set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan2 x, y = 3, and x = 0 about the line y = 3.

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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To calculate the probability a) P = (4C4 x 3C3)/(12C12) = 1/12. (b) P = (4C1 x 3C3 x 5C5)/(12C12) = 1/12. (c) P= (4C1 x 3C3 x 4C3 x 5C4)/(12C12) = 1/9. (d) P= (4C2 x 3C3 x 5C5)/(12C12) = 1/36.

(a) To calculate the probability that all hip surgeries are completed before another type of surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with four hip surgeries and three knee surgeries (4C4 x 3C3). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (b) To calculate the probability that the schedule begins with a hip surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery, three knee surgeries, and five shoulder surgeries (4C1 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (c) To calculate the probability that the first and last surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery at the start, three knee surgeries, three hip surgeries, and four shoulder surgeries (4C1 x 3C3 x 4C3 x 5C4). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/9). (d) To calculate the probability that the first two surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with two hip surgeries, three knee surgeries, and five shoulder surgeries (4C2 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/36).

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By using the box plots, each statistical value should be completed as follows;

Mean: cannot be determined.

Median: equal for data sets X and Y.

Range: greater for data set X.

Interquartile range: greater for data set Y.

Mathematically, the range of a data set can be calculated by using this formula;

Range of X = Highest number - Lowest number

Range of X = 65 - 20

Range of X = 45.

Range of Y = Highest number - Lowest number

Range of Y = 55 - 20

Range of Y = 35.

Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of X = Q₃ - Q₁

Interquartile range (IQR) of X = 55 - 35

Interquartile range (IQR) of X = 20.

Interquartile range (IQR) of Y = Q₃ - Q₁

Interquartile range (IQR) of Y = 50 - 25

Interquartile range (IQR) of Y = 25.

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In the given simultaneous linear equation, the value for x is 3 and the value for y is 2.

A system of simultaneous linear equations is any set of two or more linear equations that share the same variables involved. Obtaining values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.

In the given question,

x + y = 5.......(i)

x2 - 2y2 = 1.......(ii)

x = 5 - y.........(iii)

Substituting x in equation(ii) = (5 - y)2 - 2y2 = 1

25- 10y + y2 - 2y2 = 1

25 - 1 = y2 + 10y

y2 + 10y2 - 24 = 0

(y + 12)(y - 2) = 0

Then Either y + 12 = 0 or y - 2 = 0

= (-12, 2)

Thus, y = 2

Now, substituting the value of y in equation (i),

x + y = 5

x + 2 = 5

x = 5 - 2

x = 3

Therefore x = 3 and y = 2.

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The price of each pair of skates is given as follows:

$8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

A skating rink charges a rate of $4, hence the intercept b is given as follows:

b = 4.

Hence:

y = mx + 4.

A family rents 2 pairs of skates and pays a total of $20, meaning that when x = 2, y = 20, then the slope m, representing the cost of each pair, is obtained as follows:

20 = 2m + 4

2m = 16

m = 16/2

m = 8.

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The nearest whole number is 814. The value of 338/698 < 0.5

What is whole number?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

Given mixed number is [tex]814\frac{338}{698}[/tex].

The fraction part of the mixed number is 338/698.

2 times of 338 is 676 < 698.

Thus the value of 338/698< 0.5.

It is necessary to look at the first digit following the decimal point in order to round a number to the nearest whole number. We don't need to do anything if this digit is less than 5 (1, 2, 3, 4), but we must round up if it is 5 or higher (5, 6, 7, 8, 9).

This means the decimal value of the given number is less than 814.5.

Since the digit in the tenth place is less than 5, thus the nearest whole number of the given mixed number is 814.

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In a repeated measures design with 20 subjects, each subjected to 2 measurements (before and after stimulus presentation), the degrees of freedom in the test would be 19.

The problem is about an experiment in which a measurement is taken before and after a stimulus is presented to 20 subjects. The aim is to determine the number of degrees of freedom in the data analysis of the experiment.

Degrees of freedom (df) are a measure of the amount of variability in a set of data that is free to vary in the calculation of a statistical test. In a repeated measures design, the degrees of freedom are calculated as the number of subjects minus 1. In this case, with 20 subjects, the degrees of freedom would be 19.

The concept of degrees of freedom is used in both mathematics and physics, but the specific context of a t-test for dependent samples is commonly used in statistical analysis, particularly in the social sciences, psychology, and education research. So, it is more related to mathematics.

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The new coordinates of the point (-7, -6) are (-6, 7).

From the question, we have the following parameters that can be used in our computation:

(x, y) = (-7, -6)

The rule is given as

A rotation of 90° clockwise around the origin.

Mathematically, this can be represented as

(x, y) = (y, -x)

So, we have

Image = (-6, 7)

Hence, the image is (-6, 7)

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[tex]~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}[/tex]

Answer: x =13

Step-by-step explanation:

subtract 7 from both sides

7-7= 0

-7+20=13

x=13

Answer:

[tex] \sf \: x = 13[/tex]

Step-by-step explanation:

Given equation,

→ x + 7 = 20

Now the value of x will be,

→ x + 7 = 20

→ x = 20 - 7

→ [ x = 13 ]

Hence, the value of x is 13.

The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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The amount of money that Adrian will pay if he goes on the given amount of ride would be =$71

An amusement park is defined as the park where different recreational activities are being carried out.

The price of admission in the park = $35

The amount he pays for each ride at the amusement park= $3.

The amount for 12 rides= 3×12 = $36

Therefore the total amount of money that Adrian will pay if he goes to the amusement park for 12 rides would be = $36 + $35 =$71

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Answer: 3 rose bushes

Step-by-step explanation:

1. First we must identify the unknown. We do not know how many rose bushes he can get, we will use "x" to represent this number.

2. We must set up an equation with the given information. We know the delivery fee will remain constant.

3. 15+18.75(x)=80

4. Subtract 15 from both sides and it leaves you with 18.75x=65

5. Then you must divide both sides by 18.75, which leaves you with x=3.46

6. We cannot buy .46 of a plant so we must round down to 3

7. Jim can buy 3 rose bushes

The only one carton of pear is not enough because the sum of both Jo and Max requirement is max than the one.

There is only one carton of pear.

Jo want to buy 3/4 of it, and Max to buy 1/3 of it.

To check whether one carton of pear is enough for both Jo and Max we firstly add the part of Jo and Max to find the total pear they want. Then we check the one pear is enough y subtracting.

Now finding the total pear that Jo and Max want:

Total Pear they want = Jo want + Max want

Total Pear they want = 3/4 + 1/3

To add we equal the denominator.

Multiply and divide by 12 on both number

Total Pear they want = 3/4 × 12/12 + 1/3 × 12/12

Total Pear they want = 9/12 + 4/12

Total Pear they want = (9 + 4)/12

Total Pear they want = 13/12

Total Pear they want = 1 1/12

As we can see that the sum of both Jo and Max requirement is max than the one pear. So the only one carton of pear is not enough.

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Answer:

See below

Step-by-step explanation:

This is very easy once you understand what to do kiddo. They give you a x term, in this case -2, all you have to do is plug in this value into the equation y = x² -2x -3 which will give you your y value in this case +5 not - 5.

Heres the extra work

[tex]y = x^2 - 2x -3\\y = (-2)^2 -2(-2) -3\\y = 4 + 4 -3\\y = 5[/tex]

The length of the arc of the circle formed by the central angle of 90° is approximately 12.57 units

The length of an arc in a circle can be found using the formula:

Arc Length = (Central Angle / 360) * (2 * π * Radius)

Given a central angle of 90° and a radius of 8, the arc length can be found as follows:

Arc Length = (90 / 360) * (2 * π * 8)

Arc Length = (1/4) * (16π)

Arc Length = 4π

So, we have

Arc length = 12.57

So, the length of the arc of the circle is 12.57 (rounded to two decimal places).

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The Probability P(Green and odd) for given Sample Space is 1/5.

The likelihood of an event is expressed by probability. A random event's occurrence is the subject of this mathematical field of study. From zero to one, the value is available. In mathematics, probability is used to forecast the likelihood that events will take place.

The likelihood of something happening is referred to as a probability. The probability distribution also makes use of this basic concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event occurring.

Event's likelihood of occurring P(E) = The number of positive outcomes divided by the total number of outcomes

Now,

Total number of outcomes=10

No. of Box that are green and marked odd=2

Hence, the probability

           P(Green and odd)=2/10=1/5

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Answer: 80g

Step-by-step explanation:

we can write an equation for the weight of chocolate; 360-(2/5)x=248

when we solve that equation, we get x=280

since the total weight is 360, we can minus 280 from it to get the weight of the box

360-280=80

An expansion within a population that happens at the same pace across time is represented by the function of exponential growth.

Examples :

The analyst can determine the possible returns after three, five, and ten years if the customer deposits an initial starting capital of $5,000 into their compound savings account. The analyst decides: Using a 5% interest rate

Upon completion of three years: ($5,000)(1 + 0.05)(3) = $5,788

Upon completion of five years: ($5,000)(1 + 0.05)(5) = $6,381

A decade later, ($5,000)(1 + 0.05)(10) = $8,144

The Complete Question is exponential growth.

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The translation needed to obtain the graph of g(x) = [tex]9^{x}-4[/tex] from the graph of f(x) = [tex]9^{x}[/tex] is a shift down 4 units.

Graph is a type of data structure that is used to store and organize data in a visual representation. It consists of nodes, which store the data, and edges that connect the nodes. Graphs can be used to represent networks, relationships between different entities, or even mathematical equations. Graphs are versatile and can be used in many different applications, from engineering to data science. Graphs are also used to represent complex data structures and are often used to simplify and organize data for easier analysis.

This is because subtracting 4 from  [tex]9^{x}[/tex] is the same as shifting the graph of f(x) down 4 units on the y-axis, resulting in the graph of g(x).

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relational algebra is a sufficient tool for manipulating data in a distributed system because it provides a uniform and consistent way to access and manipulate data.

Regardless of where it is stored in the system, and because it is a declarative language that abstracts away implementation details, making it easier to maintain and evolve the system.

Relational algebra is a powerful mathematical tool used to manipulate data in a relational database. It provides a way to perform operations on data in a structured and organized manner.

In a distributed system, where multiple nodes store and process data, relational algebra is still sufficient because it provides a uniform and consistent way to access and manipulate data across the entire system.

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The actual length of the swing set area is 0.5 * 20 feet = 10 feet.

Since the scale drawing represents the actual dimensions of the park,

We can use the ratio of the scale drawing dimensions to the actual dimensions to find the actual length of the swing set area.

Let's call the actual length of the swing set area L.

Then, on the scale drawing, the length of the swing set area is 0.5 inches.

The ratio of the actual length to the scale drawing length is 20 inches : L feet.

We can set up an equation to find L:

L * (20 inches / L feet) = 0.5 inches

Solving for L, we find:

L = (0.5 inches * L feet) / (20 inches / L feet)

= (0.5 * L feet) / (20 / L feet)

= (0.5 * L feet) / (20 / L feet)

= 0.5 * (L feet / 12 inches/foot)

= 0.5 * 20 feet

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Answer:

The answer is 100 feet. I took the quiz and it was 100 feet.

Step-by-step explanation:

The equation of sphere is (x + 4)² + (y - 2)² + (z - 6)² = 49 and the intersection is a circle of radius √33 on yz - plane.

A sphere, like a ball, is defined as a perfectly spherical geometrical entity in three dimensions.

the general equation of a sphere is (x – a)² + (y – b)² + (z – c)² = r² where (a, b, c) is the centre of the sphere and r is the radius of the sphere.

Given, the centre of the sphere C(−4, 2, 6) and radius of sphere 7 units

Equation of sphere: (x - (-4))² + (y - 2)² + (z - 6)² = 7²

                                   (x + 4)² + (y - 2)² + (z - 6)² = 49

It is given that the sphere is intersecting with yz - plane which means x = 0

so, (0 + 4)² + (y - 2)² + (z - 6)² = 49

                     (y - 2)² + (z - 6)² = 33

The intersection is a circle of radius √33 on yz - plane.

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Answer:

Yes.

Step-by-step explanation:

They will be either side of the 2 circles.

Answer:

See below

Step-by-step explanation:

The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)

          so  4^x     is now  4^(x+1)

                                   then    4^(x+1) = 4^(x-h)

                                         would mean h = - 1

Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

26% = [tex]\frac{26}{100}[/tex] = 0.26

Hence, 0.26 is the multiplier.

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DeAndre should select the shape that satisfy the equation -

r(2h + r) = (190/π).

Given is that DeAndre has 190 square inches of plastic to make a cylindrical bird feeder.

He should choose the design whose total surface area is equivalent to 190 square inches. We can write the total surface area as -

2πrh + πr² = 190

πr(2h + r) = 190

r(2h + r) = (190/π)

Therefore, DeAndre should select the shape that satisfy the equation -

r(2h + r) = (190/π).

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The acceleration of an object is interpreted as the rate of change at which its speed varies with time. When the motion is vertical, the object has an acceleration when its speed varies, while when the speed is constant, the acceleration is equal to zero. The acceleration of the box is 0.614 m/s.

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This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.

The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.

There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

To find:

P(X < 5.5)

Z = -1.0

However;

P(X< 5.5) = P(Z < -1.0)

P(X< 5.5) = 0.1587

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The required multiplicative rate in the given function is 3 / 4.

Option B is correct.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

From the table of the exponential functions,

The multiplicative factor is given as,

K = y₂/y₁

K =  [9 / 8] / [3/2]

K = 3 / 4

Thus, the required multiplicative rate in the given function is 3 / 4. Option B is correct.

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