Graph the trigonometric function. y=1/2 cos(x+π/4 ) Plot all points corresponding to x-intercepts, minima, and maxima within one cycle

The company should not stop the production line, as it is highly unlikely to get exactly 6 baseballs with straight stitching.

To solve this, we need to use the binomial probability distribution to find the probability of getting exactly six out of eight baseballs with straight stitching, given that the proportion of baseballs with straight stitching is 0.938.

The probability of getting exactly k successful outcomes out of n independent trials, where each trial has probability of success p, is given by the formula:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

where "n choose k" is the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, the number of independent trials is 8, the probability of success is 0.938, and the number of successful outcomes is 6.

so, P(6) = (8 choose 6) * (0.938^6) * (1-0.938)^2

As we can see, this is a very low probability, so the company should not stop the production line, as it is highly unlikely to get exactly 6 baseballs with straight stitching.

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Answer:

\( \boxed{D. \: (f-g)(x) = {x}^{2} + 4x + 3} \)

Given:

\(f(x) =2 {x}^{2} - 5 \\ g(x) = {x}^{2} - 4x - 8\)

To find:

\((f - g)(x) = f(x) - g(x)\)

Step-by-step explanation:

\( \implies(f - g)x = f(x) - g(x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 {x}^{2} - 5) - ( {x}^{2} - 4x - 8) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 {x}^{2} - 5) + (- {x}^{2} + 4x + 8) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 {x}^{2} - 5 - {x}^{2} + 4x + 8 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 {x}^{2} - {x}^{2} + 4x - 5 + 8 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 4x + 8 - 5 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 4x + 3\)

Answer:

a=646.84   c=113.04

Step-by-step explanation:

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

\(P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320\)

where ! stands for factorial.

A formula is used to find a Center of a circle with a (h, k) center and a radius of r has the equation:

\((x-h)^2 + (y-k)^2 = r^2\)

A circle is a collection of all points in a plane that are uniformly distanced from a fixed point. The radius of a circle is the difference between the center and any point itself along the perimeter.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. The equation for a circle with a (h, k) center and a radius of r is:

\((x-h)^2 + (y-k)^2 = r^2\)

This is the equation's standard form. So, if we know the radius and center coordinates of a circle, we can rapidly determine its equation.

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Answer:

down five units, and left three units.

Step-by-step explanation:

The bottom corner moved down five units.

Then that point moved three units to the left.

It's the same for the other points too.

Answer:

Step-by-step explanation:

a^2 + b^2=c^2  so 81 + 9= 90 c= Square root of 90 which is 9.5.

let x = number of heavy equipment operators employed

38 - x = number of laborers employed

133x + 84(38 - x) = 4172

133x + 3192 -84x = 4172

49x = 980

x = 20

number of heavy equipment operators employed = 20

38 - 20 = 18

number of laborers employed = 18

Step-by-step explanation:

Given that,

The total number of apples, T, is directly  proportional to the number of baskets,n,  of apples.

(a) Mathematically, it can be written as :

\(T\propto n\\\\T=kn\) ....(1)

Put T = 120 and n = 5

So,

\(k=\dfrac{T}{n}\\\\k=\dfrac{120}{5}\\\\k=24\)

(b) k is equal to 24. It means the constant of proportionality is 24.

(c) Put k = 24 and n = 8 in equation (1).

T = 24(8) = 192 apples

Hence, this is the required solution.

A. To find the velocity vector v(t), we need to integrate the acceleration vector a(t) with respect to time t. So, we have: v(t) = ∫ a(t) dt, = ∫ (-25cos(5t))i + (-25sin(5t))j + (-3t)k dt, = (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + C.

where C is the constant of integration. To determine the value of C, we use the initial velocity v(0) = i + k. So, v(0) = (-5sin(0))i + (5cos(0))j + (-3/2)(0)^2 + C . = i + C, Therefore, C = v(0) - i = k. Substituting this value of C in the equation for v(t), we get: v(t) = (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + k

Therefore, the velocity vector is v(t) = <-5sin(5t), 5cos(5t), -3/2t^2 + 1>. B) To find the position vector r(t), we need to integrate the velocity vector v(t) with respect to time t. So, we have: r(t) = ∫ v(t) dt , = ∫ (-5sin(5t))i + (5cos(5t))j + (-3/2)t^2 + k dt = (1/25)cos(5t)i + (1/25)sin(5t)j + (-1/10)t^3 + kt + C, where C is the constant of integration. To determine the value of C, we use the initial position vector r(0) = i + j + k.

So, r(0) = (1/25)cos(0)i + (1/25)sin(0)j + (-1/10)(0)^3 + k(0) + C, = i + j + C
Therefore, C = r(0) - i - j = k. Substituting this value of C in the equation for r(t), we get: r(t) = (1/25)cos(5t)i + (1/25)sin(5t)j + (-1/10)t^3 + kt + k, Therefore, the position vector is r(t) = <(1/25)cos(5t), (1/25)sin(5t), (-1/10)t^3 + t + 1>.

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The mean of the data set is   427.5

We know that the mean of the data set as computed is obtained from; 345+340+400+625/ 4=  427.5

To obtain the variance of the data.

We now have to take the difference of the values and square it.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Thus;

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

The variance is 13556.2

For  the Standard deviation (S.D) of the data;

σ = √13556.25

σ =116.43

The Standard deviation of the data is 116.4

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Math is considered to have a sequential learning pattern because concepts and skills are introduced in a specific order, building upon previously learned material.

In math, concepts and skills are typically organized in a sequential manner, where each new topic builds upon what has been previously learned. This sequential learning pattern allows students to develop a solid foundation and gradually progress to more advanced topics.

For example, in elementary school, students first learn basic arithmetic operations like addition and subtraction before moving on to multiplication and division. These foundational skills are essential for understanding more complex mathematical concepts later on, such as algebra, geometry, and calculus. By following a sequential learning pattern, students can gradually develop their mathematical understanding and problem-solving abilities. They are able to connect new concepts to what they have already learned, reinforcing their knowledge and enabling them to apply it in different contexts. This sequential approach also ensures that students have the necessary prerequisite knowledge and skills to comprehend more advanced mathematical concepts. It helps create a logical progression in mathematical education, allowing students to build upon their previous knowledge and continually expand their mathematical abilities.

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Step-by-step explanation:

sogzglzotsoypysotaota9t8ts

It would be 120 ye  f  = 8  E = 3 1/2  

Therefore , the solution of the given problem of triangle comes out to be vertex E coordinate is (6,0) .

Triangles are regarded as polygons since they have four sides or more. It has an uncomplicated, geometric design. Together, the ABC letters create a triangles with a round angle. When the sides must not match, Euclidean geometry creates a single square or square. Triangles are polygons because they have three sides & three corners. The intersection of a triangle's three sides creates its corners. A triangle has 180 degrees worth of angles.

Here,

Given :

Triangle ACB with coordinates A (0,0) C (2,0) and B (2,4) is similar to triangle BED.

D has coordinates (6, 12)

Compare this to (2,4), same x, using C(2,0).

nonetheless,

y=0 (6, 0) compared to (6,12)

Thus , vertex E coordinate is (6,0)

Therefore , the solution of the given problem of triangle comes out to be vertex E coordinate is (6,0) .

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Answer:

A≈8758.26

Step-by-step explanation:

=π·52.8\({2}\)

value of pi is approximately 3.14 so

3.14*52.8\({2}\)

≈8758.26

Answer:

\(221.8 cm^{2}\)

Step-by-step explanation:

\(C=2\pi r\\A=\pi r^{2}\)

\(2\pi r=52.8\\r=\frac{52.8}{2\pi }\)

\(A=\pi ((\frac{52.8}{2\pi }) ^{2} )\)

\(A=\pi (70.61681215)\)

\(A = 221.8 cm^{2}\)

The number of liters it would take to cover 120 km is 8 liters.

Looking at the graph that shows the liters consumed per kilometer, or rather the number of kilometers per liter, we see that each liter enables to car to go for 15 km.

This means that if we should want to go 120 km, the number of liters needed would be:

= Distance to cover / Kilometers per liter

Distance to cover = 120 km

Kilometers per liter = 15 km

The liters needed are:

= 120 / 15

= 8 liters

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The polygons are similar but not necessarily drawn to scale the value of x is 13.

We can set up a proportion between the corresponding sides of the two similar polygons:

Polygons are two-dimensional geometric shapes that are made up of straight lines and closed loops.

Polygons are characterized by the number of sides, angles, and vertices they have. The sides of a polygon are the straight lines that connect the vertices, while the vertices are the points where the sides meet. The angles of a polygon are formed by the intersection of two adjacent sides.

(x - 3) / 2.5 = 8 / 2

=> 16 / 4

Simplifying each side of the equation:

(x - 3) / 2.5 = 4

Multiplying both sides by 2.5 to isolate x:

x - 3 = 10

Adding 3 to both sides:

x = 13

Therefore, the value of x is 13.

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Note: The full question is

The polygons are similar but not necessarily drawn to scale, find the value of x.

Bigger polygon has x - 3, 8, and 16

Smaller has 2.5, 2, 4

The sign of 'a' for the given quadratic function is positive.

We know that the vertex form of a quadratic function is given by:
\(f(x) = a(x - h)^2 + k\)
where (h, k) represents the coordinates of the vertex. In this case, the vertex is (2, 8), so we have:
\(f(x) = a(x - 2)^2 + 8\)
We are also given that the y-intercept is (0, 4). Substituting these coordinates into the equation, we have:
\(4 = a(0 - 2)^2 + 8\)
4 = 4a + 8
Simplifying the equation, we get:
4a = -4
a = -1
From this calculation, we find that 'a' is equal to -1. However, this implies that the quadratic function is facing downward, which contradicts the information given that the vertex is at (2, 8) above the y-axis. Therefore, the sign of 'a' must be positive to ensure the quadratic function opens upwards, consistent with the given vertex and y-intercept.

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If the original coordinates of the pipeline plunge are (x, y), the new coordinates after reflecting it across the x-axis would be (x, -y).

When reflecting a point or object across the x-axis, we keep the x-coordinate unchanged and change the sign of the y-coordinate. This means that if the original coordinates of the pipeline plunge are (x, y), the new coordinates after reflecting it across the x-axis would be (x, -y).

By changing the sign of the y-coordinate, we essentially flip the point or object vertically with respect to the x-axis. This reflects its position to the opposite side of the x-axis while keeping the same x-coordinate.

For example, if the original coordinates of the pipeline plunge are (3, 4), reflecting it across the x-axis would result in the new coordinates (3, -4). The x-coordinate remains the same (3), but the y-coordinate is negated (-4).

Therefore, the new location of the pipeline plunge after reflecting it across the x-axis is obtained by keeping the x-coordinate unchanged and changing the sign of the y-coordinate.

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The dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 cantered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

A scale factοr is defined as the ratiο between the scale οf a given οriginal οbject and a new οbject, which is its representatiοn but οf a different size (bigger οr smaller).

5).Tο find the cοοrdinates οf the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K, we need tο perfοrm the fοllοwing steps:

Find the cοοrdinates οf pοint K after dilatiοn.

Since the center οf dilatiοn is K, the image οf K will be itself.

Therefοre, the cοοrdinates οf the image οf pοint K will be (8, 12).

Find the cοοrdinates οf the images οf pοints J, L, and M after dilatiοn.

Tο find the image οf pοint J, we can use the fοrmula fοr dilatiοn:

(image οf J) = (center οf dilatiοn) + (scale factοr) x (vectοr frοm center tο J)

(image οf J) = (8, 12) + (1/4)(vectοr JO)(image οf J) = (8, 12) + (1/4)(-4, 0)

(image οf J) = (7, 12)Similarly, we can find the images οf pοints L and M:

(image οf L) = (8, 12) + (1/4)(vectοr ZK)(image οf L) = (8, 12) + (1/4)(-4, -12)

(image οf L) = (7, 9)(image οf M) = (8, 12) + (1/4)(vectοr KM)(image οf M) =

(8, 12) + (1/4)(-16, -8)(image οf M) = (4, 10)

Therefοre, the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).

6). Tο find the image οf triangle XYZ after a dilatiοn centered at the οrigin with a scale factοr οf k = -3/2, we need tο apply the dilatiοn fοrmula tο each vertex.

Fοr vertex X(0, 2):

x-cοοrdinate οf image = k * x-cοοrdinate οf X = -3/2 * 0 = 0y-cοοrdinate οf image = k * y-cοοrdinate οf X = -3/2 * 2 = -3

Sο the image οf vertex X is X'(0, -3).

Fοr vertex Y(4, 6):x-cοοrdinate οf image = k * x-cοοrdinate οf Y = -3/2 * 4 = -6y-cοοrdinate οf image = k * y-cοοrdinate οf Y = -3/2 * 6 = -9

Sο the image οf vertex Y is Y'(-6, -9).

Fοr vertex Z(8, 0):x-cοοrdinate οf image = k * x-cοοrdinate οf Z = -3/2 * 8 = -12y-cοοrdinate οf image = k * y-cοοrdinate οf Z = -3/2 * 0 = 0

Sο the image οf vertex Z is Z'(-12, 0).

Therefοre, the image οf triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

Hence, the dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

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The Kanizsa triangle illusion helps us understand that our perceptual experiences are not simply the sum of the individual sensory inputs, but rather the result of a complex and variable process of perceptual organization.

Gestalt is a German word meaning "shape" or "form," and in psychology, it refers to a set of principles that describe how people perceive and organize sensory information into meaningful wholes. These principles propose that the whole is greater than the sum of its parts, and that we tend to organize our perceptual experiences into coherent, holistic forms rather than isolated, unrelated sensations.

Experimental examples such as the Necker cube, visual cliff, and others help demonstrate principles of perceptual organization by highlighting how our minds naturally try to impose structure and order on sensory input. For example, the Necker cube is a two-dimensional drawing that can be perceived as a cube that can be viewed from different angles. However, as one stares at the image, it appears to flip back and forth between different possible interpretations. This phenomenon illustrates the Gestalt principle of figure-ground, which describes how we tend to perceive objects as being distinct from their surrounding context.

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Answer:

x= -4

Step-by-step explanation:

I hope this helps, have a great day/night :) !

Answer:

x = -4

Step-by-step explanation:

2x + 3 = -6x - 29

2x + 6x = -3 - 29

8x = -32

x = -32/8

x = -4

Hope this helps :D

Answer:

Please should we solve the equation or the angle?

Between 1 and 200, there are 66 numbers that are divisible by either 4 or 6.

To find the numbers between 1 and 200 that are divisible by 4 or 6, we need to determine the count of numbers divisible by 4 and the count of numbers divisible by 6, and then subtract the count of numbers divisible by both 4 and 6 (since they would be counted twice).

Divisibility by 4:

To find the count of numbers divisible by 4, we divide 200 by 4 and round down to the nearest whole number. So, 200 divided by 4 equals 50, meaning there are 50 numbers divisible by 4 between 1 and 200.

Divisibility by 6:

Similarly, to find the count of numbers divisible by 6, we divide 200 by 6 and round down. 200 divided by 6 equals approximately 33.33, so there are 33 numbers divisible by 6 between 1 and 200.

Numbers divisible by both 4 and 6:

To find the count of numbers divisible by both 4 and 6, we need to find the count of numbers divisible by their least common multiple, which is 12. We divide 200 by 12 and round down, resulting in approximately 16.67. Thus, there are 16 numbers divisible by both 4 and 6 between 1 and 200.

Finally, we add the count of numbers divisible by 4 and the count of numbers divisible by 6 and subtract the count of numbers divisible by both 4 and 6 to get the total count of numbers divisible by either 4 or 6. Therefore, there are 50 + 33 - 16 = 67 numbers between 1 and 200 that are divisible by either 4 or 6.

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Answer:

3y = 2x+6

Drawing:

Answer:

A

Step-by-step explanation:

For the function y = f(x), a reflection in the y axis is y= f(-x)

(-x)^3 = -x^3 so negate that term

(-x)^2 = x^2 so leave that as is

(-x)^1 = -x so negate that term too

Answer:

Answer: a) 23+3x < (or equal to) 50

B) x<= 9

Step-by-step explanation:

Answer:

i got 27 but im not sure if its right?

Step-by-step explanation:

The probability their sum is even without replacement is 39/52

Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

It is given that if we randomly select 4 numbers from the set of the first 16 prime numbers, without replacement, then the probability that their sum i seven is,

2,3,5,7,11,13,17,23,27,29,31,37,41,43,49,51 are the first 16 prime numbers.

Even numbers are always produced when two odd numbers are joined together.

Odd numbers are always created when Even numbers are added to Odd numbers.

In the list of 16, there is just one even number. If that is one of the options, then the outcome will only be odd. As the same number cannot be selected twice, there is a 15/16 chance that it won't be chosen the first time. There is also a 14/15 chance that it won't be chosen the second time, a 13/14 chance the third time, and a 12/11 chance the fourth time.

By multiplying these four probabilities, we may get the probability of an even sum. The odds of a total that is even are therefore,

32760/43680=39/52=0.75

The probability their sum is even without replacement is 39/52

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Answer:

I think the answer is C but i'm not an expert with this so sorry if you get it wrong :(

Step-by-step explanation:

Answer:

I think is c but I'm not really sure

Answer: -5

Step-by-step explanation: 19 -9 = 10. 10/-2 = -5

Answer:

-5=x

Step-by-step explanation:

f(x)=9-2x when f(x)=19

19=9-2x

Subtract 9 from both sides

10= -2x

Divide both sides by -2 to isolate the variable

-5=x