Determine all solutions to the equation 2sin2x = 1 − cos x on the interval [0, 2π).
a: x equals pi over 2 comma 2 times pi over 3 comma 4 times pi over 3
b: x equals 0 comma pi over 3 comma 5 times pi over 3
c: x equals pi over 2 comma pi over 3 comma 5 times pi over 3
d: x equals 0 comma 2 times pi over 3 comma 4 times pi over 3

By using the formula of a geometric sequence, the 14th term will be 125/1024

We have, the Fourth term of geometric sequence T_4= 125 and T_10 = 125/64

Let's find the first term and common ratio of the geometric sequence.

Using the formula of the nth term of a geometric sequence, we get,

T_4 = a * r^3 = 125 ....(1)

and,

T_10 = a * r^9 = 125/64 ...(2)

On dividing eq. (2) by eq. (1), we get,

(r^6) = (125/64) / 125 ⇒ 1/64

Taking the sixth root of both sides, we get:

r = (1/64)^(1/6)

r = 1/2

Now that we know the common ratio, we can use the equation for the nth term of a geometric sequence:

T_n = a * r^(n-1)

To find the 14th term, we substitute n=14 and solve:

T_14 = a * (1/2)^(14-1) ⇒ a * (1/2)^13

We don't know the value of a yet, but we can use the fact that the 4th term is 125 to solve for it:

a * r^3 = 125

a * (1/2)^3 = 125

a = 125 * 2^3

a = 1000

Substituting this value for a, we get:

T_14 = 1000 * (1/2)^13

T_14 = 1000 * 1/8192

T_14= 125/1024

Therefore, the 14th term of the geometric sequence is 125/1024.

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When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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Answer:

When x = 0, y = 2^0 + 6 = 7. So the first point is (0, 7).

When x = 1, y = 2^1 + 6 = 8. So the second point is (1, 8).

When x = 2, y = 2^2 + 6 = 10. So the third point is (2, 10).

When x = -1, y = 2^-1 + 6 = 6.5. So the fourth point is (-1, 6.5).

When x = -2, y = 2^-2 + 6 = 6.25. So the fifth point is (-2, 6.25)

The probability that a person chosen at random at age 40 or older has only completed high school is 0.2912.

Probability is the chance or likelihood that something will occur. It is quantified using numbers, ranging from 0 (no chance) to 1 (certainty). It also helps us to draw conclusions about the chances of something happening based on the available data.

The total number of people who have only completed high school

=(5394)

the total number of people in the age group 40 and over =(18521)

By dividing both the data, we get

5394/18521= 0.2912

From the given data in the table, we can calculate the probability that a person chosen at random at age 40 or older has only completed high school.

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To solve the question asked, you can say:  So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of ​​a triangle can be calculated using the formula A =​​ (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.  

here in the triangle we have sides that are 3 and 8

we can use

[tex]A^2 = B^2 + C^2\\A^2 = 3^2 + 8^2\\A^2 = 9+64\\A^2 = 73\\A = \sqrt73[/tex]

So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

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Answer:

If the store marks up the price of the diving board by 45%, the selling price will be 100% + 45% = 145% of the cost price.

Let's calculate the selling price:

Selling price = Cost price + Mark-up

Mark-up = Selling price - Cost price

Mark-up = (145% of cost price) - cost price

Mark-up = 0.45 * cost price

We know that the store paid $261 for the diving board, so:

Mark-up = 0.45 * $261 = $117.45

Therefore, the amount of the mark-up is $117.45.

well, what's 45% of 261?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{45\% of 261}}{\left( \cfrac{45}{100} \right)261}\implies \text{\LARGE 117.45}[/tex]

the statement "A Triangle with side lengths 20,21, and 28 is a right triangle" is invalidated.

As, You may simply rule out the first three options if you are familiar with specific Pythagorean triples and other triangle relationships.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most important triplets are (3,4,5).

So,

20² +21² = 400 +441 = 841 = 29²

The appropriate choice is  20, 21, and 29

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209 went to the first game.

192+17=209

Happy to help.

The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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Answer:

x = - 2

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through all points with an x- coordinate of - 2 , then

x = - 2 ← equation of line

Answer:

<b> <i>

Step-by-step explanation:

The significance of a pedigree symbol consisting of a square with a diagonal slash mark through it is that it represents the male members of the family

It is a standard symbol in a pedigree chart. This symbol represents the sex of a person, in this case, it represents the male sex. In other words, a square with a diagonal slash mark through it is used to represent the male gender in pedigree charts.

A pedigree chart is a diagram that shows the genetic relationships between individuals in a family. It is used to track genetic diseases or traits through generations. A pedigree chart can provide information about a family's medical history and can help doctors to understand how genetic disorders are inherited from one generation to the next. Each symbol used in the pedigree chart has a specific meaning.

The squares represent males while the circles represent females. The horizontal line between two symbols represents marriage, and the vertical line from a symbol represents a child of that union.

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Answer:

You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer

Step-by-step explanation:

300?

The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

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Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

----------------

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]

The entire lawn is 19124 square decimeters.

----------------

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Answer:

15/x * 100 %

Step-by-step explanation:

Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)

Answer:

the value of x is approximately 0.382 cm.

Step-by-step explanation:

Answer:

The correct order to draw 65 agle would be:

C

A

B

D

A skater has a mean score of 7. 25 points. An equation to determine the skaters total scores received from eight judges is equals to the x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

Mean is called the average of the values and is calculated by dividing the addition of values by the total number of values. It is denoted by [tex]\bar X[/tex]. That is bar above X represents mean of x number of values. Mathematically, Mean = (Sum of all the values/Total number of values).We have in a skating compotion where each skater receives score from eight judges. Now, Mean or average of score points obtained by a skater = 7.25 points. Let the skater's received score from eight judges be equals to x₁,x₂,x₃,x₄,x₅,x₆,x₇, x₈. Total score received by skater = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ and we have to write the equation to determine the skaters total scores. Now, in this case mean of scores means the sum of scores received by skaters from eight judges divided by eight (judges).

=> 7.25 = (x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈)/8

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 8× 7.25

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 58

which is equation of 8 variables for total score. Therefore, the required equation is x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

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Answer:

42x-27

Step-by-step explanation:

The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.

Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.

Using the formula for simple interest, we can calculate the interest earned in each year:

Simple interest for 3 years = (x * 5% * 3) = 0.15x

Simple interest for 4 years = (x * 5% * 4) = 0.2x

The difference between the two is:

0.2x - 0.15x = 0.05x

We are given that this difference is equal to Rs. 82, so:

0.05x = 82

Solving for x, we get:

x = 82 / 0.05 = 1640

Therefore, the principal sum is Rs. 1640.

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Value of angle x is 41 degree.

A straight line is a one-dimensional geometric object that extends infinitely in both directions. It can be defined as the shortest path between two points in a plane, and it has a constant slope (i.e., rate of change) between any two points on the line.

The standard equation for a straight line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). Another commonly used form is the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Given, total angle=236°

236°=76°+119°+x

x=236°-76°-119°

x=41°

Hence, Value of angle x is 41 degree.

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Each pair of numbers (m, h) which meet the inequality is the answer to the inequality. m < h plus 2.

A factor pair is a collection of two factors that, when multiplied together, produce a certain result in mathematics. In those other words, it's a pair of integers that we multiply to produce a result. For instance, the factor pair that yields the result in the multiplication formula 6 7 = 42 is composed of the numbers 6 and 7. 42

By adding 14 to both sides, starting with -14 + 7m 7h, we may simplify the left side:

-14 + 7m plus 14 < 7h plus 14

Even more condensed, we get at:

7m < 7h plus 14

The inequality can then be divided by 7 on both sides: m h + 2.

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The total surface area of the remaining portion is approximately 23.14 in.

To find the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, use the formula SA = 4πr2. A sphere is symmetrical, and thus, the diameter of the wooden sphere is equal to the diameter of the remaining portion. The radius of the remaining portion is equal to half the diameter of the sphere minus the radius of the cap.

The diameter of the wooden sphere is 11.8 in. As such, the radius of the sphere is 5.9 in. If two equal caps are removed, the diameter of the remaining portion is equal to 11.8 in - 2x R_cap, where R_cap is the radius of the cap. Since the caps are equal, we can simplify the formula to

D = 11.8 - 2R_cap. R_cap is equal to the radius of a circle with area equal to the surface area of one cap. As such, we can use the formula SA = 2πrh + πr2 to find the surface area of the cap. We know the diameter of the sphere is 11.8 in. Thus, the radius of the sphere is 5.9 in. We also know that the height of the cap is 5.9 in. Since the caps are equal, we can use the formula to find the surface area of one cap and multiply by 2 to get the total surface area of both caps.

SA_cap = 2π(5.9 in)(5.9 in) + π(5.9 in)

2SA_cap = 2π(34.84 in2) + π(34.84 in2)

SA_cap = 2π(34.84 in2) + 109.45 in2SA_cap ≈ 219.74 in

Since the surface area of the cap is equal to 219.74 in, we can use the formula to find the radius of the cap.

219.74 in = 2πrh + πr22(219.74 in2)

= 2π(5.9 in)h + π(5.9 in)22(219.74 in2)

= 37.699 in2 + 109.45 in23r2

= 72.533 in2r ≈ 4.545 in

Using the formula D = 11.8 - 2R_cap, we can find the diameter of the remaining portion of the wooden sphere.

D = 11.8 - 2(4.545 in)D ≈ 2.71 in

The radius of the remaining portion of the wooden sphere is equal to 5.9 in - 4.545 in. Thus, the radius of the remaining portion of the sphere is 1.355 in. Finally, we can find the total surface area of the remaining portion of the sphere.

SA = 4πr2SA = 4π(1.355 in)2SA ≈ 23.14 in

Therefore, the total surface area of the remaining portion is approximately 23.14 in.

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The coordinates of the point P is (-1,2) .

What is translation?

In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.

Finding the coordinates of the point P :

The coordinates of point P can be found by subtracting the vector from point Q.

To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).

Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:

3 - 4 = -1

Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:

-1 - (-3) = 2

Therefore, the coordinates of point P are (-1, 2).

So, the correct answer is (C) (-1, 2).

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Answer:

I got 162?

Step-by-step explanation:

I broke down each individual shape (7 rectangles and 2 triangles) and used each shapes surface area formula.

triangle surface area formula is 1/2*b*h, and there are 2 of the same triangles of the exact same size and 7 rectangles. 3 are same size rectangles, 2 are same size rectangles and the other 2 are different sized rectangles. Then add altogether.

The radius of the given circle is x = 3 and x = 3/11.

A polynomial equation of degree two is a quadratic equation, indicating that the variable's maximum exponent is 2. There are various ways to solve a quadratic equation, including factoring, completing the square, and applying the quadratic formula. Finding two quadratic expression factors that multiply to produce the constant term c and add to produce the linear term b's coefficient is known as factoring. The quadratic expression is completed by adding and removing a constant component to create a perfect square trinomial that can be factored or solved by calculating the square root.

In the given figure connect the points QF and QG using a line segment, thus forming two right angled triangle.

The perpendicular segment QA divides the base into two equal parts. Thus, the base of the triangle is 8.

Using the Pythagorean theorem we have:

(QF)² = (8)² + (4x + 3)²

QG² = 8² + (7x - 6)²

In the figure QF = QG = r thus:

(8)² + (4x + 3)² = 8² + (7x - 6)²

Expanding using the algebraic identity:

16x² + 24x + 9 = 49x² - 84x + 36

33x² - 108x + 27 = 0

3(11x² - 36x + 9) = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values a = 11, b = -36, and c = 9:

x = (-(-36) ± √((-36)² - 4(11)(9))) / 2(11)

x = (36 ± √(1296 - 396)) / 22

x = (36 ± √900) / 22

x = (36 ± 30) / 22

x = (36 + 30) / 22 = 3

x = (36 - 30) / 22 = 3/11

x = 3 and x = 3/11.

Thus, the radius of the given circle is x = 3 and x = 3/11.

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Answer:

For WXYZ to be a parallelogram, both pairs of opposite sides must be parallel.

So, we have 7m + 4 = 9m and 5y + 13 - (2n - 1) = 6y - 8 - (n + 6).

Solving the first equation, we get m = 2.

Solving the second equation, we get y - n = 4.

Thus, for WXYZ to be a parallelogram, m = 2 and y - n = 4, so option B is correct.

Answer:

Elise's average pay per hour for the year 2017 was £11.88.

Step-by-step explanation:

First, we need to calculate Elise's monthly salary in 2017 after the 3% increase:

3% of £2100 = 0.03 x £2100 = £63

Elise's new monthly salary in 2017 = £2100 + £63 = £2163

Next, we need to calculate her total earnings in 2017:

Total earnings = monthly salary x number of months worked

Elise worked for 45 weeks in 2017, which is approximately 10.4 months:

Total earnings = £2163 x 10.4 = £22,477.20

Finally, we can calculate her average pay per hour for the year:

Total number of hours worked = 42 hours/week x 45 weeks = 1890 hours

Average pay per hour = total earnings / total number of hours worked

Average pay per hour = £22,477.20 / 1890 hours = £11.88 per hour

Answer:

I got $13.73 per hour

Step-by-step explanation:

If you multiply 2100 by 12 months you get $25200 for an annual salary before percent increase.

Then you include the 3% salary increase each month 25200 x .03 = 756 then add the two 25200 + 756 = 25956 OR you can calculate the longer way by doing each individual month, either way it will be the same answer. 2100 x .03 = 63 then 2100 + 63 = 2163 then 2163 x 12 = 25956

Then you divide 25956 by the number of weeks worked in the year. 25956/45 = 576.8

So, each week $576.8 was earned.

Then to get an hourly rate, you divide this by the number of hours worked in each week. 576.8/42 = 13.73

So, the hourly rate is $13.73.

I hope this helped :)