What is the magnitude of the angle (in radians) that the minute hand sweeps before the end of class?

Answers

Answer 1

This means that the minute hand sweeps a full circle befοre the end οf class.

What is radian?

A circle tο a circle's radius. One radian is the angle that an arc with length equal tο the circle's radius subtends at its center.

Tο put it anοther way, if we draw an arc arοund a circle whοse length is equal tο its radius, r, then the angle that arc subtends at the circle's centre is οne radian. One radian is equal tο apprοximately 57.3 degrees in numerical terms

Radians are a valuable measure fοr calculating angles in physics and mathematics because they make trigοnοmetric and circular mοtiοn calculatiοns simple.

The amοunt οf time that passes thrοughοut the class is t - t0 if we suppοse that the class cοncludes at sοme arbitrary time t and set t0 as the start time. The minute hand sweeps at the fοllοwing angle:

= (t - t0) (/30) radians

Fοr instance, if the class begins at 9:00 am and cοncludes at 10:00 am, then t0 = 9:00 am and t = 10:00 am, indicating that the class lasts an hοur οr 60 minutes. Hence, the size οf the angle that the minute hand sweeps just befοre the end οf class is:

60 radians divided by 30 radians equals twο radians.

Hence, This means that the minute hand sweeps a full circle befοre the end οf class.

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Related Questions

a researcher constructs a confidence interval for a population proportion using a sample of size 50. the value of p-hat is .3, and the resulting confidence interval is determined to be (.1323, .4677). what's the level of confidence for this interval?

Answers

The level of confidence for the given confidence interval is 95% and z-score is 1.96.The calculation involves using the formula for the confidence interval and the given sample proportion and size.

We can use the formula for the confidence interval for a population proportion:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))

Where p-hat is the sample proportion, z is the z-score for the desired level of confidence, and n is the sample size.

We're given that p-hat = 0.3 and n = 50. We're also given that the confidence interval is (.1323, .4677), which means that:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n)) = (.1323, .4677)

We can use the midpoint of the confidence interval as the point estimate for p-hat, which is (0.1323 + 0.4677) / 2 = 0.3.

Substituting the values we have into the equation, we get:

0.3 ± z*(sqrt(0.3*(1-0.3)/50)) = (.1323, .4677)

Simplifying the equation, we get:

z = 1.96

Therefore, the level of confidence for this interval is 95%, since the z-score for a 95% confidence level is 1.96.

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.If P(B/A)-1, P(B)-0.5, And P(A)-0.3, What Is P(A'/B)? (A' Is A Complement) a. 0.15 b. 0.6 c. 0.85 d. 0.4

Answers

The correct answer is c. 0.85.

To find P(A'/B), we can use the formula P(A'/B) = 1 - P(A/B). We are given that P(B/A) = 1, so we can use the formula P(A/B) = P(B/A) × P(A) / P(B) to find P(A/B).
Plugging in the given values, we get:
P(A/B) = (1) × (0.3) / (0.5) = 0.6
Now we can use the formula P(A'/B) = 1 - P(A/B) to find P(A'/B):
P(A'/B) = 1 - 0.6 = 0.4
However, this answer is incorrect because the given value of P(B/A) is incorrect. It should be P(B/A) = 1, not P(B/A) - 1. With the correct value of P(B/A), we can find P(A/B) as follows:
P(A/B) = (1) × (0.3) / (0.5) = 0.6
And then we can find P(A'/B) as follows:
P(A'/B) = 1 - 0.6 = 0.4
Therefore, the correct answer is c. 0.85.

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. (5) Let x be a real number. The floor of x, denoted |, is the largest integer n such that n < x. (See the Scheinerman "Assorted Notation" section.) Let f R -R be defined by f(x) (a) Determine the domain of f. (b) Determine the image of f. (c) Is f one-to-one? Prove your answer (d) Find sets A-R and B-R which are as large as possible so that f : A → B is a bijection. Prove that f : A → В is a bijection

Answers

Let x be a real number. The floor of x, denoted |, is the largest integer n such that n < x. Therefore, (π²/10)I = 4

The meaning of cos in trigonometry defines the cosine of an angle. This angle is the acute angle in a right triangle and is considered a ratio. So in a right triangle the cosine of an angle is equal to the ratio of the side adjacent to the angle to the hypotenuse of the triangle

According to the Question:

f(x) is periodic with period 2

∴I = ∫ ⁻¹⁰₁₀  f(x)cos πx dx

    = 2∫₀¹⁰ f(x)cos πx dx

    = 2×5∫₀² f(x)cosπx dx

    = 10 [∫₀¹ (1−X)cosπx dx+∫²₁(x−1)cosπx dx ]

    = 10(I₁+I ₂)

I₁ =∫₁² (x−1)cosπxdx put x−1=t

I₂ = −∫₀¹ tcosπt dt

Therefore,

I = 10[−2∫₀¹ xcosπx dx ]

 = −20[x sinπx/π  + cosπx/π²]₀¹

​  = −20[−

Therefore,

(π²/10)I = 4

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Stephen drove at a constant speed from Town X to Town Y at 9 A.M. yesterday. Half an hour later Cole drove from Town X to Town Y at a constant speed that was 30km/h faster than Stephens. 9:30 A.M., Stephen had already travelled 40km. Cole caught up with Stephen at Town Y, arriving the same time as Stephen.

a) At what speed was Stephen driving?
b) What was the distance between the 2 towns?

Answers

Answer:

r1 = 40km/0.5h = 80 km/h = Stephen's speed.

r2=Cole's speed = 80 + 30 = 110 km/h.

r2 * t = (r1 * t) + 40km

110t = 80t + 40

30t = 40

t = 1.33 h.

D = r*t = 110 * 1.333 = 146.7 km. =

Distance between the 2 towns.

Step-by-step explanation:

It costs Alexis $212 to make candles. How many candles must she sell at $8 apiece to make a profit?
Choose all the answers that could be true
Choices

54

26

20

32

24

Answers

Therefore , the solution of the given problem of unitary method comes out to be the only feasible response is 32.

An unitary method is what?

By applying what was learned, using this varied technique, and incorporating all relevant variable data from two persons who used a particular tactic, the work can be finished. In other words, if the desired statement result occurs, either the entity mentioned in the expression will also be discovered, or both crucial processes will truly ignore the colour. A refundable fee of Rupees ($1.21) may be needed for fifty pens.

Here,

The revenue from sales of the candles must exceed the expense of production in order to turn a profit.

Assume Alexis charges $8 for each of the x candles she sells. Then, her income would increase by $8.

Alexis needs to generate more income than it costs to produce the candles in order to turn a profit. Therefore, we can create a disparity:

=> 8x > 212

We can split both sides by 8 to find the solution for x:

=> x > 26.5

Since Alexis is unable to sell small quantities of candles,

she would need to sell at least 27 candles at an average cost of $8 each in order to break even.

The only option that is higher than or equal to 27 among the options is 32. Consequently, the only feasible response is 32.

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Claude is covering the lateral surface of bug spray cans with labels. Each can is cylindrical with a height of 12.7 centimeters and a radius of 3 centimeters. If he places labels on 5 bug spray cans, how many square centimeters of labeling material will he use?

Answers

Answer:

Claude will use approximately 1196.2 square centimeters of labeling material to cover the lateral surface of 5 bug spray cans.

Step-by-step explanation:

The lateral surface area of a cylinder can be calculated using the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, each bug spray can has a height of 12.7 cm and a radius of 3 cm. So the lateral surface area of one can is:

Lateral surface area = 2πrh = 2 × 3.14159 × 3 cm × 12.7 cm ≈ 239.24 cm²

Therefore, the lateral surface area of 5 bug spray cans is:

5 × 239.24 cm² = 1196.2 cm²

In the standard (2, 4) coordinate plane, the point (2, 1) is the midpoint of CD. Point Chas coordinates (6, 8). What are the coordinates of point D?

Answers

Since (2, 1) is the midpoint of CD, we can use the midpoint formula to find the coordinates of point D.

The midpoint formula states that the coordinates of the midpoint M between two points A and B are:

M = ((x_A + x_B)/2, (y_A + y_B)/2)

In this case, we know that point C has coordinates (6, 8), and the midpoint between C and D is (2, 1). Therefore, we can set up two equations using the midpoint formula:

(6 + x_D)/2 = 2 (for the x-coordinates)

(8 + y_D)/2 = 1 (for the y-coordinates)

Solving for x_D and y_D, we get:

6 + x_D = 4 => x_D = -2

8 + y_D = 2 => y_D = -6

Therefore, the coordinates of point D are (-2, -6).

Find the indefinite integral (Use C for the constant of integration.) ∫ 1/ x√9x^2-1 dx

Answers

The indefinite integral of ∫ 1/ x√9x^2-1 dx is 1/9 √(9x^2-1) + C.

To find the indefinite integral of ∫ 1/ x√9x^2-1 dx, we can use substitution. Let u = 3x, then du = 3dx, and dx = 1/3 du. Substituting these values into the integral gives us:∫ 1/ (u/3)√u^2-1 (1/3)du= 1/9 ∫ 1/ u√u^2-1 du

Now, we can use another substitution. Let v = u^2-1, then dv = 2u du, and du = 1/2u dv. Substituting these values into the integral gives us:1/9 ∫ 1/ u√v (1/2u)dv= 1/18 ∫ 1/ √v dv= 1/18 ∫ v^(-1/2) dv

Using the power rule for integration, we get:1/18 ∫ v^(-1/2) dv = 1/18 (v^(1/2))/(1/2) + C= 1/9 √v + C

Now, we can substitute back in for v and u to get the final answer:1/9 √v + C = 1/9 √(u^2-1) + C= 1/9 √(9x^2-1) + C Therefore, the indefinite integral of ∫ 1/ x√9x^2-1 dx is 1/9 √(9x^2-1) + C.

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find the area of the region bounded by the parabola , the tangent line to this parabola at and the axis.

Answers

The area of the region bounded by the parabola, the tangent line to this parabola at the point, and the axis is 20/3.

The area of the region bounded by the parabola y=x2, the tangent line to this parabola at (1,1) and the x-axis can be calculated by using integration.

First, we note that the equation of the tangent line to the parabola at (1,1) is y=2x-1. Then, the area of the region can be calculated by the equation:
A=∫01 (2x-1) - (x2)dx
A=∫01(x-x2)dx
A=∫01x dx - ∫01x2dx
A= (x2/2) |01 - (x3/3) |01
A=(1/2) - (1/3)
A=1/6
Let the given parabola be[tex]y^2=4ax[/tex].

So, the equation of tangent at

[tex](a,a^2/4) is y=a^2/4 + (x-a)[/tex].On solving this with the parabola equation we get,

x=3a/2, y=3a/2

So, the x intercept is 3a/2 and hence the required area is :∫[tex](3a/2)(a^2/4)[/tex]dx + ∫[tex](a/2)(3a/2 - a^2/4)[/tex] dx...on solving this, we get,[tex]20a^2/12 = 5a^2/3[/tex]= 20/3.

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It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. Find the spring constant k. k = Σ N/m

Answers

It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. The spring constant k will be 212.5 N/m.

The potential energy stored in a spring is given by the formula:

PE = (1/2) kx^2

where k is the spring constant, x is the displacement from the equilibrium position, and PE is the potential energy.

In this problem, the spring is stretched from its natural length of 2 m to a length of 6 m, so the displacement is x = 6 m - 2 m = 4 m.

The work done on the spring is equal to the change in potential energy, so:

Work = PE final - PE initial

1700 J = (1/2) k(4² - (1/2) k(0)²

1700 J = 8k

k = 212.5 N/m

Therefore, the spring constant is 212.5 N/m.

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Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, why is the other zero irrational?

Answers

Another root is also irrational, and if a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational

If a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational.

Any equation of the ax² + bx + c = 0 form   where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation.

Let assume quadratic equation is:

ax² + bx + c = 0

Given that coefficients are integer and roots are distinct,

we know root of quadratic equation are,

x = -b±√b²-4ac/2a

As roots are distinct b²-4ac > 0

and one root is irrational so b²-4ac is not a perfect square,

Hence another root is also irrational, and if a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational.

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Which of the following expressions is equivalent to the logarithmic expression below log3 5/x^2

Answers

Applying the Quotient and Power rule, B is equivalent to the given expression.

Christina’s Trip Christina drove 116 miles in 2 hours 15 minutes. She used 4 gallons of gas that cost her $9. 28. Find the quantities that are expressed with each of these units. (Express a quantity with both the number-amount and the unit. ) a. Miles per hour e. Dollars per hour i. Miles per dollar b. Miles per gallon f. Quarts per minutes j. Gallons per hour c. Dollars per gallon g. Cents per minute d. Feet per second h. Cents per mile

Answers

The quantities that are expressed with each of these units are by using the following formulae.

We can use the following formulas to determine the quantities stated with each of these units:

a. Miles per hour = Distance / Time

b. Miles per gallon = Distance / Gas

c. Dollars per gallon = Cost of Gas / Gas

d. Feet per second = (Distance * 5280) / (Time * 3600)

e. Dollars per hour = Cost of Gas / (Time / 60)

f. Quarts per minute = Gas * 4 / (Time * 60)

g. Cents per minute = Cost of Gas / (Time * 60)

h. Cents per mile = (Cost of Gas / Distance) * 100

i. Miles per dollar = Distance / Cost of Gas

j. Gallons per hour = Gas / (Time / 60)

Using the given information, we can find the values of each of these quantities:

a. Miles per hour = 116 miles / (2.25 hours) = 51.56 miles per hour

b. Miles per gallon = 116 miles / 4 gallons = 29 miles per gallon

c. Dollars per gallon = $9.28 / 4 gallons = $2.32 per gallon

d. Feet per second = (116 miles * 5280 feet per mile) / (2.25 hours * 3600 seconds per hour) = 88.53 feet per second

e. Dollars per hour = $9.28 / (2.25 hours / 60 minutes) = $24.70 per hour

f. Quarts per minute = 4 gallons * 4 quarts per gallon / (2.25 hours * 60 minutes per hour) = 0.59 quarts per minute

g. Cents per minute = $9.28 / (2.25 hours * 60 minutes per hour) = 6.48 cents per minute

h. Cents per mile = ($9.28 / 116 miles) * 100 = 8 cents per mile

i. Miles per dollar = 116 miles / $9.28 = 12.50 miles per dollar

j. Gallons per hour = 4 gallons / (2.25 hours / 60 minutes) = 10.67 gallons per hour.

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Choose the statements that describe characteristics of a probability distribution?a. Half of the possible outcomes have associated probabilities grater than 0.5.b. The probability of an outcome is between 0 and 1.c. The sum of the probabilities of all possible outcomes is 1.d. The distribution is symmetrical.e. The outcomes are mutually exclusive.

Answers

the key characteristics of a probability distribution include the probability of an outcome being between 0 and 1, the sum of the probabilities of all possible outcomes equaling 1, and the outcomes being mutually exclusive.

A probability distribution is a function that describes the likelihood of different outcomes of a random event. The characteristics of a probability distribution include the following:

a. Half of the possible outcomes have associated probabilities greater than 0.5: This statement is not true for all probability distributions. The probabilities associated with each possible outcome can vary and are not necessarily evenly distributed.

b. The probability of an outcome is between 0 and 1: This statement is true for all probability distributions. The probability of any possible outcome must be greater than or equal to 0 and less than or equal to 1.

c. The sum of the probabilities of all possible outcomes is 1: This statement is true for all probability distributions. The sum of the probabilities associated with all possible outcomes must equal 1, which ensures that the probability distribution accounts for all possible outcomes of an event.

d. The distribution is symmetrical: This statement is not true for all probability distributions. The shape of a probability distribution can vary and may be symmetrical, skewed, or bimodal, depending on the nature of the event.

e. The outcomes are mutually exclusive: This statement is generally true for probability distributions. The outcomes of an event are said to be mutually exclusive if they cannot occur simultaneously. For example, in a coin toss, the outcome can either be heads or tails, but it cannot be both at the same time.

In summary, the key characteristics of a probability distribution include the probability of an outcome being between 0 and 1, the sum of the probabilities of all possible outcomes equaling 1, and the outcomes being mutually exclusive. However, the probabilities associated with each possible outcome can vary, and the distribution may not be symmetrical

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The PivotTable functionality is located in the Data tab. O True False

Answers

The PivotTable functionality is located in the Data tab. This statement is True.

What is a PivotTable? A PivotTable is a table of statistics that is used to summarize and categorize large data collections. It enables users to rearrange, categorize, and filter data from a table to produce a summary report. PivotTables can help you make sense of large amounts of data by allowing you to extract insights and patterns from it quickly and easily.

Where is the PivotTable functionality located? The PivotTable functionality is located in the Data tab. A PivotTable is a great way to analyze and present data in Excel. The Data tab contains all the commands related to the manipulation of data sources, as well as PivotTable and PivotChart tools.

In Excel, the PivotTable command is located on the Data tab. By selecting the range of data you want to summarize, you can create a new PivotTable.

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In isosceles triangle ABC, ∠B is a right angle. What are the measures of angles A, B, and C?

Answers

Answer:yes

Step-by-step explanation:yes

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS. What is the measure of ? a. 78° b. 84° c. 88° d. 96°

Answers

The measure Circle of angle ∠RTS is 96°, and the measure of ∠RTQ is 84° in . Therefore, the answer is (b) 84°.

Let's call the measure of ∠RTS as x. Then, according to the problem, the measure of ∠RTQ is 12° less than x, so it's equal to x - 12°.

We know that angles ∠RTS and ∠RTQ are on a straight line, so their measures add up to 180°. Therefore:

x + (x - 12°) = 180°

Simplifying this equation, we get:

2x - 12° = 180°

2x = 192°

x = 96°

So the measure of ∠RTS is 96°, and the measure of ∠RTQ is x - 12°, which is:

96° - 12° = 84°

Therefore, the answer is (b) 84°.

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what is 3 divided by ten using long divison

Answers

Answer:

0.3

Step-by-step explanation:

3 divided by 10

the 0 from the ten pushes the 3 to 0.3

10

3

0 ->.3

Answer:

0.3

Step-by-step explanation:

10 doesn't go into 3 in a whole number so you pit a 0 and a decimal. then you add a .0 to the 3. then 10 goes into 30 3 times so you put a 3 at the end of the 0. on the top.

5. Mrs. Walsh conducted a survey of the most popular after-school snack in the
middle school. Of the 400 students surveyed, 70 preferred muffins, 70 preferred
pretzels, 50 preferred fruit, 50 preferred yogurt, 80 preferred cheese and crackers,
and 80 preferred granola bars. Select all of the sections of a circle graph that each
represent of the entire circle.
muffins
Opretzels
fruit
yogurt
cheese and crackers
granola bars

Answers

All of the sections of a circle graph that each represent 1/8 of the entire circle including Fruit and yogurt.

What is a circle graph?

A circle graph is a chord diagram's intersection graph in graph theory. It is an undirected graph, meaning that two vertices are only nearby if and only if the corresponding chords cross each other, and its vertices may be connected with a finite system of circular chords.

Since there were 400 students are surveyed, So their preference can be calculated as follows:

Muffins = 70/400

Pretzels = 70/400

Fruit = 80/400 = 1/8

Yogurt = 80/400 = 1/8

Cheese and crackers = 80/400 = 1/5

Granola bars = 80/400 = 1/5.

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Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain.
Min 1X + 1Y
s.t. 5X + 3Y < 30
3X + 4Y > 36
Y < 7
X , Y > 0

Answers

The given linear programming problem does not exhibit infeasibility, unboundedness or alternate optimal solutions.

Linear programming is an optimization technique to solve optimization problems. Linear programming is the process of optimizing a linear objective function of several variables subject to constraints on the variables. A linear programming model always has an objective function and constraints expressed as linear equations or inequalities.

Linear programming can be solved graphically or by using the simplex algorithm. The given linear programming problem isMin 1X + 1Ys.t. 5X + 3Y < 303X + 4Y > 36Y < 7X , Y > 0There are three constraints in the given linear programming problem, and each of them can be represented by a straight line in a two-dimensional graph. The feasible region is the shaded area where all the constraints are satisfied.

The objective function can be represented by a straight line as well.The feasible region in the given linear programming problem is not empty, which means there is at least one feasible solution. The feasible region is bounded, which means the optimal solution exists.

The objective function has a finite minimum value, which means the optimal solution is unique. Therefore, the given linear programming problem does not exhibit infeasibility, unboundedness or alternate optimal solutions.

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Nina owns a condominium where she paid $3,340 in maintenance fees this year. If her property taxes are 15% of this amount, how much did Nina pay in property taxes?

Answers

Nina pay in property taxes 501. or [tex]5.01*10^{2}[/tex].

A property tax, often known as a millage rate, is an ad valorem tax based on a property's value. The tax is imposed by the administrative body of the region where the property is situated. This could be the federal government, a federated state, a county, a region of land, or a municipality. The average effective property tax rate in the Lone Star State is 1.60%, making Texas' property taxes the seventh-highest in the nation. Comparing that to the current 0.99% national average will help. Property taxes in Texas cost the average homeowner $3,797 a year. It is well known that British property owners do not pay property tax. But hold on, it's too soon to celebrate because there might still be taxes to pay.

Based on the given conditions, formulate:

3340*15%

Calculate.

501

Alternative forms.

[tex]5.01*10^{2}[/tex]

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6 of the children in Bernie's class have a blue block. 5 children have an orange block, and 3 children have both a blue block and an orange block. How many children have an orange block but not a blue block?

Answers

Answer:

Step-by-step explanation:

it might be 2.

Answer: The answer is 2

Let X and Y be two random variables with joint probability density function fx,y(x, y) = cx + 1
for x, y ≥ 0 and x + y < 1. (Note: fx,y (x, y) = 0 outside this domain.) (a) Draw the domain of (X,Y) in the xy-plane. Make sure to clearly indicate which boundaries are part of this region and which are not. Then find the value of constant c, using the fact that ∫ [infinity] ∫[infinity] fX,Y(x,y) dxdy = 1.
-[infinity] -[infinity]
(b) Find the marginal distribution fx(x). (Hint: do not forget to mention its domain!) (c) Determine the probability P(Y < 2x^2).

Answers

The probability P(Y<2X^2) is equal to (4c/3).

The domain of X and Y in the xy-plane is shown in the graph below:Explanation:As it is given, X and Y are two random variables with joint probability density function fx,y(x, y) = cx + 1 for x, y ≥ 0 and x + y < 1. Therefore, we get: $$
\int_0^{1-x}\int_0^\infty{cx + 1}dydx=1
$$$$
\int_0^{1-x}{cx + 1}dx=\frac{1}{2}$$$$
\frac{1}{2}c(1-x)^2+c(1-x)+x= \frac{1}{2}$$$$
\frac{1}{2}c(1-x)^2+c(1-x)+x-\frac{1}{2}= 0$$$$
c(1-x)^2+2c(1-x)+2x-1= 0$$$$
c=-2x^2-2x+1$$$$
\int_{-\infty}^\infty\int_{-\infty}^\infty{f_{X,Y}(x,y)}dydx=1$$$$
\int_0^1\int_0^{1-x}(-2x^2-2x+1)dydx=1$$$$
\int_0^1[-2x^2y-2xy+y]_0^{1-x}dx=1$$$$
\int_0^1{-2x^3-3x^2+3x-1}dx=1$$$$
\left[-\frac{1}{2}x^4-x^3+\frac{3}{2}x^2-x\right]_0^1=1$$$$
-\frac{1}{2}-1+\frac{3}{2}-1=-1/2$$$$
c=2a) The marginal distribution fx(x) can be found by integrating fx,y over y from 0 to 1-x:$$
f_X(x)=\int_0^{1-x}cx + 1 dy = c(1-x)+x = -2x^2-2x+2$$$$
x+1/2\leq fx(x)\leq 2$$$$
0\leq x\leq 1$$$$
b) $$P(Y<2X^2)=\int_0^1\int_0^{2x^2}f_{X,Y}(x,y)dydx$$$$
=\int_0^1\int_0^{2x^2}cx+1dydx$$$$
=\int_0^1(cx^22+2x)dx$$$$
=\frac{4c}{3}$$$$
=-\frac{8}{3}x^2-4x+4$$Therefore, the probability P(Y<2X^2) is equal to (4c/3).

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the contour map given below for a function f shows also a path r(t) traversed counterclockwise as indicated.

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The contour map for the function f shows a path r(t) that is traversed counterclockwise as indicated. A contour map is a type of map that uses lines to indicate the elevation or depth of an area. The path r(t) is shown on the contour map as a line that is traversed counterclockwise, meaning that it moves in a circular motion in the opposite direction of a clock's hands.



To find the value of the function f at any point along the path r(t), you can look at the contour lines that the path crosses. Each contour line indicates a specific elevation or depth, and the value of the function f at that point will be equal to the elevation or depth indicated by the contour line.

For example, if the path r(t) crosses a contour line that is labeled "10", then the value of the function f at that point will be 10. Similarly, if the path r(t) crosses a contour line that is labeled "20", then the value of the function f at that point will be 20.

By following the path r(t) and looking at the contour lines that it crosses, you can find the value of the function f at any point along the path.

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Consider the following communication system where the transmitter sends a binary symbol xE[-1, 1] through the channel. The received signal is given by Y = X+Z where Z is a uniform random variabel in the range of ZE [-1.5, +1.5]. Z and X are independent. After receiving Y, the receiver estimates
X = {1 If Y ≥ t
{-1 If Y < t
A communication error occurs if X ≠ Y
Given that X = +1, what is the probability X=-1?

Answers

In this communication system where X and Z are independent and Y=X+Z, and X=+1, the probability of X=-1 is (t+0.5)/3 for 1<=t<=2.5.

Since X and Z are independent, the probability distribution of Y can be found as follows:

P(Y≤t) = P(X+Z≤t) = P(Z≤t-X)

P(Y>t) = P(X+Z>t) = P(Z>t-X)

Since Z is uniformly distributed in the range of [-1.5, +1.5], its probability density function (PDF) is constant over this range, i.e., fZ(z)=1/3 for -1.5<=z<=1.5, and zero elsewhere.

Now, we can calculate the probability of X=-1 given that X=+1 as follows:

P(X=-1|X=+1) = P(Y<t|X=+1)

= P(X+Z<t|X=+1)

= P(Z<t-1)

= integral from -1.5 to t-1 of fZ(z) dz

= integral from -1.5 to t-1 of 1/3 dz

= (t-1+1.5)/3, for -0.5<=t<=1

= (t+0.5)/3, for 1<=t<=2.5

Therefore, the probability that X=-1 given that X=+1 is (t+0.5)/3 when 1<=t<=2.5.

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If cosθ=2853cos⁡=2853 with θin Quadrant IV, what is sinθsin⁡?

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If cosθ=2853cos⁡=2853 with θin Quadrant IV, sinθsin⁡ is -45/53.

If cosθ = 28/53 with θ in Quadrant IV, we can use the Pythagorean identity to find sinθ. The Pythagorean identity is a fundamental equation that relates the sine and cosine functions of an angle in a right triangle. The Pythagorean identity states that sin^2θ + cos^2θ = 1.

We can rearrange the equation to solve for sinθ:

sin^2θ = 1 - cos^2θ

sin^2θ = 1 - (28/53)^2

sin^2θ = 1 - 784/2809

sin^2θ = 2025/2809

sinθ = √(2025/2809)

sinθ = 45/53

Since θ is in Quadrant IV, where sine is negative, we need to make sure our answer is negative:

sinθ = -45/53

Therefore, the answer is sinθ = -45/53.

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What is the circumference of a circle with a diameter of 21 cm? Approximate using pi equals 22 over 7.

7 cm
33 cm
66 cm
132 cm

Answers

Answer:

circumference of a circle = 2*π*10,5=66cm

Step-by-step explanation:

Answer:

I think the answer is C 66 cm

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n= 12​,
p= 0.7​,
x= 10

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The probability of getting exactly 10 successes in 12 independent trials, given the probability of success in each trial is 0.7, is 0.0159 or approximately 1.59%.

Now, let's consider a binomial probability experiment with the given parameters: n= 12​, p= 0.7​, x= 10. Here, n represents the total number of independent trials, p represents the probability of success in each trial, and x represents the number of successful trials that we are interested in calculating the probability for.

Using the given values, we can substitute them into the formula to find the probability of 10 successes in 12 independent trials:

P(10) = [tex](^{12}C_{10}) \times 0.7^{10} \times (1-0.7)^{12-10}[/tex]

P(10) = (66) x 0.02824 x 0.0081

P(10) = 0.0159 or approximately 1.59%

This means that if we were to repeat this experiment many times, we would expect to get exactly 10 successes in about 1.59% of the trials.

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for the following distribution of quiz scores, if a score of x = 4 or lower is a failing grade, how many individuals failed the quiz?
X f
6 3
5 6
4 5
3 5
2 3
1 2
a. 15 b. 14 c. 9 d. 10

Answers

The number of individuals who failed the quiz is d. 10

For the following distribution of quiz scores, if a score of x = 4 or lower is a failing grade, the number of individuals who failed the quiz is 10.

The distribution of quiz scores is shown below:X    f6    35    64    53    52    31    2For this question, we need to find the number of individuals who failed the quiz, given that a score of x = 4 or lower is a failing grade. In other words, we need to find the frequency of the scores that are 4 or lower. To do this, we need to add the frequencies of the scores that are 4, 3, 2, 1, and 0.x  f4   53   52   31   2

The frequency of scores that are 4 or lower is 15, which means that 15 individuals received a score that is 4 or lower.

Out of these individuals, the ones who failed are the ones who received a score of 4 or lower. Hence, the number of individuals who failed the quiz is the frequency of the score that is 4 or lower, which is 10. Therefore, the answer is d. 10.

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Look at the triangles you created. What do you notice about the different lengths of line c? Write an inequality that shows the possible lengths for line c (the triangle inequality theorem will help you):​

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Answer:

I'm sorry, but I don't have any context or information about the triangles you're referring to. Please provide me with more details or clarify your question so that I can better understand what you're asking. Thank you.

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