What is the measure of the unknown angle?

Image of a full circle divided into two angles. One angle is one hundred twenty degrees and the other is unknown

210°
220°
230°
240°

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

the question is incomplete

Answer:

This would shift the equation to the right by 5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

let f(x)=y and g(x)=x

so y=x²

if y-2=(x-2)

y=x

Answer:

the answer is A)$5.12

Step-by-step explanation:

The answer can be find by step-step explanation. You are supposed to divide to get your answer.

Answer:

Step-by-step explanation:

15

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

The probability that they each have a different tens digit is 0.047.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.

Solution:- The collection contains 50 integers, hence there are \(^{50}C_5\) different ways to select 5 different integers.

Sample space = \(^{50}C_5\)

Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).

Therefore,

probability that each have a different tens digit = \(\frac{10^5}{^{50}C_5}\)

                                                                                = \(\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}\)

                                                                                = \(\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }\)

                                                                                = \(\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }\)

                                                                                 = 0.047

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a. The value corresponding to surviving the year is $0, and the value corresponding to not surviving the year is -$90,000.

b. The expected value for the 33-year-old male purchasing the policy is -$579.06.

c. Yes, the insurance company can expect to make a profit from many such policies because the expected profit per 33-year-old male insured for 1 year is $408.06.

a. The monetary value corresponding to surviving the year is $0 because the individual would not receive any payout from the insurance policy if he survives. The monetary value corresponding to not surviving the year is -$90,000 because in the event of the individual's death, the policy pays out a death benefit of $90,000.

b. To calculate the expected value for the 33-year-old male purchasing the policy, we need to multiply the probability of each event by its corresponding monetary value and sum them up. The probability of surviving the year is 0.9988, and the value corresponding to surviving is $0. The probability of not surviving the year is (1 - 0.9988) = 0.0012, and the value corresponding to not surviving is -$90,000.

Expected value = (Probability of surviving * Value of surviving) + (Probability of not surviving * Value of not surviving)

Expected value = (0.9988 * $0) + (0.0012 * -$90,000)

Expected value = -$108 + -$471.06

Expected value = -$579.06 (rounded to the nearest cent)

c. The insurance company can expect to make a profit from many such policies because the expected value for the 33-year-old male purchasing the policy is negative (-$579.06). This means, on average, the insurance company would pay out $579.06 more in claims than it collects in premiums for each 33-year-old male insured for 1 year. Therefore, the insurance company expects to make an average profit of $579.06 on every 33-year-old male it insures for 1 year.

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Answer:x=2

Step-by-step explanation:

The value of x in the equation 2.5(6x - 4) = 10 + 4(1.5 +0.5x) is 2.

The correct option is C.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

2.5(6x - 4) = 10 + 4(1.5 +0.5x)

Solving the equation for x we get

15x - 10 = 10 + 6 + 2x

15x - 2x = 16 + 10

13x = 26

Divide both side by 13 we get

13x/ 13 = 26 /13

x= 2

Thus, the value of x is 2.

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We don't have enough data to provide specific values in this situation for the population mean and standard error.

However, using the 52% probability provided, you can now discover the two values that are symmetrically distributed around the population mean using the Z-score of 0.75 and the standard error.

To determine the two values symmetrically distributed around the population mean, we need to use the concept of a confidence interval.

Given a probability of 52%, we can calculate the confidence interval as follows:
Convert the probability to a confidence level: 100% - 52% = 48%.

So, we have a 48% confidence level.
Divide the remaining probability by 2 to find the percentage of values in each tail: (100% - 48%) / 2 = 26%.

This means 26% of the values lie in each tail.
Use a Z-table or online calculator to find the corresponding Z-score for 26%.

The Z-score represents the number of standard deviations away from the mean. In this case, the Z-score is approximately ±0.75.
Apply the Z-score to the standard error formula:
  Confidence interval = population mean ± (Z-score * standard error)
However, we don't have enough information about the population mean and standard error to provide the exact values in this case.

But with the given probability of 52%, you can now use the Z-score of ±0.75 and the standard error to find the two values symmetrically distributed around the population mean.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

$86.35

Step-by-step explanation:

103.98

 17.63

 86.35

Answer:

p=103.98 + 17.63

Step-by-step explanation:

In order to find last weeks pay we must take this weeks pay and add the money that was cut from his check.

Interp2 is a MATLAB function that can be used to resize arrays of different sizes. This function is especially useful when we want to change the dimensions of an array without losing any important data.

An array is a collection of values or elements arranged in a specific order. When we want to resize an array, we essentially want to change its shape, but keep the same amount of data. This can be tricky when dealing with arrays of different sizes, because we need to find a way to map the data from one array onto another.

Interp2 helps us do this by using interpolation. Interpolation is a mathematical technique that allows us to estimate values between known data points. In the context of array resizing, interpolation is used to estimate the values of the new array based on the values of the old array.

To use interp2 to resize arrays, we need to provide it with the following inputs:

The old array (the array we want to resize)

The new size of the array (the dimensions of the new array)

The method of interpolation (how we want to estimate the values of the new array)

For example, let's say we have an array A that is 4x4, and we want to resize it to a 6x6 array. We can use interp2 as follows:

B = interp2(A, 6, 6, 'cubic');

In this case, we are telling interp2 to resize the array A to a 6x6 size using cubic interpolation. The resulting array B will have the same amount of data as A, but will be reshaped to fit the new dimensions.

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For 1+6x - 2x^3, the linear differential operator that annihilates the given function is  D^3 - 6D - 2. For e^-x + 2xe^x - x^2e^x, the linear differential operator that annihilates the given function is  D^2 - 3D + 2.

To find a linear differential operator that annihilates a given function, we need to apply the differential operator D to the function and obtain a linear combination of the function and its derivatives that is equal to zero. In other words, we need to find a differential operator of the form a_nD^n + a_(n-1)D^(n-1) + ... + a_1D + a_0, where a_n, a_(n-1), ..., a_0 are constants, that makes the given function vanish when applied to it.

In the first example, we apply D^3 - 6D - 2 to the function 1 + 6x - 2x^3, and obtain the expression 0, which means that this linear differential operator annihilates the given function.

In the second example, we apply D^2 - 3D + 2 to the function e^-x + 2xe^x - x^2e^x, and obtain the expression 0, which means that this linear differential operator annihilates the given function.

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Answer:

5 1/6 ÷ 4 2/3 = 31/28

3 3/4 ÷ 1 2/8 = 3

4 2/4 ÷ 2 1/4 = 2

5 2/5 ÷ 1 4/5 = 3

4 2/8 ÷ 3 2/4 = 17/4

3 3/9 ÷ 2 4/12 = 10/7

7 1/2 ÷ 3 3/5 = 25/12

6 2/8 ÷ 3 1/3 = 15/8

Explanation:

5 1/6 ÷ 4 2/3 = 31/6 ÷ 14/3 = (31/14) / (6/3) = (31/14) / 2 [when you divide by a certain number you multiply that number by the denominator] = 31/28

5 1/6 ÷ 4 2/3 = 31/6 ÷ 14/3 = 31/6 × 3/14

Option A is the correct answer which is t=(v-u)/a

This equation defines the behaviour of a physical scheme in order of its movement as a function of time in Newtonian mechanics

where:

v= final velocity

u= initial velocity

t= time

a= acceleration

Now from the following equation

v-u=at(rearrange the term)

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Answer:

d = 47°

Step-by-step explanation:

Image is attached

Sum of angles drawn along a straight line = 180°:

The angle drawn in pink : 180° - 112° = 68°

The angle drawn in green: 180° - 66° = 114°

The angle drawn in yellowish orange: 180° - 23° = 157°

The angle marked in purple: 180° - 102° = 78°

The figure drawn in the center is a 5-sided irregular pentagon

∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°

                                                                            = (5 - 2) × 180°

                                                                            = 540°

The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):

   68° + 114° + 78° + 157° + angle in light blue = 540°

Angle in light blue = 540° - 68° - 114° - 78° - 157°

                               = 123°

Sum of angles drawn along a straight line = 180°:

Angle marked in dark blue = 180° - 123°

                                                = 57°

Now focus on the angles present inside the triangle

Sum of interior angles of a triangle = 180°

= d + 76° + 57° = 180°

d has to be isolated and made the subject of the equation:

d = 180° - 76° - 57°

d = 47°

Answer:

Hey buddy, here is your answer. Hope it helps you.

Step-by-step explanation:

144 students enter a spelling bee contest.

Step 1

For the semi final round we are told that only 1/6 of the group will make it into that round.

This is calculated as

1/6 × 144/students = 24 students.

This means that only 24 students would make it into the semi final rounds.

Step 2

We are also told in the question that only 2/3 of THAT group would make it into the final round.

" THAT" group been referred to in the question means the number students that made it to the semi final round

This is calculated as

2/3 of that group( the group that made it to the semi finals)

= 2/3 × 24 students

= 16 students.

Therefore, the number of students that will enter the final round of the spelling bee is 16 students.

Answer: 6,192 paperclips, 3,826 paperclips

Step-by-step explanation:

a) To find the sum of all the children's paperclips, you must find each of them.

First, to start off, create some equations that represent this information:

k = j * \(\frac{6}{7}\)

m = 3k

m = j + 2552

Then, for starts you can use the equation m = 3k and plug in for the variables

m = 3k

(j+2552) = 3(j * 6/7)

j + 2552 = 3j + 2.57

2549.43 = 2j

j = 1274.715

j = 1274 (round down because you can't have a fraction of a paper clip)

Next, use j to solve the other equations

m = j + 2552

m = 1274 + 2552

m = 3826

k = j * 6/7

k = 1274 * 6/7

k = 1092

sum = k + j  + m

sum = 1092 + 1274 + 3826

sum = 6,192 paperclips

b) We already know m, which is 3826.

3,826 paperclips

The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

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The Bisection method converges to the zero at x = 0 for intervals a and b, the zero at x = 1 for interval c, and the zero at x = -1 for interval d.

The Bisection method is a numerical method for finding the roots of a function. It works by repeatedly dividing an interval in half and checking if the function changes sign in either half. If it does, then the root must be in that half and the process is repeated until the root is found to a desired level of accuracy.

To determine which zero of f the Bisection method converges to on the given intervals, we need to apply the method and see which zero is found.

a. [−1.5, 2.5]: The Bisection method will converge to the zero at x = 0, since f changes sign in the interval [−1.5, 0.5] and the method will continue to narrow in on this interval.

b. [−0.5, 2.4]: The Bisection method will also converge to the zero at x = 0, since f changes sign in the interval [−0.5, 0.5] and the method will continue to narrow in on this interval.

c. [−0.5, 3]: The Bisection method will converge to the zero at x = 1, since f changes sign in the interval [0.5, 1.5] and the method will continue to narrow in on this interval.

d. [−3,−0.5]: The Bisection method will converge to the zero at x = -1, since f changes sign in the interval [−1.5, -0.5] and the method will continue to narrow in on this interval.

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Answer:

Step-by-step explanation:

Answer:

$30.48<x<$53.34

Step-by-step explanation:

8 times per galleon: 14 times per gallon

Answer:

-4 = 2

Step-by-step explanation:

Answer:

-4 = 2

Step-by-step explanation:

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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