Use the formula to find the volume of the figure. Show your work.

The best measure of central tendency for Patrick's scores would be the median, which is 72.5.

To determine which measure of central tendency best describes Patrick's scores, let's consider the three main measures: mean, median, and mode.
1. Mean: Calculate the average by adding all scores and dividing by the number of tests.
(70 + 74 + 72 + 71 + 73 + 96) / 6 = 456 / 6 = 76
2. Median: Arrange the scores in ascending order and find the middle value.
70, 71, 72, 73, 74, 96
There are two middle values (72 and 73), so the median is their average: (72 + 73) / 2 = 72.5
3. Mode: Identify the most frequent score.
There is no mode, as all scores occur only once, except for the outlier (96).
The best measure of central tendency for Patrick's scores would be the median, which is 72.5. The median is less influenced by the outlier (96) and provides a more accurate representation of Patrick's typical performance on the science tests.

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The most general antiderivative of f(x) = 9sqrt(x) + 3cos(x) is:

F(x) = 6x^(3/2) + 3sin(x) + C

To find the most general antiderivative of the function f(x) = 9sqrt(x) + 3cos(x), we can integrate each term separately.

The antiderivative of 9sqrt(x) can be found by using the power rule of integration. We add 1 to the exponent (1/2) and divide by the new exponent:

∫9sqrt(x) dx = 9 * (2/3)x^(3/2) + C = 6x^(3/2) + C

The antiderivative of 3cos(x) can be found using the integral of the cosine function:

∫3cos(x) dx = 3sin(x) + C

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Answer:

sec² [㏑(ax + b)] X a/(ax +b)

Step-by-step explanation:

chain rule is if y = f(c) and z = f(e), and y = f[f(e)], then:

dy/de = dy/dc X dc/de

This might look complicated. Much easier with example, as in this question.

y = tan [㏑(ax + b)]

y = tan (u),

where u =㏑(v), v = ax + b

so we have y = tan (u), u = ㏑(v), v = ax + b.

dy/du = sec² (u), du/dv = 1/v, dv/dx = a.

dy/dx = dy/du X du/dv X dv/dx

        = sec² (u) X (1/v) X a

        = sec² [㏑(v)] X (1/(ax + b)) X a

        = sec² [㏑(ax + b)] X a/(ax + b)

True

False

True

1. True, the legs of a right triangle are connected to the right angle.

2. False, the hypotenuse of a right triangle is a specific side that is opposite to the right angle, and it is always the longest side of the triangle. The other two sides are called legs.

3. True, the side opposite to the right angle in a right triangle is called the hypotenuse.

Using the combination formula, we calculate that there are 133,784,560 different 7-card hands that can be chosen from a standard 52-card deck.

A standard 52-card deck has 52 unique cards, and to find the number of different 7-card hands that can be chosen, we use the combination formula, which is C(52,7). This formula represents the number of ways to choose 7 cards out of a total of 52 cards, where order does not matter.

The formula for C(52,7) is derived by using factorials. For example, 52! represents 52 x 51 x 50 x 49 x 48 x 47 x 46 x ... x 2 x 1, which is the total number of ways to arrange all 52 cards. The denominator, 7! x 45!, represents the number of ways to arrange the 7 chosen cards out of 52, and also the number of ways to arrange the remaining 45 cards that were not chosen.

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The farming conglomerate will use approximately 36,912.51 megaliters of water 5 years from now.

To calculate the amount of water the farming conglomerate will use 5 years from now, we can use the given information that its water usage increases at a rate of 7% every year.

Let's denote the current water usage as W₀ and the water usage after 5 years as W₅.

We know that W₅ = W₀ * (1 + r)^n, where r is the growth rate (in decimal form) and n is the number of years.

In this case, W₀ = 28,390 megaliters, r = 7% = 0.07, and n = 5.

Substituting these values into the formula, we have:

W₅ = 28,390 * (1 + 0.07)^5

Calculating this expression, we get:

W₅ ≈ 28,390 * (1.07)^5 ≈ 36,912.51 megaliters

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The value of sample space are:

⇒ (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)

We have to given that;

When entering class, each student is given a card labeled with either A, B or C.

And, The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}.

Hence, the possible outcomes for being given a letter over two days are:

{(A,A), (A,B), (A,C), (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)}

So, the options that would be part of the sample space are:

(B,A), (B,B), (B,C), (C,A), (C,B), (C,C)

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The volume of the solid given is 1073.88 cm³.

Given is a composite solid made up of a cone and a cylinder,

We need to find the volume of the composite solid,

So, to find the same we will add both volumes of both the solids,

V(cylinder) = π × radius² × height

V(cone) = π × radius² × height / 3

So, the volume =

= 3.14 × 6² × 6.5 + 3.14 × 6² × 9/3

= 3.14(6² × 6.5 + 6² × 3)

= 3.14(234 + 108)

= 3.14 × 342

= 1073.88 cm³

Hence the volume of the solid given is 1073.88 cm³.

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Answer:

The sample size is 30.

The sample mean is $36,900.

The sample standard deviation is $8,250.

The confidence level is 98%.

The critical value for a 98% confidence interval with 29 degrees of freedom is 2.457.

The confidence interval is calculated as follows:

(Sample mean - t-critical value * sample standard deviation / sqrt(sample size), Sample mean + t-critical value * sample standard deviation / sqrt(sample size))

(36,900 - 2.457 * 8,250 / sqrt(30), 36,900 + 2.457 * 8,250 / sqrt(30))

(21,668.25, 52,131.75)

Therefore, a 98% confidence interval for the mean account valuation of the population of customers is $21,668.25 to $52,131.75.

Step-by-step explanation:

35>28

For this problem, just replace x with seven and multiply by four.

35 > 4•7

This should get us to our new equation, 35 > 28

The variance is 7521.2 and the standard deviation is 86.7.

The variance is 18630.08 and the standard deviation is 136.4.

The variance is 0.0325 and the standard deviation is 0.18.

The variance is 252.8418 and the standard deviation is 15.91.

We have,

1)

Step 1: Find the mean

Mean = (106 + 121 + 152 + 234 + 347) / 5 = 192

Step 2: Find the variance

Variance = [(106-192)^2 + (121-192)^2 + (152-192)^2 + (234-192)^2 + (347-192)^2] / 5

Variance = 37606 / 5 = 7521.2

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(7521.2) = 86.7

2)

Step 1: Find the mean

Mean = (1450 + 1250 + 1776 + 1388 + 1340) / 5 = 1440.8

Step 2: Find the variance

Variance = [(1450-1440.8)^2 + (1250-1440.8)^2 + (1776-1440.8)^2 + (1388-1440.8)^2 + (1340-1440.8)^2] / 5

Variance = 93150.4 / 5 = 18630.08

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(18630.08) = 136.4

3)

Step 1: Find the mean

Mean = (7.7 + 7.4 + 7.3 + 7.9) / 4 = 7.575

Step 2: Find the variance

Variance = [(7.7-7.575)^2 + (7.4-7.575)^2 + (7.3-7.575)^2 + (7.9-7.575)^2] / 4

Variance = 0.0325

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(0.0325) = 0.18

4)

Step 1: Find the mean

Mean = (112 + 100 + 127 + 120 + 134 + 118 + 105 + 110) / 8 = 117.375

Step 2: Find the variance

Variance = [(112-117.375)^2 + (100-117.375)^2 + (127-117.375)^2 + (120-117.375)^2 + (134-117.375)^2 + (118-117.375)^2 + (105-117.375)^2 + (110-117.375)^2] / 8

Variance = 2022.7344 / 8 = 252.8418

Step 3: Find the standard deviation

Standard deviation = sqrt(Variance) = sqrt(252.8418) = 15.91

Therefore,

The variance is 7521.2 and the standard deviation is 86.7.

The variance is 18630.08 and the standard deviation is 136.4.

The variance is 0.0325 and the standard deviation is 0.18.

The variance is 252.8418 and the standard deviation is 15.91.

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Answer:

[tex]x^{0} =105^{0}[/tex]

Step-by-step explanation:

[tex]x^{0} =180-(180-(180-110)-(180-145))[/tex]

[tex]x^{0} =180-(180-70-35)[/tex]

[tex]x^{0} =180-75[/tex]

[tex]x^{0} =105[/tex]

Hope this helps

Answer:

x=105

Step-by-step explanation:

Two methods

Method 1. Solving with Exterior Angles

Method 2. Solving with Interior Angles

Method 1. Solving with Exterior Angles

So that we can keep things organized, let's call the angle in the bottom left of the triangle, Angle 1, the angle in the top of the triangle, Angle 2, and the angle in the bottom right of the triangle, Angle 3.

An Exterior Angle is formed by continuing the line segment of a side, and is the angle that forms a linear pair with the interior angle.

Observe that all of the angles given are Exterior Angles to the Polygon (in this case, a triangle), and only one exterior angle is given for each vertex (we don't want to double-count things).

For any polygon, the sum of its exterior angles is always 360 degrees.

Therefore, we can setup the following equation:

[tex]360^o=m \angle 1_{exterior} + m \angle 2_{exterior} + m \angle 3_{exterior}[/tex]

[tex]360^o=(145^o) + (110^o) + (x^o)[/tex]

Combining like terms on the right hand side...

[tex]360^o=x^o +255^o[/tex]

Isolating x by subtraction 255 degrees from both sides...

[tex](360^o)-255^o=(x^o +255^o)-255^o[/tex]

[tex]105^o=x^o[/tex]

So, x = 105

Method 2. Solving with Interior Angles

An Interior Angle is the angle we usually think of inside of a polygon (in this case, a triangle).

The sum of the Interior angles of any polygon is given by [tex]Interior~Angle~Sum=180^o*(n-2)[/tex], where "n" is the number of sides of the polygon.  For triangles, n=3, so

[tex]Interior~Angle~Sum=180^o*((3)-2)[/tex]

[tex]Interior~Angle~Sum=180^o*(1)[/tex]

[tex]Interior~Angle~Sum=180^o[/tex]

In this case, we're given exterior angles for two of the vertices, and we've been asked to find the exterior angle for the third vertex.  Each Exterior angle forms a linear pair with the interior angle, and thus is supplementary, meaning a pair of Interior and Exterior angles have measures that add to 180 degrees.

Keeping with our angle numbering described in Method 1, we have the following 3 true equations about each interior/exterior pair, where we can substitute in the known values, and solve for / isolate the unknown angle measure (in the last case, we'll get an expression containing "x" for its measure):

[tex]\begin{array}{ccc}180^o=m \angle 1+m \angle 1_{exterior}&180^o=m \angle 2+m \angle 2_{exterior}&180^o=m \angle 3+m \angle 3_{exterior}\\180^o=m \angle 1+(145^o)&180^o=m \angle 2+(110^o)&180^o=m \angle 3+(x^o)\\180^o-145^o=m \angle 1&180^o-110^o=m \angle 2&180^o-(x^o)=m \angle 3\\35^o=m \angle 1&70^o=m \angle 2&180^o-(x^o)=m \angle 3\end{array}[/tex]

Additionally, since the sum of the interior angles of a triangle is 180 degrees, we also have the following equation...

[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex]

Making substitutions with the quantities found above...

[tex](35^o) + (70^o) + (180^o-x^o) = 180^o[/tex]

Rewriting subtraction as addition of a negative...

[tex]35^o + 70^o + 180^o + (-x^o) = 180^o[/tex]

Adding x degrees to both sides, and subtracting 180 degrees from both sides...

[tex]35^o + 70^o =x^o[/tex]

Combining like terms..

[tex]105^o =x^o[/tex]

So, again, x=105

The volume of the inscribed cube is equal to twice the cube of the sphere's radius, which is 864 cubic units.

Let the side of the inscribed cube be 's.' The diagonal of the cube is the diameter of the sphere, which is 12 units. Therefore, by using the Pythagorean theorem, we get:

s² + s² + s² = 12²

3s² = 144

s² = 48

The volume of the cube is given by s³, which is 48√3 cubic units.

Now, the volume of the sphere is (4/3)πr³, where r is the radius of the sphere. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the diagonal of the cube, which is s√3. Hence, r = (s√3)/2.

Substituting the value of r in the volume formula, we get:

(4/3)π[(6)(√3)/2]³ = (4/3)π(54√3) = 72π√3 cubic units

Therefore, the volume of the cube is twice the volume of the sphere, which is 864 cubic units.

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Edwin eats approximately 9 kilograms of granola in a year.

To calculate how much granola Edwin eats in a year, we need to determine the total amount of granola consumed in a month and then multiply it by the number of months in a year.

Given that Edwin eats about one 750-gram bag of granola every month, we can simply multiply this by the number of months in a year, which is 12.

750 grams * 12 months = 9,000 grams

To convert grams to kilograms, we divide by 1,000 since there are 1,000 grams in a kilogram.

9,000 grams / 1,000 = 9 kilograms

Therefore, Edwin eats approximately 9 kilograms of granola in a year.

It's important to note that this calculation assumes that Edwin's granola consumption remains consistent throughout the year and that he consumes exactly one 750-gram bag each month. Variations in actual consumption may lead to slightly different results.

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Answer:

Step-by-step explanation:

We know that the original recipe is for 6 people, and it requires 800g of pineapple, 4 egg whites, and 1/2 lemon.

If Dan uses 2 1/2 lemons instead of 1/2 lemon, that means he's using 5 times as much lemon juice. Therefore, he's likely making 5 times the original recipe.

So, for Dan's pineapple sorbet, he would need:

800g x 5 = 4000g (or 4kg) of pineapple

4 x 5 = 20 egg whites

1/2 lemon x 2.5 = 1 1/4 lemons (but since we can't really use a quarter of a lemon, we'll just say he needs 1.5 lemons)

Therefore, Dan is making pineapple sorbet for 6 x 5 = 30 people.

a city with more than 100,000 residents located within a metropolitan area but that is not the central city and that has maintained a double-digit growth rate in recent years is known as an "edge city."

A suburban city refers to a city with more than 100,000 residents located within a metropolitan area but that is not the central city. These cities are often characterized by their proximity to a larger city, and they may offer a more suburban or residential feel compared to the central city. Additionally, suburban cities have maintained a double-digit growth rate in recent years due to factors such as increased economic opportunities and a higher quality of life.

Edge cities are urban areas that have emerged on the periphery of major metropolitan areas, often near major highways or other transportation hubs. These cities experience significant growth due to their strategic location, and they attract businesses, retail centers, and housing developments. This leads to a continuous increase in population and rapid expansion, which can result in a double-digit growth rate.

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Answer:

x = 8

Step-by-step explanation:

If those two given angles equal each other, then u and v are parallel.

7x - 6 = 5x + 10

2x = 16

x = 8

If x = 8, then lines u and v are parallel.

Answer:

-----------------------

The average price Jaffar paid for the 5 books is $17.

To find the total cost of the 5 books, we multiply the average price by the number of books:

Now, we'll add up the prices of the first four books:

Finally, we'll subtract the sum of the first four books from the total cost to find the price of the fifth book:

So, Jaffar paid $18 for the fifth book.

The measure of angle FCD is given as follows:

m < FCD = 28º.

First we consider that the given angles are bisected, meaning that they are divided into two equal parts, hence:

Consecutive angles on a rhombus are supplementary, hence the value of x is obtained as follows:

6x + 2 + 16x - 20 = 180

22x = 198

x = 198/22

x = 9.

Then the measure of angle E is given as follows:

m < E = 6 x 9 + 2

m < E = 56º.

Opposite angles on a rhombus are congruent, hence the measure of angle C is given as follows:

m < C = m < E = 56º.

Considering the bisection, the measure of angle FCD is given as follows:

m < FCD = 0.5 x 56º = 28º.

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Within the relevant range, a curvilinear cost function can be graphed as a curved line. A curvilinear cost function is a cost function where the total cost changes as a function of the level of activity, but not at a constant rate.

This means that as the level of activity increases, the cost per unit may increase or decrease, resulting in a curved relationship between the level of activity and the total cost. In order to determine the optimal level of activity, a manager can use calculus to find the point where the marginal cost equals the marginal revenue.

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The correct answer to the question is option c) An effect modifier.

A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).

It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.

In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.

An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.

Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.

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Nina will catch up Kevin in 1 hour.

Given that Kevin has completed 90 miles in the race and Nina completed 15 miles less, Kevin continues the race at a constant rate of 25mph and Nina continues the race at a constant rate of 30mph.

So, Nina covered the distance = 90-15 = 75 miles.

So,

When will finish the race, Kevin has already covered 15 miles,

So, Nina needs to catch Kevin by covering 15 + 15 = 30 miles

So, time taken by Nina cover 30 miles = 30/30 = 1 hours

Hence Nina will catch up Kevin in 1 hour.

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Answer:

Step-by-step explanation:

to figure out the distributive property of 13(2+9), we multiply the outside number (in this case 13), into the inside numbers (2 and 9). so, 13*2 and 13*9. in this equation the 2 and 9 are separate by a + sign meaning we separate it again by the + sign. (13*2+13*9). making D the correct answer.

Desired graph is attached below.

Steps to draw a desired angle are:

If the sum of angle ABD and angle DBC is equal to 105 degrees, then the statement is verified.

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Complete question:

Draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.

When we have two large independent samples from two populations, the difference in the two sample means will follow an approximate normal distribution.

This is due to the central limit theorem, which states that when we have a large enough sample size (typically, greater than 30), the distribution of the sample means will be normal regardless of the underlying distribution of the populations. As the two samples are independent, the difference in means will also be independent. Therefore, we can use the normal distribution to estimate the probability of observing a certain difference in means. It is important to note that this approximation may not hold for small sample sizes, and the underlying distributions of the populations can also impact the shape of the distribution. We can say that the normal distribution approximation is widely used in statistics and hypothesis testing, making it an essential concept for understanding and interpreting data.

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