To move Point A(-5, -2) to Quadrant IV, we need to apply one or more transformations that result in a reflection about the x-axis and/or a rotation of 180 degrees. The following transformations would move Point A to Quadrant IV:
Reflection about the x-axis: This transformation would change the sign of the y-coordinate, making it positive. So, the image of A after this transformation would be (−5, 2).
Rotation of 180 degrees about the origin: This transformation would change the sign of both the x and y-coordinates, making them positive. So, the image of A after this transformation would be (5, 2).
Therefore, either a reflection about the x-axis or a rotation of 180 degrees would move Point A to Quadrant IV.
Need this answer please and show work
The value of the "trigonometric-expressions' are :
(a) tan(5π/2) is undefined,
(b) sec(315°) is √2.
Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.
Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),
First, we convert 315° to radians:
Which is : 315° = (7π/4) radians;
Next, we find the value of cos(7π/4):
⇒ cos(7π/4) = cos(π/4) = (√2)/2;
Finally, we substitute in the identity for sec(θ);
So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.
Therefore, value of sec(315°) is √2.
Learn more about Trigonometric Expression here
https://brainly.com/question/26649239
#SPJ1
The given question is incomplete, the complete question is
Find the value of the trigonometric expressions :
(a) tan(5π/2)
(b) sec(315°)
Consider the data set shown. How does the outlier affect the mean, median, and mode
7, 11, 10, 8, 10, 23, 8
The outlier does not affect the mode
The outlier will increase the mean.
The outlier will not affect the median.
How does outlier affect the mean, median and mode?The outlier will increase the mean because it will significantly increase the sum of the values.
The presence of an outlier will not affect the median, as it only changes the position of the middle value.
The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.
Learn more about outliers on:
brainly.com/question/24123584
#SPJ1
find the missing sides of this triangle (Hint: is this a special right triangle?)
(10 on the adjacent and two 45° angles on both ends if anyone can’t see)
Answer:
Both sides are equal, and are equvalent to 5 square root of 2
Step-by-step explanation:
This is a special right angled triangle known as the 45-45-90 triangle
The hypotenuse of a 45-45-90 triangle is x square root 2, with x being both sides of the triangle
10=x square root of 2 (Divide both sides by square root of 2)
10/square root of 2=x (Rationalize)
x=5 square root of 2
(2x+1)^2 +(4x-4)^2 = (4x-1)^2
The quadratic equation is solved and the solution is x = 1 and x = 4
Given data ,
Let's expand the left-hand side of the equation:
(2x+1)² + (4x-4)²
= (2x)² + 2(2x)(1) + 1² + (4x)² - 2(4x)(4) + 4² (using the formula for the square of a binomial)
= 4x² + 4x + 1 + 16x² - 32x + 16
= 20x² - 28x + 17
Now let's expand the right-hand side of the equation:
(4x-1)²
= (4x)² - 2(4x)(1) + 1²
= 16x² - 8x + 1
Now we can set the left-hand side equal to the right-hand side and simplify:
20x² - 28x + 17 = 16x² - 8x + 1
4x² - 20x + 16 = 0
x² - 5x + 4 = 0
(x - 1)(x - 4) = 0
Hence , the solution is x = 1 and x = 4
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ1
. Suppose that the following represents the graph of the function f(x).
N
a. (5 points) Determine the x intercepts and give a number line for the function
f(x). Are there any horizontal or vertical asymptotes?
b. (5 points) Give a number line for f'(x) and classify any local maxima or minima.
c. (5 points) Give a number line for f"(x) and list any points of inflection.
The x intercepts are (-2, 0), (2, 0) and (3, 0) and it has vertical asymptotes at x = 4 and x = -4
Determining the x interceptsThe x intercepts are the points where the graph intersect with x-axis
In this case, the points are (-2, 0), (2, 0) and (3, 0)
So, the x intercepts are (-2, 0), (2, 0) and (3, 0)
Are there any horizontal or vertical asymptotes?The graph has no horizontal asymptotes
However, it has vertical asymptotes at x = 4 and x = -4
The local maxima or minimaFrom the graph, the local maxima or minima are
Minima (3, -1) and Maxima (-1, 12)
The point of inflectionThis is the points where the graph changes it concave-ness
From the graph, we have the point to be (1, 13/2)
Read more about functions at
https://brainly.com/question/4138300
#SPJ1
Tickets of a program at college cost $3 for general admission or $2 with student ID. If 181 people paid to see a performance and $435 was collected, how many of each type of ticket were sold.
pleaseeeee helpppppp
Find the terms: a=_1=8, r=0.7
The formula of the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)
Finding the terms of the sequence:From the question, we have the following parameters that can be used in our computation:
a=_1=8, r=0.7
Express properly
So, we have
First term, a = 8
Common ratio, r = 0.7
The above definition is of a geometric sequence that has a first term of 8 and a common ratio of 0.7
Using the above as a guide, we have the following:
f(n) = a * r^(n - 1)
substitute the known values in the above equation, so, we have the following representation
f(n) = 8 *0.7r^(n - 1)
Hence, the nth term of the sequence is f(n) = 8 *0.7r^(n - 1)
Read more about sequence at
https://brainly.com/question/6561461
#SPJ1
The ratio of children: teenagers: adults in a survey sample are 2: 11:17. a) Which is the largest group represented? b) If there are 180 people surveyed how many are:
The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented
Here, we have,
given that,
The ratio of children: teenagers: adults in a survey sample are 2: 11:17.
now, we have,
If there are 180 people surveyed
now, let , we have,
children = 2x
teenagers= 11x
adults = 17x
now, we have,
2x + 11x + 17x = 180
or, 30x = 180
or. x = 6
Hence, The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented.
To learn more on ratio click:
brainly.com/question/13419413
#SPJ1
I Need help pleaseeeeeee
Answer:
A
Step-by-step explanation:
according triangle inequality,
the sum of any two sides of a triangle is larger than the remaining side.
so a + b > c is correct
Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base?
The polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base include :
B. SquareC. RectangleE. CircleHow to find the polygons ?If a plane intersects three distinct vertices of the cube while bypassing any other vertices, a triangle is produced. To visualize this, suppose a corner of the cube were removed with a knife; picture that cut surface as a triangle.
On the other hand, if a plane coincides with four points on the cube and outlines a square shape, it creates what's called a "square cross-section." This transpires when said plane parallels one side of the cube while intersecting only the midpoints of its opposite face's edges.
Find out more on polygons at https://brainly.com/question/30956846
#SPJ1
Full question is:
Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base
A triangle
B square
C. rectangle
D pentagon
E circle
Suppose you have a 4 foot sub and you have to feed 10 people ,how many cuts will you make?
Answer: Cut 3 inch per person
Step-by-step explanation:
there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)
Answer:
7 Cuts
Step-by-step explanation:
This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.
Which of the following statements about transportation in the United States is NOT true?
A. Most Americans commute to work in a personally owned vehicle.
B. Most Americans who commute to work in car's drive alone.
C. Americans spend more income on transportation than anything else except
housing.
D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
Answer: D
Step-by-step explanation:
The answer is D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
According to the U.S. Energy Information Administration, the average price of a gallon of regular unleaded gasoline in the United States was $3.53 on March 8, 2023. This is higher than the average price of gasoline in many other countries, including Canada ($1.56), Mexico ($1.97), and the United Kingdom ($1.73). However, the cost of gasoline in the United States is lower than the average price in some countries, such as Norway ($6.62), Sweden ($5.62), and Denmark ($5.51).
Here are the facts about the other statements:
A. Most Americans commute to work in a personally owned vehicle. According to the U.S. Census Bureau, in 2019, 77.4% of workers commuted to work by driving alone.
B. Most Americans who commute to work in car's drive alone. According to the U.S. Census Bureau, in 2019, 77.4% of workers who commuted to work by driving did so alone.
C. Americans spend more income on transportation than anything else except housing. According to the U.S. Bureau of Labor Statistics, in 2020, Americans spent an average of $10,564 on transportation, more than any other category except housing ($16,916).
Match the line described on the left with the slope of the line on the right.
x=-3 , 6x-3y=18 , the line through (7,5) and (8,5) , the line through (4,-2) and (1,7)
Undefined -3 , 0 , 2
The Slope of x = -3 is undefined; 6x-3y=18 is 2; (4,-2) and (1,7) is -3; and (7,5) and (8,5) is 0.
What is the Slope of a Line?Slope of a line (m) = rise/run = change in y / change in x
Note that the slope of vertical lines are always undefined.
Therefore, we have the following:
x = -3 represents the equation of a vertical line, therefore, the slope is undefined.
6x - 3y = 18 is rewritten as y = 2x - 6 in slope-intercept form. The slope is 2.
For (4,-2) and (1,7):
Slope (m) = (7 -(-2))/(1 - 4) = 9/-3 = -3
For (7,5) and (8,5):
Slope (m) = 5 - 5/8 - 7 = 0/1 = 0
Learn more about the Slope of a line on:
https://brainly.com/question/24907633
#SPJ1
The engine in a ice cream truck has a power curve approximated by Y=-X^2/5000 + 19x/23 -26
X is the RPM, Y is the horsepower generated (notice the a and b values are fractions)
What is the maximum horsepower? Round your answer to three decimal places.
The maximum horsepower of the ice cream truck engine is 827.025.
How to find the maximum horsepower?For quadratic equation y = ax² + bx + c, the maximum value of y is given by:
y(max) = c- b²/4a
Since the horsepower generated by the ice cream truck engine power curve is approximated by Y = -X²/5000 + 19x/23 -26
In this case, a = -1/5000, b = 19/23 and c = -26
Thus, the maximum horsepower will be:
maximum horsepower = -26 - (19/23)²/[4*(-1/5000)]
maximum horsepower = 827.025 horsepower
Learn more about quadratic equation on:
https://brainly.com/question/24334139
#SPJ1
Geometry
All I need is the letter that is correct. Don’t mind the ones I already circled
The translation of ABC by (Rx + Ry) is UVW and the rigid composition of XYZ to X'Y'Z' cannot be determined
Translation image of the triangleThe rule (Rx + Ry) represents a translation image of a shape, where R is a vector representing the direction and distance of the translation, and (x, y) are the coordinates of the original shape.
To apply this rule to a shape, we simply add the vector R to each point of the shape, which moves the shape in the direction and distance specified by R.
Using the above as a guide, we have the following the translation of ABC by (Rx + Ry) to be UVW
The rigid composition of XYZ to X'Y'Z'The triangle X'Y'Z' is not given in the figure
So, the rigid composition of XYZ to X'Y'Z' cannot be determined
Read more about transformation at
https://brainly.com/question/1548871
#SPJ1
Out of 400 people sampled, 160 preferred
Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A.
Use a 90% confidence level, and give your answers as decimals, to three places. Use GeoGebra to calculate!
A rectangular classroom is 10m long and 4.6m wide. Make a scale drawing of the classroom using the following scales.
The scale drawing of the classroom have the dimensions of 10 centimeters by 4.6 centimeters
Making a scale drawing of the classroom using the scalesFrom the question, we have the following parameters that can be used in our computation:
Dimension of classroom = 10 meters by 4.6 meters
The scale of the drawing is given as
1 cm : 1 m
Using the above as a guide, we have the following:
Scale factor = 1 cm/1 m
So, we have
Scale factor = 1 cm per m
So, we have
Scale dimension of classroom = (10 meters by 4.6 meters) * 1 cm per m
Evaluate
Scale dimension of classroom = 10 centimeters by 4.6 centimeters
Hence, the scale drawing of the classroom have the dimensions of 10 centimeters by 4.6 centimeters
Read more about scale drawing at
https://brainly.com/question/25324744
#SPJ1
Complete question
A rectangular classroom is 10 m long and 4.6 m wide. Make a scale drawing of the classroom using the following scales. 1 cm : 1 m
the mean radius of the earth is 6371.0 kilometers and the mean radius of earths moon is 1737.5 kilometers. what is the approximate difference in the mean circumferences in kilometerse of the earth and earths moon
the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.
Describe circle.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.
A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. T
he line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius.
The difference in the mean circumferences of the Earth and the Moon can be found by subtracting the circumference of the Moon from the circumference of the Earth.
The circumference of the Earth is:
C earth = 2π * 6371.0 km = 40075.04 km (rounded to two decimal places)
The circumference of the Moon is:
C moon = 2π * 1737.5 km = 10921.16 km (rounded to two decimal places)
The difference in the mean circumferences of the Earth and the Moon is:
C earth - C moon = 40075.04 km - 10921.16 km ≈ 29153.88 km
Therefore, the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.
To know more about mean visit
https://brainly.com/question/31101410
#SPJ1
5. Un tanque contiene 9 litros de agua si se abre el grifo que vierte tres litros de agua por minuto y y es la cantidad de agua (en litros), que hay en el tanque después de x minutos
The equation that models the amount of water in the tank after x minutes is:
y = -3x + 9
How many liters are there after x minutes?We know that the tank contains 9 liters of water, and it loses water at a constant rate of 3 liters per minute.
Then we can model the amount of water y in the tank after x minutes with a linear equation where the y-intercept is 9 and the rate of change is -3 (the amount it loses per unit of x)
Then the equation is:
y = -3x + 9
Learn more about linear equations at:
https://brainly.com/question/1884491
#SPJ1
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 66 m wide.
Find the area of the training field. Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
0
$6 m
808
m
X
m²
5
m²
The area of the training field that has the shape of a rectangle and two semicircle would be = 9,755.46m²
How to calculate the area of the training field?To calculate the area of the training field, the area of the rectangle and the two semicircles should be determined and added together.
The area of rectangle = length×width
where:
length = 96m
width = 66m
area of rectangle = 66×96 = 6,336m²
Area of the two semicircle = Area of a circle = πr²
radius = diameter/2 = 66/2 = 33m
area of a circle= 3.14×33×33 = 3419.46m²
Therefore the area of the training field = 6,336m²+3419.46m² = 9,755.46m²
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
Olivia Jackie. Play? The game with the spinner Olivia's funny 2 out of 12 out of fift. Do you watch Jackie's fun 2 on 19 of a 100? Find each experimental probability of spinning a 2.
The experimental probability of spinning a 2 on Olivia's spinner is 0.1667.
The experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.
Olivia and Jackie are playing a game with a spinner. Olivia's spinner has 12 equal sections, two of which are marked as "funny 2". Jackie's spinner has 100 equal sections, and two of them are marked as "fun 2".
To find the experimental probability of spinning a 2 in Olivia's spinner, we first need to determine the total number of possible outcomes, which is the number of sections on the spinner. In this case, the spinner has 12 sections. Out of these, two sections are marked as "funny 2". Therefore, the number of favorable outcomes is 2.
Experimental probability of spinning a 2 in Olivia's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes
= 2 / 12
= 1 / 6
= 0.1667
Therefore, the experimental probability of spinning a 2 on Olivia's spinner is 0.1667.
To find the experimental probability of spinning a 2 in Jackie's spinner, the total number of possible outcomes is the number of sections on the spinner, which is 100. Out of these, two sections are marked as "fun 2". Therefore, the number of favorable outcomes is 2.
Experimental probability of spinning a 2 in Jackie's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes
= 2 / 100
= 0.02
Therefore, the experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.
To know more about Probability here
https://brainly.com/question/11234923
#SPJ1
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Responses
The surface area of the cube is 384 mm².
What is a cube:A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six
A = 6L²...................... Equation 1Where:
A = Surface area of the cubeL = Length of the side of the cubeFrom the question,
Given:
L = 8 mmSubstitute this value into equation 1
A = 6×8²A = 6×64A = 384 mm²Hence the right option is D. 384 mm².
Learn more about cube here: https://brainly.com/question/28776132
#SPJ1
When doubling the dimensions of a rectangle, why does the area quadruple and the perimeter only doubles?
If you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
The perimeter will be double of if we double the length and breadth of rectangle
→ When doubling the dimensions of a rectangle, why the area is quadruple:
We know that :
Area of rectangle = l × b
where, l is length and b is breadth
A = L × W
This means area equals length times width.
if you double the length and you double the width, the formula becomes:
A = 2 × L × 2 × W
A = 2 × 2 × L × W
A = 4 × L × W
if you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
→When doubling the dimensions of a rectangle, why the perimeter is doubles?
Let length be equal to ′l′
And breadth be equal to ′b′
Perimeter of rectangle = 2 (l + b) ____(equation i )
The perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one.
Double length of rectangle of initial one= 2 × l=2l
Double breadth of rectangle of initial one = 2×b=2b
So the perimeter of new rectangle whose length and breadth are double of initial one are:
As we know that:
Perimeter of rectangle = 2 (l + b)
So,
Perimeter of new rectangle= 2(2l+2b), (by taking 2 common)
Perimeter of new rectangle = 2×2(l + b) ____ equation (ii)
As from equation (i) perimeter of initial rectangle is = 2(l + b)
So from equation (i) and (ii)
Perimeter of new rectangle= 2 × 2(l + b)
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
Hence, the perimeter will be double of if we double the length and breadth of rectangle.
Learn more about Rectangle at:
https://brainly.com/question/29123947
#SPJ1
Rationalize the denominator and simplify:
4/4+√x
Answer: 16-4√x/16-x is the answer.
Step-by-step explanation:
=> 4/4+√x*4-√x/4-√x
=> 4(4-√x)/(4)²-(√x)² {using identity - (a+b) (a-b)=a² - b²}
=> 16-4√x/16-x
Please help with these to questions its urgent please!
Answer:
First problem: x = 5.7√2 = (57√2)/10
Second problem: x = 10√3
what are the answers to these questions
Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when the distance the cow must stand from the billboard x₀ = 26.
How to determine angle and distance?To find Θ, use similar triangles. Let the distance from the cow to the top of the billboard be h. Then, using similar triangles:
h / x = 5 / (x - 13)
Solving for h:
h = 5x / (x - 13)
The vertical angle subtended by the billboard at the cow's eye is equal to the angle whose tangent is given by:
tan(Θ) = h / 4
Substituting for h:
tan(Θ) = 5x / (4(x - 13))
To maximize Θ, find the value of x that maximizes tan(Θ). Taking the derivative of tan(Θ) with respect to x and setting it equal to zero:
d/dx (tan(Θ)) = 5(52 - 26x) / (4(x - 13))² = 0
Solving for x:
x₀ = 26
Substituting x₀ into the expression for Θ:
Θ(x₀) = tan⁻¹(5(26) / 4(13)) = tan⁻¹(5/2)
Therefore, Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when x₀ = 26.
Find out more on calculus here: https://brainly.com/question/24430269
#SPJ1
How many games did the team play last season?
The number of games that the team did play in the last season is 23.
What is the frequency?The frequency is the number of times an event happens. Therefore, frequency is the number of repetitions of a digit or an event.
The given frequency table represents the frequency of different runs scored by the team in the entire season.
The frequency is written in tally form, which means that each of the vertical lines represents the count of 1, while a group of fours lines such that the four lines are vertical while the fifth line cuts the other four represents a count of 5 as shown in the second column of the second row.
Therefore, the frequency table can be made as:
Number of runs Frequency
0 8
1 5
2 3
3 6
4 1
Total: 23
Hence, the team played 23 games.
Learn more about Frequency:
https://brainly.com/question/5102661
#SPJ1
A salesman earns $60,000 in commission in his first year and then has his commission reduced by 20% the second year. What percent increase in commission over the second year will give him $57,600 in the third year?
first off, let's find out how much he's making on the 2nd year, so since he's getting slashed by 20%, that means his new commission is 100% - 20% = 80%, so 80% of 60000, how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 60000}}{\left( \cfrac{80}{100} \right)60000}\implies 48000[/tex]
now, if we want to go up to 57600, that means we need to increase his commission by 57600 - 48000 = 9600.
So, if we take 48000(origin amount) to be the 100%, what's 9600 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 48000 & 100\\ 9600& x \end{array} \implies \cfrac{48000}{9600}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies 5x=100\implies x=\cfrac{100}{5}\implies \boxed{x=20}[/tex]
Bad gums may mean a bod mood. Researchers discovered that 85% of people who have suffered a bad mood had periodontal disease. Only 29% of healthy people have this disease. Suppose that in a certain community bad moods are rare, occuring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have bad mood?
Answer:
24.6%
Step-by-step explanation:
denote B: bad mood; H: healthy; D: periodontal disease
P(B|D)
=P(B,D) / P(D)
=P(B,D) / [P(D,B)+P(D,H)] ### law of total probability ###
=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]
=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]
=0.245664739