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Answer:

[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:

[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]

Set each factor equal to zero and solve for x using the unit circle.

[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]

[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]

Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:

[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]

The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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Answer:

Step-by-step explanation:

To graph the function, we'll break it down into three parts based on the given conditions.

For x ≤ -2:

The function f(x) = x + 6 is valid in this range. We'll plot a straight line with a slope of 1 and a y-intercept of 6. Since x ≤ -2, we'll extend the line towards the left indefinitely.

For -2 ≤ x ≤ 1:

The function f(x) = x² is valid in this range. We'll plot a curve representing a quadratic function. The graph starts at the point (-2, 4), curves upward, and ends at the point (1, 1).

For x > 1:

The function f(x) = -2x is valid in this range. We'll plot a straight line with a negative slope of -2. Since x > 1, we'll extend the line towards the right indefinitely.

Combining these three parts, we get the graph of the function as follows:

23(2+2+3+372+27272+"

Answer: 42

Step-by-step explanation:

The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.

The true statements about 388.33 are:

The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.

The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.

We have,

The statement "The value of the tens digit, 80, is 10 times the value of the one's digit, 8" is incorrect. The tens digit is actually 3, not 80.

The statement "The value of the hundredths digit, 0.03, is 10 times the value of the tenths digit, 0.3" is true.

The hundredth digit is 3 times smaller than the tenth digit, which means that the tenth digit is 10 times larger than the hundredth digit.

The statement "The value of the one's digit, 8, is the value of the tens digit, 80" is incorrect.

The tens digit is 3, not 80.

The statement "The value of the hundredths digit, 0.03, is to the value of the tenths digit, 0.3" is unclear and not a proper comparison, so it cannot be determined whether it is true or false.

Thus,

The true statements about 388.33 are:

The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.

The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.

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Answer:

147

Step-by-step explanation:

V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188

The probability is solved and the tree diagram is given

Given data ,

The tree diagram to draw 3 cards out of 52 cards from the given probability details are:

The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.

        _______ Draw a Spade _______

              /                              \

      ______/______                  ______\_______

     /              \                /               \

   /                  \            /                   \

 /                      \        /                       \

Spade                 Not Spade             Spade             Not Spade

 |                        |                |                   |

Draw another Spade   Not Draw a Spade  Draw another Spade  Not Draw a Spade

Hence , the probability of deck of cards is solved

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Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.

The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.

The contribution margin can be computed per unit or in total.  Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.

 Breakfast     Selling Price    Food Cost       Sales     Contribution Margin

Menu Item               ($)                  ($)           Volume         Unit         Total

А                         $10.00             $3.00           250          $7.00      $1,750

B                         $16.00             $6.00             50        $10.00        $500

C                         $18.45             $8.00             60        $10.45        $627

D                         $14.75             $4.25           300        $10.50      $3,150

E                          $8.75             $2.50             80          $6.25        $500

F                        $12.50              $5.75            180         $6.75       $1,215

G                        $9.00              $2.60           280         $6.40      $1,792

TOTAL                                                          1,200

Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.

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The length x in the triangle below is 16 m.

Length is the distance between two points.

To calculate the length of the triangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for x

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Answer:

V = π(5^2)(8) + (4/3)π(5^3)

= 200π + (500/3)π = (1,100/3)π

= about 1,151.92 cm^3

The weight of a pitaya seed in standard form is [tex]1 \times 10^-^6[/tex]ounce.

In standard form, the weight of a pitaya seed is expressed in scientific notation, where the number is a decimal between 1 and 10, and the exponent is a power of 10. The weight of a pitaya seed is given as [tex]1 x 10^-^3[/tex] ounce, which means that the seed weighs one-thousandth of an ounce.

To write this in standard form, we first convert the number to a decimal between 1 and 10 by moving the decimal point three places to the left. This gives us a decimal of 0.001. The exponent is already in the form of a power of 10, so we can leave it as [tex]10^-^3[/tex]. Thus, the weight of a pitaya seed in standard form is:

[tex]0.001 \times 10^-^3[/tex]

To simplify this expression, we can multiply the decimal and the exponent. This gives us:

[tex]1 x 10^-^6[/tex]

This means that the weight of a single pitaya seed is very small, and it takes many seeds to make up the weight of a whole pitaya fruit.

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The measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.

The measure of angle ACB can be determined using the properties of tangents and secants intersecting a circle.

Since side AC is tangent to the circle, angle BAC is a right angle (90 degrees).

According to the tangent-secant theorem, the measure of angle ACB is equal to half the difference between the intercepted arcs AB and AX.

Since angle BAC is a right angle, the intercepted arc AX is a semicircle, which means its measure is 180 degrees. The intercepted arc AB is an arc of the circle and is less than 180 degrees since it is not a full circle.

Therefore, the measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.

To find the exact measure, more information is needed about the length of arc AB or the relationship between the lengths of the sides of the triangle. Without this additional information, we cannot determine the precise measure of angle ACB.

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For the given menu, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink.

Number of choices for ordering:

Sandwich = 8

Soup = 5

Drink = 3

According to the multiplication principle, multiply the number of options for each category to find the total number of choices:

Total choices = (Number of options for Sandwich) * (Number of options for Soup) * (Number of options for Drink)

Total choices = 8 * 5 * 3

Total choices = 120

Therefore, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink from the given menu.

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When a person places $12,500 in an investment account earning an annual rate of 8.3%, compounded continuously, based on the formula V = Pe^rt, the amount of money (future value), to the nearest cent, in the account after 12 years, is $33,842.88.

Using the formula A = Pe^rt where V is the future value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.

In this situation, we can use an online finance calculator to determine the future value compounded continuously as follows:

Principal (P): $12,500.00

Annual Rate (R): 8.3%

Compound (n): Compounding Continuously

Time (t in years): 12 years

Result:

A (Future Value) = $33,842.88

A = P + I where

P (principal) = $12,500.00

I (interest) = $21,342.88

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Answer:

Hi

Please mark brainliest ❣️

Step-by-step explanation:

25/75 × 100/1

= 33.3%

If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.

Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².

We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:

x² * 17.2 cm³ = 24.768 cm³

Simplifying this equation, we get:

x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²

Taking the square root of both sides, we get:

x = 1.2 cm

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The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

Given Sample size (n) is 120 workers

Proportion of workers who are college graduates (p): 34% or 0.34

a) Mean and Standard Deviation:

The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).

Substituting the values:

μ = 120 ×0.34 = 40.8

σ = √120 × 0.34 × (1 - 0.34)) = 5.37

To find the probability that the number of workers with a college degree is at least 35

we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.

Using a binomial probability calculator or a statistical software, we can find this probability.

Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:

P(X ≥ 35) = 1 - P(X < 35)

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

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The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%

Here, we have,

Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = speeds of cars

µ = mean speed

σ = standard deviation

From the information given,

µ = 55 mi/hr

σ = 5 mi/hr

The probability that a car is driving less than 45 mi/hr is expressed as

P(x < 45)

For x = 45

z = (45 - 55)/5 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

Therefore, the percentage of cars that are driving less than 45 mi/hr is

0.023 × 100 = 2.3%

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Answer:

2.23

Step-by-step explanation:

You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.

To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.

The average rate of change for the snowfall amount is given as follows:

2.4 inches per hour.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The change in the output is given as follows:

8.1 - 3.3 = 4.8.

(output is the amount of snow).

The change in the input is given as follows:

2 - 0 = 2.

(input is the time in hours).

Hence the average rate of change of the snowfall over time is given as follows:

4.8/2 = 2.4 inches per hour.

(change in the snowfall divided by the change in time).

The table is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.

To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the cuboid, respectively.

Substituting the given values, we get:

Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)

Surface Area = 8 + 24 + 12

Surface Area = 44

This means that there are 44 square yards of material needed to cover all six faces of the cuboid.

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According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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47.17 feet is the height of the building.

We can use the Pythagorean theorem to solve the problem:

Let h be the height of the building.

Then we have a right triangle with legs 20 and h, and a hypotenuse 50.

Using the Pythagorean theorem, we have:

[tex]50^2 = 20^2 + h^2[/tex]

Simplifying and solving for h, we get:

[tex]h = \sqrt{(50^2 - 20^2)[/tex]

h ≈ 47.17 feet (rounded to two decimal places)

Therefore, the height of the building is approximately 47.17 feet.

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We cannot have a fractional number of candles, Haleigh can make a maximum of 2 five-ounce candles using the available wax from the 20-ounce and 1-ounce candles.

To determine the number of 5-ounce candles Haleigh can make using the remaining wax from her existing candles, we need to calculate the total amount of wax available and divide it by the amount of wax needed for each 5-ounce candle.

Let's calculate the total amount of wax available:

The five 20-ounce candles have 10% of their original wax remaining, so each candle has 2 ounces of wax left.

Therefore, the total wax from the five 20-ounce candles is 5 candles [tex]\times[/tex] 2 ounces = 10 ounces.

The five 5-ounce candles already have wax, so we don't need to consider them.

The twenty-five 1-ounce candles have 10% of their original wax remaining, so each candle has 0.1 ounces of wax left.

Therefore, the total wax from the twenty-five 1-ounce candles is 25 candles * 0.1 ounces = 2.5 ounces.

Adding up the wax from the 20-ounce and 1-ounce candles, we have a total of 10 ounces + 2.5 ounces = 12.5 ounces of wax available.

To determine how many 5-ounce candles can be made, we divide the total available wax by the amount of wax needed for each 5-ounce candle:

Number of 5-ounce candles = Total available wax / Wax needed per 5-ounce candle

Number of 5-ounce candles = 12.5 ounces / 5 ounces

Number of 5-ounce candles ≈ 2.5 candles.

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The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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   The solution to the system of equations is x = 1,y = -1 by using the elimination method.

  To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations. Here's how:

  Multiply the first equation by 2 to make the coefficients of y in both equations opposite each other:

Equation 1: 2(y + 2x) = 2(1) => 2y + 4x = 2

  Rewrite the second equation as:

Equation 2: 3x - 2y = 5

  Now, we can add the modified Equation 1 to Equation 2 to eliminate y:

(2y + 4x) + (3x - 2y) = 2 + 5

  Simplifying, we get:

4x + 3x = 7

7x = 7

  Divide both sides of the equation by 7 to solve for x:

x = 7/7

x = 1

  Substitute the value of x into either of the original equations. Let's use the first equation:

y + 2(1) = 1

y + 2 = 1

  Subtract two from both sides of the equation to solve for y:

y = 1 - 2

y = -1

  Therefore, the solution to the system of equations is:

x = 1

y = -1

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Answer:

Step-by-step explanation:

easy its A tell me if u got it correct good job (:

Answer:

 r=5.9

Step-by-step explanation:  

Answer:

the set of all real numbers -1≤y≤1

Step-by-step explanation:

according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.