isolating the y term. To do that, we must add 2y to both sides to get
[tex]4x=2y-12[/tex]
Now, we must add 12 to both sides and the y term will be all alone on the right side:
[tex]4x+12=2y[/tex]
Now, to have only y on the right side, we must divide by 2 to get:
[tex]y=2x+6[/tex]
In slope-intercept form, b is the y-intercept, and 'b' in this equation is 6. We have our y-intercept.
To find our x-intercept, y must be equal to zero. We can plug in that value for y and solve for x:
[tex]0=2x+6[/tex]
We can start off by subtracting 6 from both sides to get:
[tex]2x=-6[/tex]
We can then divide both sides to get [tex]x=-3[/tex] when y is equal to 0. Thus, we have our x-intercept.
Answer:
y-intercept= -6
x-intercept= 3
Step-by-step explanation:
First, rearrange the equation to be in y=mx+b.
4x-2y=12
4x-12=2y
(1/2)(4x-12)=y
y=2x-6
From here, we know that the 'b' in an equation in form y=mx+b is the y-intercept, which is -6.
To find the x intercept make y=0 and solve.
You can also solve without rearranging the equation and simply making x=0 and solving to find the y-intercept. and making y=0 and solving to find the x-intercept.
Express 456782 to 2 significant figures
Answer:
the answer for this is 45*10^4
This graph shows a portion of an odd function.
Use the graph to complete the table of values.
X
f(x)
-2.
-3
-4
-6
DONE
9514 1404 393
Answer:
-2-1-2-3Step-by-step explanation:
An odd function is symmetrical about the origin:
f(-x) = -f(x)
So, ...
f(-2) = -f(2) = -2
f(-3) = -f(3) = -1
f(-4) = -f(4) = -2
f(-6) = -f(6) = -3
Answer:
-2
-1
-2
-3
I did it on edge2020 and got it right
87.26+(-25.6)+(-5.4)
Answer:
= 87.26 + (-25.6) + (-5.4)
=87.26- 25.6 - 5.4
= 87.26 - 31
= 56.26
✌✌✌✌✌
An asset's book value is $43,200 on January 1, Year 6. The asset is being depreciated $600 per month using the straight-line
method. Assuming the asset is sold on July 1, Year 7 for $29,400, the company should record:
Assuming the asset is sold on July 1, Year 7 for $29,400, the company should record the asset's value as equal to $32,400.
The book value of the asset on January 1, Year 6 was $43,200.The asset is being depreciated at $600 per month using the straight-line method.The asset was sold on July 1, Year 7 for $29,400.The amount of time elapsed until the asset is sold is 18 months.The time elapsed can be considered as the "x-coordinate".The asset's value can be considered as the "y-coordinate".The rate of depreciation can be considered as the slope of the line.The equation formed from the given data is given below :(y-y1) = m(x-x1)y-43,200 = (-600)(18)y = 43,200-10,800y = 32,400To learn more about equations, visit :
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Can anyone help me with trig identities?
Answer:
cosA = √(21/25)
Step-by-step explanation:
We know
sin²(A) + cos²(A) = 1
Next, we know that sin(A) = 2/5. Plugging that into our equation, we get
(2/5)² + cos²A = 1
4/25 + cos²A = 1
subtract 4/25 from both sides to isolate cos²A
cos²A = 1 - 4/25 = 25/25-4/25 = 21/25
square root both sides to get
cosA = √(21/25)
We do not include -√(21/25) in our possible answer for cosA because this is in quadrant 1, so cosA must be positive.
Sophia runs twice as fast as her friend Mia. If mia runs 3 mph how long will it tske sophia to run 6 miles? 9 miles?
Answer:
It will take Sophia 1 hour to run 6 miles.
And 1 1/2 hours for 9 miles.
Step-by-step explanation:
What will be the value of median of a moderately asymmetrical distribution? If the mean and mode are 30 and 24 respectively.
The mean, the median and the mode are measures of central tendency, and they are related in some many ways, depending on the type of distribution.
The median of the moderately asymmetrical distribution is 26
The given parameters are:
[tex]Mean = 30[/tex]
[tex]Mode = 24[/tex]
For a moderately asymmetrical distribution, the mean, median and mode are related by the following equation:
[tex]Mode = 3 * Median - 2 * Mean[/tex]
Substitute known values
[tex]30= 3 * Median - 2 * 24[/tex]
[tex]30= 3 * Median - 48[/tex]
Collect like terms
[tex]3 * Median =30+ 48[/tex]
[tex]3 * Median =78[/tex]
Divide both sides by 3
[tex]Median =26[/tex]
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the perimeter of a square room is 48m,how much square carpet is requried to cover it ?
Answer:
144
Step-by-step explanation:
perimeter of square=48 ( formula= 4*a )
a= 48/4
= 12
area= a*a
=12*12
=144
PLSSSS HELPPP MEEEEEE
Hi, I'm happy to help!
Parallel means that two lines are lined up in the same directions and will never intersect even if they were extended forever in directions.
Let's look at the first option of AB, and AD. We can see that both lines intersect at point A, so AB and AD are not parallel.
For the next option of CD and BE, we can see that both lines don't intersect and won't ever even if the lines were extended. So, CD and BE are parallel.
For the third option, we have BC and DE. These lines don't intersect and aren't in line to ever do so. Therefore, BC and DE and parallel.
The last option is AD and BC. These two lines will never meet, but, they aren't line up in the same directions. AD is traveling upwards while BC isn't. Think about being able to make a road out of the two lines, it would never work. AD and BC are not parallel.
To sum it up: You should select the 2nd and 3rd options because those lines are parallel.
I hope this was helpful, keep learning! :D
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.
Required:
Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
Find the area of each shaded region.
Solve for x
X=In sqrt e
Step-by-step explanation:
e = 2.7182818 so you can just plug that in to your calculator and solve like normal
find laplace transform of t+t^2 +t^3
Recall that
[tex]L_s\left\{t^n\right\} = \dfrac{n!}{s^{n+1}}[/tex]
where [tex]L_s\left\{y(t)\}[/tex] is the Laplace transform of y(t) into the s-domain.
Then you have
[tex]L_s\left\{t+t^2+t^3\right\} = \dfrac{1!}{s^{1+1}} + \dfrac{2!}{s^{2+1}} + \dfrac{3!}{s^{3+1}} = \boxed{\dfrac1{s^2} + \dfrac2{s^3} + \dfrac6{s^4}}[/tex]
PLease Help! I will give you the brainiest and a lot of points
A survey of 104 college students was taken to determine the musical styles they liked. Of those, 22 students listened to rock, 23 to classical, and 24 to jazz. Also, 10 students listened to rock and jazz, 8 to rock and classical, and 8 to classical and jazz. Finally, 6 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions.
a. How many listened to only rock music?
n(only rock)
b. How many listened to classical and jazz, but not rock?
n(classical and jazz, not rock)
c. How many listened to classical or jazz, but not rock?
n(classical or jazz, not rock)
d. How many listened to music in exactly one of the musical styles?
n(exactly one style)
e. How many listened to music in exactly two of the musical styles?
n(exactly two styles)
f. How many did not listen to any of the musical styles?
n(none)
Answer:
A. 22
B. 8
C. 23 + 24
D. 22 + 23 + 24
E. 8 + 8 + 10
F. 104 - (sum of all the given numbers) = 3
What will the height of the firework be 3 seconds after the launch? How many seconds after the launch will it take for the firework to fall to the same height again?
Answer:
524m
Step-by-step explanation:
(x+1).(x/2 +2).(x/3+3).(x/4+4).(x/5+5)
Answer:
Please see the attached picture below to understand the steps I've typed to get to the final solution.
Simplify: (3x2 − 5xy + 2y2) − (7x2 − 3xy − 3y2) (5 points)
−4x2 + 8xy − y2
−4x2 − 8xy + y2
−4x2 + 2xy − 5y2
−4x2 − 2xy + 5y2
Answer:
-4×2-2xy+5y2
Step-by-step explanation:
(6-5xy+2y2)-(14-3xy-3y2)
=6-5xy+2y2-14+3xy+3y2
=(6-14)+(-5xy+3xy)+(2y2+3y2)
=-4×2-2xy+5y2
Answer:
−4x2 − 2xy + 5y2
Step-by-step explanation:
8/9 - Evaluating Algebraic Expressions
5. Which is equivalent to 4x - (y + x) + 2, if x = 5 and y=-3?
O 20
-20
-15
O 15
9514 1404 393
Answer:
(a) 20
Step-by-step explanation:
Put the numbers in place of the corresponding letters and do the arithmetic.
4(5) -((-3) +5) +2 = 20 -2 +2 = 20
40pts and a brainliest to the person who answers this question with detailed explanations and steps to solve shown.
Find y. Give your answer in the simplest form.
Answer:
y = 7 sqrt(2)
Step-by-step explanation:
Since this is a triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = 7/y
y sin 45 = 7
y = 7/ sin 45
y = 7 / (1/sqrt(2) )
y = 7 sqrt(2)
Answer:
the answer is y = 7 sqrt (2)
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
Which statements are true of functions? Check all that apply.
Answer:
All functions have a dependent variable.
All functions have an independent variable.
A horizontal line is an example of a functional relationship.
Mia wants to buy 3 notebooks for $1.29 each. What is the expression for the total cost?
Step-by-step explanation:
Mia want to buy 3 notebook for $1.29 each ,
then total cost =3×1.29
hence, 3×29
1\6+1/12+2/6=2+1+4/12
=7/12
find coordinate of a point on x axis which is at a distance of 5 units from (5,4)
Step-by-step explanation:
Hi there!
Please see attached picture for your answer.
Hope it helps!
The average of a group of data points is called the
Answer:
mean
Step-by-step explanation:
The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.
What function type does the table of values represent?
A) Linear
B) Exponential
C) Quadratic
D) Can't be determined
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|c|}x&y&x^2&3x^2\\---&---&---&---\\1&3&1^2&3*1^2=3\\2&12&2^2&3*2^2=12\\3&27&3^2&3*3^2=27\\4&48&14^2&3*4^2=48\\5&75&5^2&3*5^2=75\\\end{array}\\\\\\\boxed{y=3x^2\ the\ function\ is\ quadratic.}[/tex]
12
Detroit, Michigan covers an area of 142.9 square miles. There are approximately
672,800 people living in Detroit. Grand Rapids, Michigan has an area of 45.3 square
miles and has a population of approximately 195,100 people. How many more
people, per square mile, live in Detroit verses Grand Rapids? Round to the nearest
person per square mile.
Answer:
401 more people per square mile
Step-by-step explanation:
Find how many people there are per square mile in both cities by dividing the number of people by the number of square miles:
672,800/142.9
= 4708 people per square mile (Detroit)
195,100/45.3
= 4307 (Grand Rapids)
Find how many more people per square mile live in Detroit by finding the difference between these two numbers:
4708 - 4307
= 401
So, there are 401 more people per square mile living in Detroit versus Grand Rapids.
The table shows a set of conditional relative frequencies of drivers in a survey planning to buy a used vehicle next, based on how they obtained their current vehicle.
Which interpretation of the relative frequencies given is the most appropriate?
A. The greatest number of drivers who plan to buy used are those who leased their current vehicle.
B. The majority of drivers who will buy used next time bought their current vehicle used.
C. Of drivers who bought their current vehicle used, about 4 percent will buy new next time, almost 95 percent will buy used next time, and about 1 percent will lease next time.
D. Of drivers who bought new, 3.9 percent will buy used next time; of drivers who bought used, 94.8 percent will buy used again; of drivers who leased, 1.3 percent will buy used.
The majority of drivers who will buy used next time bought their current vehicle used. The correct option is B.
What are statistics?Any affiliations, financing, or financial holdings that could be seen as influencing the review's objectivity to give rise to potential bias.
Such elements might consist of, but are not limited to, the following: Employment, professional associations, paid consulting, and participation in groups that support relevant causes.
The given table is:-
Current vehicle Buy used
Bought new 0.039
Bought Used 0.948
Leased 0.013
Total 1.000
In the given table it is observed that the majority of drivers who will buy used next time bought their current vehicle used. The correct option is B.
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