PLEASE HELP!!! Solve 5sin(π/3x)=3 for the four smallest positive solutions

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

The values from figure is,

x = 2

NS = 3.5

We have to given that,

In the figure below, S is the center of the circle.

And, Suppose that JK = 16, MP = 8, LP = 2x + 4, and SP = 3.5.

Now, We know that,

By figure,

MP = LP

Substitute the given values,

8 = 2x + 4

8 - 4 = 2x

4 = 2x

x = 4/2

x = 2

Hence, We get;

LM = MP + LP

LM = 8 + (2x + 4)

LM = 8 + 2 x 2 + 4

LM = 8 + 4 + 4

LM = 16

Since, We have JK = 16

Hence, We get;

NS = SP

This gives,

NS = 3.5

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The order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:

Situation 1: Derrick rolls the die 10 times.

Situation 2: Derrick rolls the die 100 times.

Situation 3: Derrick rolls the die 1,000 times.

Situation 4: Derrick rolls the die 10,000 times.

Situation 5: Derrick rolls the die 1,000,000 times.

To determine the order of situations from the largest difference between relative frequency and actual probability to the smallest difference, we need to consider the concept of relative frequency and actual probability.

Relative frequency refers to the observed proportion of an event occurring in an experiment or trial, while actual probability represents the theoretical or expected probability of that event occurring.

Situation 1: Derrick rolls the die 10 times.

In this situation, the relative frequency of rolling a three can vary, but with a limited number of trials, the relative frequency might not accurately reflect the actual probability. Therefore, the difference between relative frequency and actual probability is likely to be larger compared to situations with more trials.

Situation 2: Derrick rolls the die 100 times.

With a larger number of trials, the relative frequency is expected to converge towards the actual probability. The difference between relative frequency and actual probability would likely be smaller compared to the previous situation.

Situation 3: Derrick rolls the die 1,000 times.

Increasing the number of trials further enhances the convergence of relative frequency to the actual probability. The difference between relative frequency and actual probability would be smaller than in the previous two situations.

Situation 4: Derrick rolls the die 10,000 times.

With an even larger number of trials, the relative frequency becomes more reliable and closely approximates the actual probability. The difference between relative frequency and actual probability would be smaller compared to the previous situations.

Situation 5: Derrick rolls the die 1,000,000 times.

In this situation, the large number of trials greatly increases the reliability and accuracy of the relative frequency. The observed relative frequency is expected to be very close to the actual probability, resulting in the smallest difference between the two.

Therefore, the order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:

Situation 1: Derrick rolls the die 10 times.

Situation 2: Derrick rolls the die 100 times.

Situation 3: Derrick rolls the die 1,000 times.

Situation 4: Derrick rolls the die 10,000 times.

Situation 5: Derrick rolls the die 1,000,000 times.

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The product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.

First, distribute the first term of the first polynomial (7x) to each term in the second polynomial (6x - 4):

7x × 6x = 42x²

7x × (-4) = -28x

Next, distribute the second term of the first polynomial (-5) to each term in the second polynomial (6x - 4):

-5 × 6x = -30x

-5 × (-4) = 20

Now, combine the like terms:

42x² - 28x - 30x + 20

Simplify the expression:

42x² - 58x + 20

Therefore, the product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.

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The probability that she selects the route of three specific capitals is 3/43

From the question, we have the following parameters that can be used in our computation:

States = 43

Capitals = 3

The probability is then calculated as

P = Capitals/States

substitute the known values in the above equation, so, we have the following representation

P = 3/43

Hence, the probability is 3/43

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You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.

The perpendicular bisector is determined by measuring the point that is equidistant from the segment.

The altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.

Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.

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Step-by-step explanation:

Cylinder LATERAL  S.A. = circ   X   Height = 132 cm  X  30 cm  = 3960 cm^2

   PLUS the two ends  =  two  X  pi r^2

  the circumference = pi * d = 132 cm

                   then  diameter = 132 / pi   then radius =  1/2  132 / pi = 66/ pi

     so end areas :  two *    pi (66/ pi)^2   = 2773.1

TOTAL = 3960  +  2773.1 =  6733.1 cm^2

Answer: Amplitude is 108 degrees

Step-by-step explanation:

To determine the amplitude of the tip of King Arthur's Sword, we need to understand the shape of the sword's blade, which consists of a regular hexagon and a regular pentagon.

A regular hexagon has six equal sides and six equal angles, each measuring 120 degrees. The regular pentagon, on the other hand, has five equal sides and five equal angles, each measuring 108 degrees.

Since the tip of the sword is formed by the meeting point of the hexagon and pentagon, it will be at the apex of the pentagon. The apex of the pentagon will have an angle of 108 degrees.

I hope this helps!!!

Answer: What is the probability that the ethical hacker will guess the pin code correctly on the first try?

Since the pin code consists of 10 possible digits (0 through 9), the probability of guessing the correct pin code on the first try is 1 in 10. This is because there is only one correct pin code out of the 10 possible options.

Therefore, the probability is 1/10 or 0.1 (or 10%).

Calculating the probability for each of the four situations:

(a) All four digits are unique (e.g., 1234):

In this case, there are 10 options for the first digit, 9 options for the second digit (since it can't be the same as the first), 8 options for the third digit, and 7 options for the fourth digit. The total number of possible combinations is given by:

10 × 9 × 8 × 7 = 5040

So, there are 5040 possible four-digit combinations when all digits are unique.

The probability of guessing the correct pin code on the first try in this situation is 1 in 5040, or 1/5040.

(b) Exactly one of the digits appears twice (e.g., 2334, 8185):

In this case, we have two scenarios to consider:

Scenario 1: The repeated digit is the first digit:

The first digit can be chosen in 10 ways, the second digit (repeated) can be chosen in 9 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:

10 × 9 × 8 × 7 = 5040

Scenario 2: The repeated digit is not the first digit:

The first digit can be chosen in 9 ways (excluding the repeated digit), the repeated digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:

9 × 10 × 8 × 7 = 5040

Combining both scenarios, we get a total of 2 × 5040 = 10080 possible combinations when exactly one of the digits appears twice.

The probability of guessing the correct pin code on the first try in this situation is 1 in 10080, or 1/10080.

(c) Two digits each appear twice (e.g., 1212, 8855):

In this case, there are two scenarios to consider:

Scenario 1: The two pairs of digits are different:

The first pair of digits can be chosen in 10 ways, the second pair of digits can be chosen in 9 ways, and the order of the pairs can be switched. So, the total number of possible combinations is:

10 × 9 × 2 = 180

Scenario 2: The two pairs of digits are the same:

The pair of digits can be chosen in 10 ways, and the order of the digits can be switched. So, the total number of possible combinations is:

10 × 1 = 10

Combining both scenarios, we get a total of 180 + 10 = 190 possible combinations when two digits each appear twice.

The probability of guessing the correct pin code on the first try in this situation is 1 in 190, or 1/190.

(d) One digit appears three times (e.g., 2226, 8188):

In this case, there are two scenarios to consider:

Scenario 1: The repeated digit is the first digit:

The first digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 9 and 8 ways, respectively. So, the total number of possible combinations is:

10 × 9 × 8 = 720

Scenario 2: The repeated digit is not the first digit:

The first digit can be chosen in 9 ways (excluding the repeated digit), and the repeated digit can be chosen in 10 ways. The remaining distinct digit can be chosen in 8 ways. So, the total number of possible combinations is:

9 × 10 × 8 = 720

Combining both scenarios, we get a total of 2 × 720 = 1440 possible combinations when one digit appears three times.

The probability of guessing the correct pin code on the first try in this situation is 1 in 1440, or 1/1440.

To summarize, the probabilities for each of the four situations are:

(a) All four digits are unique: 1/5040

(b) Exactly one of the digits appears twice: 1/10080

(c) Two digits each appear twice: 1/190

(d) One digit appears three times: 1/1440

The length of y in the right triangle is 15 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

The side y in the triangle XYZ can be found using trigonometric ratios as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite sides = y

hypotenuse side = 15√2

sin 45 = y / 15√2

cross multiply

y = 15√2 × sin 45

y = 15√2 × 1 / √2

y = 15 units

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The distance across the stream is 198 m.

We have,

ΔABC and ΔEBD are similar.

This means,

Corresponding sides ratios are the same.

Now,

AC/ED = AB/BE

Substituting the values.

x/360 = 220/400

x = 220/400 x 360

x = 22/40 x 360

x = 22 x 9

x = 198

Thus,

The distance across the stream is 198 m.

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The complete table for the function are

x  -2  -1  1  3

y  2   3  5  7

The graph is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The function equation and the incomplete table of values

This is given as

y = x + 4

From the table, the missing values are at

x = -2, x = -1, 1 and x = 3

So, we have

y = -2 + 4 = 2

y = -1 + 4 = 3

y = 1 + 4 = 5

y = 3 + 4 = 7

The graph is added as an attachment

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The pair of figures are similar because:

• Both figures are parallelograms

• All sides are congruent.

• Scale factor 1: 2.5

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The pair of figures are similar because:

• Both figures are parallelograms

• All sides are congruent

• Angles W and Y are congruent with angles P and R

• Angles X and Z are congruent with angles S and Q

• Scale factor 1 : 2.5

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Answer:

The maximum value of the profit function occurs at the corner point with the highest value, which is P2 = 25.

Therefore, the maximum profit is $25.

Step-by-step explanation:

The values of x and y in simplest radical form are :

5) x = 3 and y = 3√3

6) x = 5√3 and y = 10√3

7) x = 21 and y = 14√3

Given are three right angled triangles, whose angles are 30° - 60° - 90°.

The measures of sides for a 30° - 60° - 90° triangle is in the ratio 1 :√3 :2.

That is if length of the shorter leg which is the side opposite to 30° is k, then the length of the longer leg, which is the side opposite 60° will be √3k and the length of the hypotenuse, which is the side opposite to 90° will be 2k.

5) Using the above fact, here,

2k = 6

⇒ k = 6/2 = 3

So, x = 3 and y = 3√3

6) √3 k = 15

k = 15 /√3 = 5√3

So, x = 5√3 and y = 2 × 5√3 = 10√3

7) k = 7√3

So, x = √3 × 7√3 = 21

y = 2 × 7√3 = 14√3

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The value of x for the second triangle if it is the reduction of the first drawing is 6.3 feet.

Given two triangles.

Also given that, the scale drawings given are the reduction of the figure.

Most probably, the second triangle must be formed after a reduction with a scale factor of k.

Let k be the required scale factor.

The value of k can be found by taking the ratio of the corresponding sides.

k = 5.2 / 10.4

  = 0.5

So all the corresponding sides will be half of the first triangle.

x = 0.5 × 12.6

  = 6.3 feet

Hence the value of x is 6.3 feet.

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Examining the word problem we can say that, Molly used 160 beads to make the necklace.

Let's assume the number of beads used to make the bracelet is x.

We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,

x + 5x = 192

6x = 192

solve for x

x = 192 / 6

x = 32

Molly used 32 beads to make the bracelet.

number of beads used to make the necklace

Number of beads used for the necklace = 5 * 32

Number of beads used for the necklace = 160

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The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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a) The volume of the hemisphere is V₁ = 261.80 km³

b) The volume of the hemisphere is V₂ = 1,526.81 feet³

Given data ,

a)

Let the volume of the hemisphere be represented as V₁

where the radius of the hemisphere is r₁ = 5 km

And , volume of hemisphere is V = ( 2/3 )πr³

On simplifying , we get

V₁ = ( 2/3 )π ( 5 )³

V₁ = 261.80 km³

b)

Let the volume of the hemisphere be represented as V₂

The diameter of the hemisphere = 18 feet

where the radius of the hemisphere is r₁ = 9 feet

And , volume of hemisphere is V = ( 2/3 )πr³

On simplifying , we get

V₂ = ( 2/3 )π ( 9 )³

V₂ = 1,526.81 feet³

Hence , the volume of the hemisphere is solved

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f(x) is the quadratic function.  

g(x) is tripling its output for each 1-unit increase in x and g(x) = 3^x.

A quadratic function always grows more slowly than an exponential function.

So the best answer is:
f(x), because it grows slower than g(x)

The graph that shows only a translation is (c)

From the question, we have the following parameters that can be used in our computation:

The list of options

The general rule of translation it that

Using the above as a guide, we have the following:

the graph that shows only a translation is (c)

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No, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

To form a triangle considering three lengths of sides, the sum of the lengths of any two sides must be greater than the length of the third side.

Checking the above condition

1. The sum of 7.5,8.5 is 16, which is greater than 14.5. So, the condition is satisfied.

2. The sum of 7.5, 14.5 is 22, which is greater than 8.5. So, the condition is satisfied.

3.  The sum of 8.5 and 14.5 is 23, which is less than 7.5. The condition is not satisfied.

Since the sum of the two shorter sides 8.5 and 14.5 is not greater than the longest side 7.5 these three sides with given lengths cannot form a triangle.

Therefore, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

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The image of point A after the reflection is A'(3, -4).

The image of point B after the reflection is B'(2, -3).

To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.

For point A(3, 4):

After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.

Therefore, the image of point A after the reflection is A'(3, -4).

To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.

For point B(-2, -3):

After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.

Therefore, the image of point B after the reflection is B'(2, -3).

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The Horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.

We can use trigonometry and the concept of angles of depression. We can consider the height of the observation deck as the opposite side and the horizontal distance to the ship as the adjacent side of a right triangle.

Given that the angle of depression is 67 degrees and the height of the observation deck is 955 feet, we want to find the horizontal distance (adjacent side).

Using the trigonometric function tangent, we can set up the following equation:

tan(67°) = opposite/adjacent

tan(67°) = 955/adjacent

To find the value of the adjacent side (horizontal distance), we can rearrange the equation:

adjacent = 955/tan(67°)

Using a calculator, we can evaluate the tangent of 67 degrees:

tan(67°) ≈ 2.3693

Now we can substitute this value into the equation:

adjacent = 955/2.3693

adjacent ≈ 403.81

Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.

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The area of triangle ABC is 19 square units.

To find the area of a triangle, we can use different formulas depending on the information available. Since we have the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can use the Shoelace Formula (also known as the Gauss's area formula) to calculate the area of the triangle.

The Shoelace Formula states that if the coordinates of the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the area (A) of the triangle can be calculated as:

Area = 0.5 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|

Using the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can substitute these values into the formula to calculate the area.

Let's calculate step by step:

x1 = -9

y1 = -8

x2 = -2

y2 = -9

x3 = -8

y3 = -5

Area = 0.5 * |(-9 * (-9 - (-5)) + (-2) * (-5 - (-8)) + (-8) * ((-8) - (-9)))|

Area = 0.5 * |(-9 * (-4) + (-2) * (3) + (-8) * (-1))|

Area = 0.5 * |(36 + (-6) + 8)|

Area = 0.5 * |(38)|

Area = 0.5 * 38

Area = 19

Therefore, the area of triangle ABC is 19 square units.

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The value of x is equal to 10 degrees.

In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

By applying the alternate interior angles theorem to parallel lines p and q, we have the following congruent angles:

(5x - 65) = (x - 25)

5x - x = 65 - 25

4x = 40

x = 40/4

x = 10 degrees.

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The length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.

To calculate the length of the sides of the square base of the pyramid, we can use the formula for the volume of a square pyramid:

V = (1/3) * (side length)^2 * height

Given that the volume of the pyramid is 2,000,000 m³ and the height is 100 m, we can substitute these values into the formula:

2,000,000 = (1/3) * (side length)^2 * 100

To isolate the side length, we can rearrange the equation:

(side length)^2 = (2,000,000 * 3) / 100

(side length)^2 = 60,000

Taking the square root of both sides, we find:

side length ≈ √60,000

side length ≈ 244.95

Therefore, the length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.

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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

12) Volume of semi - sphere = 261.67 km³

13) Volume of semi - sphere = 8574.29 feet³

We have to given that;

12) Radius of sphere = 5 km

13) Radius of sphere = 16 feet

Since, We know that;

Volume of sphere = 4/3 πr³

Hence, We get;

Volume of semi - sphere = 2/3πr³

12) Here, Radius of sphere = 5 km

Volume of semi - sphere = 2/3πr³

Volume of semi - sphere = 2/3 × 3.14 × 5³

Volume of semi - sphere = 261.67 km³

13) Here, Radius of sphere = 16 feet

Volume of semi - sphere = 2/3πr³

Volume of semi - sphere = 2/3 × 3.14 × 16³

Volume of semi - sphere = 8574.29 feet³

Thus, We get;

12) Volume of semi - sphere = 261.67 km³

13) Volume of semi - sphere = 8574.29 feet³

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