suppose a = {0,2,4,6,8}, b = {1,3,5,7} and c = {2,8,4}. find: (a) a∪b (b) a∩b (c) a −b

Answer:

-6

Step-by-step explanation:

By looking at the graph, you can see that the graph intersects the x-axis at (-6,0), that is the zero of g.

Answer:

-9

Step-by-step explanation:

The graph's y-intercept is -9, which is the zero of g.

The speed of the faster cyclist is 14\ miles/hr.

What is speed?

It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.

Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,

\(2s+s=42\\3s=42\\s=14\)

Now, distance coverd by the first cyclist is \(2s=2\times 14\\=28 \ $miles\).

Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.

\(Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr\)

Hence, the speed of the faster cyclist is 14\ miles/hr.

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Answer: 10%

Step-by-step explanation:

As per given ,

Initial number of people went to pool = 1060

After 4 weeks periods, number of people went to pool = 1060 - 100 +140 -146  ['+' for addition . '-' for decrease]

= 954

The percent decrease in the number of people who went to the pool over these four​ weeks = \(\dfrac{1060-954}{1060}\times 100\)

\(=\dfrac{106}{1060}\times100\\\\=10\%\)

Hence, the percent decrease in the number of people who went to the pool over these four​ weeks = 10%

The scores from least to greatest is -8. -6, 4, 7

The absolute value of the scores from least to greatest is 4, 6, 7, 8

A negative number is a number that is less than zero. Negative numbers are denoted with a minus sign in front of the number. The further away from zero a negative number is, the smaller the number. Examples of negative numbers are -2, -9.

A positive number is a number that is greater than zero. The further away from zero a positive number is, the greater the number. Examples of negative numbers are 2, 9.

The scores from least to greatest is: -8. -6, 4, 7

The absolute value of a number is when the negative signs from the numbers are removed.

The absolute value of the scores from least to greatest is: 4, 6, 7, 8

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The length and width of the rectangular field is 316 ft and 133 ft respectively.

An algebraic equation is a mathematical statement that equalises two expressions. A variable, coefficients, and constants are common components of an algebraic equation. Also look into Algebraic Expressions. Equality is represented by equations or the equal sign.

It is balanced because both sides are equal in value. To avoid making an error that throws the equation out of balance, ensure that any change on one side is reciprocated on the other.

Given,

perimeter of rectangular field = 898 ft

let width be 'x'

then,

length = x+183

The perimeter of a rectangle is,

\(P = 2(length + width)\\\\898 = 2( ( x + 183 ) + x )\\\\898 = 2(2x+183)\\\\898 = 4x + 366\\\\4x = 898 - 366\\\\4x = 532\\\\x=\frac{532}{4}\\\\x=133\)

Thus, the width is 133 ft and length is (133+183)=316 ft.

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Your question is incomplete, here is the complete question.

A certain field is a rectangle with a perimeter of 898 ft. The length is 183 ft more then the width. Find the width and length of the rectangular field?

Answer:

2/5

Step-by-step explanation:

Answer:

10 : 4, 15 : 6, 20 : 8,

Step-by-step explanation:

increase the first number by 5 then add two to the second number

Answer:

8.6615988

Step-by-step explanation:

f(x) = 3 sin (x) / ( 1 + cos x)

To find the derivative   bottom * d/ dx top  - top d/dx bottom  all over the bottom squared

d/dx = 3 ( ( 1 + cos x)  cos x - sin x( - sin x))   / ( 1 + cos x) ^2

         = 3 ( cos x + cos ^2 x + sin ^2 x)   / ( 1 + cos x) ^2

         = 3 ( 1 + cos  x) /  ( 1 + cos x) ^2

         = 3 / ( 1 + cos x)

Let x = 4

3  /  ( 1 + cos 4)

Assuming x is in radians

3/.346356

8.6615988

Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. When the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s are as follows:

a) For t=0 to t=0.1s:

Average value, y_avg = 25

RMS value, y_RMS = 25.1987

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

b) For t=0.4 to t=0.5s:

Average value, y_avg = 25

RMS value, y_RMS = 28.2843

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

c) For t=0 to t=1/3 s:

Average value, y_avg = 25

RMS value, y_RMS = 23.7176

Comment: RMS value is less than the average value. This means that the signal has a lesser amount of high-frequency content. It can be inferred that the function y(t) oscillates slowly.

d) For t=0 to t=20 s:

Average value, y_avg = 25

RMS value, y_RMS = 25

Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.The results indicate that the function y(t) oscillates rapidly at the start and end of the time period and slowly in the middle. When the RMS value is greater than the average value, it means that the signal has a considerable amount of high-frequency content.

On the other hand, when the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Furthermore, if the RMS value is equal to the average value, it means that the signal does not have any high-frequency content.

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Answer:

Step-by-step explanation:

if the number is higher then 5 it goes over to the tenth

Answer:

2x(x + 3)

2x^2 + 6x

Answer:  2x²+6x

Step-by-step explanation:

A = bh

A = 2x(x+3)

A = 2x²+6x

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

The equation of motion of the spring-mass-damper system is given by2x'' + 8x' + 26x = 0

            where x is the displacement of the mass from its equilibrium position, x' is the velocity of the mass, and x'' is the acceleration of the mass.

The characteristic equation for this differential equation is:

                          2r² + 8r + 26 = 0

Dividing by 2 gives:r² + 4r + 13 = 0

Solving this quadratic equation, we get the roots: r = -2 ± 3i

The general solution of the differential equation is:

                    x = e^-2t (c₁ cos(3t) + c₂ sin(3t))

where c₁ and c₂ are constants determined by the initial conditions.

Using the initial conditions x(0) = -1 m and x'(0) = 2 m/s,

we get:-1 = c₁cos(0) + c₂

              sin(0) = c₁c₁ + 3c₂ = -2c₁

              sin(0) + 3c₂cos(0) = 2c₂

Solving these equations for c₁ and c₂, we get: c₁ = -1/2c₂ = 1

Substituting these values into the general solution, we get:x = e^-2t (-1/2 cos(3t) + sin(3t))

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

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Given:

Since the area of the semi-circle is the area of half the circle, the formula of finding the area of the circle will be divided by 2 to find the area of the semi-circle.

This means that:

Now, let's substitute the radius into the formula to find the area.

Substituting the radius into the equation:

Simplifying the RHS:

Substituting π as 3.14:

Simplifying the RHS:

Before we find the area of the triangle, we need to know the base, which is the diameter of the semi-circle.

Now, let's find the area of the triangle.

The area of the figure is basically the sum of the semi-circle and the triangle.

Thus, the area of the figure is 26.13 ft².

If you have any questions or any confusions, post them in the comments.

Answer:

See below for answers and explanations

Step-by-step explanation:

Top left: Since y can't be greater than 0 but is equal to 0, then the range is (-∞,0] and the domain is (-∞,∞) since there are no domain restrictions

Top right: Since both x and y have no restrictions, then the domain is (-∞,∞) and the range is (-∞,∞)

Bottom left: Since y cannot be less than 2 but equal to it, and x holds no domain restrictions, then the domain is (-∞,∞) and the range is [2,∞)

Bottom right: Since both x and y have no restrictions, then the domain is (-∞,∞) and the range is (-∞,∞)

A domain has [-1, 1]

Now, According to the question:

Let's know:

How do you find the domain?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

A square root with a negative number under the root cannot produce a real number. This means that \(1-x^2\) must be greater than or equal to zero.

Squaring a real number will always produce a positive number, so \(x^{2}\)must be equal to or smaller than 1. This means x is between 0 and 1, giving the domain of [0,1].

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The complete question is this ;

What is the domain of \(\sqrt{1-x^2}\)

The given statement that Survey Timeline Indicates The Date For Activation Of The Measurement Instrument is true.

The measurement instrument's activation date is shown on a survey timeline. A survey timeline shows the beginning and end dates of data collector training. The responsibility for ensuring proper instrument disposition always rests with the interviewer's instructions.

A huge population's characteristics can be described through surveys. No other research methodology can offer such a wide range of capabilities, which guarantees a more accurate sample to collect focused results from which to draw conclusions and make significant judgments.

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Answer:

5/8

Step-by-step explanation:

→ Work out how many red

8 - ( 2 + 1 + 2 ) = 3

→ Add up red and purple

3 + 2 = 5

→ Divide over total number of beads

5/8

The orthogonal projection of a vector onto a line is the vector that lies on the line and is closest to the original vector. We are given the line in \(R^{3}\) that consists of all scalar multiples of the vector (2, 1, 2) , We need to find orthogonal projection of the vector.

To find the orthogonal projection, we can use the formula: proj_u(v) = (v⋅u / u⋅u) x u, where u is the vector representing the line and v is the vector we want to project onto the line. In this case, the vector u = (2, 1, 2) represents the line. To find the orthogonal projection of a given vector, let's say v = (x, y, z), onto this line, we substitute the values into the formula: proj_u(v) =  \((\frac{(x, y, z).(2, 1, 2)}{(2, 1, 2).(2, 1, 2)} ) (2, 1, 2)\) . Simplifying the formula, we calculate the dot products and divide them by the square of the magnitude of u: proj_u(v) = \(\frac{(2x + y + 2z)}{9} (2, 1, 2)\). The resulting vector, \(\frac{(2x + y + 2z)}{9} (2, 1, 2)\), is the orthogonal projection of vector v onto the given line in \(R^{3}\).

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Answer:

Because she found it improves division.

Step-by-step explanation:

Answer:

1234567891011121314151617181920

Answer:

B. (1, -2)

Step-by-step explanation:

In order to for it to be a function, the inputs need to have only one output.

The table shows:

(-1, 2), (0, -4), (1, -2), (1, 5), (2, 0), (3, 2), (4, 9)

If a x-value is repeating it is not a function.

The expression that is in simplest form is: 49√a

The probability that only one bus will arrive within a thirty-minute period is 0.0337

We can model the arrival of shuttle buses as a Poisson process with a rate of λ= 10 buses per hour. Since we want to find the probability of only one bus arriving within a 30-minute period, we need to calculate the Poisson probability mass function for  λ = 5 (since 30 minutes is half an hour):

P(X=k) =  ( λ^k × e^- λ ) / k!

where X is the number of shuttle buses arriving within the 30-minute period

k is the number of buses, which in this case is 1.

Substituting the values, we get:

P(X = 1) = ( 5^1 × e^-5 ) / 1!

≈ 0.0337

Therefore, the probability is 0.0337

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21.2 because you use the area of a circle formula which is pi times r squared and divide it by four to get each quarter and then multiply by three because there are 3 quarters of the circle.

Answer:

5 hrs

Step-by-step explanation:

7 1/2 hours equates to 450 minutes total

2/3 of 450 = 300 total minutes

turning the minutes back into hours, 300 / 60 = 5

She was 5 hours on her computer

Number of hours worked = \(7\frac{1}{2}\)

This is an improper fraction so first we convert it

\(7\frac{1}{2} = > \frac{15}{2}\)

Time spent on her computer = \(\frac{2}{3}\) \(of working hours\)

∴ time spent on computer = (15/2)*(2/3)

= 5 hours

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Answer:

Step-by-step explanation:

none of these the corrct answer is 5

The difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

The correct answer is (d): In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance alpha.

The z-test is a statistical test used to assess whether a sample mean or proportion significantly differs from a hypothesized population mean or proportion. The difference between the z-test for mu (population mean) using rejection region(s) and the z-test for p (population proportion) using a P-value lies in the approach used to make the inference.

In the z-test using rejection region(s), the test statistic (calculated from the sample) is compared with critical values based on the chosen level of significance alpha. The critical values are determined from the standard normal distribution or a z-table, and if the test statistic falls within the rejection region (beyond the critical values), the null hypothesis is rejected.

On the other hand, in the z-test for p using a P-value, the test statistic is compared with the P-value. The P-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true. If the P-value is smaller than the chosen level of significance alpha, the null hypothesis is rejected.

Therefore, the difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

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Answer:

Step-by-step explanation: Square feet