Answer:
The probability that the target will be detected at least once in n surveillance cycles is given by the following expression: [tex]1 - (1-p_0+p(p_1-p_0))^{n}[/tex]
Step-by-step explanation:
For each surveillance cycle, there are only two possible outcomes. Either it detects the target, or it does not. Cycles are independent. This means that the binomial probability distribution is used to solve this question:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
Probability of detecting a target:
p0 of 1-p (without interference)
p1 of p(with interference). So
[tex]\pi = p_0(1-p) + p_1p = p_0 + p(p_1-p_0)[/tex]
Find the probability that the target will be detected at least once in n surveillance cycles.
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}[/tex]
[tex]P(X = 0) = C_{n,0}.(p_0+p(p_1-p_0))^{0}.(1-p_0+p(p_1-p_0))^{n} = (1-p_0+p(p_1-p_0))^{n}[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - (1-p_0+p(p_1-p_0))^{n}[/tex]
The probability that the target will be detected at least once in n surveillance cycles is given by the following expression: [tex]1 - (1-p_0+p(p_1-p_0))^{n}[/tex]
Which condition would prove ΔJKL ~ ΔXYZ?
The condition that will prove the two triangles similar is
side JL = 8 * side ZX
angle L = angle Z
What are similar triangles?Similar triangles are triangles which have the similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.
This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.
In the figure, the scale is 8
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What are the solutions to the system of equations graphed?
Answer:
(- 2, 0 ) , (1, - 3 )
Step-by-step explanation:
the solutions to the system of equations are at the points of intersection with the curve and the straight line.
points of intersection are at (- 2, 0 ) and (1, - 3 ) , then
solutions are (- 2, 0 ) , (1, - 3 )
Olivia, Muhammad, and Cameron had a challenge to see who could bike the farthest in one day. Olivia biked 8 miles, Muhammad biked 2 times as many miles as Cameron and Cameron biked 4 times as many miles as Olivia. How many miles did Muhammad bike?
Answer:
Muhammad biked 64 miles
Step-by-step explanation:
Olivia biked 8 miles.
Cameron biked 4 times as many miles as Olivia, and Muhammad biked 2 times as many miles as Cameron.
Cameron: 4 x 8 = 32
Cameron biked 32 m.
Muhammad: 32 x 2 = 64
Muhammad biked 64 miles.
every year 5 rows and 5columns are increased . derive the formula for the number of students in each row
The number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.
Assuming that the increase in rows and columns is uniform every year, we can derive the formula for the number of students in each row as follows:
Let's start with the initial number of rows and columns, which we'll call R0 and C0, respectively, and the number of students in each row, which we'll call S.
After one year, the number of rows and columns will increase by 5, so we'll have R1 = R0 + 5 and C1 = C0 + 5. The total number of students will be R1 x S. We can also express this in terms of the initial number of rows and columns as:
R1 x S = (R0 + 5) x S
Expanding the brackets, we get:
R1 x S = R0 x S + 5 x S
Subtracting R0 x S from both sides, we get:
(R1 - R0) x S = 5 x S
Dividing both sides by 5 x (R1 - R0), we get:
S = 5 / (R1 - R0)
We can use this formula to calculate the number of students in each row after any number of years, as long as the increase in rows and columns is uniform every year.
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What is the domain of the function
Answer:
xs7
Step-by-step explanation:
A small toy rocket is launched from a 48-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t2 +0t + 48. How long will it take the rocket to hit the
ground?
t =
Okay, here are the steps to solve this problem:
1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48
2) We want to find the time (t) when the rocket hits the ground (h = 0)
3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0
4) Factor the left side: - 3(t2 - 0t) + 48 = 0
5) Solve for t2 - 0t: t2 - 0t = 16
6) Add 0t to both sides: t2 = 16 + 0t
7) Take the square root of both sides: t = 4
Therefore, the time for the rocket to hit the ground is 4 seconds.
So in this case, t = 4
Let me know if you have any other questions!
Answer:
4 seconds.
Step-by-step explanation:
When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]
Now set this equal to 0
[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.
[tex]-48 = -3t^2[/tex]
[tex]16 = t^2[/tex]
From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.
Hope this helps
Mary has a lemonade stand.Last week she spent $18.00 on supplies,but earned only $12.00.Did Mary make a profit ?Explain and show problem as a mathematical equation.
They need to sell at least 13 cups to gain profits.
Here, we have,
Givens
The initial cost is $1.20.
Each cup of lemonade costs 6 cents to make.
May's children sell 10 cents a cup.
First, we need to represents the cost of their investment.
0.06x = 1.20, because each cup costs 6 cents, and the initial costs of all is $1.20.
That means,
x= 20
They can produced 20 cups.
However, they already sell a cup for 10 cents. So, how many cups they need to sell to gain profits? We need to establish a similar relation,
0.10 x = 1.20
x = 12
This means if they sell 12 cups, they will just cover the investment, that is, zero profits.
Therefore, they need to sell at least 13 cups to gain profits.
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complete question
Mary's children decide to run a lemonade stand to earn some extra money.The cost to start the business is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup,how many cups must Mary's children sell to make a profit?----Apply systems of equations
A chambered nautilus is a marine animal that lives in the outermost chamber of its shell
The chambered nautilus is a fascinating marine animal that belongs to the family of cephalopods.
It is notable for its unique, spiral-shaped shell that is divided into a series of chambers.
The nautilus lives in the outermost chamber of its shell, which it can control by adjusting the amount of gas and fluid inside it. This allows the nautilus to regulate its buoyancy and move up or down in the water column.
The nautilus has been around for millions of years and is sometimes called a "living fossil" because of its ancient lineage.
Unfortunately, due to overfishing and habitat destruction, many species of nautilus are now endangered.
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The given question is incomplete, the complete question is:
A chambered nautilus is a marine animal form which family?
The cosine of θ is −0.95. What is sin(θ)?
The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.
cos(θ) = -0.95
To calculate the value of sin(θ), we can use the Pythagorean theorem:
[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1
We can rearrange the Pythagorean identity to solve for sin(θ):
[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)--------- (equation 1)
Substitute the value of the cosine of θ = −0.95 in Equation 1
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)
sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]
sin(θ) = ±[tex]\sqrt{0.0975}[/tex]
The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.
sin(θ) = [tex]\sqrt{ 0.0975}[/tex]
sin(θ) = 0.312
Therefore, we can conclude that the value of sin(θ) is 0.312.
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Ciara needs 4 yards of fabric for a dress. She already had 2 1/4 yards of fabric Convert 32/5 to a mixed number
Can someone help me with this problem please
Suppose M is a matrix of size 9x10, c is a scalar, and the matrix computation cM is defined. What is the size of matrix cM?
----------------
If the size of matrix "M" is 9×10, and a scalar "c" is multiplied by matrix, then the size of "cM" will be 9×10.
We know that when a scalar is multiplied to a matrix, each element of the matrix gets multiplied by that scalar.
In this case, the scalar "c" is multiplied with the Matrix "M";
So if a scalar "c" is multiplied by a matrix "M" of size 9×10, then the resulting matrix "cM" will also have the same number of rows and columns as the original matrix "M".
Therefore, the size of "cM" will also be 9×10.
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Work out the area of the shaded shape on the millimetre (mm) grid.
State the units with your answer.
The diagram is not drawn to scale.
The requried area of the shaded shape is 5 square millimeters.
From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:
= 5 * 1 = 5 square millimeters.
Thus, the requried area of the shaded shape is 5 square millimeters.
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please help with geometric series
Answer:
[tex]C. -5.15\cdot10^{13}[/tex]
Step-by-step explanation:
[tex]Common\ ratio\ (r)=\frac{a_{n+1}}{a_n}=(-3)\\\\Sum\ (S_n)=\frac{a(r^n-1)}{r-1}\ \ (r\neq1)\\\\\implies S_n=\frac{1\ (\ (-3)^{30}-1\ )}{-4}\\\\\implies S_n=\frac{205891132094649-1}{-4}\\\\\approx\frac{206\cdot10^{12}}{-4}\\\\\approx-5.15\cdot10^{13}[/tex]
A triangle has side lengths of 13, 18, and 24. Is it a right triangle?
Answer:
No, it is not a right triangle.
[tex] \sqrt{ {13}^{2} + \ {18}^{2} } = \sqrt{169 + 324} = \sqrt{493} [/tex]
√493 is not equal to 24.
Answer:
it doesn't
Step-by-step explanation:
it doesn't follow pythagoras theorem
a² = b² + c²
S and P are the midpoints of the
legs, RT and QU, of trapezoid QRTU.
If QR
TU =
X?
= -6x + 37, PS = x + 33, and
= 2x + 41, what is the value of
The value of x in the trapezoid is 2.
How to find the side of a trapezoid?The mid points of a trapezoid is a line that goes across from the middle of one leg to the middle of the other leg.
Using the mid point theorem, let's find the value of x in the trapezoid as follows:
PS = 1 / 2 (QR + TU)
PS = x + 33
QR = -6x + 37
TU = 2x + 41
Therefore,
x + 33 = 1 / 2 (-6x + 37 + 2x + 41)
x + 33 = 1 / 2 (-4x + 78)
x + 33 = -2x + 39
x + 2x = 39 - 33
3x = 6
divide both sides by 3
x = 6 / 3
x = 2
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The nth term of an arithmetic sequence is given by un=15-3n.
a. [1 mark] State the value of the first term, u1.
b. [2 marks] Given that the nth term of this sequence is -33, find the value of n.
c. [2 marks] Find the common difference, d.
a. The first term of the arithmetic sequence is 12.
b. The value of n for which the nth term is -33 is 16.
c. The common difference of the arithmetic sequence is -3.
a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:
u1 = 15 - 3(1) = 12
b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:
un = 15 - 3n = -33
Adding 3n to both sides, we get:
15 = -33 + 3n
Adding 33 to both sides, we get:
48 = 3n
Dividing both sides by 3, we get:
n = 16
c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:
u2 = 15 - 3(2) = 9
u1 = 15 - 3(1) = 12
d = u2 - u1 = 9 - 12 = -3
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2) Factor by CTS: x² +12
please show work
The factored form of x² + 12 using the difference of squares formula is
(x + 2√3)(x - 2√3).
We have,
To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:
x² + 12 = x² + (2√3)²
Now we can use the difference of squares formula, which states that:
a² - b² = (a + b)(a - b)
In this case, we have a = x and b = 2√3. So we can write:
= x² + 12
= x² + (2√3)²
= (x + 2√3)(x - 2√3)
Therefore,
The factored form of x² + 12 using the difference of squares formula is
(x + 2√3)(x - 2√3).
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Which equation can be used to solve for � xx in the following diagram?
Equation which can be used to solve for the value of x is
3x° + 2x° + 80 °= 180° .
Straight angle pair is the sum of two or more angles that are in pair of angles that form a straight line is always equal to 180°.
As shown in the diagram angle on the lines are -
3x ° , 80° , 2x° respectively
Sum of all these angle will be equal to 180°.
3x° + 2x° + 80° = 180
The correct equation to find the value of x is 3x° + 2x° + 80° = 180° .
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An Inverse Variation Includes The Points(3, 3)and(1, n).Find
n .
The inverse variation is y = 9/x, using that equation we can see that n = 9.
How to find the value of n?An inverse variation between two variables x and y can be written as:
y = k/x
Where k is a constant.
We know that this inverse variation contains the point (3, 3), replacing these values we have:
3 = k/3
3*3 = k
9 = k
Then the inverse variation is:
y = 9/x
Now we want to find n such that (1, n) is on the relation above, then we will get:
n = 9/1
n = 9
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Is this negative and odd or even and positive or negative and even and positive and odd?
Answer:
Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load
Step-by-step explanation:
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What is the measure of this angle?
60
80
120
125
Answer:
60
Step-by-step explanation:
180 - 120 = 60
Can someone help me with this? Thank you
The area of the triangle is 6 sq units.
What is the area of the triangle?The area of the triangle is calculated by applying the following formula;
A = ¹/₂ x b x h
where;
b is the base of the triangleh is the height of the triangleThe base of the triangle = 3 - 0 = 3
The vertical height of the triangle = 5 - 1 = 4
Area = ¹/₂ x 4 x 3
Area = 6 sq units.
Thus, the area of the triangle is a function of base and height.
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You are considering a 5/1 ARM. What does the 1 represent?
A. The total number of years in the loan
B. The number of years that a fixed interest rate will be applied to the
loan
OC. The number of years between adjustments in the interest rate
D. The interest rate of the initial, fixed-rate loan period
SUBMIT
As far as a 5/1 ARM is concerned, note that the "1" refers to how often the rate can be adjusted after the initial fixed-rate period ends.
What is 5/1 ARM?A 5/1 ARM is an adjustable rate mortgage loan (ARM) that has a fixed interest rate for the first five years. Following that, the 5/1 ARM transitions to an adjustable interest rate for the remainder of its term. The terms "variable" and "adjustable" are frequently used synonymously.
If you want a low monthly payment and don't expect to stay in your house for long, a 5/1 adjustable-rate mortgage (ARM) loan may be worth considering. For the first five years, rates on 5/1 ARMs are typically lower than rates on 30-year fixed-rate mortgages.
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The community health clinic you volunteer for aims to develop a strategy allowing the most vulnerable members of the community to have first access to the Flu vaccine. The clinic has collected data finding that the total number of people in their service area is 50,000, 27% of the community is over the age of 65 and immunocompromised, and 11% of the community under 65 is immunocompromised. While the clinic wishes to market to all members of the community, immunocompromised people over 65 are their current priority.2. Explain in a one well-written paragraph, how you will analyze the data in this scenario to arrive at the answer you will provide in number 2.
In order to understand and prioritize the vaccination strategy for the community health clinic, first accurately assess the demographics of the community based on the data provided.
How to analyze the data ?Calculating the absolute numbers of people in each group: over 65 and immunocompromised, and under 65 and immunocompromised. For this, we'll apply the given percentage to the total population of 50,000.
Knowing the total number of people in each category will help us understand the size of each target group and prioritize accordingly. The clinic's current priority is immunocompromised people over 65, so having the exact figure will aid in planning for vaccine supply and outreach strategies.
Furthermore, the analysis of this data can also aid in projecting the needs for future vaccine campaigns for the remaining community members. Finally, this detailed analysis will help in crafting an effective communication plan that emphasizes the clinic's priority of serving the most vulnerable first, while still acknowledging the needs of all community members.
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Find the y intercept for a line with a slope or 2 that goes through (5, 4)
Answer:
y- intercept = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (5, 4 ) into the partial equation
4 = 2(5) + c = 10 + c ( subtract 10 from both sides )
- 6 = c
that is the y- intercept c = - 6
please answer all 3 questions
1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ
2. His stamp should be worth approximately $7,851.47 after 6 years.
3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵
How did we get our values?1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:
y = 81 x (¹/₃)ˣ
2. The increase in value of the stamp can be calculated using the formula:
V = P(1+r)ᵗ
where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.
Substituting the given values:
V = 4900(1+0.075)⁶
V ≈ $7,851.47
Therefore, the stamp should be worth approximately $7,851.47 after 6 years.
3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:
y = (1/16) x 2²ˣ ⁺ ⁵
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60% of the books in a library are for adults, 5% are for young people and the rest are for children. If there are 280 books for children, how many books are there altogether?
Answer:
800 books
problem solving steps：
adults:60%
young people:5%
children=100%-60%-5%
=35%
35%=280 books
1%=280÷35
=8
100%=800
so,there are 800 books
Find the greatest common factor of 56xy and 16y³.
Answer:
8y
Step-by-step explanation:
Lets put these two parts into addition to make it easier.
(y)56x + 16y^2
(8y)7x + 2y^2
8y is the GCF(grates common factor)
209 g = ___ kg
0.0209
0.209
20,900
209,000
Following is a table for the present value of an annuity of $1 at compound interest