Find the mass of the solid bounded by the xy-plane, yz-plane, xz-plane, and the plane (x/2)+(y/3)+(z/6)=1, if the density of the solid is given by δ(x,y,z)=x+4y.
mass=?

The volume of the frustum of right circular cone =  7730 cube

The volume of the frustum of the right circular cone:

The formula for the Volume of Frustum of Cone (V)=[tex]\frac{1}{3} \pi H (R^2+r^2+Rr )[/tex]

where,

         H = Height of frustum

         R = Radius of lower base

         r = Radius of top base

According to given question,

      Height of frustum(H) = 30 units

       Radius of lower base(R) = 21 units

        Radius of top base (r) = 11 units

Substituting all the given values in the formula of volume of the frustum of the cone we will get,

    The volume of a frustum of a right circular cone(V)   =[tex]\frac{1}{3} \pi H (R^2+r^2+Rr )[/tex]

                                                                            [tex]=\frac{1}{3}*30(21^2+11^2+21*11)\\\\=10*(441+121+211)\\=10*(773)\\=7730 unit^3[/tex]  

The volume of the frustum of the right circular cone =  271.22

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By looking at the vertex of the graph, we can see that the fourth graph is the correct option.

Here we want to see which one of the given graphs represents the given absolute value function.

Remember that for the absolute value function:

f(x) = |x - a| + b

Has a vertex at the point (a, b) and opens up.

Then in this particular case, with the function f(x)=∣x+1∣−3, the vertex will be at the point (-1, -3), so we just need to identify which one of the given graphs has that vertex, we can see that the correct option is the fourth option.

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If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is the measure of the likelihood or chance of an event or set of events occurring.

If Jackson does not take the final exam, the average of his three highest scores would be:

(72 + 73 + 70)/3 = 71.67.

If Jackson takes the final exam, there are two possibilities:

If Jackson scores lower than any of his previous exam scores, then his lowest score will be dropped, and his grade will be calculated based on his four highest scores, which would be:

(73 + 72 + 70 + X)/4.

where X is his score on the final exam. In this case, taking the final exam would not benefit Jackson, as his grade would be based on his three highest scores (72, 73, and 70) regardless of his performance on the final exam.

If Jackson scores higher than any of his previous exam scores, then his lowest score will be the lowest of his first four exams, and his grade will be calculated based on his four highest scores, which would be:

(73 + 72 + X1 + X2)/4.

Therefore, If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.

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The area of the composite shape using the area formula for the different shapes is 460.48ft².

The area of composite shapes refers to the space occupied by any composite shape. A composite shape is a shape that is made by connecting a few polygons to form the required shape.

These figures or shapes can be built from a wide range of shapes, such as triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.

Now in the question,

First let us find the area of the semi-circle.

Area of semi-circle = πr²/2

= [3.14 × (16/2) ²]/2

= (3.14 × 8²)/2

= 200.96/2

= 100.48ft²

Now coming to the rectangle,

area of the rectangle = l × b

= 20 × 15

= 300ft²

Now for calculating the area of the triangle,

area = 1/2 × b × h

= 1/2 × 12 × 10

= 60ft²

Therefore, the area of the total figure = 100.48 + 300 + 60 = 460.48ft².

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This is the linear approximation of f(x) = 5th root of x when x = 32. To find the linear approximation of f(x) = 5th root of x when x = 32, we need to first find the equation of the tangent line at x = 32.

The derivative of f(x) = 5th root of x is: f'(x) = 1/(5x⁴/⁵)

So, at x = 32, we have f(32) = 2 and f'(32) = 1/80.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - 2 = (1/80)(x - 32)

Simplifying this equation, we get:

y = (1/80)x + (79/40)

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The slope of tangent line is, m= [tex]-\frac{1}{14}[/tex]

Equation of tangent line, for m= [tex]-\frac{1}{14}[/tex] and b= [tex]\frac{53}{7}[/tex] is, 14y = -x + 106

The slope of a line is a measure of how steeply it rises or falls as it moves horizontally. It is calculated by dividing the change in the vertical coordinate by the change in the horizontal coordinate between two points on the line.

Slope of tangent, m = [tex]\frac{dy}{dx}[/tex]

f(x) = y = [tex]\sqrt{57-x}[/tex]

y = [tex](57-x)^{\frac{1}{2}}[/tex]  

Differentiate the above equation y with respect to x.

[tex]\frac{dy}{dx} = \frac{1}{2} * (57-x)^{1-\frac{1}{2} }* (-1)[/tex]

[tex]\frac{dy}{dx} = -\frac{1}{2} * (57-x)^{-\frac{1}{2} }[/tex]

[tex]\frac{dy}{dx} = -\frac{1}{2\sqrt{57-x} }[/tex]

Therefore, the slope (m) of tangent line f(x) at point (8, 7) is,

[tex]\frac{dy}{dx} | _{(8, 7)} = -\frac{1}{2\sqrt{57-8} } = - \frac{1}{14}[/tex]

Equation of tangent line f(x) at point (8, 7) is,

y = mx + b

7 = [tex]-\frac{1}{14}[/tex] × 8 + b

b = [tex]\frac{53}{7}[/tex]

So, Equation is, y = [tex]-\frac{1}{14}x + \frac{53}{7}[/tex]

Therefore, 14y = -x + 106

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Answer:

B) False

Step-by-step explanation:

Perpendicular lines form right angles. It does not form acute angles.

Step-by-step explanation:

The volume of the rectangular fish tank is:

V = l x w x h = 60 cm x 15 cm x 34 cm = 30,600 cm³

Since the tank is 1/3 full, the volume of water in the tank is:

V_water = (1/3) x V = (1/3) x 30,600 cm³ = 10,200 cm³

To find the volume of water needed to fill the tank completely, we can subtract the volume of water already in the tank from the total volume of the tank:

V_needed = V - V_water = 30,600 cm³ - 10,200 cm³ = 20,400 cm³

Therefore, 20,400 cm³ of water is needed to fill the tank completely.

Answer:

Step-by-step explanation:

2

Answer: To determine the number of accidents on highways and rural roads after 4 years, we need more information. The given data only tells us about the distribution of accidents in a sample of 100 accidents investigated, but it doesn't provide any information about the rate of change or trend of accidents over time.

Assuming that the rate of accidents on highways and rural roads remains the same, we can make a projection based on the given data. If 60% of the road accident deaths occur on highways and 40% on rural roads, we can estimate the number of accidents on highways and rural roads after 4 years as follows:

Number of accidents on highways after 4 years = 80 * (100/60) = 133.33 (rounded to 133)

Number of accidents on rural roads after 4 years = 20 * (100/40) = 50

Note that this is only a projection based on the assumption that the rate of accidents remains the same. In reality, the number of accidents can vary depending on various factors such as changes in traffic volume, weather conditions, road infrastructure, and driver behavior, among others. Therefore, this projection should be taken as an estimate and not as an accurate prediction.

Step-by-step explanation:

Answer:

center: (-2,-6)

radius: 5

Step-by-step explanation:

You have to complete the square again. This time the x's and the y's both need work. So first, organize. Put the x's together and put the y's together. Leave a little room to work. Take the x term and the y term and CUT them in HALF and Square 'em. That is what you add in to complete the square. Add the same thing to both sides.

see image.

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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so here we get two outcomes one is 2 and other is 4.

so there is total 2 outcomes.

total no. of possibility is 5

so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.

The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.

The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.

To solve this problem, we must use the z-score formula to standardise the values:

z = (x - μ) / σ

where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.

The lower bound is -0.08°C:

z1 = (-0.08 - 0) / 1.00 = -0.08

1.68°C is the upper bound:

z2 = (1.68 - 0) / 1.00 = 1.68

We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.

The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:

P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854

As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

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a)There are total 25 data values so for the given data, 100% data lies within 3 standard deviations of mean.

b). Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities

a) Here we have μ=61.52 and [tex]\sigma=4.58[/tex]

The 68-95-99.7% rule states that 68% of the data must be within one standard deviation of the mean. Thus, 68% of the data should fall between 61.52-4.58=56.94 and 61.52+4.58=66.1. 19 data values in the provided data are within one standard deviation of the mean. As there are a total of 25 data points, 76% of the data for the given data (19/25)*100=1 standard deviation of the mean.

The 68-95-99.7% rule states that 95% of the data should be within two standard deviations of the mean.

Specifically, 95% of the data should fall between 61.52+2*4.58=70.68 and 61.52-2*4.58=52.36. 24 data values in the provided data are within two standard deviations of the mean.

As there are a total of 25 data points, (24/25)*100=96% of the data for the given data is contained within two standard deviations of the mean.

The 68-95-99.7% rule states that 99.7% of the data should be within three standard deviations of the mean.

It follows that 99.7% of the data should fall between 61.52+3*4.58=75.26 and 61.52-3*4.58=47.78. 25 data values in the provided data are within three standard deviations of the mean.

As there are a total of 25 data points, (25/25)*100=100% of the data falls within three standard deviations of the mean for the given data.

Although not exactly, it appears that the distribution of height follows a normal distribution.

b) Both graphs demonstrate that the height distribution is essentially normal. Second graph demonstrates that there is strong linear relationship between the theoretical and sample quantities.

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The complete question is:

Heights of female college students. Below are heights of 25 female college students.

(a) The mean height is 61.52 inches with a standard deviation of 4.58 inches. Use this information to determine if the heights approximately follow the 68-95-99.7% Rule.

(b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.

The net realizable value οf the inventοry is the anticipated sale price in the nοrmal cοurse οf business less the prοjected cοsts fοr cοmpletiοn, destructiοn, and transpοrtatiοn after the LCM adjustment has been made.

The rightmοst place in an integer οr the number οne can be cοnsidered a unit in mathematics. The unit number inside the number 6713 in this case is 3. The standard measuring units can alsο be referred tο as a unit.

1. We must evaluate the price per piece and selling price per unit and select the lesser οf the twο in οrder tο get the lοwer οf price οr marketplace (LCM) fοr each item. The calculatiοns lοοk like this:

Speakers: LCM = min($105, $113) = $105 per unit

Stereοs: LCM = min($116, $126) = $116 per unit

Amplifiers: LCM = min($101, $110) = $101 per unit

Subwοοfers: LCM = min($57, $67) = $57 per unit

Alarms: LCM = min($155, $165) = $155 per unit

Lοcks: LCM = min($98, $108) = $98 per unit

Cameras: LCM = min($327, $337) = $327 per unit

Tripοds: LCM = min($89, $99) = $89 per unit

Stabilizers: LCM = min($110, $120) = $110 per unit

2. We must evaluate the entire cοst οf inventοry as well as the tοtal selling price οf inventοry in οrder tο determine whether an LCM adjustment is required. We must change the value οf the inventοry tο reflect the lesser οf the cοst οr market if indeed the market value falls shοrt οf the cοst. The calculatiοns lοοk like this:

Tοtal cοst οf inventοry = (350 x $105) + (265 x $126) + (331 x $101) + (209 x $67) + (485 x $165) + (296 x $108) + (217 x $327) + (190 x $89) + (175 x $110)

= $70,657

Tοtal market value οf inventοry = (350 x $113) + (265 x $116) + (331 x $110) + (209 x $57) + (485 x $155) + (296 x $98) + (217 x $327) + (190 x $99) + (175 x $110)

= $70,273

We must make an LCM mοdificatiοn tο the Merchandise Accοunting system because the market price is lοwer than the cοst. The distinctiοn amοng the tοtal cοst and the tοtal market value is the adjustment amοunt, which is:

$70,657 - $70,273 = $384

The LCM adjustment's jοurnal entry is as fοllοws:

Merchandise Inventοry 384

LCM Adjustment 384

The LCM adjustment reduces the inventοry value tο its net realizable value, which is the estimated selling price in the οrdinary cοurse οf business, less the estimated cοsts οf cοmpletiοn, dispοsal, and transpοrtatiοn.

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"The rate at which the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall is calculated to be 3.464 ft/s."

At a pace of 2 feet per second, the lower end of the ladder is being pulled away from the wall.

At a specific moment, when the lower end of the ladder is 4 feet from the wall, we should determine the rate at which the bottom of the ladder is lowering.

From the point t, the bottom of the ladder is x m, the top of the ladder is y m from the wall.

x² + y² = 64

Differentiating the given relationship with regard to t,

2x dx/dt + 2y dy/dt = 0

x dx/dt + y dy/dt = 0

We need to find out dx/dt at x = 4.

dy/dt = -2

At x = 4, we have,

x² + y² = 64

16 + y² = 64

y² = 48

y = 4√3

Put in the known values to find out dx/dt,

x dx/dt + y dy/dt = 0

4 dx/dt + 4√3 (-2) = 0

4 dx/dt = 8√3

dx/dt = 2√3 = 3.464

Thus, the bottom of the ladder is calculated to be moving at the rate 3.464 ft/s.

The figure can be drawn as shown in the attachment.

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Answer:

The required length is 10 feet

Step-by-step explanation:

Let the required length be l

From pythogras theorem;

[tex]{ \tt{l {}^{2} = {6}^{2} + {8}^{2} }} \\ { \tt{ {l}^{2} = 36 + 64}} \\ { \tt{ {l}^{2} = 100 }} \: \: \: \: \: \: \: \: \\ { \tt{ \sqrt{ {l}^{2} } = \sqrt{100} }} \\ { \tt{l = 10 \: feet}}[/tex]

Answer:

slope is -2

Step-by-step explanation:

100% correct :)

The slope is what is next to the x in y=mx+b

so if it was like this y=3x + 2

3 is the slope

hope that makes sense

The mean bonus paid by large companies to their executives is $5 million and the modal class is 3.5-6.5.

To find the mean, we need to find the midpoint of each class and multiply it by the frequency, then add up all of these values and divide by the total frequency:

Class boundaries Midpoint Frequency Midpoint x Frequency

0.5-3.5 2                          11                                         22

3.5-6.5 5                          12                                        60

6.5-9.5 8                           4                                        32

9.5-12.5 11                           2                                       22

12.5-15.5 14                           1                                        14

Total 150  

Mean = (Midpoint x Frequency) / Total Frequency

Mean = 150 / 30

Mean = 5

Therefore, the mean bonus paid by large companies to their executives is $5 million.

To find the modal class, we need to look for the class with the highest frequency. In this case, the class with the highest frequency is 3.5-6.5, with a frequency of 12. Therefore, the modal class is 3.5-6.5.

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The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is  (-0.19i - 0.34j + 0.15k) N.m.

To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.

To determine the couple moment acting at point O, we can use the formula:

M = r x F

where r is the position vector from point O to any point on the line of action of force F.

Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.

Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.

Now, let’s calculate M using M = r x F.

M = (OA) x F1

M = (A - O) x {-300i + 170j + 190k}N M

= (-0.19i - 0.34j + 0.15k) N.m

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Complete question is:

Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N

Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.

Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.

Answer:

-32,723.92295785232

Answer:

Step-by-step explanation:

I don’t know how to do that it

The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.

1. 5 beers per week: z-score = -1

2. 8 beers per week: z-score = +1

3. 10 beers per week: z-score = +2

4. 4 beers per week: z-score = -2

5. 6 beers per week: z-score = -0.5

6. 12 beers per week: z-score = +3

To calculate a z-score, we need to know the mean (μ) and standard deviation (σ) of the population. In the given problem, the mean is 7 beers per week, and the standard deviation is 1.5.

A z-score is the number of standard deviations away from the mean. Therefore, to calculate the z-scores, we subtract the mean from the given data point and divide by the standard deviation.

For example, for 5 beers per week, the z-score is (-1). This is calculated by subtracting the mean (7) from the data point (5) and dividing by the standard deviation (1.5). Therefore, (5-7)/1.5 = -1.

Similarly, the z-score for 8 beers per week is (+1). This is calculated by (8-7)/1.5 = +1. The z-score for 10 beers per week is (+2). This is calculated by (10-7)/1.5 = +2. The z-score for 4 beers per week is (-2). This is calculated by (4-7)/1.5 = -2. The z-score for 6 beers per week is (-0.5). This is calculated by (6-7)/1.5 = -0.5.The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.

the complete question is :

The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5), calculate the corresponding z-scores for the following 6 Americans’ weekly beer intake:

a) Bob drinks 9 beers per week

b) Sarah drinks 6 beers per week

c) John drinks 4 beers per week

d) Emily drinks 8 beers per week

e) Michael drinks 10 beers per week

f) Rachel drinks 5 beers per week

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A) Relative frequency is number of times an event happened over total number of events:

Answer is 21/50 = 0.42

B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50

C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.

Answer:

To find the equation of the ellipse, we need to use the standard form of the equation for an ellipse centered at the origin:

((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to the end of the major axis, and b is the distance from the center to the end of the minor axis.

Step 1: Find the center of the ellipse

The center of the ellipse is halfway between the two foci:

center = ((2+2)/2, (4-8)/2) = (2,-2)

Step 2: Find the length of the major axis

The distance between the two foci is 12 units (the absolute value of the difference in the y-coordinates):

c = 12

The length of the minor axis is the distance between the two co-vertices, which is 16 units:

2b = 16

b = 8

To find the length of the major axis, we use the relationship between a, b, and c in an ellipse:

c^2 = a^2 - b^2

a^2 = b^2 + c^2

a^2 = 8^2 + 12^2

a^2 = 256

a = 16

Step 3: Plug in the values to the standard form of the equation

((x-2)^2)/16^2 + ((y+2)^2)/8^2 = 1

Therefore, the equation of the ellipse is:

((x-2)^2)/256 + ((y+2)^2)/64 = 1

The number of ways to select half dozen donuts from 10 varieties is 210 ways.

The total number of varieties of donuts is = 10 varieties;

we have to select half a dozen donuts, which means we have to select 6 varieties of donuts from the total of 10 varieties of donuts.

Using formula of Combination, we can compute the number of ways to choose a half dozen donuts from 10 varieties:

which is written as :

⇒ ¹⁰C₆ = 10! / (6!×4!) = (10×9×8×7)/(4×3×2×1) = 210,

Therefore, there are total of 210 ways in which half dozen donuts can be selected from 10 varieties, where no two donuts are of the same variety.

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The given question is incomplete, the complete question is

How many ways are there to choose a half dozen donuts from 10 varieties,  If there are no two donuts of the same variety (means you need to select 6 varieties without replacement from 10)?