Find the value of
�
xx in the triangle shown below.
�
=
x=x, equals

∘
∘
degrees
A triangle with angle x degrees and its opposite side has a length of ten point four, an angle of sixty-two degrees and its opposite side has a length of twelve, and its third side has a length of twelve.


A triangle with angle x degrees and its opposite side has a length of ten point four, an angle of sixty-two degrees and its opposite side has a length of twelve, and its third side has a length of twelve.

1. When lab = 0:  f_0 = f(lab = 0, cde, ac, ad) Here, we substitute lab with 0 in the function.
2. When lab = 1: f_1 = f(lab = 1, cde, ac, ad) Here, we substitute lab with 1 in the function.
So, the cofactors of the given function f with respect to lab are f_0 and f_1.

To find the cofactors of f with respect to lab using Shannon's Expansion Theorem, we need to consider two cases:

1. When lab = 0:

In this case, we need to remove the term that contains lab. So we can rewrite f as follows:
f = (ab ac ad) + (cde)

To find the cofactor of f with respect to lab = 0, we need to remove the terms that contain both lab and its complement (la!b):
Cofactor of f with respect to lab = 0 = (ac ad) + (cde) = acd + cde + ace + ade

2. When lab = 1:

In this case, we need to set lab to 1 and remove the term that contains its complement (la!b).

So we can rewrite f as follows: f = (ab ac ad) + (cde)

Setting lab to 1 gives us: f|lab=1 = ac ad cde

To find the cofactor of f with respect to lab = 1, we need to remove the terms that contain both lab and its complement (la!b):
Cofactor of f with respect to lab = 1 = ad cde

Therefore, the cofactors of f with respect to lab are acd + cde + ace + ade and ad cde.

Using Shannon's Expansion Theorem, we can determine the cofactors of the given function f with respect to the variable lab.

The theorem states that any function can be expressed as the sum of its cofactors.

Visit here to learn more about Cofactors:

brainly.com/question/12120216

#SPJ11

The composite function in the form f(g(x)) is: y = f(g(x)) = 5e⁶ˣ

To write y = 5 ex 6 as a composite function in the form f(g(x)), we need to identify the inner function u = g(x) and the outer function y = f(u).

Let u = 6x, which means g(x) = 6x.
Now we need to find f(u).

Let f(u) = 5e^u.

Substituting u = 6x in f(u), we get:
f(u) = 5e⁶ˣ

Therefore, the composite function in the form f(g(x)) is:
y = f(g(x)) = 5e⁶ˣ

To learn more about composite function here;

brainly.com/question/5614233#

#SPJ11

The approximate solution for the system of equations is x = -48/29

From the question, we have the following parameters that can be used in our computation:

f(x) = 5/8x + 2

g(x) = -3x - 4

To calculate the solution for the system of equations, we have the following

f(x) = g(x)

Substitute the known values in the above equation, so, we have the following representation

5/8x + 2 = -3x - 4

Multiply through by 8

So, we have

5x + 16 = -24x - 32

Evaluate the like terms

29x = -48

Evaluate

x = -48/29

Hence, the solution is x = -48/29

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

Answer: At least 96 OR 340 students.

Explanation:

1) Since we know that at least 96 students of the survey have at least one sibling, it is safe to assume that 96 students of the total 425 students have at least one sibling.

2) Since we know that 80% of respondents to the survey have at least one sibling, we could apply that percentage to the whole school:

80% × 425 students = 340 students.

Hence, we could conclude that 340 students have at least one sibling.

The largest level of confidence for which the confidence interval will not contain 2 is "A 99% confidence level". Therefore the answer is option (E).

Since the p-value of 0.67 is quite large, we fail to reject the null hypothesis at any reasonable level of significance, and we cannot conclude that the population mean is different from 2.

As we cannot reject the null hypothesis at any reasonable level of significance, we cannot conclude that the population mean is different from 2. Therefore, the confidence interval for µ will always include 2, regardless of the level of confidence.

Therefore, the confidence interval for µ will always contain 2, regardless of the level of confidence. This means that the answer is (E) A 99% confidence level.

Learn more about confidence interval :

https://brainly.com/question/29537989

#SPJ4

If the vertices of triangle PQR, are rotated 90 degree in counter-clockwise direction, then the new vertices of triangle P'Q'R' is P'(1,-3), Q'(3,-3) and R'(2,-6), the correct option is (b).

To rotate a point (x,y) 90 degrees counterclockwise about the origin, we can use the following formula:

(x', y') = (-y, x)

that means if the coordinate of triangle PQR is (x,y) , then after 90 degree counter clockwise rotation , the coordinate will be = (-y,x);

Using this formula for each vertex, we get:

⇒ P' = (-(-1), -3)) = (1, -3),

⇒ Q' = (-(-3), -3)) = (3, -3),

⇒ R' = (-(-2), -6)) = (2, -6),

Therefore, the coordinates of the triangle after the rotation are P'(1,3), Q'(3,3), and R'(2,6), Option(b) is correct.

Learn more about Rotation here

https://brainly.com/question/2271360

#SPJ1

The given question is incomplete, the complete question is

Triangle PQR has vertices P(-3, -1), Q(-3, -3), and R(-6, -2). The triangle is rotated 90° counterclockwise using the origin as the center of rotation. Which graph shows the image, triangle P’Q’R’?

Group of answer choices

(a) On a coordinate plane, triangle P'Q'R' has points (-3, -1), (-3, -3), (-6, -2).

(b ) On a coordinate plane, triangle P'Q'R' has points (1, -3), (3, -3), (2, -6).

(c) On a coordinate plane, triangle P'Q'R' has points (3, -1), (3, -3), (6, -2).

(d) On a coordinate plane, triangle P'Q'R' has points (-1, 3), (-3, 3), (-2, 6).

Required length of the ST is 35 feet.

What is circle?

A circle is a geometrical shape in which all points on its boundary or circumference are equidistant from a fixed point called the center. It can also be defined as the locus of all points that are at a fixed distance from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter.

First, we notice that since PS is a diameter, angle PXS is a right angle (90 degrees) since it subtends the diameter. Therefore, angle QXT = 180 - angle PXT - angle RXS = 180 - 125 - 97 = 38 degrees.

Since X is the center of the circle, PX = RX = SX = TX (the radius of the circle), and so triangle PXS is an isosceles triangle with PS = 28 feet as its base. We can find PX as follows:

cos(125/2) = (PS/2) / PX

PX = (PS/2) / cos(125/2) = 28 / cos(62.5) = 60.1 feet (rounded to one decimal place)

Now we can use the law of cosines to find ST:

ST² = PS² + PT² - 2(PS)(PT)cos(QXT)

ST² = 28² + 2(PX² - 14²) - 2(28)(PX)cos(38)

ST² = 784 + 2(3602 - 196) - 2(28)(3602 - 196)cos(38)

ST² = 784 + 6806 - 2(28)(3406)cos(38)

ST²= 784 + 6806 - 64687.5

ST² = 1245.5

ST ≈ 35.3 feet (rounded to the nearest ten)

Therefore, the length of ST is approximately 35 feet.

Learn more about circle here,

https://brainly.com/question/29673128

#SPJ1

The box-and-whisker plot for the data set, 18, 30, 24, 19, 22, 34, 13, 12, 20, 25, 28, 17, is shown in the diagram attached below.

In order to make a box-and-whisker plot for the data given, we have to find the five-number summary of the data, which would be displayed on the box-and-whisker plot.

Given the data as: 18, 30, 24, 19, 22, 34, 13, 12, 20, 25, 28, 17

Minimum: 12 (smallest data value)

First Quartile: 17.5 (middle of the first half of the data when ordered)

Median: 21 (center of the data set)

Third Quartile: 26.5 (middle of the second half)

Maximum: 34 (largest data value)

The box-and-whisker plot is shown below in the attachment.

Learn more about the box-and-whisker plot on:

https://brainly.com/question/3209282

#SPJ1

The sum of the convergent geometric series is 1/7.

The geometric series in question is given by the formula: (−3)(n-1) / (4n), with n starting from 1 to infinity. To determine if it's convergent or divergent, we need to find the common ratio, r.

The common ratio, r, can be found by dividing the term a_(n+1) by the term a_n:

r = [(−3)n / (4(n+1))] / [(−3)(n-1) / (4n)]

After simplifying, we get:

r = (-3) / 4

Since the absolute value of r, |r| = |-3/4| = 3/4, which is less than 1, the geometric series is convergent.

To find the sum of the convergent series, we use the formula:

Sum = a_1 / (1 - r)

In this case, a_1 is the first term of the series when n = 1:

a_1 = (−3)(1-1) / (4) = 1/4

Now we can find the sum:

Sum = (1/4) / (1 - (-3/4)) = (1/4) / (7/4) = 1/7

Know more about geometric series here:

https://brainly.com/question/4617980

#SPJ11

The value of Lucas number L(4) is 4.

To find L(4) using the recursive definition of Lucas numbers, we'll follow these steps:

1. L(n) = 1 if n = 1
2. L(n) = 3 if n = 2
3. L(n) = L(n-1) + L(n-2) if n > 2

Since we want to find L(4), we need to first find L(3) using the recursive formula:

L(3) = L(2) + L(1)
L(3) = 3 (from step 2) + 1 (from step 1)
L(3) = 4

Now we can find L(4):

L(4) = L(3) + L(2)
L(4) = 4 (from L(3) calculation) + 3 (from step 2)
L(4) = 7

So, the value of L(4) in the Lucas numbers is 7.

Explanation;-

STEP 1:-  First we the recursive relation of the Lucas number, In order to find the value of the L(4) we must know the value of the L(3) and L(2)

STEP 2:- Value of the L(2) is given in question, and we find the value of L(3) by the recursion formula.

STEP 3:-when we get the value of L(3) and L(2) substitute this value in L(4) = L(3) + L(2) to get the value of L(4).

Know more about the "Recursion formula" click here:

https://brainly.com/question/8972906

#SPJ11

a. The marginal PMFs of U and V can be obtained by summing over all possible values of the other random variables: P(U = u):[tex]= sum_{v=-u}^{u} P(U = u, V = v), P(V = v) \\\\= sum_{u=|v|}^{2-|v|} P(U = u, V = v).[/tex]

and b. P(V = -1) = P(X = 1, Y.

a. The joint probability mass function (PMF) of U and V, we can use the definition of U and V and the fact that X and Y are independent Bernoulli(0.5) random variables:

For U = X + Y and V = X - Y, we have:

U = 0 if X = 0 and Y = 0

U = 1 if (X = 0 and Y = 1) or (X = 1 and Y = 0)

U = 2 if X = 1 and Y = 1

V = 0 if X = 0 and Y = 0

V = 1 if (X = 0 and Y = 1) or (X = 1 and Y = 0)

V = -1 if X = 1 and Y = 1

Using the above equations, we can write the joint PMF of U and V as:

P(U = u, V = v) = P(X = (u+v)/2, Y = (u-v)/2)

Since X and Y are independent Bernoulli(0.5) random variables, we have:

P(X = x, Y = y) = P(X = x) * P(Y = y) = 0.5 * 0.5 = 0.25

Therefore, we can write the joint PMF of U and V as:

P(U = u, V = v) =

{ 0.25 if u+v is even and u-v is even, and u+v >= 0

{ 0 otherwise

The marginal PMFs of U and V can be obtained by summing over all possible values of the other variable:

[tex]P(U = u) = sum_{v=-u}^{u} P(U = u, V = v)\\P(V = v) = sum_{u=|v|}^{2-|v|} P(U = u, V = v)[/tex]

b. To check if U and V are independent, we need to show that their joint PMF factorizes into the product of their marginal PMFs:

P(U = u, V = v) = P(U = u) * P(V = v) for all u and v

Let's consider the case where u+v is even and u-v is even:

P(U = u, V = v) = 0.25

P(U = u) * P(V = v) =

[tex]sum_{v'=-u}^{u} P(U = u) * P(V = v') * delta_{v,v'}[/tex]

= P(U = u) * P(V = v) + P(U = u) * P(V = -v) if u > 0

= P(U = u) * P(V = 0) if u = 0

delta_{v,v'} is the Kronecker delta function that equals 1 if v = v' and 0 otherwise.

Therefore, U and V are independent if and only if P(U = u) * P(V = v) = P(U = u, V = v) for all u and v.

Now let's compute the marginal PMFs of U and V:

P(U = 0) = P(X = 0, Y = 0) = 0.25

P(U = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = 0.5

P(U = 2) = P(X = 1, Y = 1) = 0.25

P(V = -1) = P(X = 1, Y

Learn more about random variables visit: brainly.com/question/17217746

#SPJ4

Answer:

Step-by-step explanation:

Classical probability assumes that all outcomes in the sample space are equally likely to occur. For example, when a single die is rolled, each outcome has the same prob- ability of occurring.

Answer:

B

Step-by-step explanation:

The method that assures random selection is:

The supervisor should select one grade level and survey randomly selected students from that grade.

Option A is the correct answer.

It is the way of choosing a number of required items from a number of populations given.

Each item has an equal of being chosen.

We have,

Option A would be the best method to assure the random selection of a sample population because it involves selecting a specific group (one grade level) and then randomly selecting individuals from that group.

This ensures that all individuals within the chosen group have an equal chance of being selected for the survey.

Option B may not provide an accurate representation of the entire student population as some grades may have a higher or lower percentage of students bringing their lunch.

Option C is not feasible as it would be time-consuming and resource-intensive to survey all students enrolled in the school.
Option D is not a random selection method as it only involves selecting one grade level and surveying all students in that grade, which may not be representative of the entire student population.

Thus,

The supervisor should select one grade level and survey randomly selected students from that grade.

Learn more about random sampling here:

https://brainly.com/question/12719656

#SPJ5

(a) A basis for the subspace { (w, x, y) ∈ R³ : 2w + x - y = 0 } is {(1, 0, 2), (0, 1, 1)}.

(b) A basis for the subspace { (x, y, z) ∈ R³ : x - 2y + z = 0, x + 2z = 0 } is {(-2, 1, 1)}.

(a) To find a basis for the subspace { (w, x, y) ∈ R³ : 2w + x - y = 0 }, we can first rewrite the equation as y = 2w + x. Then any vector (w, x, y) in the subspace can be written as (w, x, 2w + x) = w(1, 0, 2) + x(0, 1, 1). Therefore, a basis for the subspace is {(1, 0, 2), (0, 1, 1)}.

(b) To find a basis for the subspace { (x, y, z) ∈ R³ : x - 2y + z = 0, x + 2z = 0 }, we can use the equations to solve for x, y, and z in terms of a free variable. Using z as the free variable, we get x = -2z and y = z. Therefore, any vector (x, y, z) in the subspace can be written as (-2z, z, z) = z(-2, 1, 1). Since there is only one free variable, z, we have a one-dimensional subspace. Therefore, a basis for the subspace is {(-2, 1, 1)}.

Learn more about Subspace :

https://brainly.com/question/31392995

#SPJ4

Answer:

To determine if MaryKate has enough paint without calculating, we would need to know the surface area of the birdhouse she wants to paint. If the surface area of the birdhouse is less than or equal to 39.5ft^2, then MaryKate has enough paint. However, if the surface area of the birdhouse is greater than 39.5ft^2, then MaryKate will not have enough paint to cover the entire birdhouse and will need to purchase more paint.

Answer:

We can tell that MaryKate has enough paint without calculating by comparing the amount of paint needed to the amount of paint she has available. If the amount of paint she has available is greater than or equal to the amount of paint needed to cover the birdhouse, then she has enough paint.

To determine the amount of paint needed to cover the birdhouse, we need to know the surface area of the birdhouse. Without knowing the surface area, we cannot make a definitive conclusion about whether MaryKate has enough paint or not.

However, if we assume that the surface area of the birdhouse is less than or equal to 39.5 square feet, then we can say that MaryKate has enough paint because a pint of paint that covers 39.5 square feet of surface can cover at least the entire birdhouse.

Hope this helps!

Answer:

28

Step-by-step explanation:

You must divide 20 by 100 to get 1 percent, then multiply it by 140.

Randy ate 28 pop-tarts this month.

To find out how many pop-tarts Randy ate this month, we first need to calculate 40% of the pop-tarts he ate last month.

To do this, we can multiply 20 by 0.4 to get 8.

Next, we can add this amount to the original number of pop-tarts Randy ate last month (20), giving us a total of 28 pop-tarts for this month.

Therefore, Randy ate 28 pop-tarts this month, which is 40% more than he ate last month.  

Learn more about percentage:

https://brainly.com/question/24877689

The convergence set of the power series ∑n=1∞ [tex](x-2)^n/n^2[/tex] is [1, 3). The series converges for x values in the interval [1, 3), and diverges for x values outside of this interval.

At the endpoints x = 1 and x = 3, the series converges for x = 1 and diverges for x = 3.

To find the convergence set of a power series, we can use the ratio test:

lim[n→∞] |[tex](x - 2)(n+1)^2 / n^2[/tex]| = lim[n→∞] |[tex](x - 2)(1 + 2/n)^2[/tex]| = |x - 2| lim[n→∞] [tex](1 + 2/n)^2[/tex]

Since lim[n→∞] [tex](1 + 2/n)^2 = 1[/tex], the series converges if |x - 2| < 1, and diverges if |x - 2| > 1.

If |x - 2| = 1, then the ratio test is inconclusive, so we need to check the endpoints x = 1 and x = 3 separately.

For x = 1, the series becomes:

∑n=1infinitynn2 = ∑n=1infinitynn2

which is the alternating harmonic series, which converges by the alternating series test.

For x = 3, the series becomes:

∑n=1infinitynn2 = ∑n=1[infinity]nn2

which diverges by the p-series test with p = 2.

Therefore, the convergence set of the series is:

1 ≤ x < 3

In interval notation, this can be written as:

[1, 3)

Learn more about convergence set of a power series

brainly.com/question/31440916

#SPJ11

False. If the null hypothesis is rejected using a two-tailed test, it does not necessarily mean it would be rejected if the researcher had used a one-tailed test.

One-tailed tests have more power to detect an effect in a specific direction, but they also have a higher risk of making a Type I error (rejecting the null hypothesis when it's actually true). The decision to use a one-tailed or two-tailed test should be based on the research question and prior knowledge of the expected direction of the effect.

A two-tailed test is more conservative and examines both tails of the distribution, while a one-tailed test focuses on only one direction. The outcome depends on the direction of the effect and the specific hypothesis being tested.

To know more about direction click here

brainly.com/question/31451833

#SPJ11

Answer:3.5/1     14/4     21/6

Step-by-step explanation:

это вопрос 10 класса? Вопрос старшеклассника??

Answer: I think its reflected

Step-by-step explanation:

it will take the band 50 minutes to walk 10 blocks.

So the answer is (B) 50 minutes.

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

The marching band is marching at a rate of 3 blocks in 15 minutes. To find how long it will take them to walk 10 blocks, we can set up a proportion:

3 blocks / 15 minutes = 10 blocks / x minutes

where x is the time it will take to walk 10 blocks.

Simplifying the proportion:

3/15 = 10/x

Cross-multiplying:

3x = 150

x = 50

Therefore, it will take the band 50 minutes to walk 10 blocks.

So the answer is (B) 50 minutes.

Learn more about proportion on:

https://brainly.com/question/870035

#SPJ1

Answer:

D) 72 cm squared

Step-by-step explanation:

Separate into to shapes, a right triangle and a rectangle

Rectangular area = 6 x 8

6 x 8 = 48

Triangle area, you have to find the length

Equation A + B = C

B = 8 and C = 10

A + 8^2 = 10^2

Need to find A

10^2 - 8^2=

10 x 10 = 100

8 x 8 = 64
100 - 64= 36

Now we have to find the square root of 36
Finding the square root of means finding 2 numbers that are the same and multiplying them to get 36

6 x 6 = 36

So the 6 is A

Now to solve the triangle area

6 x 8 x 1/2 =

48 x 1/2 = 24

Now add the two areas

48 + 24 = 72 cm squared

please mark brainliest :)

The system of inequalities that best represent the shaded feasible region shown on the graph is

x - 4y > -2

x + 2y > 4

Here, we have,

to determine the equation of the guess game

information gotten from the question include

inequality graph showing shaded regions

some interpretation on the information from the question include

shading above a line is greater than

dotted lines mean the inequality do not have equal to

This interpretation removes the first, the second and the last options

making the third option the correct choice

other consideration is the intercept

the first equation at x= 0, x - 4y > -2,  y > 2

the second equation at x= 0, x + 2y > 4,  y > 1/2

Learn more about inequality interpretation:

brainly.com/question/29045926

#SPJ1

An operating system such as Windows or Linux is an example of the software component of an information system. So, the correct option is A. Software.

An operating system such as Windows or Linux is an example of the software component of an information system. Software is a set of instructions or programs that tell the hardware what to do and how to do it. In the case of an operating system, it is the software that manages the computer's hardware resources, provides services for applications, and enables users to interact with the computer. An operating system acts as an intermediary between the hardware and other software programs that run on the computer.

In addition to managing hardware resources, an operating system provides several other key functions, such as memory management, file management, security, and network connectivity. These functions are essential for the effective and efficient operation of an information system. Therefore, an operating system plays a crucial role in the overall functioning of an information system.

Therefore, Option A. Software is the correct answer.

To learn more about Software, visit:

https://brainly.com/question/27359435

#SPJ11

The linear Taylor polynomial is l(x,y) = x-1, and the quadratic Taylor polynomial is q(x,y) = x-1.

To find the linear and quadratic Taylor polynomials for f(x, y) = sin(x-1)cos(y) near (1, 0), we need to find the partial derivatives of f with respect to x and y, evaluated at (1,0):

f(x, y) = sin(x-1)cos(y)

[tex]\dfrac{\partial f}{\partial x}[/tex] = cos(x-1)cos(y)

[tex]\dfrac{\partial f}{\partial y}[/tex] = -sin(x-1)sin(y)

Evaluated at (1,0), we get:

f(1,0) = sin(0)cos(0) = 0

[tex]\dfrac{\partial f}{\partial x}(1,0)[/tex] = cos(0)cos(0) = 1

[tex]\dfrac{\partial f}{\partial y}(1,0)[/tex] = -sin(0)sin(0) = 0

The linear Taylor polynomial is:

l(x,y) = f(1,0) + [tex]\dfrac{\partial f}{\partial x}(1,0)[/tex](x-1) + [tex]\dfrac{\partial f}{\partial y}(1,0)[/tex](y-0)

l(x,y) = 0 + 1(x-1) + 0(y-0)

l(x,y) = x-1

The quadratic Taylor polynomial is:

[tex]q(x,y) = l(x,y) + \dfrac{1}{2} \dfrac{\partial^2f}{\partial x^2}(1,0)(x-1)^2 + \dfrac{\partial^2f}{\partial y^2}(1,0)(y-0)^2 + \dfrac{\partial^2f}{\partial x \partialy}(1,0)(x-1)(y-0)[/tex]

We need to find the second-order partial derivatives:

[tex]\dfrac{\partial^2f}{\partial x^2}[/tex] = -sin(x-1)cos(y)

[tex]\dfrac{\partial^2f}{\partial y^2}[/tex] = -sin(x-1)cos(y)

[tex]\dfrac{\partial^2f}{\partial x \partial y}[/tex] = -cos(x-1)sin(y)

Evaluated at (1,0), we get:

[tex]\dfrac{\partial^2f}{\partial x^2}(1,0)[/tex]= -sin(0)cos(0) = 0

[tex]\dfrac{\partial^2f}{\partial y^2}(1,0)[/tex] = -sin(0)cos(0) = 0

[tex]\dfrac{\partial^2f}{\partial x \partialy}(1,0)[/tex] = -cos(0)sin(0) = 0

Substituting into the quadratic Taylor polynomial formula, we get:

q(x,y) = (x-1) + (1/2)(0)(x-1)² + (1/2)(0)(y-0)² + (0)(x-1)(y-0)

q(x,y) = x-1

Therefore, the linear Taylor polynomial is l(x,y) = x-1, and the quadratic Taylor polynomial is q(x,y) = x-1.

To know more about Taylor polynomial, here

brainly.com/question/31419648

#SPJ4

The following parts can be answered by the concept of Sets.

a.  f is not injective.
b. f is surjective.

(a) To prove or disprove that f is injective, we need to determine whether for every x1, x2 in R such that f(x1) = f(x2), it must be the case that x1 = x2.

Assume f(x1) = f(x2). Then, for any Y in R, we have y^2 < x1 if and only if y² < x2. However, this does not guarantee that x1 = x2. For example, let x1 = 2 and x2 = 3. Both f(x1) and f(x2) include all Y such that y² < 2 and y^2 < 3, respectively, but x1 ≠ x2.

Therefore, f is not injective.

(b) To prove or disprove that f is surjective, we need to determine whether for every set S in P(R), there exists an x in R such that f(x) = S.

Consider an arbitrary set S in P(R). If S is the empty set, then we can choose x = 0, since there are no Y in R such that y² < 0, and f(x) = S. If S is non-empty, let m = sup{y² | y in S}. Then for all Y in R, y² < m if and only if Y in S. Thus, we can choose x = m and f(x) = S.

Therefore, f is surjective.

Therefore,

a.  f is not injective.
b. f is surjective.

To learn more about Sets here:

brainly.com/question/29805748#

#SPJ11

Answer:

The triangle is obtuse.

Step-by-step explanation:

Using the sine rule to determine the other angle:

[tex]\frac{sinA}{a} =\frac{sinB}{b} \\\frac{sin90}{10} =\frac{sinB}{8} \\10sinB=8sin90\\sinB=\frac{8}{10} \\B=sin^{-1} (\frac{8}{10} )\\B=53.1301[/tex]

180 - 53.1301 - 90 = 36.8699

Using sine rule again to determine the unknown length:

[tex]\frac{sinA}{a} =\frac{sinB}{b} \\\frac{sin90}{10} =\frac{sin36.8699}{b} \\10sin36.8699=bsin90\\b=6[/tex]

Answer:

-157

Step-by-step explanation:

8-5[(4+3)^2-(2^3+8)], Your Answer Should Be "-157"

Hope this helps!