The number of fish in a small bay is modeled by the function F defined by F(t)=10 (t3 â 12t2 + 45t +100), where t is measured in days and 0
(a) Using correct units, interpret the meaning of F' (4)= -30 in the context of the problem.
(b) Based on the model, what is the absolute minimum number of fish in the bay over the time interval 0
(C) For what values of t, 0
(d) For 0
Answers
The graph of the given function is attached showing characteristics of the function.
The correct responses are;
(a) F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at a rate of 30 fish per day.(b) Over the interval 0 ≤ t ≤ 8 the absolute minimum number of fish in the bay is; 1,000.(c) The values of t at which the rate of change is decreasing is; 3 ≤ t ≤ 8(d) The rate of change of the number of pelicans flying near is; P' = 10·(3·c² - 24·c + 45)Reasons:
The given function is; f(t) = 10·(t³ - 12·t² + 45·t + 100)
Where;
t = Number of days
0 ≤ t ≤ 8
(a) The derivative of the given function is presented as follows;
F'(t) = 10 × (3·t² - 2×12·t + 45) = 10·(3·t² - 24·t + 45)
Therefore;
F'(4) = 10 × (3 × 4² - 24 × 4 + 45) = -30
Therefore F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at 30 fish per day.
(b) The absolute minimum is given as follows;
At a minimum or maximum value, F'(t) = 10·(3·t² - 24·t + 45) = 0
Which gives;
3·(t - 5)·(t - 3) = 0
t = 5, or t = 3
At t = 5, we have;
f(5) = 10 × (5³ - 12 × 5² + 45 × 5 + 100) = 1,500
At t = 3, we have;
f(3) = 10 × (3³ - 12 × 3² + 45 × 3 + 100) = 1,540
Therefore, f(5) = 1,500 is a local maximum
However, at x = 0, we have;
f(0) = 10 × (0³ - 12 × 0² + 45 × 0 + 100) = 1000
At x = 8, we have;
f(8) = 10 × (8³ - 12 × 8² + 45 × 8 + 100) = 2,040
Therefore, the absolute minimum is given at t = 8, where f(t) = 1,000
(c) The values of t at which the rate of change in the number of fish in the
bay is decreasing is between the local maximum at t = 3, and the local
minimum at t = 5, which gives;
The rate of change of the number of fish is decreasing for values of t in the range;
3 ≤ t ≤ 5(d) P = 10·(t³ - 12·t² + 45·t + 100)
P' = 10·(3·t² - 24·t + 45)
At time t = c, we have;
P' = 10·(3·c² - 24·c + 45)Based on a similar question online, we have;
(c) The interval over which the rate of change is decreasing
(d) The rate of change of the number of pelicans flying near the bay at t = c
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Related Questions
The temperature in Birmingham is 5°C colder than in London ( London temperature is 6 ). What is the temperature in Birmingham
Answers
Answer:
1˚C
Step-by-step explanation:
First, you take 5 away from 6
5 = 5°C colder than in London
6 = The temperature in London
1ºC. 6 minus 5 equals 1.
and also that is quite easy for high school.
Which table shows a proportional relationship between x and y?
Answers
Answer:
The 2nd table.
Step-by-step explanation:
It is the only one that makes sense.
Please mark me brainliest I need it!!!!
Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models (this is the product mix). The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.’s sales product mix for a week is?
Answers
Each model should be produced on a weekly basis to maximize net profit is $75,900.
What is Net profit?
In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.
As given,
Number of products sold:
T ≥ 1.5G
Maximize Profit Z = 150T + 130G
Labor Constraint:
Labor hours Available:
Production Department:
Number of labor hours available per day = 58 × 7 = 406
Number of days in a week = 5
Number of lobor ours available per week = 406 × 5 = 2030
Assembly Department:
Number of labor hours available per day = 25 × 7 = 175
Number of days in a week = 5
Number of labor hours available per week = 175 × 5 = 875.
Labor hours Required:
Labor hours required for G1 model:
Labor hours required at Production department = 3.5G
Labor hours required at assembly department = 2G
Labor hours required for T1 model:
Labor hours required at Production department = 4T
Labor hours required at Assembly department = 1.5T
Total labor hours required at Production department = 3.5G + 4T
Total labor hours required at Assembly department = 2G + 1.5T.
Constraint:
Labor hours required ≤ Labor hours Available.
Production department Labor constraint
3.5G + 4T ≤ 2030
Assembly department Labor constraint:
2G + 1.5T ≤ 875
The function:
Maximum Profit Z = 150T +130G
Constraint:
3.5G +4T ≤ 2030
2G + 1.5T ≤ 875
T ≥ 1.5G
Suppose that for example:
10.5G +12T = 6090
16G + 12T = 7000
Solve both equations simultaneously,
5.5G = 7000 - 6090
5.5G = 910
G = 910/5.5
G = 363
Since, T > G
Hence,
T = 363,
G = 165
Calculate Profit:
150T + 130G = 150 × 363 + 130 × 165
= 54450 + 21450
= 75900
Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.
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a person leaves home and walks 4 miles west, then 5 miles southwest. how far from home is she? miles in what direction must she walk to head directly home? degrees north of east
Answers
The person is 8.325 miles far from her home and she should walk in the direction of 64.86° North Of East to head directly home .
In the question ,
from the figure ,
we see that point O is home of the person ,
it is given that person leaves the home and walks 4 miles west to point A , then 5 miles in south west direction to the point B .
So ,distance OA = 4 miles
AB = 5 miles .
In triangle OAB ,
angle OAB = 45+90 = 135°
Using Cosine Rule ,
OB² = OA² + AB² - 2*OA*AB*Cos(135)°
= 16 + 25 + 28.2843 = 69.2843
So ,OB = √69.2843 = 8.325 miles .
Now using Sine Rule ,
Sinθ/OA = Sin(135°)/OB
Sinθ = 4*Sin(135°)/8.324
Sinθ = 0.339792
So , θ = 19.86°
hence the direction from North of East is
= 45° + θ
= 45° + 19.86°
= 64.86° North Of East .
Therefore , the distance is 8.325 miles and the direction is 64.86° North Of East .
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The equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds
of apples. What does the number 4.3 represent in the equation?
Answers
the 4.3 represents The number of apples in 1 pound
The 4.3 in the equation represents the number of apples in 1 pound
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds of apples.
Here we can see that y = 4.3x
4.3 = y/x
then we can say that 4.3 is slope of striaght line in term os linear equation.
4.3 in the equation represents the number of apples y, in dollars, of x pounds.
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To make a batch of four dozen cookies, Denis needs 1 3/4 cups of four, 1 cup of sugar, and 1/3 cup of milk. Calculate the amount of each ingredient that Denis needs to make 12 dozen cookies
Answers
Answer:
Flour = 5 1/4 Cups
Sugar = 3 Cups
Milk = 1 Cup
Step-by-step explanation:
4 Dozens = Respectively 1 3/4, 1, and 1/3 Cups -->
4(3) = 12 Dozens --> Otherwise A Gross
--> Multiply the formula by 3
7/4 x 3 = 21/4
1 x 3 = 3
1/3 x 3 = 1
Convert to a mixed number
Thus You have your answers
Hope this helps!
suppose and are two vectors that form the sides of a parallelogram. then the lengths of the two diagonals of the parallelogram are . separate answers with a comma.
Answers
The lengths of the two diagonals of the parallelogram are D1 and D2, where:
D1 = ||A + B||
D2 = ||A - B||
Let's denote the vectors as vector A and vector B. The lengths of the two diagonals of the parallelogram can be calculated using vector operations.
The length of the first diagonal (D1) can be calculated using the formula:
D1 = ||A + B||
The length of the second diagonal (D2) can be calculated using the formula:
D2 = ||A - B||
Here, ||A|| represents the magnitude (length) of vector A, and ||B|| represents the magnitude of vector B.
Therefore, the lengths of the two diagonals of the parallelogram are D1 and D2, where:
D1 = ||A + B||
D2 = ||A - B||
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In a sport is added time played at the end of the match
Answers
Answer:
depending on what is happening then ye
Step-by-step explanation:
2 . let r be noetherian and let b be an r-module satisfying the ascending chain condition on submodules. then the following are equivalent : (i) there exists exactly one associated prime of b (see exercise 9); (ii) b 0 and for each r e r one of the fol lowing is true: either rx = 0 implies x = 0 for all x e b or for each x e b there exists a positive integer n(x) such that r" dx>x = 0.
Answers
The statements (i) and (ii) are equivalent in the given context. To prove the equivalence of the statements (i) and (ii) in the given context, we'll use the definitions and properties related to Noetherian modules and associated primes.
Let's proceed with the proof.
Statement (i): There exists exactly one associated prime of b.
Statement (ii): b ≠ 0, and for each r ∈ r, one of the following is true: either rx = 0 implies x = 0 for all x ∈ b, or for each x ∈ b, there exists a positive integer n(x) such that rⁿ(x) · x = 0.
We'll first prove that (i) implies (ii).
Proof: (i) ⟹ (ii)
Assume that there exists exactly one associated prime of b. Let P be this associated prime.
Since r is a Noetherian ring and b is a Noetherian r-module satisfying the ascending chain condition on submodules, we know that b can be written as the intersection of its primary components:
b = ∩\((P_i)b_i\),
where P_i are the associated primes of b and \(b_i\) are the corresponding primary components. In this case, there is only one associated prime, P, so we have:
b = (P)b',
where b' is the primary component associated with P.
Now, consider an element r ∈ r. We need to show that one of the following holds for any x ∈ b:
(i) rx = 0 implies x = 0, or
(ii) There exists a positive integer n(x) such that rⁿ(x) · x = 0.
Let's consider the element x ∈ b.
Since b = (P)b', x ∈ (P)b'. By the definition of primary components, this means that for some positive integer n(x), Pⁿ(x) · x = 0.
Now, if r · x ≠ 0, then r does not belong to the associated prime P. Since P is the only associated prime of b, it means that r does not belong to any associated prime of b.
Therefore, rx = 0 implies x = 0, satisfying (i).
Hence, (i) implies (ii).
Next, we'll prove that (ii) implies (i).
Proof: (ii) ⟹ (i)
Assume that b ≠ 0 and for each r ∈ r, one of the following holds:
(i) rx = 0 implies x = 0 for all x ∈ b, or
(ii) There exists a positive integer n(x) such that rⁿ(x) · x = 0 for each x ∈ b.
We need to show that there exists exactly one associated prime of b.
Let P be any prime ideal of r such that P ∈ As(r/b). We'll show that there exists a unique prime ideal P' such that P' ∈ As(b).
Consider the localization of the ring r with respect to P, denoted as \(r_P\). Similarly, consider the localization of the module b with respect to P, denoted as b_P.
Since b ≠ 0, there exists an element x ∈ b that is not zero. Now, by assumption (ii), there exists a positive integer n(x) such that rⁿ(x) · x = 0.
Consider the element r ∈ r. If r · x = 0, then by assumption (i), we have x = 0, which contradicts our choice of x. Therefore, r · x ≠ 0.
Now, let's consider the localization of the equation \(r^n(x) x = 0\) with respect to P. We have:
\((r_P)^n(x_P) x_P = 0\).
Since r · x ≠ 0, it follows that \((r_P) x_P \neq 0\) in the localized module \(b_P\).
Therefore, the element r_P does not belong to the annihilator of \(x_P\) in b_P, which means that the localized prime ideal P_P does not belong to the associated primes of b_P.
Since this holds for any prime ideal P ∈ As(r/b), it implies that there are no associated primes of \(b_P\).
Now, consider the inverse image of \(P_P\) under the natural projection from b to \(b_P\). Let's denote this prime ideal as P'. We claim that P' is the associated prime of b.
To prove this, we need to show that for any x ∈ b, if x_P = 0 in b_P, then x belongs to P'.
Let x ∈ b be such that x_P = 0 in b_P. This means that there exists an element r ∈ r - P such that r · x = 0.
By assumption (ii), we have two cases:
Case 1: rx = 0 implies x = 0 for all x ∈ b.
In this case, since r · x = 0, it follows that x = 0. Hence, x belongs to every prime ideal, including P'.
Case 2: There exists a positive integer n(x) such that rⁿ(x) · x = 0 for each x ∈ b.
Since r · x = 0, we have rⁿ(x) · \(x = r^{(n-1)}(x) (r x) = 0\). By induction, we can show that rⁿ(x) · x = 0 implies r · x = 0. Thus, we reach a contradiction because r was chosen to be outside the prime ideal P.
Therefore, in both cases, x belongs to P'.
Hence, we have shown that there exists a unique prime ideal P' such that P' ∈ As(b).
Since this holds for any prime ideal P ∈ As(r/b), it implies that there exists exactly one associated prime of b.
Therefore, (ii) implies (i).
Combining both directions of the proof, we conclude that the statements (i) and (ii) are equivalent.
Thus, we have established the equivalence between the statements (i) and (ii) in the given context.
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The info is in the picture
Answers
Answer:
no it isn't the inverse.
Find the measure of the missing angle.
Answers
Answer:
Hi
U should do like this
90-51=39...
Answer: 39 degrees
Step-by-step explanation:
Right angle is 90 degrees so 51 plus a will equal 90
A is 39 degrees
In physics lab, you measure three quantities: x, y, and z. Suppose that x=2.5 kg, y=0.8 m, and z=4.9 kg/m. Which of the mathematical combinations might be meaningful?(x/y) - z(x/z) - yx+y+z(xz) + yxyzx - (y/z)xy/z(x-y)/z
Answers
not meaningful: x+y+z, x - (y/z), (x-y)/z, (xz) + y
In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:
(x/y) - z(x/z) - yx - (yz)In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.
Based on the given quantities' scale, we know that x, y, and z have a relationship where:
z = x/y
Then, the mathematical combinations that might be meaningful are:
- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
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working together, it takes two different sized hoses 40 minutes to fill a small swimming pool. if it takes 60 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Answers
It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.
Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40
Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60
Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60
The amount of swimming pool filled in 1 minute = (60 - 40)/2400
The amount of swimming pool filled in 1 minute = 20/2400
The amount of swimming pool filled in 1 minute = 1/120
Total time taken to fill swimming pool = 1 ÷ (1/120)
Total time taken to fill swimming pool = 120 minutes
Thus, 120 minutes are required.
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The histogram shows the number of broken light bulbs in each shipment a retail chain received from the manufacturer. The histogram represents how many shipments
Answers
Answer:
its 16
Step-by-step explanation:
on the graph just count how many shipments they had like 1-10 it was at 4 at 11-20 it was at 5 at 21-30 was at 4 at 31-40 was at 1 and 41-50 was at 2 so just add all of though's together 4+5+4+1+2= which gives 16
Answer:
16
Step-by-step explanation:
If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.
Answers
Answer: \(26.4\ \text{days}\)
Step-by-step explanation:
Given
Half life of radioactive substance is \(T_{\frac{1}{2}}=20\ \text{days}\)
Initial amount \(A_o=2\ \text{days}\)
Amount left at any time is given by
\(\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}\)
It takes 26.4 days to reach 2 gm.
(5-√x)² = y-20√2
Solve for x and y.
Answers
Answer:
33
Step-by-step explanation:
(
5
−
√
x
)
2
=
5
2
−
(
2
×
5
×
√
x
)
+
x
=
25
−
10
√
x
+
x
=
(
x
+
25
)
−
10
√
x
In order to eliminate the irrational
−
20
√
2
term with
x
and
y
being integers, we must have:
−
10
√
x
=
−
20
√
2
Divide both sides by
−
10
to get:
√
x
=
2
√
2
So
x
=
(
2
√
2
)
2
=
8
y
=
x
+
25
=
8
+
25
=
33
ANSWER NOW AND YOU GET 12 and ill answer one of ur questions
Answers
Answer Im going to geuss the last, Im not sure but it looks right.
Step-by-step explanation: heres my question--> https://brainly.com/question/20473783
a person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. determine the total distance in meter (1 mile
Answers
8 laps time 1/4 mile is 2 miles .
Average speed in miles per hour:
2 mi / 12.5 min * 60 min/hour = 9.6 mph
Average velocity is zero, since velocity is directional and the person jogged around a track. [I mention that in case this was set up as a trick question.]
But if we're really looking for average speed in m/s we can easily convert:
A mile is about 1.6 km, so it's about 1600 m.
(2 mi * 1600 m/mi) / (12.5 min * 60 s/min) = 1800 / 750 = 2.4 m/s
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
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A square pyramid and its net are shown below. What is the surface area of the pyramid?
17 cm
16 cm
Type the answer in the box.
square centimeters
17 cm
16 cm
...15 sm
15 cm.
Answers
Check the picture below.
so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.
\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)
If4x-2y=6, then y =?
Answers
4x-2y=6, move the x to the other side by subtracting 4x from both sides
-2y=-4x+6, leave the y by itself and divide by -2, since that’s what y is being multiplied by
you get y=2x-3
please help fast :(
A box contains five $1 bills, three $5 bills, one $10 bill and one $20 bill. Construct a PROBABILITY DISTRIBUTION for the data and DRAWA GRAPH. (Take a picture and submit with the test when you are done)
Answers
Answer:
Step-by-step explanation:
yes
Rosa and Albert receive the same amount of allowance
each week. The table shows what part of their allowance
they each spent on video games and pizza
A: Who spent more or their allowance no video games? Write an inequality to compare the portion spent on video games.
Answers
Answer:
0.4x < 0.5x
Step-by-step explanation:
Let x = Amount of money Rosa and Albert earn each week
Rosa:
Rosa spends 0.4(x) and 2/5(x) each week on video games and pizza
That equals to :
0.4x + 0.4x0.8xRosa spends 0.8x, or 80% of her allowance on video games and pizza
Albert
Albert spends 1/2(x) and 0.25(x) each week on video games and pizza
0.5x + 0.25x0.75xAlbert spends 0.75x, or 75% of her allowance on video games
Rosa spends 0.4x on video games, and Albert spends 0.5x.
0.4x ≤ 0.5x
-Chetan K
A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $9 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth
$4 a pound?
To get a mixture worth $4 a pound, pounds of coffee should be added.
(Type an integer, proper fraction, or mixed number)
Answers
prove that if a symmetric matrix is invertible, then its inverse is symmetric also.
Answers
Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, \(B = B^{T}\)
To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:
\(AB^{T} = I^{T}\)
Using the transpose rules, we can rewrite this as:
\(B^{T} * A^{T}\) = I
Now, we can multiply both sides of this equation by A:
\(B^{T} * A^{T}\)* A = A
Since A is invertible, we can multiply both sides by A⁻¹ to get:
\(B^{T}\) = A⁻¹
Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = \(B^{T}\), which is the transpose of the matrix B.
Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.
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g(x) = f(x - 6) = 10(-6)
OA.
OB.
OC.
O D. The graph of g(x) is the graph of f(x) shifted 6 units up.
The graph of g(x) is the graph of f(x) shifted 6 units down.
The graph of g(x) is the graph of f(x) shifted to the left 6 units.
The graph of g(x) is the graph of f(x) shifted to the right 6 units.
Answers
The Option D. The graph of g(x) is the graph of f(x) shifted to the right 6 units. is correct.
The function G(x) is defined as G(x) = f(x - 6). This means that the function G(x) is obtained by taking the function f(x), and shifting it to the right by 6 units.
To see this, consider the effect of the argument of f(x) in G(x). When x = 6, the argument of f(x) becomes (6 - 6) = 0, and when x = 0, the argument becomes (0 - 6) = -6. This means that the graph of G(x) is the graph of f(x) shifted 6 units to the right.
Therefore, the correct option is:
The graph of g(x) is the graph of f(x) shifted to the right 6 units. (Option D)
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Select Independent or Not independent for each description of events.
P(A) = 0.6, P (B) = 0.5, P (AB) = 0.6
P(A)=0.8, P (B) = 0.2. P(AB) = 0.4
P(A) = 0.4, P (B) =0.3, P(AB) = 0.12
Answers
Step-by-step explanation:
If A and B are independent, then P(A and B) = P(A) * P(B).
Then the probability that A occurs given that B occurs, for example, reduces to the probability that A occurs by itself:
P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A)P(B)}{P(B)}=P(A)P(A∣B)=P(B)P(A∩B)=P(B)P(A)P(B)=P(A)
So all you need to do is check that P(A|B) = P(A). If so, then A and B are independent. This is true only for the second case.
As per the given events, the first one is dependent, and the other two are not independent.
What is Probability?Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.
As per the given information in the question,
As we know that,
P(A ∩ B) = P(A | B) P(B)
Then, we will get,
P(A | B) = P(A) and P(B | A) = P(B)
Now, let's check the computation for 1st probability:
P(A | B) = 0.6
P(A) = 0.6
So, P(A | B) = P(A), it is dependent.
Now, check the computation for 2nd probability:
P(A | B) = 0.4
P(A) = 0.8
P(A | B) ≠ P(A), so it is not independent.
Check for the computation for 3rd probability:
P(A | B) = 0.12
P(A) = 0.4
P(A | B) ≠ P(A), so it is not independent.
To know more about Probability:
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Mai spent $2 and has less than $20.
Answers
Answer:
Mai has $18
Step-by-step explanation:
Answer:
x−2 < 20
Step-by-step explanation:
the diameter of a circle is 2 cm. What is the circumference
Answers
Answer:
4π cm
Step-by-step explanation:
The circumference of a circle is equal to Pi π times the diameter d . Since the diameter d is equal to 2 times the radius r , the formula for circumference using radius is 2πr 2 π r .
An acute angle in one right triangle has the same measure as an acute angle in another right triangle. Name the theorem or postulate that is the most direct way to prove the triangles similar.
Answers
Answer:
Step-by-step explanation:
Right Triangle Similarity
Acute Angle Similarity
If one of the acute angles of a right triangle is congruent to an acute angle of another right triangle, then by Angle-Angle Similarity the triangles are similar.
In the figure, ∠M≅∠Y , since both are right angles, and ∠N≅∠Z .
So, ΔLMN∼ΔXYZ .
Leg-Leg Similarity
If the lengths of the corresponding legs of two right triangles are proportional, then by Side-Angle-Side Similarity the triangles are similar.
In the figure, ABPQ=BCQR .
So, ΔABC∼ΔPQR .
Hypotenuse-Leg Similarity
If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar. (You can prove this by using the Pythagorean Theorem to show that the third pair of sides is also proportional.)
In the figure, DFST=DESR .
So, ΔDEF∼ΔSRT .
Taking Leg-Leg Similarity and Hypotenus-Leg Similarity together, we can say that if any two sides of a right triangle are proportional to the corresponding sides of another right triangle, then the triangles are similar.
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