1 1/12-7/10 greater than 1/2 or less than 1/2

the antiderivative of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x) is F(x) = 2x + C.

To find the antiderivative F(x) of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x), we can simplify the expression and integrate each term individually.

We know that csc(x) = 1/sin(x), cot(x) = 1/tan(x), sec(x) = 1/cos(x), and tan(x) = sin(x)/cos(x).

Substituting these values into the expression:

f(x) = 2 * (1/sin(x)) * (1/tan(x)) * (1/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (1/(sin(x)/cos(x))) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (cos(x)/sin(x)) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * 1

= 2

The antiderivative of a constant function is simply the constant multiplied by x. Therefore:

F(x) = 2x + C

where C represents the constant of the antiderivative.

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Answer:

acute angle

Step-by-step explanation:

The value of x in the triangle is 11.62

The complete question is in the attached image

From the image, we have the following tangent function

tan(71) = x/4

Make x the subject

x = 4 * tan(71)

Evaluate the expression

x = 11.62

Hence, the value of x is 11.62

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Answer:

11.62

Step-by-step explanation:

took the test

Whether the two ratios are 2: 3 and 2: 3 or a proportion

4: 6 and 12: 18

\($\frac{4}{6}$\)   and

\($\frac{12}{18}=\frac{2}{3}$\)   and

2/3

=2: 3 and 2: 3

Yes the given two ratios form a proportion.

The complete question is:

Check whether the given two ratios form a proportion or not: 4: 6  12: 18

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The general strategy for solving an equation of the form

is to multiply both sides by a, provided a and b are numerical constants, and x is unknown. This gives

Hence, the correct option is C

To solve the problem of a vibrating string with damping using numerical methods and time steps, follow these steps:

1. Discretize the string into a set of points along its length.

2. Use a finite difference method, such as the central difference method, to approximate the derivatives in the equation.

3. Apply the difference equation to each point on the string, considering the damping force and given parameters.

4. Set up the initial conditions for the string's displacement and velocity at each point.

5. Iterate over time steps to update the displacements and velocities at each point using the finite difference equation.

6. Compute and store the values of the solution at selected points for analysis.

7. Compare the numerical solution with the analytical solution, if available, to assess accuracy.

8. Plot the results to visualize the behavior of the vibrating string over time.

9. If using MATLAB, write a script to implement the numerical method and generate plots.

Note: The specific equation and initial conditions are missing from the given question, so adapt the steps accordingly.

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Answer:

You would need 1256 flowers.

Answer:

Ans:157

Step-by-step explanation:

\( \frac{628.4}{4} = 157.1\)

round off 157

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Here given that radius of circle is 11 feet. Using the formula of area of circle we will get the required area of circle

On substituting the required values:

Area = 3.14 × (11)²

Area = 3.14 × 121

Area = 379.94 feet²

Hence,

Answer:

The boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Step-by-step explanation:

Let x be the time (in hours) that the boat traveled at 10 miles per hour, and let y be the time (in hours) that it traveled at 30 miles per hour.

We know that:

x + y = 6 (the total time the boat traveled)

We also know that the boat traveled a total distance of 140 miles, which can be expressed as:

10x + 30y = 140

We can use the first equation to solve for one of the variables in terms of the other:

y = 6 - x

Substituting this expression for y into the second equation, we get:

10x + 30(6 - x) = 140

Simplifying and solving for x, we get:

10x + 180 - 30x = 140

-20x = -40

x = 2

Therefore, the boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.

Step-by-step explanation:

The y - intercept is 1 . Since the line goes through the point ( 0 , 2 ) and ( -1 , -2 ) the slope is m = ( - 2 - 2 ) / ( - 1 - 0 ) = -4/-1. so the equation will be y = -4/1x + 1

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

  a.  9.56 × 10^3

Step-by-step explanation:

You want the sum (3.45 × 10^3)+ (6.11 ×10^3).

Distributive property

The distributive property works when adding numbers in scientific notation:

  (3.45 × 10^3)+ (6.11 × 10^3) = (3.45 +6.11) × 10^3 = 9.56 × 10^3

Answer:

8x+140=180

8x=40

x=5°

Step-by-step explanation:

Sum of angles in a straight line=180°

Answer:

-\(\frac{y}{2.5}\) < 10.5

Step-by-step explanation:

All the above can represent stable interhalogen compounds. Interhalogen compounds are formed when different halogens combine with each other.

The general formula for interhalogen compounds is given by XYn, where X and Y represent different halogens, and n represents the number of Y atoms bonded to the X atom. The interhalogen compounds can have different stoichiometries, resulting in different values of n. Therefore, all the given formulas, XY, XY2, XY3, and XY5, can represent stable interhalogen compounds, depending on the specific combination of halogens and their bonding arrangements.

Hence, none of the given formulas does not exist for interhalogen compounds, as all of them can be valid representations of stable interhalogen compounds.

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Answer:

 g(x) = f(5x)

Step-by-step explanation:

We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).

Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...

 g(x) = f(x/(1/5))

 g(x) = f(5x)

The measure of angle A remains as (4x + 20) degrees until we have more information or the specific value of x.

The measure of angle A is given by the expression (4x + 20) degrees. To find the specific measure of angle A, we need to determine the value of x or be provided with additional information.

The given information provides the measure of angle D as (5x - 65) degrees, but it does not directly give us the measure of angle A.

Without knowing the value of x or having any additional information, we cannot determine the specific measure of angle A.

The expression (4x + 20) represents the general form of the measure of angle A, but we need more information or the value of x to evaluate it.

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Answer:

4

Step-by-step explanation:

\(\frac{1}{2} * 4\) = 2

Answer: (b+5)(b-5)

Step-by-step explanation:

both b^2 and 25 are square numbers, so square root both of them to give b and 5, then put into brackets with a + and -

Answer:

Step-by-step explanation:

Volume of a rectangular prism = l x w x h

I am reading the width as 12 1/2 ft

Treat the depth of the ball pit as height

Vol = l x w x h

875 = (20)(12 1/2)(h)

875 = 250(h)

875/250 = 250h/250

3 1/2 = height

depth of the ball pit is 3 1/2 ft

The ball pit is 3.5 feet deep. This can be answered by the concept Surface area.

To find the depth of the ball pit, we can use the equation: Volume = length x width x depth.

The volume of the ball pit is given as 875 cubic feet, the length is 20 feet and the width is 12.5 feet. Let d be the depth of the ball pit. Therefore, the equation we can use is:

875 = 20 x 12.5 x d

To solve for d, we can divide both sides of the equation by (20 x 12.5):

d = 875 / (20 x 12.5)

d = 3.5 feet

Therefore, the ball pit is 3.5 feet deep

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The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

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We are 95% confident that the true population proportion is between 0.479 and 0.521.

The margin of error (ME) is inversely proportional to the square root of the sample size (n). So, to cut the margin of error in half, we need to quadruple the sample size.

In the case of the question, the initial sample size was 2,228. To cut the margin of error in half, we would need to quadruple the sample size to 8,832.

The 95% confidence interval for the population proportion is calculated using the following formula:

CI = p ± ME

In the case of the question, the sample proportion is 0.5. The margin of error is 0.5/✓2,228) = 0.021. So, the 95% confidence interval is:

CI = 0.5 ± 0.021

[0.479, 0.521]

This means that we are 95% confident that the true population proportion is between 0.479 and 0.521.

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To derive the analytical expressions for the optimal portfolio weights of the first and second assets, we need to maximize the expected utility function.

Let's assume the weights of the first and second assets are denoted by w1 and w2, respectively. Since there is no risk-free security available, the sum of weights must be equal to 1: w1 + w2 = 1.

To find the optimal portfolio weights, we need to maximize the expected utility function with respect to w1 and w2. This can be done using optimization techniques, such as Lagrange multipliers or calculus.

We can start by taking the derivative of the expected utility function with respect to w1 and set it equal to zero to find the critical points. Similarly, we take the derivative with respect to w2 and set it equal to zero.

Next, we solve these equations to find the values of w1 and w2 that satisfy the equations. These values will give us the optimal portfolio weights for the first and second assets.

Ihe analytical expressions for the optimal portfolio weights of the first and second assets can be derived by maximizing the expected utility function and solving the resulting equations.

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Answer:

-5+(-6 )= -11 so you would pinpoint -11 on the number line

Step-by-step explanation:

Answer:

F = (7,-5)

Step-by-step explanation:

Coordinates are written as:

(x, y)

So the x value, ( the number on the horizontal axis) is 7

The y value, ( the number on the vertical axis) is -5

So lets input.

F = (7,-5)

If my answer is incorrect, pls correct me!

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-Chetan K

Given the system of equations below:

\( \large{ \begin{cases} x + 2y = 12 \\ x = y - 12 \end{cases}}\)

For the second equation, x-term is isolated and can be substituted in the first equation.

\( \large{(y - 12) + 2y = 12}\)

The equation above is when we substitute x = y-12 in the first equation. Cancel the brackets.

\( \large{y - 12 + 2y = 12}\)

Add up the like term and isolate y-term.

\( \large{3y - 12= 12} \\ \large{3y - 12 + 12 = 12 + 12}\)

Add both sides by 12 to get rid of 12 from the left side to isolate y-term.

\( \large{3y = 24}\)

Divide both sides by 3 so we can finally isolate the term.

\( \large{ \frac{3y}{3} = \frac{24}{3} } \\ \large{ \frac{ \cancel{3}y}{ \cancel{3}} = \frac{ \cancel{24}}{ \cancel{3}} } \\ \large{y = 8}\)

Next, find the x-value because in system of equations - we have to answer as in an ordered pairs or coordinate point. We know y-value now but we don't know x-value yet. To find x-value, we substitute the y-value in one of two equations that are given. You can substitute in both equation but it's not necessary to substitute in both equations at one. I will choose to substitute in x = y-12.

\( \large{x = y - 12}\)

Substitute y = 8 in the equation.

\( \large{x = 8 - 12} \\ \large{x = - 4}\)

Now that we know the both values. We finally have an answer to this problem. Hence.

Answer

The second answer is in ordered pair form. Let me know if you have any doubts!

Answer:

1.5gallons

Step-by-step explanation:

Here,

no. of bottles(a) : 12

no. of cups (b) :a*2

=12*2

=24

Now,

No. of gallons. :24/16

:1.5gallons

.·.A cartoon contains 1.5 gallons of lemon tea.