somebody help me find m∠DEC.

Answer:

\( \frac{6}{x} = \frac{8}{24} \)

\(8x = 144\)

\(x = 18\)

\( \frac{8}{24} = \frac{y}{12} \)

\(24y = 96\)

\(y = 4\)

So x = 18 and y = 4.

Answer:

6.85565

Step-by-step explanation:

Answer: 40 seconds per worksheet

Step-by-step explanation:

From the information given in the question, we are informed that Robert took 8 minutes to complete his 12 worksheets.

Based on this, his unit rate of completing worksheets will be given as:

= 8 minutes / 12

= 480 seconds / 12

= 40 seconds per worksheet

Note 1 minute = 60 seconds

8 minutes = 8 × 60 = 480 seconds

2÷100=0.02

1500×0.02=30

30×3=90

Answer:

£90

Step-by-step explanation:

Simple interest (I ) is calculated as

I = \(\frac{PRT}{100}\) ( P is principal, R is rate of interest and T time in years )

Here P = 1500, R = 2 and T = 3 , then

I = \(\frac{1500(2)(3)}{100}\) = 15 × 2 × 3 = 30 × 3 = £90

Answer:

Nine hundred and eighty six million two hundred and eighteen thousand

three hundred and twenty

986,218,320 in word form is "Nine hundred eighty-six million, two hundred eighteen thousand, three hundred twenty."

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The derivative of the function f(x) = 3x^2 - 1 using the first principle (definition of the derivative) is f'(x) = 6x.

To find the derivative of the function f(x) = 3x^2 - 1 using the first principle (definition of the derivative), we need to evaluate the limit of the difference quotient as h approaches 0.

The difference quotient is given by:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

Substituting the function f(x) = 3x^2 - 1 into the difference quotient, we have:

f'(x) = lim(h->0) [3(x + h)^2 - 1 - (3x^2 - 1)] / h

Expanding and simplifying the numerator, we get:

f'(x) = lim(h->0) [3(x^2 + 2hx + h^2) - 1 - 3x^2 + 1] / h

      = lim(h->0) [3x^2 + 6hx + 3h^2 - 1 - 3x^2 + 1] / h

      = lim(h->0) (6hx + 3h^2) / h

Now, we can cancel out the common factor of h:

f'(x) = lim(h->0) 6x + 3h

Taking the limit as h approaches 0, we obtain the derivative:

f'(x) = 6x

Therefore, the derivative of f(x) = 3x^2 - 1 using the first principle is f'(x) = 6x.

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The polynomial B is represented by:

B = 20m + 28n - 32

The given expressions are:

A = 6m + 2n - 1

C = 14m + 26n - 31

B is the sum of the expressions A and C

It can be represented mathematically as:

B. = A + C

B = 6m + 2n - 1 + 14m + 26n - 31

Collect like terms

B = 6m + 14m + 26n + 2n - 1 - 31

B = 20m + 28n - 32

Therefore, the polynomial B is represented by:

B = 20m + 28n - 32

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The complete question demands that we find B from; B = A+C

The expression which represents the polynomial B is; B = 20m +28n -32.

The given polynomials are;

Since, B= A +C; we have;

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

Step-by-step explanation:

It remains 1/6

because you replace it, it stays as 1/6

Answer:

-1/7

Step-by-step explanation:

\((-1/4)/(7/4) \\\\= (-1/4) * (4/7)\\ \\=-4/28\\=-1/7\)

Answer:

-0.14285714285

Step-by-step explanation:

Answer:

$375

Step-by-step explanation:

$13,500÷36=$375

Hope this helps! :)

Answer:

Step-by-step explanation:

13500 divided by 36

Answer:

x(x²+x+1)

Step-by-step explanation:

im not surewhat answer u want but take note this is FACTORIZATION

Answer:

84

Step-by-step explanation:

x/2=3*28/2=3*14 = 42

x=84

The second solution to the given differential equation is y2(x) = \(e^{5x/4}\) * x + C, where C is a constant of integration.

To find the second solution, we'll use the formula

y₂(x) = y₁(x) ∫[y1(x)⁻² * \(e^{-\int P(x)dx}\)dx]

Given the differential equation: 16y'' - 40y' + 25y = 0 and y₁(x) = \(e^{5x/4}\), we need to find y₂(x).

First, let's find the integral of P(x)

P(x) = -40 / 16 = -5/2

∫P(x)dx = ∫(-5/2)dx = (-5/2)x + C

Now, substitute the values into the formula

y₂(x) = \(e^{5x/4}\) ∫[\(e^{5x/4}^{-2}\) * \(e^{-(-5/2)x}\)dx]

= \(e^{5x/4}\) ∫[\(e^{-5x/2}\) * \(e^{-5x/2}\)dx]

= \(e^{5x/4}\) ∫[1 dx]

= \(e^{5x/4}\) * x + C

So, the second solution to the differential equation is y₂(x) = \(e^{5x/4}\) * x + C, where C is the constant of integration.

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--The given question is incomplete, the complete question is given below "  The indicated function y 1​

(x) is a solution of the given differential equation. Use reduction of order  y 2

​=y 1​

(x)∫ y 1

2​

(x)

e −∫P(x)dx

​

dx as instructed, to find a second solution y 2

​

(x). 16y ′′

−40y ′

+25y=0;y 1

​

=e 5x/4

y 2

​

= "--

Answer B

scajgvbcxns djavhgvdscjv

Answer: 5/9 of the capacity of a tank has been used and there are still 108L left. What is the capacity of the deposit?

Step-by-step explanation:

Answer:

take a better pic

Step-by-step explanation:

Answer:

it would be x = 9

Step-by-step explanation:

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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To fully answer this question, I would need the information presented in Figure 3.14 that provides the computer solution. Unfortunately, I cannot access or view specific figures or external sources. However, I can explain the general approach to solving such a problem and provide a LaTeX code snippet to format the question.

To solve the given problem, it appears to be a linear programming problem where the goal is to optimize the total annual return subject to certain constraints. The decision variables are the number of shares of US Oil (U) and Huber Steel (H) to be purchased.

a. The optimal solution would provide the values of U and H that maximize the total annual return while satisfying the given constraints. The value of the total annual return would be the objective function value at the optimal solution.

b. The binding constraints are those that are active and determine the solution. These constraints limit the risk index, the total investment amount, and the maximum number of shares of US Oil. Interpretation of these constraints would depend on the specific problem and its context.

c. The dual values for the constraints represent the marginal values or shadow prices associated with each constraint. They indicate the rate of change in the objective function value for a small change in the right-hand side of the constraint. Interpretation of dual values would also depend on the specific problem and its context.

d. The impact of increasing the maximum amount invested in US Oil would depend on the objective function and the constraints. It could lead to a higher total annual return if US Oil has a higher return rate and the constraint on the risk index or total investment amount allows for it. However, if the maximum number of shares of US Oil is already binding, increasing the maximum investment amount would not be beneficial.

Please provide any additional information or specific values from Figure \(3.14\) if you have access to it, and I can assist further.

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Answer:

Step-by-step explanation:

Fed Raises Interest Rate Target By 0.5%

Fed Raises Interest Rate Target By 2%

The Taylor Rule states that interest rates should be raised when inflation rises. If a country's gross domestic product growth is high and above potential, the Fed should raise interest rates. Fed funds should raise his Fed by 2% if inflation exceeds target by 2%.

The product of Taylor's law consists of his three numbers: interest rate, inflation rate and GDP rate. They are all based on equilibrium interest rates to estimate the exact equilibrium of the monetary authorities' interest rate forecasts.

Prices and inflation are determined by three factors: the consumer price index (CPI), producer prices and the employment index. Most countries now focus on headline CPI instead of core CPI. This method excludes food and energy prices from the core CPI, allowing observers to see the full picture of the economy in terms of prices and inflation. Higher prices mean higher inflation, so Taylor recommends looking at inflation over a year (or four quarters).

He recommends raising the real interest rate to 1.5 times his rate of inflation. This is based on the assumption of an equilibrium interest rate that offsets real inflation against expected inflation. Taylor calls this equilibrium his 2% steady state, which equates to a rate of about 2%. But that's only part of the equation

Output should also be considered.

To better assess inflation and price levels, use moving averages of different price levels to determine trends and smooth out fluctuations. Run the same function for monthly interest rate charts. Identify trends according to Federal Funds rates.

Prices and inflation are determined by three factors: the consumer price index (CPI), producer prices and the employment index. Most countries now look at the entire CPI rather than the core CPI. With this method, the core CPI does not include food and energy prices, allowing observers to see the full picture of the economy in terms of prices and inflation.

Higher prices mean higher inflation, so Taylor recommends looking at inflation over a year (or four quarters) to get the full picture.

He recommends making the real interest rate 1.5 times his inflation rate. This is based on the assumption of an equilibrium interest rate that offsets real inflation against expected inflation. Taylor calls this equilibrium the 2% steady state, which corresponds to a rate of about 2%. But that's only part of the equation. Output should also be considered.

To better assess inflation and price levels, use moving averages of different price levels to determine trends and smooth out fluctuations.

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Answer:

501,000 adults 976,000 people total

Step-by-step explanation:

First step is adding 26,000 to 475,000 to find the number of adults, you get 501,000

Then you add 501,000 to 475,000 to get the total number of people, you get 976,000

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

If 501,000 grownups total then 976,000 people.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in some terms have a number in front of them. A coefficient is the number placed before a term.

Given:

There were 475,000 children at a state fair.

There were 26,000 more adults than children at the state fair.

Number of adults = 26,000 × 475,000 = 501,000

Total number of people = 501,000 × 475,000 = 976,000

501,000 grownups total 976,000 people

Therefore, 501,000 grownups total 976,000 people.

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The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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The perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

The complete length of a semicircle's boundary is referred to as the circumference of a semicircle, which is another name for its perimeter. The diameter's length and one-half of the original circle's circumference are added to determine it. Linear units such as "inches," "feet," "metres," or "centimetres," etc. are used to indicate the circle's circumference.

Given that the radius of the semicircle is 3cm.

The formula for the perimeter of a semicircle is:

P = pi(r) + 2r

Substituting the value of r = 3 we have:

P = pi(3) + 2(3)

P = 6 + 3pi

Hence, the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

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To conduct a hypothesis test to determine if there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode, we can follow these steps:

1. Define the null hypothesis (H0) and alternative hypothesis (Ha):
  - Null hypothesis (H0): The true percentage of those in the first group who suffer a second episode is the same as the true percentage of those in the second group who suffer a second episode.
  - Alternative hypothesis (Ha): The true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode.

2. Determine the significance level: The significance level is given as 0.1, which means we need to find evidence that is strong enough to reject the null hypothesis with a 10% chance of making a Type I error (incorrectly rejecting a true null hypothesis).

3. Calculate the test statistic: We need to compare the observed proportions in both groups to determine if they are significantly different. The test statistic used for this situation is the z-test for comparing proportions.

4. Calculate the test statistic value: The formula for the z-test for comparing proportions is:
  - Test statistic value = (p1 - p2) / √((p * (1 - p)) * ((1/n1) + (1/n2)))
  - where p1 and p2 are the observed proportions of second episode occurrences in the first and second groups respectively, n1 and n2 are the sizes of the first and second groups respectively, and p is the pooled proportion calculated as (x1 + x2) / (n1 + n2), where x1 and x2 are the number of second episode occurrences in the first and second groups respectively.

5. Determine the critical value(s): The critical value(s) depend on the significance level and the type of test (one-tailed or two-tailed). Since the alternative hypothesis is two-tailed, we will find the critical values for a two-tailed test with a 0.1 significance level.

6. Compare the test statistic value with the critical value(s): If the absolute value of the test statistic value is greater than the critical value(s), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

7. Draw a conclusion: Based on the results of the hypothesis test, we can draw a conclusion regarding whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode.

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There are 84 ways to choose five balls in order from a bag that contains 4 identical white balls, 3 identical red balls, and 3 identical blue balls.

To determine the number of ways to choose five balls in order, we can use the concept of combinations. In this scenario, we have a total of 10 balls (4 white + 3 red + 3 blue) in the bag.

To choose five balls, we need to consider different combinations of white, red, and blue balls. We can calculate this using the formula for combinations:

C(n, r) = n! / (r!(n - r)!)

Where n is the total number of balls and r is the number of balls to be chosen.

In this case, we want to choose 5 balls, so the formula becomes:

C(10, 5) = 10! / (5!(10 - 5)!)

Simplifying the calculation:

C(10, 5) = (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1) = 252

Therefore, there are 252 ways to choose five balls in order from the given bag.

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Answer:

7.81

Step-by-step explanation:

Answer:

\( \sqrt{66} \)

Step-by-step explanation:

By geometric mean property:

\(BD = \sqrt{6 \times 5} = \sqrt{30} \\ \\ In \: \triangle ABD: \\ by \: pythagoras \: theorem : \\ \\ AD^2 = AB^2 + BD^2 \\ \\ {x}^{2} = {6}^{2} + {( \sqrt{30}) }^{2} \\ \\ {x}^{2} = 36 + 30 \\ \\ {x}^{2} = 66 \\ \\ x = \sqrt{66} \)

The third and fourth options are the correct answers using probability.

Pablo has 0 pieces of candy and wants to divide them into 6 equal piles.

Pablo has 6 pieces of candy and wants to divide them into 0 equal piles.

Probability refers to potential. However, a random event's occurrence is the subject of this area of mathematics. The range of the value calculated is from 0 to 1. Hence to forecast how likely occurrences are able to occur, probability has been introduced in mathematics. How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.

Pablo has 0 pieces of candy. So he cannot divide to equal piles. Also Pablo cannot divide his 6 candies to 0 piles. It is not possible to divide 0 with 6. So the statements 3 and 4 do not have a solutions.

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