Solve. Show all steps.
1/8 x = 1/2

Last option is the correct answer

Answer:

ASA Postulate

Step-by-step explanation:

\( In\: \triangle TKS\: \& \: \triangle TLR\\

\angle 1 \cong \angle 2....(given) \\

TK \cong TL... (given) \\

\angle 3 \cong \angle 4....(given) \\

\therefore \triangle TKS\: \cong \: \triangle TLR.. (ASA \: Postulate) \\\)

Answer:

First option is the correct choice.

Step-by-step explanation:

AAS theorem applies here to prove the claim.

Best Regards!

Answer:

1:3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It's one or the other, so the two on the graph won't connect, and each of them are greater/less than, NOT "or equal to" so both the circles would be closed. When thinking of these, forget about the x and just read greater than 5. On a graph the greater numbers are to the right, so the arrow would be pointing that way

The work done by the force field on the particle moving along the given helix is 60π units of work.

To find the work done by the force field F on the particle that moves along the helix r, we use the formula:

W = ∫ F · dr

where · denotes the dot product, and dr is the differential displacement vector along the path of the particle.

First, we need to calculate dr. Since the particle moves along the helix r, we can write:

dr = dx i + dy j + dz k

where dx, dy, and dz are the differentials of x, y, and z with respect to t, respectively. We have:

dx = -2sin(t) dt

dy = 2cos(t) dt

dz = 5 dt

Therefore, we can write:

dr = (-2sin(t) i + 2cos(t) j + 5k) dt

Next, we need to calculate F · dr. We have:

F · dr = (6x i + 6y j + 2k) · (-2sin(t) i + 2cos(t) j + 5k) dt

= -12sin(t) + 12cos(t) + 10 dt

Finally, we can integrate F · dr over the interval 0 ≤ t ≤ 2π to obtain the work done by the force field F on the particle that moves along the helix r:

W = ∫ F · dr = ∫ (-12sin(t) + 12cos(t) + 10) dt

= [-12cos(t) + 12sin(t) + 10t]0\(^(2π)\)

= (-12cos(2π) + 12sin(2π) + 10(2π)) - (-12cos(0) + 12sin(0) + 10(0))

= 20π

Therefore, the work done by the force field F on the particle that moves along the helix r is 20π.

Learn more about work

brainly.com/question/18094932

#SPJ11

Possible equations of functions \(\(f\)\) and \(\(g\)\) such that \(\(h(x) = (g \circ f)(x)\)\) are: \(\(f(x) = x^2\)\) and \(\(g(x) = \frac{1}{x^2 + 4}\)\).

Let's find the functions f and g such that \(\(h(x) = (g \circ f)(x)\)\), where \(\(h(x) = \frac{x^2}{x^2 + 4}\)\).

We can rewrite h(x) as:

\(\[h(x) = \frac{x^2}{x^2 + 4} = \frac{x^2}{(x + 2)(x - 2)}\]\)

Now, let's consider f and g as follows:

\(\[f(x) = x^2\]\)

\(\[g(x) = \frac{1}{x^2 + 4}\]\)

Substituting these functions into the composition \(\((g \circ f)(x)\)\), we have:

\(\[(g \circ f)(x) = g(f(x)) = g(x^2) = \frac{1}{x^2 + 4}\]\)

Thus, we have found functions \(\(f(x) = x^2\)\) and \(\(g(x) = \frac{1}{x^2 + 4}\)\) such that \(h(x) = \((g \circ f)(x)\)\).

To know more about equations, refer here:

https://brainly.com/question/12951744

#SPJ4

Complete Question:
Given the function \(\( h(x)=\frac{x^{2}}{x^{2}+4} \)\), find possible equations of functions f and g such that \(\( h(x)=(g \circ f)(x) \)\).

Based on the equation that is given, the total cost for the group to attend a play will be 2842.

From the information given, the cost in dollars for a group to attend a play is represented by 72p + 250.

Therefore, when the number of people are 36, the cost will be:

= 72p + 250

= 72(36) + 250

= 2592 + 250

= 2842

Learn more about equations on:

https://brainly.com/question/1214333

Answer:

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the answer.

3 * 17 = 51

The square root of 51 is: 7.141

7.141 is the geometric mean of 3 and 17.

Step-by-step explanation:

Hope it helps! =D

= 2x² + 7/x

Step-by-step explanation:

2x³ + 7/x

= 2 • x • x • x + 7/x

= 2 • x • x • x/x + 7/x

= 2 • x • x + 7/x

= 2x² + 7/x

-TheUnknownScientist

Answer:

2x^2 + 7/x................

The probability that the sweet is a cherry sweet is given as follows:

p = 4/11.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability that it is an apple sweet is 2/11, and the ratio of apple sweets to pear sweets is 2: 5, hence the probability of a pear sweet is given as follows:

p = 5/11.

Then the probability that the sweet is a cherry sweet is given as follows:

p = 1 - (5/11 + 2/11)

p = 1 - 7/11

p = 11/11 - 7/11.

p = 4/11.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

8 x 3 = 24 for should be 24

Only because 8 times larger than three seems like a multiplication problem..

I hope this helps if it is correct!

Answer:

(8+1) x 3 = 27

Step-by-step explanation:

this is correct rather than 8 x 3 = 24 because both sides of 8x3=24 are equal rather than the sum being greater than the statement.

Our answer is A = [5 -2; -10 4]/7.

We know that if λ is an eigenvalue of matrix A, then the eigenvectors corresponding to it satisfy the equation (A - λI)X = 0 where X is the eigenvector matrix and I is the identity matrix

.Using this equation, we can find the matrix A as:

For eigenvalue λ = 3, [A - 3I][x y]T = 0⟹[(a-3) b; c (d-3)][x y]T = 0⟹(a-3)x + by = 0; cx + (d-3)y = 0

We know that the eigenvector [−1, 2] corresponds to this eigenvalue.

So, [x y]T = [-1, 2]T. Therefore, (a-3)(-1) + b(2) = 0 and c(-1) + (d-3)(2) = 0.⟹ a - 3 + 2b = 0 and c - 2d + 6 = 0.Let's solve this system of equations to find a and b in terms of c and d.

⟹ a = 2b + 3 and c = 2d - 6.

Substituting these in the matrix A, we get A = [2b+3 b; 2d-6 d] = b[2 1; 0 0] + d[3 0; 2 -2]

It can be observed that the matrix A can be expressed as a linear combination of eigenvectors corresponding to λ1 = 3 and λ2 = -2.For eigenvalue λ = -2, [A + 2I][x y]T = 0⟹[(a+2) b; c (d+2)][x y]T = 0⟹(a+2)x + by = 0; cx + (d+2)y = 0We know that the eigenvector [2, -5] corresponds to this eigenvalue.

So, [x y]T = [2, -5]T. Therefore, (a+2)(2) + b(-5) = 0 and c(2) + (d+2)(-5) = 0.⟹ 2a - 5b + 4 = 0 and 2c - 5d - 10 = 0.

Let's solve this system of equations to find a and b in terms of c and d.⟹ a = (5b-4)/2 and c = (5d+10)/2.

Substituting these in the matrix A, we get A = [5b-4 b; 5d+10 d] = b[1 1/5; 0 0] + d[2 -1; 5 5]

It can be observed that the matrix A can be expressed as a linear combination of eigenvectors corresponding to λ1 = 3 and λ2 = -2.

Since we now know the eigenvectors corresponding to the eigenvalues of A, we can find P and D matrices.

P is formed using the eigenvectors as its columns and D is a diagonal matrix having the corresponding eigenvalues on its diagonal.

Therefore, P = [−1 2; 2 -5] and D = [3 0; 0 -2]

.We know that A = PDP-1.

Therefore, A = [−1 2; 2 -5][3 0; 0 -2][1/7 -2/7; -2/7 -1/7] = [5 -2; -10 4]/7.A = [5 -2; -10 4]/7.

Therefore, our answer is A = [5 -2; -10 4]/7.

Know more about the matrix here:

https://brainly.com/question/27929071

#SPJ11

The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

To learn more about probability visit

https://brainly.com/question/9793303

#SPJ4

I disagree with Eva. The pool will be full at 11:45 pm thus option (D) will be correct.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given table,

The pool filled out 1000 gallons every 15 minutes.

In 1 hour = 1000 x 4 = 4000 gallons,

To fill out a full pool of 15000 gallons,

15000/4 = 3 + 2000/3

3 hour + (15 + 15 + 15) minutes

⇒ 3 hours and 45 minutes

Since, it begins at 8:00 am thus 8 + 3 + 45 minutes = 11:45 am.

Hence "I don't concur with Eva. At 11:45 p.m., the pool will be filled".

For more information about the work and time relation,

brainly.com/question/6912604

#SPJ1

The volume of the largest right cylinder that fits in a sphere of radius 4 units is 143 m².

Let the diameter of the cylinder be “d" and the height of the cylinder be “h".

Given radius of the sphere = r = 4m

Diameter of the sphere = d = 2r = 2×4 = 08 m

As the cylinder is inscribed in the sphere

Therefore, the diameter of the cylinder be “d" is equal to the height of the cylinder be “h".

i.e, d = h

By Pythagoras Theorem, In triangle ABC

AB²+BC²=AC²

Or, d²+h² = (8)²

Or, h²+h² = 64

Or, 2h² = 64

Or, h² = 64/2

Or, h = √32

And d =√32

Or, r = d/2

       = √32/2 =16/√32

Or, r = 16/√32

Volume of the cylinder = πr²h

                                       =22/7 × (16/√32 )² × √32

                                       = 22/ 7 × 8 ×√32

                                       = 142.229

Rounding up the value 142.229 in 143 m³

Therefore, the largest volume of the cylinder = 143 m³

Learn more about  Volume of Cylinder:

https://brainly.com/question/16788902

#SPJ4

Answer:

your answer is 5^9

Step-by-step explanation:

first you would multiply the terms with the same base by adding their exponents it should look like this:5^3 + 6

then you add the numbers and you should get 5^9

Answer:

4 1/2

Step-by-step explanation:

Matt mixed 2/3 cups of strawberries.

1 1/2 cups of pineapples

2 1/3 cups of grapes

The first step is the calculate the total mixture

= 2/3 + 1 1/2 + 2 1/3

= 2/3 + 3/2 + 7/3

= 27/6

= 9/2

Therefore the amount of 1-cup serving of salad made by Matt can be calculated as follows.

= 9/2 /1

= 9/2

= 4 1/2

Hence Matt made 4 1/2 of 1-cup servings of salad

The dimensions of the rectangle are either 10cm x 24cm or

24cm x 10cm having perimeter 68 cm.

What is Pythagorean theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

A rectangle has 4 angles measure of each is 90°.

A diagonal of rectangle divides it into two right angled triangles.

Pythagorean theorem can be applied on these triangles to get the desired values.

According to the given question:  

Let the length and breadth of rectangle be  x  and  y .

Perimeter:  2x + 2y = 68 (Given)

Using Pythagorean theorem diagonal:  \(x^2+y^2=26^2\)

Using perimeter,  x + y = 34

∴ x = 34 - y

Substituting this is the equation for diagonal

\((34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0\)

Therefore dimensions of rectangle are either 10cm x 24cm or

24cm x 10cm.

To know more about Pythagorean theorem visit

https://brainly.com/question/3346664

#SPJ1

The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as \(e^{-x}\).

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Learn more about exponential at https://brainly.com/question/2456547

#SPJ1

Answer:

the measure of C is 90°

Step-by-step explanation:

it's a right angle

all right angles are 90°

Answer:

f(x)= -3x+14

Step-by-step explanation:

the question gives you

f(x)+1=-3(x-5)

the first thing you want to do is distribute the -3 to the (x-5)

f(x)+1=-3x+15

then you going to subtract the 1 and move it to the other side

f(x)=-3x+14

The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.

What is system of equations?

A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.

A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.

According to given question, x represents the number

So, The number would be 6x ≥ 8x - 4

To know more about system of equations visit,

https://brainly.com/question/2088661

#SPJ1

The probability of a right-handed student being forced to use a left-handed arm tablet is 0.085 or 8.5% using either the binomial or normal model.

A binomial model is appropriate to use for this problem since there are two possible outcomes (left or right-handed) and the probability of each outcome is independent of the other. The probability of a right-handed student being forced to use a left-handed arm tablet is calculated by subtracting the number of left-handed arm tablets (30) from the total number of students in the class (188) and dividing that by the total number of arm tablets (200). This yields a probability of 0.085 or 8.5%.

Using the normal model, the probability of a right-handed student being forced to use a left-handed arm tablet can also be calculated. This model is appropriate since there are a large number of students (188) and the probability of a student being right or left-handed is close to the population average (13%). The probability can be calculated by subtracting the number of left-handed arm tablets (30) from the total number of students in the class (188) and dividing that by the total number of arm tablets (200). This yields a probability of 0.085 or 8.5%.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

Know more about multiplication principle here:https://brainly.com/question/10275154

#SPJ1

Answer: Jacinta

Step-by-step explanation: But the fraction still can be simplified to 1/7

Answer: j is correct

Step-by-step explanation:

Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.

Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.

the complete question is :

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

Learn more about residual plot here

https://brainly.com/question/2876516

#SPJ1

Pua will use 13, 1/4 cups of oatmeal.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Pua needs 3\(\frac{1}{4}\) cups of oatmeal.

The number of 1/4 cups of oatmeal,

she will use,

= 13/4 ÷ 1/4

= 13

Therefore, she will use 13 cups.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ1

Answer:

100

Step-by-step explanation:

1+3+5+7+9+11+13+15+17+19

=1+19 +3+17 ... + 9+11

= 20+20+...20

=5*20 =100

The dynamical stability of the box-shaped vessel at a 20-degree heel is approximately 5,510,350 Nm.

To calculate the dynamical stability of the box-shaped vessel at a 20-degree heel, we need to consider the changes in the center of buoyancy (B) and the center of gravity (G) due to the heeling angle.

Given:

- Length (L) = 65 m

- Breadth (B) = 10 m

- Depth (D) = 6 m

- Draft (T) = 4 m

- GM = 0.6 m (metacentric height)

To determine the dynamical stability, we need to calculate the righting moment (RM) at a 20-degree heel. The formula for calculating the righting moment is:

RM = (GZ) * (W)

Where:

- GZ is the righting arm, which is the horizontal distance between the center of gravity (G) and the vertical line passing through the center of buoyancy (B)

- W is the weight of the vessel

First, let's calculate the weight of the vessel (W):

W = Density of water * Volume of the immersed portion of the vessel

W = Density of water * Length * Breadth * Draft

Assuming the density of saltwater is approximately 1025 kg/m³, we can calculate the weight as follows:

W = 1025 kg/m³ * 65 m * 10 m * 4 m

W = 26,650,000 kg

Next, we need to calculate the righting arm (GZ) at a 20-degree heel. The formula for calculating GZ is

GZ = GM * sin(heel angle)

GZ = 0.6 m * sin(20°)

GZ ≈ 0.207 m

Finally, we can calculate the dynamical stability (RM) using the formula mentioned earlier:

RM = GZ * W

RM = 0.207 m * 26,650,000 kg

RM ≈ 5,510,350 Nm (Newton-meters)

Therefore, the dynamical stability of the box-shaped vessel at a 20-degree heel is approximately 5,510,350 Nm.

for more such question on dynamical visit

https://brainly.com/question/32952661

#SPJ8

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The function f(x, y) = 2x^2 + 2y^2 corresponds to the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2."

A gradient vector field represents the direction and magnitude of the gradient of a function at each point in the plane. The gradient vector field can be visualized by plotting vectors at different points, with the vectors pointing in the direction of the steepest ascent of the function.

In this case, the function f(x, y) = 2x^2 + 2y^2 represents a quadratic function with the coefficients 2 for both x^2 and y^2 terms. The gradient vector field plot that corresponds to this function would show vectors pointing away from the origin (0, 0) in all directions, indicating the direction of steepest ascent.

By matching the function f(x, y) = 2x^2 + 2y^2 with the gradient vector field plot labeled with the equation "f(x, y) = 2x^2 + 2y^2," we can visually observe the direction and magnitude of the gradient vectors associated with the function at each point in the plane.

Learn more about quadratic function here:

https://brainly.com/question/18958913

#SPJ11