Use a Double- or Half-Angle Formula to solve the equation in the interval \( [0,2 \pi \) ). (Enter your answers as a comma-separated list.) \[ \cos (\theta)-\sin (\theta)=\sqrt{2} \cdot \sin \left(\fr

The value of 402€ after increasing by 23% is 494.46€. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, often known as "arithmetic operations," are said to be able to adequately explain all the real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given a value as 402€ which is to be increased by 23%.

So, by using the addition operation, we get the value as,

⇒ 402€ + 23%

⇒ 402€ + 92.46€

⇒ 494.46€

Hence, the value of 402€ after increasing by 23% is 494.46€.

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Question: Find the value of 402€ when increased by 23%.

Answer: 11550

Step-by-step explanation:

First you add 475+2650=11550

Therefore, the number of measurements falling into each of the measurement classes are:

00.5-2.50: 45

02.5-4.50: 30

04.5-6.50: 30

06.5-8.50: 15

08.5-10.5: 30

10.5-12.5: 60

12.5-14.5: 60

14.5-16.5: 30

What is relative frequency ?

Relative frequency is a measure used to calculate the proportion or percentage of occurrences of an event in relation to the total number of events or observations. It is calculated by dividing the frequency of an event by the total number of observations in a dataset. The relative frequency is expressed as a decimal, fraction, or percentage. It is useful for comparing the occurrence of events in different datasets or for comparing the distribution of events in a single dataset.

According to the question:
To calculate the number of measurements that fall into each class, we need to multiply the relative frequency of each class by the total number of measurements, which is 300.

For the 00.5-2.50 class: 0.15 x 300 = 45

For the 02.5-4.50 class: 0.1 x 300 = 30

For the 04.5-6.50 class: 0.1 x 300 = 30

For the 06.5-8.50 class: 0.05 x 300 = 15

For the 08.5-10.5 class: 0.1 x 300 = 30

For the 10.5-12.5 class: 0.2 x 300 = 60

For the 12.5-14.5 class: 0.2 x 300 = 60

For the 14.5-16.5 class: 0.1 x 300 = 30

Therefore, the number of measurements falling into each of the measurement classes are:

00.5-2.50: 45

02.5-4.50: 30

04.5-6.50: 30

06.5-8.50: 15

08.5-10.5: 30

10.5-12.5: 60

12.5-14.5: 60

14.5-16.5: 30

To graph a frequency histogram for these data, we can plot the number of measurements in each class on the vertical axis and the measurement classes on the horizontal axis, with the bars for each class touching each other. The resulting histogram should have eight bars of varying heights, with the tallest bars representing the classes with the most measurements.

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125 cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inch.

A cube is a 3-dimensional solid shape with six square faces that are all congruent, and with all edges of equal length.

The volume of a cube is calculated by cubing the length of one of its edges.

To find the number of cubes with an edge length of 1/5 inch that are needed to build a cube with an edge length of 1 inch, we need to calculate the ratio of the volumes of the two cubes.

The volume of the larger cube with an edge length of 1 inch is:

V_large = (1 inch)^3 = 1 cubic inch

The volume of the smaller cube with an edge length of 1/5 inch is:

V_small = (1/5 inch)^3 = 1/125 cubic inches

To find the number of small cubes, we need to divide the volume of the larger cube by the volume of the smaller cube:

Number of small cubes = V_large / V_small = 1 cubic inch / (1/125 cubic inches) = 125

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Answer:

fourth option

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]

and

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]

The perimeter of the triangle jeg is 60 units where the sides of the triangle are given.

Perimeter is the total distance around the outer boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

EK = x + 5

KJ = x +5

FG = 2x

GH = 3x - 5

Assuming that the triangle is equilateral:

equate GH = FG

3x - 5 = 2x

solve for x

x = 5

therefore, one side of the triangle is

(x + 5) + (x + 5) = 20

and the equilateral triangle's perimeter is

3×one side = 3 ×20 units

Thus, Perimeter = 60 units.

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The complete question is What is the perimeter of triangle JEG?

60 units

65 units

70 units

75 units

The midpoint of the line segment with the endpoints is (-2, 5).

option B.

To find the coordinates of the midpoint of a line segment with endpoints K(-9, 3) and H(5, 7), we can use the midpoint formula:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Where;

Plugging in the coordinates of K and H, we get:

Midpoint = [(-9 + 5)/2, (3 + 7)/2]

= [-2, 5]

Therefore, the midpoint of the line segment with endpoints K(-9, 3) and H(5, 7) is (-2, 5).

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An equation of this line in slope-intercept form is y = 5x - 15.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

At data point (3, 0) and a slope of 5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 5(x - 3)  

y - 0 = 5x - 15

y = 5x - 15

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Answer:

Option B.

Step-by-step explanation:

Convert the word problem into an equation.

[tex](x)(5x-2) = 72[/tex]

Simplify this to get

[tex]5x^2-2x=72[/tex]

Option B.

The value of x, y, z are 14√2, 4√7, 2√21

Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Tan (45) = 14√2/x

1 = 14√2/x

x =14 √2

the third side(hypotenuse) = √14√2)²+14√2)²

= √56+56

= √112

= 4√7

sin(30) = y/4√7

1/2 = y/4√7

2y = 4√7

y = 2√7

cos 30 = z/4√7

√3/2 = z/4√7

2z = 4√21

z = 2√21

therefore the value of x , y , z are 14√2, 4√7, 2√21

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75% of the time, a dart will fall inside a square rather than on the circular dartboard.

The ratio of the area of the circle to the square is 16/64 = 1/4. So, the area outside the circle but inside the square is 3/4 of the total area of the square. The probability of landing the dart in this region is 3/4.

To find the percentage, we can multiply by 100:

3/4 × 100 = 75%

Therefore, to the nearest percent, the probability that the dart lands inside the square but not on the circular dartboard is 75%.

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Answer:

18 bc there a 9 angles and below is is another angle so u do 9 + 9 or 9(2) and u will get 18

The line segment that shows the base that corresponds to the given height of the triangle is; Line segment A

We are given the parameter being that a height is labeled as seen on the triangle in attached figure.

Now, what we want to achieve is to find the specific segment which tells us the specific base that corresponds to the given specific height of the triangle

We know that the base of the triangle is that particular side of the triangle on which the height is perpendicular.

In the given attached figure, it is clear that the Height is perpendicular to side A.

Therefore, side A will represent the base of triangle.

Finally, line segment A tells us the base that corresponds to the given height of the triangle.

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Answer:

There are 4 queens in a pack of 52 cards, and there are also 13 diamonds and 26 black cards (13 clubs and 13 spades).

To find the probability of getting a queen or a diamond or a black card, we need to add the probabilities of each event happening and subtract the probability of getting a card that is both a queen and a diamond (the queen of diamonds).

Probability of getting a queen = 4/52 = 1/13

Probability of getting a diamond = 13/52 = 1/4

Probability of getting a black card = 26/52 = 1/2

Probability of getting the queen of diamonds = 1/52

So, the probability of getting a queen or a diamond or a black card is:

(1/13) + (1/4) + (1/2) - (1/52) = 51/52 or approximately 0.98

Therefore, the probability of getting a queen or a diamond or a black card is approximately 0.98.

Hence, the answers are a) 9.14 and b) 7.

a) What is the expected number of times the die comes up 6, when it is rolled 32 times?b) What is the expected number of times the die must be rolled until the first 6 comes up?Solutions:Part a) Let X be the number of times the die comes up 6 when it is rolled 32 times.To find the expected number of times the die comes up 6, we'll apply the formula E(X) = np, where n is the number of trials and p is the probability of success on any given trial.If we look at the bias in this particular cubic die, we see that when the event is {6}, then p({6}) = p = 2p/4. This implies that p = 2/7, therefore: E(X) = np = 32*2/7 = 9.14285714286 = 9.14Part b) Let Y be the number of times the die must be rolled until the first 6 comes up.Let's use the geometric distribution to calculate the expected number of rolls E(Y).Since the event "6" has a probability of 1/7, then p = 1/7. Thus, the expected number of times the die must be rolled until the first 6 comes up is given by E(Y) = 1/p, which is 7 rolls.Hence, the answers are a) 9.14 and b) 7.

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The solution to the equation x² + 3x = 0 when solved for variable x are x = -3 and 0

Equations are statements with equal values

Given the following equation

x² + 3x = 0

Factor out x from the equation

So, the equation becomes

x(x + 3) = 0

The above equation means that

x = 0

Also, it means that

x + 3 = 0

When the equation is evaluated, we have

x = 0 and x = -3

Now that we have the values of x, we can conclude that the solutions are x = 0 and x = -3

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Answer:

2(x+6)(x+9)

Step-by-step explanation:

Factor out a 2.

The result is 2(x^2+15x+54).

From here, many ways are possible, but for simplicity, we’ll go for a guess and check method. Assuming you know how it works, 2 numbers (we’ll call them a and b) satisfy a+b=15 and ab=54. After a bit of guessing, we can derive that the 2 numbers are 6 and 9. Our factored expression resembles 2(x+a)(x+b), so our factored expression is

2(x+6)(x+9)

The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.

Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.

Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.

This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.

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Answer: six minutes

Step-by-step explanation: 8 / 4 = 2 , 3 x 2 = 6

Answer:

54

Step-by-step explanation:

So a right angle has one right angle and each angle is equal to ninety degrees. So you have 90+36=126. Sum of angles in a triangle is 180 so subtract 126 from it to get 54.

Have a wonderful day and feel free to ask me again. Peace

The scale factor on the map is 1 unit = 557 miles. This means that for every 1 unit on the map, it corresponds to 557 miles in the real world.

A map is a visual representation of an area. It shows physical features such as landforms, bodies of water, and other geographical features. It can also represent political boundaries, transportation networks, and population density. Maps are useful tools for navigation, planning, and communication. They are also used for research, education, and leisure activities.

For example, if Seattle to San Jose on the map is 1 unit, then it is equivalent to 557 miles in the real world. Similarly, if Denver to El Paso is 2 units, then it would be equivalent to 1114 miles in the real world.

This scale factor is important when planning a journey because it helps travelers to accurately calculate the distance they need to travel. Knowing the exact distance can help travelers plan their stops along the way, choose the most efficient route, and estimate the amount of time it will take to get to their destination. Additionally, it can help travelers to plan their budget accordingly, since they will have an idea of how much gas they need to buy and how much accommodation costs they need to cover.

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The length of one side of a square face is 5 inches

The surface area of a cube is given by 6s^2, where s is the length of one side of a square face. If the net for a cube has a total surface area of 150 in^2, we can set up an equation:

6s^2 = 150

Dividing both sides by 6, we get:

s^2 = 25

Taking the square root of both sides, we get:

s = 5

Therefore, the length of one side of a square face is 5 inches.

So, the answer is (b) 5 in.

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Answer:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Step-by-step explanation:

To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.

For x less than 0:

f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)

For x greater than or equal to 0:

f(x) = sqrt(7x^2 + 9)

Therefore:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

In response to the query, we can state that Hence, the bigger polygon's equation circumference measures around 54.86 inches.

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.

Area of a smaller polygon is equal to (k * side of a smaller polygon)2.

bigger polygon's area is equal to (k * side of larger polygon)2.

Area of bigger polygon / area of smaller polygon = (k * side of larger polygon) / (k * side of smaller polygon) /

[tex]\sqrt(128/98) k * 42 = (48 / side of smaller polygon) * 42 = 48 * (42 / side of smaller polygon) = (k * side of bigger polygon) / (k * 42)[/tex]

Greater polygon's perimeter is equal to 48 * (42 / smaller polygon's side) [tex]= 48 * (42 / (42k)) = 48 * (1/k).[/tex]

We may utilize the fact that the ratio of the two polygons' surface areas is to calculate k:

bigger polygon's area divided by smaller polygon's area equals 128/98, or 64/49.

the ratio of the sides of the two polygons is 8/7.

K thus equals 7/8.

Hence, the bigger polygon's circumference measures around 54.86 inches.

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Quadrilateral A: Parallelοgram, Rectangle, Rhοmbus, Square.

Quadrilateral B: Trapezοid, Isοsceles Trapezοid

Quadrilateral C: Kite, Trapezοid

Square and Rectangle:

Bοth have fοur right angles, but the square has fοur cοngruent sides, while the rectangle dοes nοt necessarily have cοngruent sides. Therefοre, a square is a rectangle, but nοt all rectangles are squares.

Rhοmbus and Square:

Bοth have all sides cοngruent, but the square alsο has fοur right angles, while the rhοmbus dοes nοt necessarily have right angles. Therefοre, a square is a rhοmbus, but nοt all rhοmbuses are squares.

Parallelοgram and Rhοmbus:

Bοth have οppοsite sides parallel, but the rhοmbus alsο has all sides cοngruent, while the parallelοgram dοes nοt necessarily have cοngruent sides. Therefοre, a rhοmbus is a parallelοgram, but nοt all parallelοgrams are rhοmbuses.

Trapezοid and Kite:

Bοth have twο pairs οf adjacent sides that are cοngruent, but the kite alsο has οne pair οf οppοsite cοngruent sides, while the trapezοid dοes nοt. Therefοre, a kite is a type οf trapezοid, but nοt all trapezοids are kites.

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a. The probability of a correct decision on each trial is 0.1.

b. The expected number of correct decisions in seven trials is 0.7.

c. The probability of no correct decisions in seven trials is approximately 0.478.

d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.

Therefore, the probability of a correct decision on each trial is -

p = 1/10 = 0.1

b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -

E(X) = np = 7 × 0.1 = 0.7

Therefore, the number of correct decisions is 0.7.

c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -

[tex]P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}[/tex]

In this case, n = 7, x = 0, and p = 0.1.

Substituting these values into the formula, we get -

[tex]P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478[/tex]

Therefore, the probability value is 0.478.

d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -

q = 1 - p

q = 1 - 0.5

q = 0.5

The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -

[tex]P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}[/tex]

In this case, n = 7, x = 7, p = 0.5, and q = 0.5.

Substituting these values into the equation, we get -

[tex]P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078[/tex]

Therefore, the probability value is 0.0078.

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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)

a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?

b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?

c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?

d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.

According to the question the value of ST is 3 + 4x.

Value is the worth or importance that is placed on something. It can refer to tangible items such as money, goods, or services, or intangible concepts such as a person's beliefs, attitude, or sense of self-worth. Values are essential for guiding decisions and behaviour. They provide a framework for understanding what is important to an individual or a society, and can inform how people interact with their environment.

Given equation : 4x + 3 = ST
To find the value of ST, we need to subtract 4x from both sides of the equation.
4x + 3 - 4x = ST - 4x
3 = ST - 4x
Now, add 4x to both sides of the equation.
3 + 4x = ST
Therefore, the value of ST is 3 + 4x.

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Dividing by a larger fraction (8/5) instead of 4/5 results in a smaller answer (2), because we are dividing the same amount (16/5) into more parts (8) compared to dividing by 4/5.

If you divide 3 and one fifth by four fifths, you can first convert the mixed number to an improper fraction:

3 and 1/5 = (3 x 5 + 1) / 5 = 16/5

Then, you can perform the division as follows:

(16/5) / (4/5) = (16/5) x (5/4) = 4

So, we get an answer of 4.

If we divide by 8/5 instead of 4/5, we can use the same process but with the new fraction:

(16/5) / (8/5) = (16/5) x (5/8) = 2

So, the answer would be 2.

This is because when we divide by a smaller fraction, we are dividing the same amount into fewer parts, which results in a larger answer.

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The length of the diagonals AC and BD are 28 and 18 units respectively.

A parallelogram is a quadrilateral that has opposite sides equal to each other and opposite sides parallel to each other. The diagonal of a parallelogram are not equal but they bisect each other.

Therefore,

AE = EC

EB = ED

Hence,

2x + 4   = 15 - y

2x + y = 11

6 + 3y = x + 4

x - 3y = 2

Combine the equation

2x + y = 11

x - 3y = 2

multiply equation(ii) by 2

2x + y = 11

2x - 6y = 4

7y = 7

y = 7 / 7

y = 1

Let's find x

x = 2 + 3y

x = 2 + 3(1)

x = 2 + 3

x = 5

Therefore,

x = 5 and y = 1

AE = EC = 2(5) + 4 = 14

AC = 14(2) = 28 units

EB = ED = 6 + 3(1) = 9

BD = 9(2) = 18 units

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