Answer:
23
Step-by-step explanation:
There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism. Suppose a particular surveillance system has a 96% chance of correctly identifying a future terrorist and a 99.8% chance of correctly identifying someone who is not a future terrorist. If there are 1,000 future terrorists in a population of 200 million, and one of these 200 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist
Answer:
0.9976 = 99.76% probability that he/she actually is a future terrorist
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Person identified as a future terrorist
Event B: Person is actually a future terrorist.
Probability that a person is identified as a future terrorist:
96% of [tex]\frac{1000}{200000000}[/tex]
100 - 99.8 = 0.2% of [tex]\frac{200000000-1000}{200000000}[/tex]
So
[tex]P(A) = 0.96\frac{1000}{200000000} + 0.002\frac{200000000-1000}{200000000} = 0.002[/tex]
Probability of being identified and being a future terrorist:
100 - 99.8 = 0.2% of [tex]\frac{200000000-1000}{200000000}[/tex]
[tex]P(A \cap B) = 0.002\frac{200000000-1000}{200000000} = 0.00199999[/tex]
What is the probability that he/she actually is a future terrorist
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.00199999}{0.00200479} = 0.9976[/tex]
0.9976 = 99.76% probability that he/she actually is a future terrorist
Simplify the expression 10 + 2(n + 5) + 4n
Answer:
6n + 20
Step-by-step explanation:
10 + 2n + 10 +4n
6n +20
Answer:
[tex]10 + 2n + 10 + 4n \\ 6n + 20 \\ 2(3n + 10)[/tex]
54 1/2-42 3/4
45 3/8- 13 3/4
Answer:
11 3/4
31 5/8
Step-by-step explanation:
1. 54 1/2 - 42 3/4
= 109/2 -171/4
= 218-171/4
= 47/4
= 11 3/4
2. 45 3/8 - 11 3/4
= 363/8 -55/4
= 363-110/8
= 253/8
= 31 5/8
The vector matrix [-3,-5] is rotated at different angles. Match the angles of rotation to the vector matrices they produce.
Answer: The above answer is correct.
Step-by-step explanation: I got this correct on Edmentum.
Answers
[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex], [tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex], [tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex], [tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex], [tex]\theta = \frac{\pi}{2}[/tex]
This exercise consist in finding the resulting Vector Matrix for each Angle of Rotation and a given Vector Matrix. The result is found by multiplying the given Vector Matrix for a Rotation Matrix, defined below as follows:
[tex]A' = R\cdot A[/tex] (1)
Where:
[tex]A[/tex] - Given vector matrix.
[tex]R[/tex] - Rotation matrix.
[tex]A'[/tex] - Resulting vector matrix.
For 2-dimension Vector Matrices, The Rotation Matrix is defined by the following entity:
[tex]R = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\\\end{array}\right][/tex] (2)
Where [tex]\theta[/tex] is the Angle of Rotation, in radians.
Let be [tex]A = \left[\begin{array}{cc}x\\y\end{array}\right][/tex], the resulting vector matrix is found by (1) and (2):
[tex]A' = \left[\begin{array}{cc}\cos \theta&-\sin \theta\\\sin \theta&\cos \theta\end{array}\right] \cdot \left[\begin{array}{cc}x\\y\end{array}\right][/tex]
[tex]A' = \left[\begin{array}{cc}x\cdot \cos \theta - y\cdot \sin \theta\\x\cdot \sin \theta +y\cdot \cos \theta \end{array}\right][/tex]
If we know that [tex]A = \left[\begin{array}{cc}-3\\-5\end{array}\right][/tex], then the resulting vector matrix for each angle is, respectively:
[tex]\theta = \frac{\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}1.414\\-5.657\end{array}\right][/tex]
[tex]\theta = \frac{\pi}{2}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex]
[tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex]
[tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex]
[tex]\theta = \frac{5\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.83\\0.098\end{array}\right][/tex]
[tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex]
Therefore, we have the following answers:
[tex]A' = \left[\begin{array}{cc}5.830\\-0.098\end{array}\right][/tex], [tex]\theta = \frac{2\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}-5.657\\-1.414\end{array}\right][/tex], [tex]\theta = \frac{7\pi}{4}[/tex]
[tex]A' = \left[\begin{array}{cc}-2.83\\5.098\end{array}\right][/tex], [tex]\theta = \frac{4\pi}{3}[/tex]
[tex]A' = \left[\begin{array}{cc}5\\-3\end{array}\right][/tex], [tex]\theta = \frac{\pi}{2}[/tex]
Related question: https://brainly.com/question/11815899
1. Luis went to the bank. He deposited
$20 into his savings account and
withdrew $40 from his checking
account. Write integers to describe
both transactions.
А_______is part of the population chosen to
represent the entire group.
Answer:
mean.
Step-by-step explanation:
since this is a math question i'm assuming you want a mathematical term. the mean of a set of data represents the entire set of data.
factorise ab+cb+ad+cd
Answer:
ab=a×b
cb=c×b
ad=a×d
cd=c×d
Answer:
well the factor: Add and subtract the second term to the expression and factor by grouping. (a+c)(b+d)
Step-by-step explanation:
Hope this is helpful! God Bless you !
Find the area of the triange below
units given are cm, cm^2, cm^3
Answer:
[tex]A=150\ cm^2[/tex]
Step-by-step explanation:
The Hypotenuse of triangle, H = 25 cm
Base = 15 cm
Height = 20 cm
We need to find the area of the triangle. The area of a right-angled triangle is given by :
[tex]A=\dfrac{1}{2}\times b\times h\\\\A=\dfrac{1}{2}\times 15\times 20\\A=150\ cm^2[/tex]
So, the area of the triangle is equal to [tex]150\ cm^2[/tex].
PLS HELP
WILL GIVE BRAINIEST
The points plotted below are on the graph of a polynomial. Which of the
following x-values is the best approximation of a root of the polynomial?
Check all that apply.
A. X-1.1
B. X= 4.3
C. x=2.4
D. X=6
E.X=1
Answer:
I don't know the answer but have a site that helps me with math, its called
Step-by-step explanation:
Just check it out
patterns A and B are generated using these rules pattern a start with 12 and add six pattern be start with 4 and add 2
How many chicks hiding? Explain how you know.
Whats 4 5/6 + 5 7/8 thank you for answering
Answer:
4 5/6 + 5 7/8= 10 17/24
Step-by-step explanation:
pretty sure I answered this exact question like minutes ago
Answer: 257/24, or 10 and 17/24.
Step-by-step explanation:
First, we need to turn the fractions into improper fractions and then find the common denominator.
4 and 5/6 = 29/6
5 and 7/8 = 47/8
The common denominator is 24. Now, we convert the fractions and add. Hope this helps!
I am confused on how to solve this. NOTE: the lower limit for the second function is (-6) NOT 6. Wouldn't let me type it in correctly.[tex]\int\limits^6_3 {|x-4|} \, dx + \int\limits^0_6 {\sqrt{36-x^2} } \, dx[/tex]
I think how you approach this depends on your knowledge of calculus.
If you don't know how to compute definite integrals yet, but you do know that they represent signed areas under curves, then you can plot both curves |x - 4| and √(36 - x ²), then recognize that the areas represented by these integrals are areas of geometric shapes. (See attached images)
First integral: if you plot |x - 4| on the interval [3, 6], you'll see that the integral corresponds to the area of two triangles. One of them has base = height = 1, and the other has base = height = 2. Then
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac12\times1\times1+\frac12\times2\times2=\frac52[/tex]
Second integral: if [tex]y=\sqrt{36-x^2}[/tex], then [tex]x^2+y^2=6^2[/tex], meaning this curve is the upper half of a circle with radius 6. On the interval [-6, 0], the area amounts to 1/4 of the total area of such a circle, so that
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\frac{\pi\times6^2}4=9\pi[/tex]
* * *
If you already know a few things about calculus and integration, you can compute these areas directly.
First integral:
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\int_3^4(4-x)\,\mathrm dx+\int_4^6(x-4)\,\mathrm dx[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(4x-\frac{x^2}2\right)\bigg|_{x=3}^{x=4}+\left(\frac{x^2}2-4x\right)\bigg|_{x=4}^{x=6}[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(\left(4\times4-\frac{4^2}2\right)-\left(4\times3-\frac{3^2}2\right)\right)+\left(\left(\frac{6^2}2-4\times6\right)-\left(\frac{4^2}2-4\times4\right)\right)[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac52[/tex]
Second integral:
Substitute x = 6 sin(t ) and dx = 6 cos(t ) dt, then
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\int_{-\frac\pi2}^0\sqrt{6^2-(6\sin(t))^2} (6\cos(t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{1-\sin^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{\cos^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) |\cos(t)| \,\mathrm dt[/tex]
For t ∈ [-π/2, 0], cos(t ) > 0, so |cos(t )| = cos(t ) :
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos^2(t)\,\mathrm dt[/tex]
Recall the half-angle identity,
cos²(t ) = (1 + cos(2t )) / 2
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\int_{-\frac\pi2}^0(1+\cos(2t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(t+\frac{\sin(2t)}2\right)\bigg|_{t=-\frac\pi2}^{t=0}[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(\left(0+\frac{\sin(2\times0)}2\right)-\left(-\frac\pi2+\frac{\sin\left(2\times\left(-\frac\pi2\right)\right)}2\right)\right)[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=9\pi[/tex]
Can someone help with these questions?
¿Alguien puede ayudar con estas preguntas?
9514 1404 393
Answer:
63/94$6857.14Step-by-step explanation:
a) The fraction is ...
2(5 1/4)/(15 2/3) = (21/2)/(47/3) = 63/94
Two streamers will require 63/94 of the original material.
__
b) $4800 is 70% of Sara's salary, so that salary is ...
4800 = 0.70s
4800/0.70 = s = 6857.14
Sara's salary is about $6857.14.
You roll a number cube twice. What is the probability of rolling a 2 first and then rolling an odd number?
A) 1/12
B) 1/36
C) 1/4
D) 1/9
Log x^4-logx^3=log 3x-log2x solve
Answer:
x = 3/2
Step-by-step explanation:
Log x^4-logx^3=log 3x-log2x solve
log(x^4/x^3) = log(3x/2x)
Log cancels out
x^4/x^3 = 3x/2x
x^3 * x/x^3 = 3/2
x^3/x^3 * x = 3/2
x = 3/2
Hence the required value of x is 3/2
Laurent is preparing a fruit salad. She wants the total carbohydrates from pineapple and watermelon to equal 24 g. Pineapple has 3 g of carbohydrates per ounce and watermelon has 2 g of carbohydrates per ounce. Write and graph an equation to model this situation.
Answer:
3x+2y=24
Step-by-step explanation:
I made the x value be the pineapples and the y value be the watermelon. And it said in the problem that it should equal 24g so I made it equal 24. Next You would need to find the x and y intercepts in order to graph it.
2y=24 and 3x=24, so x=8 and y=12. Now unfortunately I can't add a graph here but if you input those intercepts in an app like desmos or photomath, you'll get a graph. Hope this helps!
Can someone please help meee
Answer:
20
Step-by-step explanation:
Because this angle is 90 and we have 70
If h(x) = sqrt 7 + 6f(x), where f(3) = 7 and f '(3) = 4, find h'(3).
Answer:
we should find the value of h(3) and do invers
Evan uses 1/3 of his tickets to ride the loop-d-loop. how many tickets does he use?
Answer: 1/3 of 24 tickets is 8
Step-by-step explanation:
1/3 of 24 is 8.
The way I usually find this is by multiplying different numbers by three and seeing if it equals (in this case) 24.
8 x 3 = 24
Because eight goes into twenty-four three times, eight is one-third of twenty-four.
Hope this helps✨
Rounding to the first decimal place, calculate the mean for the following distribution of homicide rates in the 12 metropolitan areas with the lowest homicide rates (homicides per 100,000 population) in the U.S. in 2017.
Mesa, AZ: 4.1 Seattle, WA: 3.8 Portland, OR (tie): 3.4 New York, NY (tie): 3.4 Virginia Beach, VA: 3.3 San Jose, CA: 3.1 El Paso, TX: 2.9 Austin, TX: 2.6 San Diego, CA: 2.4 Suffolk County, Long Island, NY: 2.2 Montgomery County, MD: 2.0 Fairfax, VA: 1.7
Solution :
Given :
X = homicide rate (homicides per 100,00 population)
n = 12 = metropolitan areas
Area X (homicides per 100,000 population)
Mesa, AZ 4.1
Seattle, WA 3.8
Portland, OR (tie) 3.4
New York, NY(tie) 3.4
Virginia beach, VA 3.3
San Jose, CA 3.1
EI, Paso, TX 2.6
Austin, TX 2.6
San Diago, CA 2.4
Suffolk County 2.2
Montgomery, MD 2.0
Fairfax, VA 1.7
Therefore, the mean of X = [tex]$\bar X = \frac{\sum X_i}{n}$[/tex]
[tex]$=\frac{34.9}{12}$[/tex]
= 2.9
Therefore, the mean of homicide rater in the 12 metropolitan areas is 2.9 homicide per 100,000 population.
What is the slope and y-intercept of the line whose equation is y + 4x =
8?
Answer:
The slope is -4 and the y-intercept is 8.
Step-by-step explanation:
y+4x=8
y=8-4x
y=-4x+8
y=mx+b where m=slope and b=y-intercept.
Hello!
The equation of this line is written in slope-intercept form (y=mx+b)
Where
m is the slope
b is the y-intercept
m is 4
b is 8
Hope it helps!
If you have any questions, feel free to ask! :)
~An excited gal
[tex]MagicalNature[/tex] here to help
true or false help please pre cal
Answer:
True
Step-by-step explanation:
Please help!
Note that common contexts are listed toward the top, and less common contexts are listed toward the bottom. According to O*NET, what are common work contexts for Film and Video Editors? Check all that apply.
(1) extremely bright or inadequate lighting
(2) spend time sitting
(3) exposed to disease or infections
(4) indoors, environmentally controlled
(5) face-to-face discussions
(6) deal with physically aggressive people
Answer:
2,4,5 got it right on egde2021
Step-by-step explanation:
Before dividing, decompose 420 to make it easier to divide by 4.
what is the greatest common factor of 10, 30 and 45
Answer:
5
Step-by-step explanation:
Which inequalities will have an open circle at -3
Find the slope on the line.
Answer: -2 is the slope
(0,0) (1,4) (rise over run) *Y2 - Y1/X2 - X1*
X1= 0
Y1= 4
X2= 1
Y2= 2
2-4= -2
1-0= 1
-2/1= -2
the slope is -2
PLS help i've been trying this for an hour i still don't get it
Layla is saving money to buy a bicycle that costs $249. She has already saved $193. She saves
$7 each week. Which inequality shows the solution set for the number of weeks that Layla will
need to save money to be able to buy the bicycle?
Answer: It would take her another 8 weeks to get a total of $249.
Step-by-step explanation: