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What is the sum of the moments of the component areas around the Y-axis?
Said another way, what is Sax?"

The cartesian vector form of \(F\) is \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\). We call x + yi the Cartesian form for a complex number.

Given that \(i,j,p\) and \(q\) are unit vectors and the angle \(\alpha = 222\)°, we can express the cartesian vector form of \(F\) as \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\).

To calculate the components of \(F\) , we use the trigonometric functions \(cos(\alpha )\) and \(sin(\alpha )\) with the given angle \(\alpha = 222\)°.

\(cos(222) = -0.766\\sin(222) = -0.643\)

Substituting these values into the cartesian vector form, we have:

\(F = (-31cos(222)i + 102sin(222)j)\\F = (-31 * -0.766i + 102*-0.643j)\\F = (23.746i - 65.586j)\)

Therefore, the cartesian vector form of \(F\) is \(F = (23.746i - 65.586j)\).

The cartesian vector form of \(F = (23.746i - 65.586j)\)

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The minimum number of cutting planes that can divide the plank into 4 parts of equal volume is 3.

Now, We need to make two cuts that divide the wooden plank into three equal parts, then another cut that splits one of those three portions in half in order to divide the board into four equal pieces.

We must be cautious not to cut through the rectangular hole that is present in the wooden board.

As a result, we can cut the plank twice: once along its length and once across its width. The plank will be divided into three equal pieces by these two cuts.

The final cut, which splits one of the three portions in half, is what we need to do next.

To do this, we can split the plank in half vertically by making a cut through its center.

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Answer:

To divide the rectangular wooden plank into 4 parts of equal volume, we can achieve this with a minimum of (2) cutting planes. Here's how:

1. Start by drawing a straight line across the plank, passing through the center of the smaller rectangular hole. This line should be parallel to one of the longer sides of the plank.

2. When you cut along this line, you will obtain two equal halves of the plank. Each half will contain half of the smaller rectangular hole.

3. Now, cut each of these halves along a line that is perpendicular to the first cutting line, passing through the center of the smaller rectangular hole. This will result in four parts: two larger rectangular pieces and two smaller rectangular pieces.

4. By rearranging the pieces, you can create four parts of equal volume. Place one larger piece together with one smaller piece, and do the same with the other two pieces. Each pair will now have equal volumes.

Using this method, we have successfully divided the plank into 4 parts of equal volume using 2 cutting planes.

It's important to note that while this is one possible solution, there may be other ways to achieve the same result. The key is to ensure that each part has an equal volume.

Step-by-step explanation:

<3

Answer:

55 is c

Step-by-step explanation:

what number times 4 equals 20? ...5

so times 11 and 5 and you'll get 55

Answer:

c=55

20/4 is 5

11*5=55

Answer:

The answer is D 3x+y=1 and 3x-2y=16

Step-by-step explanation:

Answer:

116

Step-by-step explanation:

10324 divided by 89!!

The probability that more than 5 engines are defective is approximately 0.1685 using the binomial approximation.

The binomial approximation is used to approximate the probability of a given event occurring a certain number of times in a specified number of trials, given a certain probability of the event occurring on each trial.

We can use this approximation to calculate the probability that more than 5 engines are defective.

Let X be the number of defective engines out of 40.

Then X follows a binomial distribution with n = 40 and p = 0.03, where p is the probability that any given engine is defective.

Using the binomial approximation, we can approximate the distribution of X with a normal distribution with mean

μ = np and standard deviation σ = √(np(1-p)).

We can then use the normal distribution to approximate the probability that more than 5 engines are defective.

P(X > 5) = P(X >= 6)

We can use the normal distribution to approximate this probability as follows:

Z = (X - μ) / σZ

= (6 - (40*0.03)) / √(40*0.03*(1-0.03))Z

= 0.9577

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 0.9577 is approximately 0.1685.

Therefore, P(X > 5) = P(X >= 6) ≈ 0.1685.

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Answer:

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In graphing inequalities, the first thing to do is graph the equation first irregardless of the inequality symbol. In the given problem, the equation to be graphed is f(x) = 2/9x + 3. Since it has a general form of y=mx + b, this is a linear function. Plot the graph by assigning arbitrary points of x, then you get the corresponding f(x) values. Graph the x values against the f(x) values. The blue line the attached picture will be formed.

Next, you solve the equation by finding x. Just don't mind the inequality symbol:

2/9 x + 3 > 4 5/9

2/9x > 4 5/9 - 3

2/9x > 14/9

x > 14/9 ÷ 2/9

x > 7

Hence, the value of x must be greater than 7. To show this in the graph, find the line where x=7. Create a partition using that line, then shade the rest of the portion where x is greater than 7 until infinity.

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Answer:

the range is the set of possible output of values

Step-by-step explanation:

The range is the set of y-values (OUTPUT) that map to the set of x-values (INPUT).

The value of m∠5 = m∠4 + 10° or  m∠3 + 20°.

The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. The measure of each exterior angle of a polygon is equal to the sum of the interior angles of the polygon divided by the number of sides of the polygon.

Solution:

The given value of m∠4 = m∠3+ 10°

The value of m∠5 is increase in 10° of m∠4

The answer is m∠5 = m∠4 + 10°.

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The angles, 60°, \(\displaystyle \frac{\pi}{4}\) and \(\displaystyle \frac{\pi}{6}\) are special angles that have known trigonometric ratio values.

First part;

Second part;

Third part;

Reasons:

First Part;

Considering a unit circle with the center at the origin of the graph, we have;

The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.

The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;

The coordinates of point P = (cos(θ), sin(θ))

In the four quadrant, we have;

First Quadrant; All trigonometric ratios are positive

Second Quadrant; sine is positive

Third Quadrant; Tan is positive

Fourth Quadrant; Cosine is positive

Second part;

We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;

sin(60°) = sin(120°) = 0.5·√3

However, the x-coordinate of the point P is in the negative direction, therefore, we get;

cos(120°) = -cos(60°) = -0.5

Similarly from the quadrant relationship, we have;

240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;

sin(240°) = -sin(60°) = -0.5·√3

cos(240°) = -cos(60°) = -0.5

300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;

sin(300°) is negative and cos(300°) is positive

Which gives;

sin(300°) = -sin(60°) =  -0.5·√3

cos(300°) =  cos(60°) = 0.5

Third part;

\(\displaystyle \frac{\pi}{4} =45^{\circ}\)

\(\displaystyle \frac{\pi}{6} =30^{\circ}\)

The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°

Also, due to the mid location of the angle 45° on the quadrant, we have;

Another angles is the sines and cosine of (90° + 45°) = 135°

Therefore, \(\displaystyle \frac{\pi}{4}\), can be used to find the sine and cosine of 135°, 225°, and 315°

\(\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}\), \(\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}\), \(\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}\)

Therefore,

\(\displaystyle \frac{\pi}{4}\) can be used to find the sine and cosine of \(\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}\), \(\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}\), and \(\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}\)

Similarly, the sine and cosine of, \(\displaystyle \frac{\pi}{6}\)  = 30° can be used to find the sine and cosine of 150°,  210°, and 330°.

\(\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}\), \(\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}\), and \(\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}\)

\(\displaystyle \frac{\pi}{6}\), can be used to find the sine and cosine of \(\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}\), \(\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}\), and \(\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}\)

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Answer:

Step-by-step explanation:

The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.

Answer:

768

Step-by-step explanation:

Answer:

The answer is 75.4

Step-by-step explanation:

I hope it helps

Answer: C) 50

Step-by-step explanation:

The smallest number on the plot is 43.  The largest is 93.  The range of a chart is the largest number - the smallest number.  Thus, simply do 93-43 to get 50.

Hope it helps <3

Answer:

C. 50

Step-by-step explanation:

Range is the highest value minus the lowest value:

Highest value: 93

Lowest value: 43

93 - 43 = 50

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Answer:

10 1/8

Step-by-step explanation:

through similar triangles

8 : 9

9 : y

y = 9 * 9/8 = 81/8

reduced : 10 1/8

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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As M is directly proportional to r³, the value of r when M equals 540 is 6.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Given that, M is directly proportional to r³.

we can write:

M = k × r³

Where k is the constant of proportionality.

To find the value of k, we can use the given information that when r = 4, M = 160:

160 = k × 4³

160 = k × 64

k = 160/64

k = 2.5

Now we can use this value of k to find r when M = 540:

540 = 2.5 × r³

r³ = 540/2.5

r³ = 216

Taking the cube root of both sides, we get:

r = 6

Therefore, when M = 540, the value of r is 6.

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Answer:

The median is: 5

Hope this helps! <3

Answer:

Step-by-step explanation:

5

The answer is 10.

please see the attached picture for full solution

hope it helps

Good luck on your assignment..

Answer:

\( = 10\)

Step-by-step explanation:

\( \sqrt{20} \times \sqrt{5} \\ \sqrt{2 \times 2 \times 5} \times \sqrt{5} \\ 2 \sqrt{5} \times \sqrt{5} \\ 2 \sqrt{ {5}}^{2} \\ = 10\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

$562.5

Step-by-step explanation:

1250*45%= 562.5     o      1250*45/100=562.5

el 100 representa el %

To determine the control limits for the fraction of defective batteries using three sigma limits, we will follow certain steps. A sample of 50 batteries was used to collect data and the data below shows how many batteries out of each sample failed the test. Sample Number of Failed Batteries 1 4 2 2 3 5 4 2 5 4 6 8 7 3 8 2.

First, we need to find the mean of the sample size of the failed batteries and use it to calculate the upper and lower control limits (UCL and LCL). Next, we will calculate the fraction of batteries that failed for each sample, which is value = (number of failed batteries)/50.

Now, let us find the mean and standard deviation of these fractions. First, we will calculate the sum of all the values and divide it by the number of values to get the mean. Mean = (4 + 2 + 5 + 2 + 4 + 8 + 3 + 2)/400 = 0.0375. Then, we will find the standard deviation of these values, which is 0.0172.

The upper and lower control limits will now be calculated. Upper control limit = 0.0375 + 3(0.0172) = 0.0891. Lower control limit = 0.0375 - 3(0.0172) = -0.0141.

However, we can see that the lower control limit is negative, which is not possible since the fraction value cannot be negative. Thus, we will set the lower control limit to zero. The final control limits for the fraction of defective batteries are: Upper control limit = 0.0891 and Lower control limit = 0.0000 (or 0).

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6:15 to 7:45 is 1 hour and 30 minutes.

Dividing 1 hour and 30 minutes by 15 minute intervals equals 6

They rang the bell 6 times

The probability that exactly one of the bridges will collapse in the next year in Dystopia county is 0.2988 (rounded to four decimal places).

To calculate the probability of exactly one bridge collapsing, we need to consider the probabilities of each bridge collapsing and not collapsing. Let E, Y, and A represent the events of the Elder, Younger, and Ancient bridges collapsing, respectively.

The probability of exactly one bridge collapsing can be found by considering three cases:

Only the Elder bridge collapses: P(E) * P(Y') * P(A') = 0.18 * (1 - 0.06) * (1 - 0.28) = 0.18 * 0.94 * 0.72.

Only the Younger bridge collapses: P(Y) * P(E') * P(A') = 0.06 * (1 - 0.18) * (1 - 0.28) = 0.06 * 0.82 * 0.72.

Only the Ancient bridge collapses: P(A) * P(E') * P(Y') = 0.28 * (1 - 0.18) * (1 - 0.06) = 0.28 * 0.82 * 0.94.

Summing up the probabilities from these three cases gives the total probability of exactly one bridge collapsing: 0.18 * 0.94 * 0.72 + 0.06 * 0.82 * 0.72 + 0.28 * 0.82 * 0.94 ≈ 0.2988.

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Answer: 1, 2, 5

Step-by-step explanation: Move the decimal two times to the left if you divide by 100.

Answer:2y+y-4+9

Step-by-step explanation:

2y+y-4+9

The answer is Demographic data

The researcher includes the following material in a research report: The seven males varied in age from 32 to 45 (M = 38), had a high school education (two had high school diplomas, one had an associate degree, three had an undergraduate degree, and one had a master's degree), and had yearly incomes ranging from $20,000 to $100,000 (M = $52,000). Demographic data refers to information on the characteristics of the individuals being investigated.

What is Demographic data?

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Answer: 2^(3) equals to 8.

So the x value is 3.

Step-by-step explanation: Hope this Helps!

Answer:

The answer is b= 7/2

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

4b-4+4=10+4

4b=14

4b/4 =14/4

B=7/2

Answer:

its the eleventh letter of the alphabet

Step-by-step explanation:

The function f(x) = 8x² + 4x written in vertex form include the following: A. f(x) = 8(x + 0.25)² - 1/2.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

In order to write the given function in vertex form, we would have to apply completing the square method as follows;

f(x) = 8x² + 4x

f(x) = 8[x² + 0.5x]

f(x) = 8[x² + 0.5x + (0.5/2)² - (0.5/2)²]

f(x) = 8[(x² + 0.5x + 1/16) - 1/16]

f(x) = 8[(x + 0.25)² - 1/16]

f(x) = 8(x + 0.25)² - 8/16

f(x) = 8(x + 0.25)² - 1/2

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Complete Question:

What is f(x) = 8x² + 4x written in vertex form?

f(x) = 8(x + 0.25)² - 1/2

f(x) = 8(x + 0.25)² - 1/16

f(x) = 8(x + 0.5)² - 2

f(x) = 8(x + 0.5)² - 4

Answer:

d

Step-by-step explanation: