Answer: x = -3, y = -4, or (-3, -4)
Step-by-step explanation:
To solve the system of equations, we can substitute the first equation into the second equation, replacing y with 3x + 5:
x + (3x + 5) = -7
Simplifying:
4x + 5 = -7
Subtracting 5 from both sides:
4x = -12
Dividing by 4:
x = -3
Now that we know x = -3, we can substitute that value into either of the original equations to find y:
y = 3(-3) + 5 = -4
Therefore, the solution to the system of equations is x = -3, y = -4, or (-3, -4).
Given the triangle below, what is mA, rounded to the nearest tenth? B 12 Triangle not drawn to scale A. 60.4° B. 2.2° 10 O C. 58.2° OD. 55.8° C SUBMIT
Answer:
C
Step-by-step explanation:
2. problem 4.3.4 for a constant parameter , a rayleigh random variable x has pdf what is the cdf of x?
The cumulative distribution function (CDF) for given random variable fx(x) is given by F(x) = 1 - e^[(-a²)(x²/2)] x > 0,
F(x) = 0 x ≤ 0.
The cumulative distribution function (CDF) F(x) for a Rayleigh random variable X is defined as,
F(x) = P(X ≤ x)
To find the CDF of X, we integrate the PDF of X over the interval [0, x],
F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx
Using the substitution u = (-a²x²/2),
Simplify the integral as follows,
F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx
= ∫₀^((-a²x²)/2) -e^u du (where u = (-a²x²/2) and x = √(2u/a²))
= [e^u]₀^((-a²x²)/2)
= 1 - e^[(-a²)(x²/2)]
Therefore, the CDF of X for the Rayleigh random variable X has PDF fx (x) is equal to,
F(x) = 1 - e^[(-a²)(x²/2)] x > 0,
F(x) = 0 x ≤ 0.
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The above question is incomplete, the complete question is:
For a constant parameter a > 0, a Rayleigh random variable X has PDF
fx (x) = a²xe^[(-a²)(x²/2)] x > 0
0 otherwise.
What is the CDF of X?
The relative housing cost for a US city is defined to be the ratio nationalaveragehousingcost
averagehousingcostforthecity
, expressed as a percent.
The scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005. The line of best fit is also shown and has equation y=0.0125x+61. Which of the following best explains how the number 61 in the equation relates to the scatterplot?
In 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.
We know that the relative housing cost for a US city is defined to be the ratio average housing cost for the city /national average housing cost, expressed as a percent also the scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005, therefore,
the equation is y = 0.0125x + 61
Therefore, with this we know that in 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.
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PLEASE HELP!!!!!!!!!
△DEF is similar to △YZX
A) which side corresponds to ED? (this one is already answered)
B) write a proportion that you could use to find XZ
C) what is XZ?
Step-by-step explanation:
B) 20:23
C) 6,0375
hope this helps
Find the measures of angles 1 through 5 in the figure shown !
Answer:
55 degrees angles on a rights angle triangle. 1 and 3 they are equal cause they are vertical opp angles 55 degrees
mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each
Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".
Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".
Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".
Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".
Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.
Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".
Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".
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WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!
The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.
you can use Newtons's Method or Bisection to help but you don't have to.
Answer:Approximately
(0.58975,0.34781)
Step-by-step explanation:
If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:
√(x−1)2+(y−0)2=√x4+x2−2x+1
To minimize this, we want to minimize
f(x)=x4+x2−2x+1
The minimum will occur at a zero of:
f'(x)=4x3+2x−2=2(2x3+x−1)
graph{2x^3+x-1 [-10, 10, -5, 5]}
Using Cardano's method, find
x=3√14+√8736+3√14−√8736≅0.58975
y=x2≅0.34781
place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.
A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.
So, as per the given option, the correct sequence should be, B, A, E, C, D, F.
We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.
When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.
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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
A. Select the level of significance
B. setup null and alternative hypothesis
C. Establish the decision rule
D. performance computation
E. select the test statistics
F. Draw conclusions
PLEASE HELPPP ME MATH
The coordinates of the image of point D that ensures that the triangles are congruent is (-2, 2)
How to determine the coordinates of point DGiven the triangle ABC and the incomplete triangle DEF
From the triangle transformation of points B and C, we can see that
The points of the triangle ABC are translated to the left by 6 units and downward by 4 units
Mathematically, this can be represented as
(x, y) = (x - 6, y - 4)
Given that
A = (4, 6)
So, we have
D = (4 - 6, 6 - 4)
Evaluate the difference
D = (-2, 2)
Hence, the position is (-2, 2)
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5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)
Answer:
Player Efficiency Rating (PER)
Step-by-step explanation:
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.
PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.
PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.
On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.
Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.
Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.
So, correct option is D.
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Write a quadratic inequality represented by the graph.
Using the concept of parabola, the quadratic inequality represented by the graph can be written as:
y = x² -2x +2.
Define parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.
The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.
The general equation for a parabola is given as:
y = a(x-h) ² + k
Now here we have:
(x,y) = (2,5)
(h,k) = (1,1)
Putting these values in the equation,
5 = a (2-1) ² + 1
a = 5-1
=4
Substituting the values:
y = (x-1) + 1
y = x² -2x +2
Therefore, the quadratic inequality can be written as: y = x² -2x +2.
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A pollster recorded the size of households in his
area. The table below shows the distribution for
820 families. How many of the 820 families has at
least 3 people in the household?
Number of people in
a household
1
2
3
4
5
6 or more
% of Households
27%
33%
24%
10%
4%
2%
✩
Step 1: Calculate the number of families with 1 person in the household by multiplying the percentage (27%) and the total number of families (820) - 27% x 820 = 220.4.
Step 2: Calculate the number of families with 2 people in the household by multiplying the percentage (33%) and the total number of families (820) - 33% x 820 = 271.6.
Step 3: Calculate the number of families with 3 people in the household by multiplying the percentage (24%) and the total number of families (820) - 24% x 820 = 196.8.
Step 4: Calculate the number of families with 4 people in the household by multiplying the percentage (10%) and the total number of families (820) - 10% x 820 = 82.
Step 5: Calculate the number of families with 5 people in the household by multiplying the percentage (4%) and the total number of families (820) - 4% x 820 = 32.8.
Step 6: Calculate the number of families with 6 or more people in the household by multiplying the percentage (2%) and the total number of families (820) - 2% x 820 = 16.4.
Step 7: Add the numbers calculated in Steps 1 - 6 to get the total number of families with at least 3 people in the household - 220.4 + 271.6 + 196.8
A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4sin4t. If the mass is pulled down 6 in and then released, determine the position of the mass at any time t. (Use g=32ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)
The position of the mass at any time t is given by u(t) = -1/2 cos(2√2 t) + sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t), and the first four times at which the velocity of the mass is zero, excluding t = 0, are t = 0.0567, 0.283, 0.510, and 0.736.
To solve this problem, we need to use Newton's second law of motion which states that the force acting on an object is equal to its mass times its acceleration. In this case, the force acting on the mass is the sum of the force due to gravity and the external force, and the acceleration is given by the second derivative of the displacement.
Using Hooke's law, the force due to the spring is proportional to the displacement u of the mass from its equilibrium position, with a proportionality constant k
F_spring = -k u
where k is the spring constant. Since the mass is pulled down 6 in. from its equilibrium position, the initial displacement is u(0) = -0.5 ft. The spring stretches 24 in. under a weight of 8 lb, so the spring constant is
k = F_spring / u = (8 lb) / (2 ft) = 4 lb/ft
The force due to gravity is
F_gravity = m g
where m is the mass of the object and g is the acceleration due to gravity. The mass is given in pounds, so we need to convert it to slugs:
m = 8 lb / (32.2 ft/s^2) = 0.248 slugs
Thus, the force due to gravity is
F_gravity = (0.248 slugs) (32 ft/s^2) = 7.94 lb
The equation of motion for the displacement u(t) is
m u''(t) = F_gravity + F_spring + F_external
where F_external = 4 sin 4t lb is the external force. Substituting the expressions for these forces and dividing by m, we get
u''(t) + 8 u(t) = 2 sin 4t
This is a homogeneous linear second-order differential equation with constant coefficients, which can be solved by finding the roots of the characteristic equation:
r^2 + 8 = 0
The roots are r = ±2i√2. The general solution of the differential equation is then
u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + u_p(t)
where u_p(t) is a particular solution of the nonhomogeneous equation. Since the right-hand side of the equation is a sinusoidal function with frequency 4/π, we can guess a particular solution of the form
u_p(t) = A sin(4t) + B cos(4t)
Substituting this into the equation and equating coefficients, we get
16 A - 16 B + 8 A = 2, or A = 1/2
-16 A - 16 B + 8 B = 0, or B = -1/2
Therefore, the particular solution is
u_p(t) = 1/2 sin(4t) - 1/2 cos(4t)
The general solution is then
u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t)
We can use the initial conditions u(0) = -0.5 and u'(0) = 0 to determine the values of c1 and c2
u(0) = c1 + 1/2 = -0.5, or c1 = -1/2
u'(0) = -2√2 c1 + 2√2 c2 - 2 = 0, or c2 = 1
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The given question is incomplete, the complete question is:
A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time t. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)
u(t) = 1/2sin(4t)+1/2cos(4t)-2tcos(4)
Determine the first four times at which the velocity of the mass is zero. (Exclude t = 0 as trivial.)
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D:please !!!!
If the top of Bria's bookcase has a length-to-width ratio of 3:1, the width of the top should be about 10 inches to provide an area of 300 square inches for her soap carving collection.
How to find the dimension of the top of the bookcaseThe top of the bookcase is a rectangle, the area of the top can be expressed as the product of its length and width:
Area of the top = length × width
Area of the top = 300 square inches
length × width = 300 square inches
width = 300 square inches / length
Assuming that the top of the bookcase is with a length-to-width ratio of
3 : 1
length = 3 × width
substituting the value gives
width = 300 / (3 × width)
Simplifying, we have:
width² = 100 square inches (the polynomial)
Taking the square root of both sides, we get:
width = √100 ≈ 10 inches
Then the length will be = 30 inches
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I will mark you brainiest!
If the triangles above are reflections of each other, then ∠D ≅ to:
A) ∠F.
B) ∠E.
C) ∠C.
D) ∠A.
E) ∠B.
Answer:
D I believe
Step-by-step explanation:
what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}
Answer:
[tex]b) \quad(-1,0,2)[/tex]
Step-by-step explanation:
The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation
Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value
Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]
What are the zeros of the function f(x)= 240x -2x^2
Answer:
What are the zeros of the function f(x)= 240x -2x^2
Step-by-step explanation:
To find the zeros of the function f(x) = 240x - 2x^2, we need to set f(x) equal to zero and solve for x:
240x - 2x^2 = 0
We can factor out 2x from the left side:
2x(120 - x) = 0
So either 2x = 0 or 120 - x = 0. Solving for x in each case gives:
2x = 0 => x = 0
120 - x = 0 => x = 120
Therefore, the zeros of the function are x = 0 and x = 120.
Find the 6th term of the geometric sequence described below.
m₁ = -3(-5)-1
Show your work here
Hint: To add an exponent (z"), type "exponent" or press "A"
Answer:
m₆ = 9375
Step-by-step explanation:
Given sequence is
[tex]m,_i = -3(-5)^{i - 1}[/tex]
To find the 6th term, all you have to do is substitute i = 6 and compute
For i = 6 we get
[tex]m_6 = -3(-5)^{6 - 1}\\= -3(-5)^5\\\\= -3(-3125) \\\\= 9375[/tex]
A negative number raised to an odd number is negative that is why (-5)⁵ is negative
each of the cars on the left has th esame solution as on of the card ont the right find the cards with macthing solutions to coplete the sentece below.[tex]6x - 72 = -18[/tex]
Answer:
x=9
Step-by-step explanation:
this is solved by using cover and cancel so we can isolate the x variable
1) first add 72 to both sides.
6x=54
2) second divide both sides by 6
3) x=9
Find the value of Tan 15 without using a table or calcutator
Answer:
Step-by-step explanation:
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What are the coordinates of point G on the coordinate grid below?
A
(-4,3)
(4,-3)
-2
4
2
O
-2
4
B
AY
D
2
(4,3)
(-4,-3)
4
G
XA
Answer:
The answer is G = (4,3)
Step-by-step explanation:
G = (4,3)
the solution set is
5r+20/10=3r-6/3
Answer:
r = -2
Step-by-step explanation:
5r + 20/10 = 3r -6/3
5r + 2 = 3r - 2
2r + 2 = -2
2r = -4
r = -2
Answer: r = -2
Step-by-step explanati
consider the funciton f given by f(t)=log49(t7). find values for a and b such that f(t)=a+logb(t).
The values for a and b such that f(t) = a + logb(t) are,
a = log(1/log(49))
b = 49
Therefor
We can start by simplifying the expression for f(t)
f(t) = log49(t7)
f(t) = log(t7)/log(49) [Using the change of base formula]
Now we can rewrite f(t) as:
f(t) = log(t)/log(b) + a [Using the logarithmic properties log(ab) = log(a) + log(b)]
Comparing this expression with f(t) = a + logb(t), we can see that:
a = log(1/log(49)) [since log(b) = 1/log(49)]
b = t
Therefore, we have
f(t) = log(t7)/log(49) = log(t)/log(b) + log(1/log(49))
= log(t)/log(49) + log(1/log(49))
= log(1/log(49)) + log(t)/log(49)
So, a = log(1/log(49)) and b = 49.
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At a community college, a survey was taken to determine where students study on campus. Of the 250 students surveyed, it was determined that
170 studied in the library
135 studied in the cafeteria
76 studied in both the library and the cafeteria
How many studied in library or cafeteria (including both)?
Answer:
Step-by-step explanation:
To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.
So, the number of students who studied in library or cafeteria is:
170 + 135 - 76 = 229
Therefore, 229 students studied in the library or cafeteria (including both).
|x+6|<3 absolute value inequality, write an equivalent compound inequality.
An equivalent cοmpοund inequality is -9 < x < -3.
What is an absοlute value inequality?An inequality with an absοlute value algebraic expressiοn and variables is knοwn as an absοlute value inequality. An expressiοn using absοlute functiοns and inequality signs is knοwn as an absοlute value inequality.
Here, we have
Given: |x+6|<3 is an absοlute value inequality.
Apply absοlute rule
if |u|<a, a>0 then -a<u<a
-3 < x+6 <3
x+6 > -3 and x+6 <3
x> -9 and x< -3
-9 < x < -3
Hence, an equivalent cοmpοund inequality is -9 < x < -3.
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A rectangular fish tank 60 cm x 15 cm x 34 cm is 13 full of water. Find the volume of water needed to fill the tank completely.
Step-by-step explanation:
The volume of the rectangular fish tank is:
V = l x w x h = 60 cm x 15 cm x 34 cm = 30,600 cm³
Since the tank is 1/3 full, the volume of water in the tank is:
V_water = (1/3) x V = (1/3) x 30,600 cm³ = 10,200 cm³
To find the volume of water needed to fill the tank completely, we can subtract the volume of water already in the tank from the total volume of the tank:
V_needed = V - V_water = 30,600 cm³ - 10,200 cm³ = 20,400 cm³
Therefore, 20,400 cm³ of water is needed to fill the tank completely.
PLS HELP FAST 20 POINTS + BRAINLIEST
Answer:
£22
Step-by-step explanation:
50% of 88=88/100 ×50=44
44÷2=25%=22
75% of £88 is deducted, so that 88-66=£22
Don't forget my Brainliest9x+6=24
8x-4=28
-18-x=57
-4-8x=8
3x+0.7=4
Answer:
Step-by-step explanation:
To solve each of these equations, we need to isolate the variable (x) on one side of the equation. Here are the steps to solve each equation:
9x + 6 = 24
Subtract 6 from both sides:
9x = 18
Divide both sides by 9:
x = 2
Therefore, the solution to the equation is x = 2.
8x - 4 = 28
Add 4 to both sides:
8x = 32
Divide both sides by 8:
x = 4
Therefore, the solution to the equation is x = 4.
-18 - x = 57
Add 18 to both sides:
-x = 75
Multiply both sides by -1:
x = -75
Therefore, the solution to the equation is x = -75.
-4 - 8x = 8
Add 4 to both sides:
-8x = 12
Divide both sides by -8:
x = -1.5
Therefore, the solution to the equation is x = -1.5.
3x + 0.7 = 4
Subtract 0.7 from both sides:
3x = 3.3
Divide both sides by 3:
x = 1.1
Therefore, the solution to the equation is x = 1.1.
a triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square
The cοst οf painting the triangle bοrder at the given rate is Rs. [tex]108\sqrt{(2)[/tex].
What is a triangle?A triangle is a geοmetric shape that cοnsists οf three line segments, οr sides, that are cοnnected tο fοrm three angles.
Tο find the cοst οf painting the triangle bοrder, we first need tο find its area. Let's call the third side οf the triangle "x".
We knοw that the perimeter οf the triangle is 24cm, sο we can write an equatiοn:
6cm + 8cm + x = 24cm
Simplifying this, we get:
x = 10cm
Nοw we can use Herοn's fοrmula tο find the area οf the triangle:
s = (6cm + 8cm + 10cm)/2 = 12cm
Area [tex]= \sqrt{(s(s-6cm)(s-8cm)(s-10cm))[/tex]
[tex]= \sqrt{(12cm6cm4cm*2cm)[/tex]
[tex]= 2\sqrt{(72cm^2)[/tex]
[tex]= 12\sqrt{(2) cm^2[/tex]
Finally, we can calculate the cοst οf painting the bοrder at a rate οf Rs. 9 per square cm:
Cοst = (Area) x (Rate)
[tex]= (12\sqrt{(2)} cm^2) x (Rs. 9/cm^2)[/tex]
[tex]= Rs. 108\sqrt{(2)[/tex]
Therefοre, the cοst οf painting the triangle bοrder at the given rate is= [tex]Rs. 108\sqrt{(2)[/tex]
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What is the probability that someone who does not take vitamins is a female? Round to three decimal places.
Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500
Answer:
A) 0.374
Step-by-step explanation:
Let event A be that the person is female.
Let event B be that the person does not take vitamins.
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, from the given table:
[tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]
[tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]
[tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]
To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]
[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]
