Consider a binary classification problem in which we want to determine the optimal decision surface. A point x is on the decision surface if P(Y = 1|x) = P(Y = 0x). = = (a) (20 pts) Find the optimal decision surface assuming that each class-conditional distri- bution is defined as a two-dimensional Gaussian distribution: = (2 – m.)".:(– m. = = = = > 1 1 p(xly = i) = exp (2π/, mi) (27)d/2/2;11/2 where i € {0,1},and mo = (1, 2), mı = (6,3) and further 20 = 1 = 12, and P(y=0) = E mi Eo P(Y = 1) = 1/2, Id is the d-dimensional identity matrix, and E;is the determinant of matrix Σ. (b) (20 pts) Generalize the solution from part (a) to arbitrary covariance matrices Eo and 1. Discuss the shape of the optimal decision surface.
Answers
(a) To find the optimal decision surface, we need to find the equation that satisfies P(Y = 1|x) = P(Y = 0|x). In this problem, we are given that each class-conditional distribution is defined as a two-dimensional Gaussian distribution with mean mi and covariance matrix Σi:
P(x|Y = i) = (2π|Σi|)^(-1/2) exp[-1/2 (x - mi)ᵀΣi^(-1)(x - mi)] where i ∈ {0,1}, mi = (1,2) for Y = 0 and mi = (6,3) for Y = 1, and Σi = Σ for i ∈ {0,1}. We are also given that P(Y = 0) = P(Y = 1) = 1/2.
Using Bayes' rule, we can find the posterior probability of Y = 1 given x:
P(Y = 1|x) = P(x|Y = 1)P(Y = 1) / [P(x|Y = 0)P(Y = 0) + P(x|Y = 1)P(Y = 1)]
Substituting the Gaussian distributions and simplifying, we get:
P(Y = 1|x) = [1 + exp(-q(x))]^(-1)
where q(x) = (1/2)[(x - m1)ᵀΣ^(-1)(x - m1) - (x - m0)ᵀΣ^(-1)(x - m0) + 2log(π/2)]
The decision surface is the set of points x such that P(Y = 1|x) = P(Y = 0|x), or equivalently, q(x) = 0.
Solving for q(x) = 0, we get:
(x - m1)ᵀΣ^(-1)(x - m1) - (x - m0)ᵀΣ^(-1)(x - m0) + 2log(π/2) = 0
Expanding and simplifying, we get:
xᵀΣ^(-1)(m1 - m0) - 1/2(m1ᵀΣ^(-1)m1 - m0ᵀΣ^(-1)m0) = 0
Plugging in the given values, we get:
x₁ + 5x₂ = 13.5
Therefore, the optimal decision surface is the line x₁ + 5x₂ = 13.5.
(b) To generalize the solution to arbitrary covariance matrices Σ0 and Σ1, we can derive the decision surface equation by following the same steps as in part (a), but using the general expressions for the Gaussian distributions:
P(x|Y = i) = (2π|Σi|)^(-1/2) exp[-1/2 (x - mi)ᵀΣi^(-1)(x - mi)]
where Σi is the covariance matrix for class i, and mi is the mean vector for class i.
Using Bayes' rule and simplifying, we get:
P(Y = 1|x) = [1 + exp(-q(x))]^(-1)
where q(x) = (1/2)[(x - m1)ᵀΣ1^(-1)(x - m1) - (x - m0)ᵀΣ0^(-1)(x - m0) + log(|Σ0|/|Σ1
Learn more about Gaussian distribution here:
https://brainly.com/question/29734279
#SPJ11
Related Questions
Anybody can I know is this the working and the answer are right? If any wrong plssss tell me..
Answers
Answer:
\(\boxed{Domain = \{3,6,9\}}\)
\(\boxed{Range = \{9,18\}}\)
Step-by-step explanation:
The relation is:
=> {(3,9)(3,18)(6,18)(9,18)}
Domain => x inputs of the ordered pair
Domain = {3,6,9}
Range => y inputs of the ordered pair
Range = {9,18}
1
Select the correct answer from each drop-down menu.
Consider the function RX) = 3x + 1 and the graph of the function gx) shown below.
Y
A
6
+
2
-6
.
- 2
2
6
-27
-6
Answers
Answer:
The graph of g(x) is the graph of f(x) translated 6 units down, and
g(x) = f(x) - 6
Step-by-step explanation:
Let us revise the vertical translated of a function f(x)
If f(x) translated k units up, then its image g(x) = f(x) + kIf f(x) translated k units down, then its image g(x) = f(x) - kThe form of the linear function is f(x) = m x + b, where
m is the slope of the lineb is the y-intercept (value y at x = 0)We will the rules above to solve the question
∵ f(x) = 3x + 1
→ Compare f(x) with the form of the function above
∴ m = 3 and b = 1
∴ The y-intercept is (0, 1)
∴ The graph of f(x) intersects the y-axis at point (0, 1)
From the graph
∵ The graph of g(x) intersects the y-axis at the point (0, -5)
→ That means the y-intercept of g(x) is down the y-intercept of f(x)
∵ The difference between the y-intercepts g(x) and f(x) = -5 - 1 = -6
∴ The graph of f(x) is moved down by 6 units
∴ The image of f(x) is g(x) = f(x) - 6
The graph of g(x) is the graph of f(x) translated 6 units down, and
g(x) = f(x) - 6
The shapes of the horizontal cross-sections of the cone below are not all
congruent.
A. True
B. False
Answers
Answer:
B. False
Step-by-step explanation:
We are given the statement,
'The shapes of the horizontal cross-sections of the cone are all congruent'.
Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.
Further, the radius of the circle vary depending on the position form where the cone is cut i.e.
If cut from the top, the circle is approximately equal to a point.
If cut from the middle, the radius of the circle is less than the radius of the cone.
If cut from the bottom, the radius of the circle is equal to the radius of the cone.
Now, 'two figures are congruent if they overlap each other'.
Since, the circles have different radius, they will not overlap each other.
Thus, all the cross-sections of the cone would not be congruent.
Hence, the given statement is false.
Step-by-step explanation:
The solution is, the given statement is B. False.
What is a cross-section of any shape?A cross-section is a shape formed by cutting a solid (such as a cone, cylinder, or sphere) with a plane. If a cylinder-shaped object is cut by a plane parallel to its base, the resulting cross-section is a circle. As a result, the object intersected.
here, we have,
We are given the statement,
'The shapes of the horizontal cross-sections of the cone are all congruent'.
Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.
Further, the radius of the circle vary depending on the position form where the cone is cut i.e.
If cut from the top, the circle is approximately equal to a point.
If cut from the middle, the radius of the circle is less than the radius of the cone.
If cut from the bottom, the radius of the circle is equal to the radius of the cone.
Now, 'two figures are congruent if they overlap each other'.
Since, the circles have different radius, they will not overlap each other.
Thus, all the cross-sections of the cone would not be congruent.
Hence, the given statement is false.
To learn more about the cross-section of the shapes, visit:
brainly.com/question/13028300
#SPJ7
geometry, finding angle
Answers
Answer:
See below
Step-by-step explanation:
Angle a cos = adj leg / hyp
arcos(28/35) = a = 36.9 °
angle b you could just say
a + 90 + b = 180° (angles in triangle sum to 180 )
36.9 + 90 + b = 180 b = 53.1°
or angle b = arcsin (opp/hyp) = arcsin (28/35) = 53.1°
What is the value?
90.5=
1/81
4.5
3
Answers
Answer:181/2
Step-by-step explanation:
90.5 as a fraction is 181/2
PLEASE HURRY, TEST QUESTION!!!!
Question- The original radius of a sphere is 6 centimeters. Explain how the surface area of the sphere would change if the radius was halved to 3 centimeters. Round your answers to the nearest whole number.
Answers
Step-by-step explanation:
Refer to pic.............
Please Answer all if you do I give brainly
Answers
Answer:
Squares:
1 is 12.4in
6.2 x 6.2 = 12.4
2 is 21 in
5 1/2 x 4 = 21
Triangles:
1 is 48 in
16+16+16=48
2 is 21 in
\(A = \frac{h\x_{b} }{2} = \frac{7 * 6}{2} = 21\)
hoped that helped:P
Step-by-step explanation:
Do NOT type the $ sign in your answers. Make sure you round correctly, to the nearest DOLLAR, or the quiz will not recognize your answer as correct.
$1925 in invested into an account that pays 0.44% interest compounded monthly, for 3.5 years.
a) What is the value of the investment after 3.5 years?
b) How much interest was earned?
Answers
Answer:
Step-by-step explanation:
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
Answers
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
To learn more about the midpoint;
https://brainly.com/question/28224145
#SPJ4
how to do this question plz?
Answers
Answer:
y+y-8=<41,I think that's the answer
A new health drink has 150% of the recommended daily allowance (RDA) for a certain vitamin. The
RDA for this vitamin is 20 mg. How many milligrams of the vitamin are in the drink?
There are mg of the vitamin in the drink.
Answers
Multiply 1.5 times the 20 mg = 30 mg in the drink.
150% is one and a half times a value.
x+4=3x+9 how to solve this?
Answers
Answer:
x = - \(\frac{5}{2}\)
Step-by-step explanation:
x + 4 = 3x + 9 ( subtract x from both sides )
4 = 2x + 9 ( subtract 9 from both sides )
- 5 = 2x ( divide both sides by 2 )
- \(\frac{5}{2}\) = x
Please help ASAP !! :)
Answers
Answer:
temperature is decreasing as time passesx-axishot drink temperature (°C)Step-by-step explanation:
1. Each value of temperature is lower than the one previous, so we can say the temperature is decreasing. We also notice that the rate of decrease is getting smaller, possibly because the temperature is approaching a horizontal asymptote.
__
2. The horizontal axis, where temperature is plotted, is conventionally called the x-axis.
__
3. The label on the vertical axis is "temperature" and the graph title is "cooling a hot drink ...", so we presume the dependent variable is the temperature of a hot drink.
Please help pre algebra it’s super hard
Answers
Answer:
a reflection and then a translation
a translation and then a rotation
a rotation and then a reflection
Hope this helps
x represents a positive interger
X < 7
How should I solve this? It would help with a step by step guide
Answers
If x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
The x represents a positive integers
Positive integers are the integers greater than 0. In number line the positive number will be at the right side of the 0. The negative integers are the integers less than 0. In number line the negative number will be at the left side of the 0.
The given inequality is
x<7
The inequality is the mathematical expression represents the relation between the two values that is not equal
Here x is less than 7 and a positive integer
Therefore,
x = {1, 2, 3, 4, 5, 6}
Hence, if x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
Learn more about inequality here
brainly.com/question/28823603
#SPJ1
Is my answer correct?
Answers
Answer:
yes $56 is correct
Step-by-step explanation:
The 3 part of the ratio relates to $42 , then
$42 ÷ 3 = $14 ← value of 1 part of the ratio , then
4 parts = 4 × $14 = $56
Find the missing side of each triangle
Answers
Answer:
B) x = √118 mi
Step-by-step explanation:
This is a right triangle, so we can the measure of x using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
a and b are the shorter legs,and c is the hypotenuse (longest side opposite the right angleIn the figure, the sides measuring x mi and √26 mi are the legs, so we plug these in for a and b in the theorem,and the side measuring 12 mi is the hypotenuse, so we plug it in for c in the theorem:Step 1: Plug in x and √26 for a and b and 12 for c and simplify:
x^2 + (√26)^2 = 12^2
x^2 + 26 = 144
Step 2: Subtract 26 from both sides to isolate x^2:
(x^2 + 26 = 144) - 26
x^2 = 118
Step 3: Take the square root of both sides to isolate x:
√(x^2) = √118
x = √118 mi
Find the area of the shape 11cm 14cm 9cm 20cm who ever answers correctly gets brainlist
Answers
Answer:
Step-by-step explanation:
Given : shape 14cm 11cm 9cm 20cm
To Find : Find area
Solution:
20 - 1 1 = 9 cm
We can divide figure in 2 parts
rectangle = 14 cmx 11 cm
square = 9 cm x 9 cm
Area of rectangle = 14 * 11 = 154 cm²
Area of square = 9 * 9 = 81 cm²
Total area = 154 + 81
= 235 cm²
Learn More :
Find the area of the given figure withTU = 6 cm, SR = 8 cm, UR = 15 ...
brainly.in/question/14804329
In the figure, triangle ABC in the semi circle . Find the area if the ...
brainly.in/question/13845921
Answer:
Area = 235 square cm
Step-by-step explanation:
Given : shape 14cm 11cm 9cm 20cm
To Find : Find area
Split the figure into rectangle and square:
Rectangle : 14 x 11
Square : 9 x 9
\(Area \ of \ rectangle : 14 \times 11 = 154 \ cm^2\)
\(Area \ of \ square = 9 \times 9 = 81 \ cm^2\)
\(Total \ area = 154 + 81 = 235 \ cm^2\)
The area of the surface of the swimming pool is 210 square feet. what is the length of the deep end?
Answers
The length of the deep end is 12 feet of the swimming pool.
Given: Area of the swimming pool is 210 square feet
Width of the pool = 10 feet
The length of the shallow end is 9 feet and the length of the deep end is d.
To find the value of d.
Let's solve the problem.
The area of the swimming pool is 210
The width is 10
The deep end length is d
The shallow end length is 9
The total length of the swimming pool = The length of the deep end + The length of the shallow end
=> d + 9
Therefore, the total length of the swimming pool is d + 9
The surface of the swimming pool is rectangular, so
The area of rectangle = width × length
Therefore,
area of swimming pool = width of the pool × length of the swimming pool
=> 210 = 10 × (9 + d)
or 10 × (9 + d) = 210
Dividing both sides by 10:
10 × (9 + d) / 10 = 210 / 10
9 + d = 21
Subtracting 9 on both sides:
9 + d - 9 = 21 - 9
d = 12
Therefore the length of the deep end is 12 feet
Hence the length of the deep end is 12 feet of the swimming pool.
Know more about "areas" here: https://brainly.com/question/27683633
#SPJ4
The length of the deep end of the swimming pool is 12 feet.
We are given that:
The Area of the swimming pool = 210 square feet
width of the swimming pool = 10 feet
Length of shallow end = 9 feet
Let the length of the deep end be d.
Total length of the swimming pool = length of deep end + length of shallow end = d + 9
Area of swimming pool = width × length
Substituting the values, we get that:
210 = 10 × (9 + d)
9 + d = 21
d = 12
Therefore the length of the deep end of the swimming pool is 12 feet.
Learn more about area here:
brainly.com/question/27683633
#SPJ4
-7–2.1n=-3.5n PLEASE ANSWER
Answers
Answer:
n=5
Step-by-step explanation:
-7-2.1n=-3.5n
+2.1n +2.1n
-7 = -1.4n
/-1.4 /-1.4
n=5
Hope this helps!
If not, I am sorry
Answer:
b = - 1.25
Step-by-step explanation:
-7 - 2.1n = 3.5n
-7 = 3.5n + 2.1n
-7 = (3.5+2.1)n
-7 = 5.6n
-7/5.6 = n
n = -1.25
Check:
-7 -(2.1*-1.25) = 3.5*-1.25
-7 + 2.625 = -4.375
a local travel office has 10 employees. their monthly salaries are given below. find the mean. 1550, 1710, 1630, 1000, 1400, 1610, 1890, 1300, 2700, 5800
Answers
The mean is a measure of central tendency that represents the average value of a set of data. To find the mean of the monthly salaries of the 10 employees in the local travel office, we need to add up all the salaries and divide by the total number of employees.
So, if we add up all the salaries, we get:
1550 + 1710 + 1630 + 1000 + 1400 + 1610 + 1890 + 1300 + 2700 + 5800 = 19,940
Then, we divide this sum by the total number of employees, which is 10.
Mean = 19,940 / 10 = 1,994
Therefore, the mean monthly salary for the 10 employees in the local travel office is $1,994.
It's important to note that the mean is a useful measure of central tendency, but it can be affected by outliers. In this case, the salary of $5,800 is significantly higher than the other salaries, which may skew the mean. To get a better understanding of the distribution of salaries, it may be useful to also look at other measures such as the median and mode.
To find the mean monthly salary of the 10 employees at the local travel office, follow these steps:
1. Add up all the monthly salaries: 1550 + 1710 + 1630 + 1000 + 1400 + 1610 + 1890 + 1300 + 2700 + 5800 = 20,590.
2. Divide the total sum by the number of employees (10): 20,590 / 10 = 2,059.
The mean monthly salary of the 10 employees at the local travel office is 2,059. The mean represents the average salary of the employees, providing a general idea of the salary level at the office. In this case, the mean gives a local perspective on the financial situation of the employees within the travel office, allowing for comparisons with other companies or the industry standard.
More on Mean: https://brainly.com/question/1136789
#SPJ11
nolan has too for 26 bedding plants in his garden. he can get pansies for $1.99 each, marigolds for $1.39 each, and zinnias for $0.74 each. he plans to buy 10 of one type and 8 each of the other two types of plants.
a) what is the minimum (in $) edward will have to spend?
b) what is the maximum (in $) edward could spend
Answers
Using proportions, it is found that:
a) The minimum Edward will have to spend is of $34.44.
b) The maximum Edward will have to spend is of $36.94.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Since a zinnia is the least expensive plant, for the minimum, he buys 10 zinnias and 8 of the other 2, hence, considering the price of each plant, the minimum amount spent is given by:
Min = 10 x 0.74 + 8 x (1.99 + 1.39) = $34.44.
For the maximum, we buy 10 pansies, hence:
Max = 10 x 1.99 + 8 x (0.74 + 1.39) = $36.94.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Given the random set of four numbers, X1=1,2,3, and 5 , what's the value ΣX
2
= ? ( 2 pts.) a. 25 b. 30 c. 39 d. 121 (3) None of the above 2. Given the random set of three numbers, Xi=2,3, and 4 , what's the value of Σ(X+1)
2
= ? (3 pts. ) a. 8 b. 14 (4) 50 d. 64 e. None of the above (2+1)
2
+(3+1)
2
+(4+1)
2
=9+16+25=50 3.. Given the following two pairs of observations, What's the value of ∑XY ? ( 3 pts.)
X
1 2×
2
Y
=4=8 3×6=18 4. Lee estimated the students' self-diagnostic test scores for the special quiz of OM class during this semester. What is the expected test score in the test results? ( 3 pts.)
Test score (x) Prob. P(x)
10…
20…
30…
40…
0.2=2
0.3=6
0.3=9
0.2=8
a. 10 b. 20 c. 12.5 6. 25 e. None of the above 5. Given the following probability distribution of X, What's the value of (1) expected value (=μ) lpts. and (2) standard deviation (=σ)3pts..(4pt.) a. 2.3 and 1.005 b. 2.3 and 1.010 \&. 2.5 and 1.025 \&. 2.5 and 1.050 e. None of the above
Answers
For the given random set of four numbers the value ΣX² = 39. For the given random set of three numbers the value ΣX² = 50. The expected test score is 25. The value of the expected value (μ) is 2.0 and Standard deviation (σ) is 1.095.
Given the random set of four numbers, X1=1,2,3, and 5, the value ΣX² = ?
The formula for the sum of the squares of n natural numbers is given by,
n∑X² = n(n+1)(2n+1)/6
For X1=1,2,3, and 5, the sum of squares is,
ΣX² = 1² + 2² + 3² + 5²
ΣX² = 1 + 4 + 9 + 25
ΣX² = 39
Therefore, the correct option is c. 39.
Given the random set of three numbers, Xi=2,3, and 4, the value of Σ(X+1)² = ?
The formula for the sum of squares of n natural numbers is given by,
n∑(X+1)² = n(n+3)(2n+3)/6
For Xi=2,3, and 4, the sum of squares is,
Σ(X+1)² = (2+1)² + (3+1)² + (4+1)²
Σ(X+1)² = 3² + 4² + 5²
Σ(X+1)² = 9 + 16 + 25
Σ(X+1)² = 50
Therefore, the correct option is (4) 50.
The expected test score is given by the formula,
Expected test score (μ) = Σ(x * P(x))
where x is the test score and P(x) is the probability for x.
Lee estimated the students' self-diagnostic test scores for the special quiz of OM class during this semester. The test scores and their respective probabilities are,
Test score (x) Prob. P(x)
10 0.2 20 0.3 30 0.3 40 0.2
Expected test score (μ) = Σ(x * P(x))
Expected test score (μ) = (10 * 0.2) + (20 * 0.3) + (30 * 0.3) + (40 * 0.2)
Expected test score (μ) = 2 + 6 + 9 + 8Expected test score (μ) = 25
Therefore, the expected test score is 25. The correct option is None of the above.
Given the following probability distribution of X,
What's the value of (1) expected value (=μ) and (2) standard deviation (=σ)
The formula for the expected value is given by,
μ = Σ(x * P(x))
where x is the test score and P(x) is the probability for x.
The formula for the standard deviation is given by,
σ = sqrt(Σ(x² * P(x)) - μ²)
The probability distribution table of X and its probabilities are given below,
X 1 2 3 4
Probability 0.4 0.3 0.2 0.1
Expected value (μ) = Σ(x * P(x))
Expected value (μ) = (1 * 0.4) + (2 * 0.3) + (3 * 0.2) + (4 * 0.1)
Expected value (μ) = 0.4 + 0.6 + 0.6 + 0.4
Expected value (μ) = 2.0
The value of the expected value is 2.0.
Standard deviation (σ) = sqrt(Σ(x² * P(x)) - μ²)
Standard deviation (σ) = sqrt((1² * 0.4) + (2² * 0.3) + (3² * 0.2) + (4² * 0.1) - 2.0²)
Standard deviation (σ) = sqrt(0.4 + 1.2 + 1.8 + 1.6 - 4)
Standard deviation (σ) = sqrt(1.2)
Standard deviation (σ) = 1.095
Therefore, the correct option is a. 2.3 and 1.005.
Learn more about the standard deviation from the given link-
https://brainly.com/question/475676
#SPJ11
Given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of z), the absolute value of y, and the square root of (xy to the power of z).
Answers
\(x^y^z\) , \(|x|\) are the output of 1st 2 question and for the second question
the final computation SquareRoot(RaiseToPower(x*y, z)) is doing this:
\(\sqrt{(xy)^z}\)
float x , float y , float z
x = Get new line of input
y = Get new line of input
z = Get new line of input
Place RaiseToPower(x, y) in the output.
Place RaiseToPower(x, RaiseToPower(y, z)) to get output
Put abs(x) to output
where abs(x) is absolute value of x
Place SquareRoot(RaiseToPower(x*y, z)) to get disired output
The very first three lines of code simply declare the float type (a number with decimal points) data type of the x, y, and z variables.
After the initial three lines, the user's input is asked in the following three lines.
Coral's Put instruction is used to output an expression for display on the console.
I'm using Coral's built-in RaiseToPower math function to instruct the interpreter to output the value of x raised to the power of y to the console for the initial Put command.
Although the subsequent calculation RaiseToPower(x, RaiseToPower(y, z)) appears to be nested, it actually performs this: \(x^y^z\)
The next computation is AbsoluteValue(x) is doing this \(|x|\)
And the final computation SquareRoot(RaiseToPower(x*y, z)) is doing this:
\(\sqrt{(xy)^z}\)
To know more about squareroot click below:
https://brainly.com/question/15054169#
#SPJ4
Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.cos115 cos65° - sin115 sin65°
Answers
We can use the following identity to solve the exercise:
\(\cos a\cos b-\sin a\sin b=\cos (a+b)\)In this case, we have:
\(\begin{gathered} a=115\degree \\ b=65\degree \end{gathered}\)\(\begin{gathered} \cos a\cos b-\sin a\sin b=\cos (a+b) \\ \cos 115\degree\cos 65\degree-\sin 115\degree\sin 65\degree=\cos (115\degree+65\degree) \\ \cos 115\degree\cos 65\degree-\sin 115\degree\sin 65\degree=\cos (180\degree) \\ \cos 115\degree\cos 65\degree-\sin 115\degree\sin 65\degree=-1 \end{gathered}\)Therefore, the exact value of the given expression is -1.
You’re taking a 33 question multiple choice test. Each question has 4 choices. Clueless on 1 question, you decide to guess. What’s the chance you’ll get it right?
Answers
Please help me solve this, and show your work
Answers
Answer:
16. 25/45 ; 18/45
17 4/7; 4/7
Step-by-step explanation:
5/9 and 2/5
The common denominator is 45
5/9 * 5/5 = 25/45
2/5 *9/9 = 18/45
4/7 and 12/21
Simplify 12/21 by dividing by 3 in the numerator and denominator
12/21 = 4/7
4/7; 4/7
The common denominator is 7
16:25/45;18/45
17: 4/7;4/7
Answer:
16:5/9;2/5
Common denominator is 9*5=45
now
make a equal denominator
5/9=5/9*5/5=25/45
2/5=2/5*9/9=18/45
and
17: 4/7;12/21
common denominator =7
4/7
12/21=4/7
f(−1) : f(3) + f(1).
Answers
Find the volume of the composite solid 3 in. 8 in. 11 in.
Answers
You just multiply at three numbers
A coral reef grows 0.18m every week. how much does it grow in 9 weeks? write your answer in millimeters
Answers
ANSWER
EXPLANATION
The reef grows 0.18m every week
hence,
after 9weeks, it grows:
\(undefined\)