2 BEC = 74°. What is 2 AED?

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Yes, the cost of t* you would use for a 90% self-belief interval with a pattern length of 30 is 1.645.

To compute a 90% self-belief c programming language for the mean of a population with an unknown population well-known deviation, you would use the t-distribution. The vital fee, denoted as t*, is primarily based on the preferred self-assurance stage and the degrees of freedom, that's the same as the sample size minus 1 (n - 1).

In this situation, the pattern size is 30, so the tiers of freedom are 30 - 1 = 29. To locate an appropriate fee of t* for a 90% confidence stage, you could talk to the t-distribution table or use a statistical software program.

For a 90% confidence level and 29 tiers of freedom, the price of t* is approximately 1.645. This approach that 90% of the t-distribution falls inside ±1.645 trendy deviations from the suggestion.

Using this cost of t*, you can compute the confidence c language by taking the sample suggested and including/subtracting the margin of mistakes, which is fabricated from t* and the same old errors of the mean.

Remember that the t* cost may additionally vary slightly depending on the level of precision required and the precise table or software used, however, 1.645 is a normally used approximation for a 90% self-assurance c program language period with a sample size of 30.

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The correct question is:

"You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. Is the value of t* you would use for this interval is Group of answer choices 1.645?"

A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. The speed of the bug is equal to the tangential speed of a point on the rim of the disk, which can be given by: v = rωWhere:r = 0.1 m (the radius of the disk)ω = 10 rad/sec (the angular speed of the disk)Therefore, the speed of the bug is: v = rω= 0.1 m x 10 rad/sec= 1 m/s

The acceleration of the bug can be given by: a = rαWhere:α = α (angular acceleration)The angular acceleration is zero because the disk is spinning at a constant angular speed. Hence, the acceleration of the bug is zero or a = 0 m/s². Therefore, the correct option is option 2) 1 m/s and 0 m/s² (Disk spins at a constant speed).

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Answer:

y > −x − 3

Step-by-step explanation:

Answer:

The proper equation is, y = -5x + 35

The mistake Amy made, was that she used the x-intercept instead of the y intercept

1. a function that could be used to model the data in the table. Make sure to use h for height and d for distance is d = -0.425h + 39.25

2. If the balloon is 800 meters high,  the farthest distance that you would be able to see is  48 km

3. at the  height  of  67 does the balloon have to rise for the building to be visible.

The table in the question shows a relationship between the height of a balloon and the distance away from the balloon that can be seen. Using this data, a linear function can be determined that models this relationship. The function is d = -0.425h + 39.25, where h is the height of the balloon in meters and d is the distance in kilometers. Using this function, if the balloon is 800 meters high, the farthest distance that can be seen is 48 km, which is the y-intercept of the equation.

Inversely, if a building is 16 km away from the balloon, the height the balloon must rise for the building to be visible is 67 m. This can be determined by substituting 16 for d in the equation and solving for h.   Overall, the linear function d = -0.425h + 39.25 models the relationship between the height of the balloon and the distance away from the balloon that can be seen. The equation can be used to determine the height of the balloon needed to see a certain distance or the distance away from the balloon that can be seen when the balloon is at a certain height.

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Height in meters 15 30 45 60 75 90 105 , Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598

1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.

2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round the answer to the nearest whole number

3. Round answer to the nearest whole number A building is 16 km away. What height does the balloon have to rise for the building to be visible?

The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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Answer:

I hope the image helps!

Answer:

Step-by-step explanation:

· To provide some context, for an employee who earns $4,000 in each bi-weekly pay period in September through December, approximately $2,200 of Social Security taxes would be deferred. This same amount, of course, will need to be repaid beginning in 2021 and the employee’s paycheck would be reduced accordingly.

The given equations are as follows

\(\begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned}\)

(1) First, multiply both sides of equation A by 4, we have

\(4\times\left(\frac{x}{4} +1\right)=4\times(-3)\)

Then, rewrite the left-hand side of the above equation by using the distributive property, we have

\(4\times\frac{x}{4}+4\times1=4(-3)\)

\(\Rightarrow x+4=-12\)

This is the required equation B.

In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.

Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.

(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.

As both the equations are the same, so both will have the same solution.

Yes, they have the same solution.

To start, you would need the relevant data, such as the number of successful attempts and the total number of trials for each group or time interval. Then, you can perform a statistical test, like the chi-square test or a two-proportion z-test, to evaluate if the difference in probability is statistically significant at the 0.05 level. If the resulting p-value is less than 0.05, it would indicate a significant difference in the probability of solving the puzzle within one minute.

To answer your question, we would need to conduct a statistical analysis to compare the probability of solving the puzzle within one minute in two different groups or conditions. We would also need to establish a null hypothesis and an alternative hypothesis and use a statistical test such as a t-test or a chi-square test to determine whether the observed difference in probability between the two groups is statistically significant at the 0.05 level, which means that there is less than a 5% chance that the observed difference is due to chance alone. Without more information about the specific groups or conditions being compared, it is difficult to provide a definitive answer.

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Answer:

Look below

Step-by-step explanation:

1) x = 14, because 14 * 14 = 196

2) x = 3 / 16, because ( 3 / 16 ) * ( 3 / 16 ) = 9 / 256

3) x = 8, because 8 * 8 * 8 = 512

4) x = 4 / 7, because ( 4 / 7 ) * ( 4 / 7 ) * ( 4 / 7 ) = 64 / 343

Answer:

sin

Step-by-step explanation:

sin=O opposite/hypotenuse

Answer:

A.

Step-by-step explanation:

A function is a relation in which every input or value in the domain is paired with exactly one output or value in range.

Draw vertical to check if there is one output for one input.

Hope it is useful...

Answer:

So, the prime factors of 50 are 2 × 5 × 5 or 2 × 52, where 2 and 5 are the prime numbers.

Answer:

The prime factorization of 50 is \(2 * 5^{2} \)

Step-by-step explanation:

When the number of ounces is 9, the cost per ounce would be 40 cents. To solve , we can use the concept of inverse variation, which states that two variables are inversely proportional if their product remains constant.

Let's denote the cost per ounce as C and the number of ounces as N. According to the problem, we know that when N = 6, C = 60 cents per ounce. Using the inverse variation equation, we have: C × N = k, where k is the constant of variation. Substituting the given values, we get: 60 × 6 = k; k = 360.

Now, we can find the cost per ounce when N = 9: C × 9 = 360. Dividing both sides by 9, we have: C = 360 / 9; C = 40. Therefore, when the number of ounces is 9, the cost per ounce would be 40 cents.

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Answer:

x <1

Step-by-step explanation:

3x < 3.

Divide each side by 3

3x/3 < 3/3

x <1

The population size at t = 6 hours is approximately 1349.9 individuals.

To solve this differential equation, let's denote the population at time t as P(t). We know that the growth rate is proportional to the current population, so we can write the differential equation as:

dP/dt = k * P

where k is the proportionality constant.

To solve the equation, we can separate variables and integrate both sides:

1/P dP = k dt

∫1/P dP = ∫k dt

ln|P| = kt + C

where C is the constant of integration.

To find the value of C, we can use the initial condition that the population starts with 1000 individuals at t = 0:

ln|1000| = 0 + C

C = ln|1000|

Substituting the value of C back into the equation, we have:

ln|P| = kt + ln|1000|

ln|P| - ln|1000| = kt

ln(P/1000) = kt

\(P/1000 = e^(kt)\\P = 1000 * e^(kt)\)

Now, if the growth rate is 0.05 per hour, we have k = 0.05. So the equation becomes:

P = 1000 * e^(0.05t)

To find the population size at t = 6 hours, we substitute t = 6 into the equation:

\(P(6) = 1000 * e^(0.05*6)\\P(6) ≈ 1000 * e^0.3\)

P(6) ≈ 1000 * 1.3499

P(6) ≈ 1349.9

The population size at t = 6 hours is approximately 1349.9 individuals.

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Complete question:

A population of bacteria starts with 1000 individuals and grows at a rate proportional to the current population. If the growth rate is 0.05 per hour, find the equation that models the population growth and determine the population size at t = 6 hours.

Answer:

6/5

Step-by-step explanation:

The given series is:[infinity] (−1)n2n 4n(2n)! n = 0The sum of this series can be found as follows:The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4.The sum of the given series is cos 4. The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4. The sum of the given series is cos 4.

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The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.

Given curve,  x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).

To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.

To calculate the tangent vector, the following steps are taken:

Equation of the curve is given as,

x=5sin(3t),

y=t,

z=5cos(3t).

Differentiating above equation with respect to t, we get;

dx/dt = 15 cos(3t)

dy/dt = 1

dz/dt = -15 sin(3t)

The unit tangent vector T is given by,

T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)

Substituting the given values, we get

T = (3√10/10) i + (1/√10) j - (3/√10) k

Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.

Let's differentiate T to obtain N:

dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]

On substituting, we get,

N = (-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.

To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.

The equation of the osculating plane is then written as follows:

xT + yN = c,

where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,

To find the value of P, we substitute t=π in the given curve,

Thus,

x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5

Therefore, the point of tangency P is (0, π, -5).

From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the unit principal normal vector is given by,

B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]

= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k

= (24/√10) i + (12√10/10) j - (3/√10) k

The osculating plane equation is given by,

xT + yB = c

Now substituting x=0, y=π and z=-5 in above equation, we get

c = π(12√10/10) = (6π√10/5)

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Answer:

\(ln(\frac{8}{5x} )=ln(8)-ln(5)-ln(x)\)

Step-by-step explanation:

Use the properties of logarithms on each step:

First use the property for the logarithm of a quotient:

\(ln(\frac{a}{b} )=ln(a)-ln(b)\)

So we get: \(ln(\frac{8}{5x} )=ln(8)-ln(5x)\)

Now, we can expand the last term using the property of logarithm of a product:

\(ln(a\,*\,b)=ln(a)+ln(b)\)

Therefore we write \(ln(5x)=ln(5)+ln(x)\)

No we insert this result in the subtraction we had before:

\(ln(\frac{8}{5x} )=ln(8)-ln(5x)=ln(8)-(ln(5)+ln(x))=ln(8)-ln(5)-ln(x)\)

Answer: it has to be \(36\\50\)

Step-by-step explanation:you have to add them all

The travel time x is 41.162 min such that 17.36% of the 60 days have a travel time that is at least x.

We have to determine the travel time such that 17.36% of the 60 days have a travel time that is at least.

Total work days to work = 60 days

The travel mean time = 35.6

Standard deviation = 10.3

For normal distribution,

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X > x) = 0.2946

P(X < x) = 1 - 0.2946 = 0.7054

P(Z < (x - 35.6)/10.3) = 0.7054

Take the z value that corresponds to 0.7054 in the table of the standard normal distribution.

(x - 35.6)/10.3 = 0.54

x = 41.162 min

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Answer:

2/21.

Step-by-step explanation:

\(\frac{2}{7}\) ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.

Hope this helps!

Write 3 as 3/1

Now you have 2/7 / 3/1.

When you divide by a fraction change the divide to multiply and flip the second fraction over

Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get

2/21

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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The dependent variable in this study is the incidence of aggressive behavior displayed by the children during the period of free play.

The dependent variable is the outcome that is being measured and observed based on the independent variable, which in this scenario is the type of television program watched (violent or nonviolent). By observing and recording the incidence of aggressive behavior in each group, the researcher can determine if exposure to violent television programs has an effect on children's behavior. In this study, the dependent variable is essential to determining if there is a significant difference between the groups, and it allows for the researcher to draw conclusions about the relationship between exposure to violent television and aggressive behavior in children. In this scenario, the dependent variable is the incidence of aggressive behavior observed in the children during the period of free play. The dependent variable is the outcome or response that is measured in a study, and it is influenced by the independent variable(s). In this case, the independent variables are the type of television program (violent or nonviolent) and the gender of the participants (boys and girls). The researcher is investigating the relationship between exposure to violent or nonviolent television content and the occurrence of aggressive behavior among boys and girls.

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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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The cost to repair a bicycle equals 150X, where X has the following probability function: f(x)=20x(1−x)3 Thus standard deviation of the repair cost is approximately 0.267.

To calculate the standard deviation of the repair cost, we need to find the variance first. The variance of a random variable X can be calculated using the formula:

Var(X) = E(X^2) - [E(X)]^2

First, let's calculate E(X):

E(X) = ∫(x * f(x)) dx, integrated from 0 to 1

E(X) = ∫(x * 20x(1−x)^3) dx, integrated from 0 to 1

E(X) = ∫(20x^2(1−x)^3) dx, integrated from 0 to 1

E(X) = 20 * ∫(x^2(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X) = 4/7.

Next, let's calculate E(X^2):

E(X^2) = ∫(x^2 * f(x)) dx, integrated from 0 to 1

E(X^2) = ∫(x^2 * 20x(1−x)^3) dx, integrated from 0 to 1

E(X^2) = ∫(20x^3(1−x)^3) dx, integrated from 0 to 1

E(X^2) = 20 * ∫(x^3(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X^2) = 4/15.

Now, we can calculate the variance:

Var(X) = E(X^2) - [E(X)]^2

Var(X) = (4/15) - (4/7)^2

Var(X) = 4/15 - 16/49

Var(X) = 40/105 - 48/105

Var(X) = -8/105

The standard deviation (σ) is the square root of the variance:

σ = sqrt(-8/105)

Thus, the standard deviation of the repair cost is approximately 0.267.

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