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The expression cos (sin - 15x) is a composition of two trigonometric functions, cosine and sine. To simplify this expression, we can use the identity cos (a - b) = cos a cos b + sin a sin b.

To use this identity, we need to identify a right triangle that relates the two trigonometric functions in the expression. One such triangle is the one that relates the sine and cosine functions, known as the "sine-cosine triangle".

This triangle relates the sine and cosine functions through the following identities:

sin a = y/r

cos a = x/r

Where a is the angle opposite to the side of length y, x is the side opposite to angle a and r is the hypotenuse of the triangle.

We can use these identities to write the given expression as:

cos (sin - 15x) = cos (y/r - 15x) = cos y/r cos(-15x) - sin y/r sin(-15x)

This is by using the identity cos (a-b) = cos a cos b - sin a sin b

The expression cos (sin - 15x) can be written as cos y/r cos(-15x) - sin y/r sin(-15x)

It's important to note that this simplified expression is still not in its final form as we have no information about the value of y and r, this is only possible if we have a specific angle or triangle that we are working with.

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Function Table:

x f(x)

0 1

1 3

2 5

3 7

4 9

5 11

6 13

7 15

8 17

9 19

And so on, f(x) will always be 2x + 1.

Answer:

-9,-6,6,12

Step-by-step explanation:

Using the LCM, the numbers that Ivan could choose between 55 and 101 which are multiples of 4, 10, and 20 are 60, 80, and 100.

A multiple of numbers is the lowest common multiple (lcm) of two or more numbers.

The LCM shows the numbers into which the given numbers can divide without a remainder.  The result is always an even integer.

Between 55 and 101, we know that 4, 10, and 20 can each divide 60, 80, and 100 without leaving a remainder.

For example, when 4 divides 60, 80, and 100, we have 15, 20, and 25.

When 10 divides 60, 80, and 100, we have 6, 8, and 10.

Lastly, when 20 divides 60, 80, and 100, we have 3, 4, and 5.

Thus, Ivan can choose 60, 80, and 100, which are between 55 and 101 as the multiples of 4, 10, and 20.

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The vertices are A, B, C, D, E, F. The edges are AB, BC, CA, ED, DF, FE, BD, CF, and AE and the faces are DBCF, DEAB, EFCA, EDF, and ABC.

The three-dimensional shape's vertices are the points at which the edges converge. Edges are the lines where two faces converge, while faces are flat surfaces.

Vertices are the locations where the sides of a polyhedron constructed of line segments connect.

According to the definition given above, the vertices are A, B, C, D, E, and F.

Line segments from which the formation of a polyhedron takes place are known as edges.

Hence in the given figure, AB, BC, CA, ED, DF, FE, BD, CF, and AE are the edges.

Two-dimensional surfaces in a three-dimensional figure are known as faces.

In the given prism, DBCF, DEAB, EFCA, EDF, and ABC are the faces of the prism.

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1. Yes, this is a binomial distribution.

2. n = 200, p = 0.25.

3. The mean of X is 50. This means that we can expect to get 50 cherry flavored Starburst candies on average.

4. The standard deviation of X is 7.07. This means that the number of cherry flavored candies is likely to be close to the mean of 50, but it could vary by up to 7.07 in either direction.

5. The probability of getting exactly 60 cherry flavored Starburst is 0.108.

6. The probability of getting at most 60 cherry flavored Starburst is 0.619.

A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies since there are 4 flavors. The probability that each Starburst is cherry flavor is 0.25. Since we are buying one bag of Starburst, the number of cherry flavored candies in the bag can be represented by a binomial distribution with n = 200 and p = 0.25. This means that the mean of X (the number of cherry flavored candies) is 50. The standard deviation of X is 7.07, which means that the number of cherry flavored candies is likely to be close to the mean of 50, but could vary by up to 7.07 in either direction. The probability of getting exactly 60 cherry flavored Starburst is 0.108, and the probability of getting at most 60 cherry flavored Starburst is 0.619.

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Super would need 2 premium cars to achieve a productivity ratio of 7.

Let's call the number of premium cars "x".

The total revenue from the regular cars would be $1500 * 19 = $28,500 per month.

The total revenue from the premium cars would be $2500 * x.

The total cost of the regular cars would be $100 * 19 = $1900 per month.

The total cost of the premium cars would be $500 * x.

The Chief of Operations wants the revenue to be 7 times the cost of service operations, so we can write the following equation:

($28,500 + $2500x) / ($1900 + $500x) = 7

Expanding and simplifying the equation, we get:

$2500x + $28,500 = 7($1900 + $500x)

$2500x + $28,500 = $13,300 + 7$500x

$11,200 = 6$500x

$11,200 / $6,500 = x

x = 1.723

Rounding up, Super would need 2 premium cars to achieve a productivity ratio of 7.

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Answer:

The perimeter of a circle is equal 2 * pi * radius. So, if we let "d" be the diameter of the circle, we can use the following to solve for the radius:

Perimeter = 2 *p * radius = 51.42 cm

we can then use the relationship between the diameter and the radius to solve for the diameter:

d = 2 * radius

substitute the value of the perimeter equation into the diameter equation:

d= 2 * (51.42 cm / 2 * 3.142)

d= 33.49 cm

therefore, the diameter d is 33.49 cm

The required expression is 4w4w² or Aw.Bw².

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

An expression,

16w³.

To write an answer in the form A or AB, where A and B are constants or variable expressions that have no variables in common:

16w³,

= 4w 4w²

Where A = 4 and B = 4.

So, 16w³ = Aw.Bw².

Therefore, the expression is 4w4w² or Aw.Bw².

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The measure of an angle which is 5 times its supplement is 150.

Supplementary Angles. When the sum of the measures of two angles is 180 then the angles are called supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other.

thus, x and y two angle which sum is 180 then x and y supplement to each other.

According to the problem,

The measure of an angle which is 5 times its supplement.

Supplementary angles means , sum of angles is 180.

⟹x=5(180 −x)

⟹x=5×180 −5x

⟹6x=5×180

⟹x=5×30

       =150

Hence, x=150

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Whether a discrete or continuous quantity is used. the lowest temperature recorded on January 1st in Cheyenne, Wyoming, in degrees Fahrenheit

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The volume of the large container of popcorn is 56.52 in³

This is 2.25 times the volume of the small container.

The volume of a cylinder is given by the formula:

V = πr²h

where r and h represent the radius and height respectively

Volume of small container = 3.14 × 2² × 4.5 = 56.52 in³

For large container:

diameter = 1.5 × 4 = 6 in and radius = 3 in

Volume of large container = 3.14 × 3² × 4.5 = 127.17 in³

Volume of large container/Volume of small container = 127.17/56.52 = 2.25

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A function named "sum three(x, y, z)" that accepts three integer arguments and returns their sum is defined in the aforementioned code.

The function first determines whether any two or three of the three integers (x, y, and z) are equal and if so, it assigns 0 to the variable "sum".

If not, the variable "sum" is set to the sum of the three integers.

It then gives the value of "sum" back.

The function is finally run four times with various inputs, printing the sum of the inputs each time.

def sum_three(x, y, z):

if x == y or y == z or x==z:

sum = 0

else:

sum = x + y + z

return sum

print(sum_three(2, 1, 2))

print(sum_three(3, 2, 2))

print(sum_three(2, 2, 2))

print(sum_three(1, 2, 3))

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A store sells 5 oranges and 10 apples.

What is the cost amount?

The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.

Here, we have

Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.

We have to determine how many of each type of fruit were sold.

We, let the oranges be x.

let the apples be y.

x + y = 15...(1)

1x + 2y = 25...(2)

We subtract equation(2) from equation(1), we get

y = 10

Now we put the value of y in equation (1) and we get

x + 10 = 15

x= 5

Hence, a store sells 5 oranges and 10 apples.

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The data are reported with a mean and standard deviation of 3 and 1.72, respectively.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given a histogram and we need to find the values of the Mean and standard deviation.

For mean:

Step 1: Multiply the category (number) by the height of each bar in our histogram (how many of each number we have).

Step 2: To obtain the total of our data, add each of the goods determined in Step 1 together.

Step 3: To determine our mean, divide this amount by the total of the bars' heights.

Multiply each category by its respective height.

1* 60 = 60

2 * 30 = 60

3*10 = 30

4 * 30 = 120

5 * 60 = 300

Add the products from Step 1 together.

Adding these products together, we get: 60 + 60 + 30 + 120 + 300

Sum = 570

Divide this sum by the sum of the heights of the categories.

The sum of the heights of the categories will tell us how many individual pieces of data we have. In this case, this is:

60 + 30 + 10 + 30 +60

Sum of frequency = 190

So, we need to divide the sum of the products in Step 2 by the sum of the heights given above to get our mean.

Mean  = 570 /190

Mean = 3

Therefore, the Mean and standard deviation of the given data are 3 and 1.72 respectively.

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Answer:

Bacteria Growth The number N of bacteria in culture is modeled by N= 250e^kt where t is the time in hours. If N = 280 when t= 10, estimate the time required for the population to double in size.

Step-by-step explanation:

(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)

Answer:

A = 30 yd²

Step-by-step explanation:

the figure is a trapezium whose area (A) is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between bases b₁ and b₂

here h = 5 , b₁ = 8 , b₂ = 4 , then

A = [tex]\frac{1}{2}[/tex] × 5 × (8 + 4) = 2.5 × 12 = 30 yd²

The equations that are equivalent are:

2 + x = 5

x + 1 = 4

-5 + x = -2

If any two or more equations are equivalent, they would have the same value when evaluated.

To find which equations are equivalent, solve to find the value of x in each given equation.

A. 2 + x = 5

x = 5 - 2

x = 3

B. x + 1 = 4

x = 4 - 1

x = 3

C. 9 + x = 6

x = 6 - 9

x = -3

D. x + (-4) = 7

x  = 7 + 4

x = 11

E. -5 + x = -2

x = -2 + 5

x = 3

The equivalent equations are:

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Triangles that are congruent have the same size and form.Triangle HGK is congruent to triangle KHJ.

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Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJ

Triangles that are congruent have the same size and form.

Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.

Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.

The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels:

Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle

HG = HK and GK = KJ

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Answer:

V=a2h3

Step-by-step explanation:

Answer:

n(A) = 5

n(B) = 8

Step-by-step explanation:

Cardinality of a set is the number of elements in that set

A has 5 elements so n(A) = 5

The set of integers >- 5 but less than 4 is
B: {- 4, - 3, - 2, - 1, 0, 1, 2, 3}

There are 8 elements in set B so n(B) = 8

The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 40 percent of battery remaining.

The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:

When x = 0, y = 40, hence the intercept of this function is of 40, representing the initial value of 40 of the percentage of battery remaining.

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The height, x, in the triangle is 0 units.

What to find perpendicular distance?

Perpendicular distance is a measure of the distance between a point and a line. It is the shortest distance between the point and the line, and it is always perpendicular to the line. The perpendicular distance is also known as the "altitude" or "height" in geometry.

In the triangle, the side OB is 5 units and the side OC is 5√2 units. The height, x, is the perpendicular distance from the vertex O to the line segment OB.

Using the Pythagorean theorem, we can find the value of x:

x^2 + (5)^2 = (5√2)^2

x^2 = (5√2)^2 - (5)^2

x^2 = 25 - 25

x^2 = 0

x = 0

Therefore, the height, x, in the triangle is 0 units.

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y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

Two lines are parallel if they have the same slope (or no slope at all), and two lines are perpendicular if the product of their slopes is -1. To determine if lines are parallel or perpendicular, you can find their slopes and check if they are equal or if the product of their slopes is -1.

The first line y-1/7x-2 can be rewritten in slope-intercept form y = mx + b as y = 1/7x + 2

The second line x-7y=4 can be rewritten in slope-intercept form y = mx + b as y = x/7 - 4/7

The slopes of the two lines are 1/7 and -1/7 respectively. The product of the slopes of two lines is 1/49 which is not -1, that means that the two lines are not perpendicular. Also, the slopes are not equal, which means that the lines are not parallel.

Therefore, the two lines y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

The perimeter of the triangle is 28 cm. The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the length of the sides.

Let the two sides of the right triangle be x and x+2

Apply the Pythagorean Theorem:

(x)^2 + (x + 2)^2 = 24

x^2 + x^2 + 4x + 4 = 24

2x^2 + 4x = 20

2x(x + 2) = 20

x(x + 2) = 10

x = 5 and x + 2 = 7

Therefore the perimeter of the triangle is 5 + 7 + 7 = 19 cm.

The perimeter of the triangle is 28 cm.

The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the b of the sides. The equation 2x(x + 2) = 20 can be used to solve for x, which is equal to 5. Therefore, the two sides of the triangle are 5 cm and 7 cm. Adding these lengths together, the perimeter of the triangle is 5 + 7 + 7 = 28 cm.

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Estimating : Ft( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30⁰c

when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c  that the actual temperature rises

estimating:  Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15⁰c

when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by 0.15⁰c for every km/h that the wind speed

A) Estimating the values of Ft(−15, 40) and fv(−15, 40)

To estimate the value of Ft( -15,40 ) we have to take an average value hence Ft ( -15,40 ) = ( 1.2 + 1.4 ) / 2 = 1.30

and this means that when the actual temperature is -15⁰c and the wind speed is 40 km/h the apparent temperatures increase by 1.3⁰c  that the actual temperature rises

To estimate the value of Fv(-15,40 )  we have to take an average value

hence Fv ( -15,40 ) = (-0.2 + -0.1 ) / 2 = -0.15

and this means that when the actual temperature -15⁰c and the wind speed is 40 km/h the apparent temperature decreases by about 0.15⁰c for every km/h that the wind speed.

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The complete question is :

The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). (a) Estimate the values of fT(−15, 40) and fv(−15, 40). (Round your answers to two decimal places.) fT(−15, 40) ≈ fv(−15, 40) ≈ What are the practical interpretations of these values? When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature ---Select--- by about °C for every degree that the actual temperature rises. When the actual temperature is −15°C and the wind speed is 40 km/h, the apparent temperature.

The zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.

A second-degree algebraic equation known as a quadratic equation can be found in mathematics (having one or more variables raised to the second power). Ancient Babylonian cuneiform texts from the time of Hammurabi demonstrate a knowledge of how to solve quadratic equations, but it seems that ancient Egyptian mathematicians were not familiar with this technique.

They have played a significant role in the physics of accelerated motion, such as free fall in a vacuum, ever since Galileo's time. The general quadratic equation in one variable is written as ax2 + bx + c = 0, where a, b, and c are arbitrary constants (or parameters) and an is not equal to 0.

Given to solve the quadratic equation

[tex]{\displaystyle x={\frac {6\pm {\sqrt {(-6)^{2}-4(1)(1)}}}{2(1)}}}[/tex]

[tex]{\displaystyle x={\frac {6\pm {\sqrt {36-4}}}{2}}}[/tex]

[tex]{\displaystyle x={\frac {6\pm {\sqrt {32}}}{2}}}[/tex]

[tex]{\displaystyle x={\frac {6-4{\sqrt {2}}}{2}}}[/tex]

[tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex]

x = 0.171573

[tex]{\displaystyle x={\frac {6+4{\sqrt {2}}}{2}}}[/tex]

[tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex]

x = 5.828427

Thus, the zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.

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The probability that a randomly selected student will either be a woman or a business major will be 76%.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, at the college, 51% of the students are women, 25% are business major, the probability that a randomly selected student will either be a woman or a business major will be:

= 25% + 51%

= 76%

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P(at least n times) = 1 - (1 - p)^k, where p is the probability of the event happening and k is the number of trials.

The probability of an event happening at least n times out of k trials can be calculated using the formula P(at least n times) = 1 - (1 - p)^k. Here, p is the probability of the event happening, and k is the number of trials. The formula is based on the principle that the probability of an event happening at least n times is equal to one minus the probability of it happening less than n times. The probability of it happening less than n times is calculated by taking the probability of the event happening once, and then multiplying it by itself k times. This is because each trial is independent, and the probability of the event happening for each trial is the same. The result of this multiplication is then subtracted from one, which gives us the probability of it happening at least n times out of k trials

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