Which of the following are solutions to the equation sinx cosx = S? Check all that apply. . 13. 51 12 . c.플 EN D. + 12

To find the ratio of the length to the perimeter of a rectangle, we need to calculate the perimeter of the rectangle first.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Breadth)

Given that the length of the rectangle is 20 cm and the breadth is 14 cm, we can substitute these values into the formula:

Perimeter = 2 * (20 cm + 14 cm)

Perimeter = 2 * 34 cm

Perimeter = 68 cm

Now, we can find the ratio of the length to the perimeter:

\(Ratio = \frac{Length}{Perimeter}\)

\(Ratio = \frac{20 cm}{68 cm}\)

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 4:

\(Ratio = \frac{\frac{20 cm}{4} }{\frac{68 cm}{4} }\)

\(Ratio = \frac{5 cm}{17 cm}\)

Therefore, the ratio of the length to the perimeter of the rectangle is 5:17.

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Let's simplify the above expression :

The solutions are:

a) A ∪ B = {a, b, c, d, e, f, g, i, o, u, t}

b) A ∩ B = {e, f}

c) A′ = {a, h, i, j, k, l, o, t, u, v, z}

d) A - B = {b, c, d, g}

a) A ∪ B: The union of sets A and B is the set that contains all the elements from both A and B without repetition.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A ∪ B = {a, b, c, d, e, f, g, i, o, u, t}

b) A ∩ B: The intersection of sets A and B is the set that contains only the elements that are common to both A and B.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A ∩ B = {e, f}

c) A′: The complement of set A refers to all the elements in the universal set U that are not in set A.

A = {b, c, d, e, f, g}

U = {a, b, c, d, e, f, g, h, i, j, k, l, o, t, u, v, z}

A′ = {a, h, i, j, k, l, o, t, u, v, z}

d) A - B: The set difference between A and B is the set that contains the elements that are in A but not in B.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A - B = {b, c, d, g}

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Answer:

the 2nd

Step-by-step explanation:

Answer: 3/5

Step-by-step explanation:

First prime factor to get GCF:

36= 2 x 2 x 3 x 3

60= 2 x 2 x 3 x 5

GCF= 2 x 2 x 3 = 12

Therefore u divide each number by 12 to get your answer.

36/12=3     60/12=5

Fraction in lowest terms= 3/5

Answer:

non-proportional

Step-by-step explanation:

non-proportional because it doesn't pass through the origin.

The overall worst-case time complexity of the algorithm is O(n).

To analyze the worst-case time complexity of the algorithm from exercise 35 of section 3.1, we can follow these steps:

1. Review the algorithm: Recall the algorithm designed in exercise 35, which aims to find the first term of a sequence less than the immediately preceding term.

2. Identify the loop: The main part of the algorithm is a loop that iterates through the sequence of numbers, comparing each term to the previous one.

3. Count the operations: For each iteration of the loop, there are a constant number of operations, such as comparisons and variable assignments.

4. Determine the number of iterations: In the worst-case scenario, the algorithm has to iterate through the entire sequence to find the first term that is less than the immediately preceding term. If the sequence has n elements, the algorithm will have n-1 iterations, since we compare each element with its previous one.

5. Calculate the time complexity: Since each iteration takes a constant amount of time, and there are n-1 iterations in the worst case, the overall worst-case time complexity of the algorithm is O(n). This means that the time complexity grows linearly with the length of the input sequence.

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Answer:

Step-by-step explanation:

Let's see how well I can explain this. \(\frac{\pi}{6}\) is the same as a 30 degree angle which is in quadrant 1. If you picture the unit circle, right in the center of it is the origin. If you draw a straight line from 30 degrees and through the center (the origin), you will automatically "connect" with the reference angle of 30 (this is true for ALL angles on the unit circle). This puts us in quadrant 3. In quadrant 3, x is negative and so is y. So the terminal point of the reference angle for 30 degrees has the same exact values, but both of them are negative (again, because both x and y are negative in quadrant 3). I can't see your choices but the one you want looks like this:

\((-\frac{\sqrt{3} }{2},-\frac{1}{2})\)

The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

524.30

Step-by-step explanation:

Answer:

40.9

Step-by-step explanation:

In ΔRST, the measure of ∠T=90°, ST = 71 feet, and RS = 94 feet. Find the measure of ∠S to the nearest tenth of a degree.

to fulfill manifest destiny, the American dream to expand, as well as reach the ocean on the west in order to have more options for trade

As the number of years increases, the percentage of married women with children ages 6 to 17 in labor force increases

To do this, we enter the number of years after 1900 and the percentage of labor force on a graphing calculator

See attachment for the scatter plot

Using the graphing calculator, we can find a linear model to fit the data

From the line on the scatter plot, the equation is

y = 1.12x - 28.48

This means that x = 82

So, we have:

y = 1.12 * 82 - 28.48

Evaluate

y = 63.36

Hence, the percentage in the labor force in the year 1982 is 63.36%

This means that y = 85

So, we have:

85 = 1.12x - 28.48

This gives

1.12x = 113.48

Divide by 1.12

x = 101.32

Approximate

x = 101

Year = 1900 + 101

Year = 2001

Hence, the year is 2001

To do this, we enter the number of years after 1900 and the percentage of labor force on a graphing calculator

Using the graphing tool;

The value of correlation coefficient for this data is 0.9962.

This is a strong positive correlation, which means that as the number of years increases, the percentage of married women with children ages 6 to 17 in labor force increases

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To plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

To determine what sample volume should yield a countable plate, we need to calculate the appropriate dilution factor.

The sample has a density of 7.9 x 10^9 CFU/mL, and we want to plate 1 mL of a 10^-8 original dilution, which means we need to dilute the sample by a factor of 10^8 to obtain a countable plate.

We can calculate the required dilution factor using the following formula:

Dilution factor = (Volume of sample plated) / (Total volume of diluted sample)

To dilute the sample by a factor of 10^8, we can calculate the total volume of diluted sample as follows:

Total volume of diluted sample = (Volume of sample plated) x (Dilution factor)

Substituting the values, we get:

10^8 = 1 mL / (Total volume of diluted sample)

Total volume of diluted sample = 1 mL / 10^8

Total volume of diluted sample = 0.00000001 mL

Therefore, to obtain a countable plate, we need to plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

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These are the values of the step function for the given inputs:

A step function is a function that has constant values on given intervals, with the constant value varying between intervals. The name of this function comes from the fact that when you graph the function, it looks like a set of steps or stairs.

To find the value of a step function at a given input, find the interval that the input falls into. If the input is greater than or equal to the upper bound of the interval, then the value of the function is 1. If the input is less than the lower bound of the interval, then the value of the function is 0. If the input falls within the interval, then the value of the function is the constant value for that interval.

For the given inputs, the following intervals are used:

[7.8] falls within the interval [0, 10] so the value of the function is 1.

[0.75] falls within the interval [0, 1] so the value of the function is 0.75.

[-6.56] falls within the interval (-∞, 0] so the value of the function is 0.

[101.2] falls within the interval [0, 10] so the value of the function is 1.

[-93.6] falls within the interval (-∞, 0] so the value of the function is 0.

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The solution to the system of given linear equations is x = 0 and y = 2.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The system of equations is given in the question, as follows:

2x + 2y = 4  .....(i)

8x - 2y = -4  .....(ii)

To eliminate y, add the two equations together:

2x + 8x = 4 - 4

10x = 0

Solve for x:

x = 0

Now that we have x, we can substitute it back into one of the original equations to find y:

2x + 2y = 4

2(0) + 2y = 4

2y = 4

y = 4/2

y = 2

Thus, the solution is x = 0 and y = 2.

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The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

5

Step-by-step explanation:

You first start by finding the acceleration of the problem.

a=f/m

Which this case is 45.

The question is asking " How many times greater must it be than A?"

You then divide

45/9

Your final answer is 5.

The acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

We have a table that gives the values of mass, acceleration and force of object A and object B.

We have to find by how many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true.

The formula to calculate the force is -

F = m x a

In the table, for Object B -

Mass = 40 Kg

Force = 1800 N

Substituting the values -

a = \(\frac{F}{m}\) = \(\frac{1800}{40}\) = 45 \(m/s^{2}\)

The acceleration of Object A is 9 \(m/s^{2}\).  On comparing the acceleration of both the objects, we can see that the acceleration of Object B is 5 times the acceleration of Object A.

Hence, the acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

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Thus, the dimensions that will give the maximum enclosed area are:  x = (320 - 3w)/4 and y = 80 - 3w/2.

To find the dimensions that will give the maximum enclosed area, we need to use the formula for the area of a rectangle, which is A = lw (where A is the area, l is the length, and w is the width).

Let's call the length of one corral x and the length of the other corral y. Since the corrals are adjacent, they share a common side, which we'll call w.

So we have two equations:

2x + y + 3w = 320 (the total amount of fencing)

A = xy (the area we want to maximize)

We can solve the first equation for y:

y = 320 - 2x - 3w

Then substitute that into the equation for the area:

A = x(320 - 2x - 3w)

Now we need to find the value of x that will give us the maximum area. To do this, we'll take the derivative of A with respect to x, set it equal to zero, and solve for x:

dA/dx = 320 - 4x - 3w = 0

4x = 320 - 3w

x = (320 - 3w)/4

Now we can substitute that value of x back into our equation for y:

y = 320 - 2(320 - 3w)/4 - 3w

y = 80 - 3w/2

We know that w must be positive, so we can find the maximum value of the area by taking the second derivative of A with respect to x:

d^2A/dx^2 = -4

Since this is negative, we know that we have a maximum.

So the dimensions that will give the maximum enclosed area are:

x = (320 - 3w)/4

y = 80 - 3w/2

w > 0

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If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

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Step-by-step explanation:

Area= 1/2 * b*h

h= 3 2/3 = 11/3

Area = 1/2*2*11/3 = 11/3 square feet or 3 3/2 square feet

Using the Pythagorean theorem:

6^2 = 5^2 + x^2

Simplify:

36 = 25 +x^2

Subtract 25 from both sides:

11 = x^2

Square root of both sides:

x = sqrt(11) (exact) or 3.316625 as a decimal

Answer:

distributive property is in the middle going straight up (read it going from the bottom up)

Answer:

hii

Step-by-step explanation:

18.75 answer

is

correct

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Step-by-step explanation:

The given decision problem can be represented as:5X + 60Y ≤ 300X + 4Y ≥ 7X + Y ≤ 10To plot the feasible region for this problem, we can use the intercepts method:Let's consider the equation 5X + 60Y = 300:At X = 0, 5(0) + 60Y = 300, Y = 5At Y = 0, 5X + 60(0) = 300, X = 60The point of intersection is (0, 5) and (60, 0).Let's consider the equation X + 4Y = 7:At X = 0, 4Y = 7, Y = 1.75At Y = 0, X = 7The point of intersection is (0, 1.75) and (7, 0).Let's consider the equation X + Y = 10:At X = 0, Y = 10At Y = 0, X = 10The point of intersection is (0, 10) and (10, 0).Therefore, the feasible region is the triangle formed by the points (0, 5), (7, 1.75), and (5, 5).

The total mass of the 1 meter rod with the given linear density function is 11/2 kg.

The given linear density function of a 1 meter rod is:

p(x) = 11/(x + 1)^2 kg/m

Here, p(x) represents the mass per unit length of the rod at a distance x from one end, in kg/m. To find the total mass of the rod, we need to integrate the linear density function over the entire length of the rod, which is from x = 0 to x = 1:

m = ∫₀¹ p(x) dx

Substituting the given linear density function, we get:

m = ∫₀¹ 11/(x + 1)^2 dx

We can solve this integral by making the substitution u = x + 1, which gives us du/dx = 1 and dx = du. Substituting these values, we get:

m = ∫₁² 11/u^2 du

Evaluating the integral using the power rule of integration, we get:

m = [-11/u]₁²

m = [-11/(2+1) + 11/(1+1)]

Simplifying the expression, we get:

m = (-11/3 + 11/2) kg

m = (22/6 - 33/6) kg

m = -11/6 kg

However, mass cannot be negative. Therefore, we made a mistake while evaluating the integral. The mistake is that we reversed the limits of integration while substituting u for x + 1. To correct this mistake, we need to change the limits of integration from [1, 2] to [0, 1]:

m = ∫₀¹ 11/(x + 1)^2 dx

Substituting u = x + 1, we get:

m = ∫₁² 11/u^2 du

Now, evaluating the integral using the power rule of integration, we get:

m = [-11/u]₀¹

m = [-11/(1+1) + 11/(0+1)]

Simplifying the expression, we get:

m = (-11/2 + 11) kg

m = 11/2 kg

Therefore, the total mass of the 1 meter rod with the given linear density function is 11/2 kg.

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The required number is 94.

Let the digit on unit's place be 'x'

Digit on ten's place be 'y'

Therefore,

Original number = 10y + x

Given, the sum of the digits = 11

=> x + y = 11 →(I)

When the digits are reversed, new number = 10x + y

Therefore,

(10y + x) - (10x + y) = 63

10y + x - 10x - y = 63

9y - 9x = 63

=> y - x = 7 →(II)

Adding (I) and (II) we get

2y = 18

y = 9

Substituting the value of y in (I) we get

x + 9 = 11

x = 2

Therefore,

Original number = 10y + x = 10(9) + 4 = 94

The required number is 94.

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The standard deviation of the critical path is 6.

To calculate the standard deviation of the critical path, we need to use the concept of variance and consider the activities on the critical path.

The variance of a project or critical path is the sum of the variances of the activities on that path.

Since the variances are given as the squares of the standard deviations, we can square the standard deviations of each activity and sum them to find the variance of the critical path. Finally, we take the square root of the variance to obtain the standard deviation.

Given the standard deviations of the activities on the critical path:

Activity 1: Standard deviation = 1 day

Activity 2: Standard deviation = 3 days

Activity 3: Standard deviation = 1 day

Activity 4: Standard deviation = 4 days

Activity 5: Standard deviation = 3 days

Calculating the variance of the critical path:

Variance = (1^2) + (3^2) + (1^2) + (4^2) + (3^2) = 1 + 9 + 1 + 16 + 9 = 36

Taking the square root of the variance, we find the standard deviation of the critical path:

Standard deviation = √(36) = 6

Therefore, the standard deviation of the critical path is 6.

The correct choice is A. 6.

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