Find the volume of the solid formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8

Answer:

3 + 7 = 10

Step-by-step explanation:

I hope this answers your question. :)

Answer: 3+7=10

Step-by-step explanation:

maybe this is it but this question is really unclear

Any counting number can be written as the sum of distinct powers of 2.(proved).

What is counting number?

Counting numbers are nothing but  the natural numbers that can be used for counting. The numbers start from 1 and the series continues as 1, 2, 3, 4, 5, 6,-- and so on. Zero can not be included in counting numbers because we cannot count 0.

To prove this statement we have to consider two cases.

Let, n be any counting number or natural number. Then the power of 2 can be written as 2ⁿ.

n can be even or odd.

n=1:

If n=1 then it can be written as 2⁰

Let us assume that for n≤ k that n can be written as the sum of distinct powers of 2.

Now let us take, n= k+1.

Here one case is n is odd.

Then n≤ k+1

   so, n-1≤ k

By the induction hypothesis n-1 can be written as distinct power of 2.

n is the sum of these distinct powers of 2 as well 2⁰, which is not among them. as n-1 is even.

Now if n is even,

so n=2m (say) for m≤ k

Thus, by the induction hypothesis m can be written as distinct power of 2.

If for each power of 2 in this sum , increment the exponent by 1 then the resulting sum of distinct powers of 2 equals n= 2m

Hence, the statement is true.

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The loan that will have a lower balance and the amount is D. The Stafford loan will have a lower balance by $274.54 at the time of repayment.

First, find the future balance of the PLUS Loan by the formula :

= Principal x ( 1 + monthly interest rate ) ^ number of months

= $ 11, 443.63 x ( 1 + 0. 005458 ) ⁶

= $ 11, 443.99

Then, find the future balance of the unsubsidized Stafford Loan with the same formula :

= 10, 720 x (1 + 0. 004958) ¹⁸

= $ 11, 169.46

This shows that the unsubsidized Stafford Loan would have a lower balance and the difference would be :

=  $11, 443.99 - $11, 169.46

=  $ 274.54

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Answer:

x = -3

Step-by-step explanation:

[tex]-4x-5-11x=40\\-15x=40+5[/tex]

[tex]x=\frac{45}{-15}[/tex]

[tex]x=-3[/tex]

Hope this helps.

Method of predicting a continuous dependent variable on the basis of two or more independent variables. The correct answer is (b)

Multiple regression is a statistical technique used to examine the relationship between a single dependent variable and multiple independent variables.

It is a type of regression analysis that can help to identify which independent variables are related to the dependent variable and to what extent.

The goal of multiple regression is to create a model that can be used to predict the value of the dependent variable based on the values of the independent variables.

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Answer:

62.5%

Step-by-step explanation:

The number of states do not use nuclear: 20 + 12 = 32

The number of states that do not use nuclear and use coal: 20

so 20/32 = 5/8 = 62.5%

Answer: 81mi^2

Step-by-step explanation:

Area Formula for Square: side * side

9*9 = 81

Answer:

11.502

Step-by-step explanation:

Yes, the project consists on single set of ordered pairs numbered 1 through 30 on coordinate planes for all class students is a suitable one.

Ordered pair is a composition of the x- coordinate (i.e., abscissa) and the y coordinate (i.e, ordinate), that's two values written in a fixed order within. In mathematics, an ordered pair ( pair means two objects) so, (a, b) is a pair of objects in particular order. The order in the pair is very significant, that is ordered pair (a, b) is different from the ordered pair (b, a). Now, Ms. todd provide a project to students which consists a single set of ordered pairs numbered 1 through 30, for all students in her class. We can easily graph a ordered pair on coordinate plane. Coordinate plane is a 2-D graph made using x-coordinate and y-coordinate. There is two axis x-axis and y-axis. So, first they collect all possible ordered pairs from 1 to 30 like ( 1,1),( 1,2),(1,3),..........(1,30), (30,1),.....,(30,30) ... etc. In this coordinate plane consists 30 numbers value on y-axis and 30 on x-axis. Then, draw on graph. Hence, it is suitable.

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Before doing calculations we can predict rectangular prism A has greater surface area to volume ratio than that of rectangular prism B.

The surface area of rectangular prism A is 136 square inches and that of B is 170 square inches. And  the ratio of surface area to volume of rectangular prism A is 1.4167 square inches/ cubic inches (approximately) and that of B is 1.1334 square inches/ cubic inches (approximately).

Rectangular prism A has dimension as,

length = 3 inches , breadth = 4 inches and height = 8 inches

Rectangular prism B has dimension as,

length = 5 inches , breadth = 5 inches and height = 6 inches

The surface area of rectangular prism can be calculated using the formula = 2( length*breadth + length*height + height*breadth)

Therefore, surface area of rectangular prism A = 2{ (3*4) + (3*8) + (4*8)} square inches =136 square inches (that is, 136 [tex]inches^{2}[/tex])

Surface area of rectangular prism B = 2{ (5*5) + (5*6) + (5*6)} square inches =170 square inches (that is, 170 [tex]inches^{2}[/tex])

The volume of rectangular prism can be calculated using the formula = length * breadth * height (in cubic unit)

Therefore, volume of rectangular prism A = (3)(4)(8) cubic inches =96 cubic inches (that is, 96 [tex]inches^{3}[/tex] )

Volume of rectangular prism B = (5)(5)(6) cubic inches =150 cubic inches (that is, 150 [tex]inches^{3}\\[/tex] )

Therefore, ratio of surface area to volume of rectangular prism A = (136/96) square inches/ cubic inches = 1.4167 square inches/ cubic inches (approximately)

Ratio of surface area to volume of rectangular prism B = (170/150) square inches/ cubic inches = 1.1334 square inches/ cubic inches (approximately)

Thus,  ratio of surface area to volume of rectangular prism A is greater than that of rectangular prism B.

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The volume of the solid figure bis 1465. 33 in³

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

From the information given, we have;

Volume = 3.14 × 4² × 18

Multiply the values

Volume = 904. 32 in²

Volume of the smaller cylinder

Volume = 3.1 4 × 4 × 18

Volume = 226. 08 in³

Volume of a cone = πr²h/3 = 3.14 × 8² × 5/3

Multiply the values

Volume = 334. 93 in³

Then, the volume of the solid = 904. 32 + 226. 08 + 334. 93 = 1465. 33 in³

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The fewest number of minutes it will take Jeremy and Michael to solve 10 Rubik's cube is 16 with a speed such that Jeremy solve one in 4 minutes and Michael solves 5 in 12 minutes.

To solve the following word problem,

Time taken by Jeremy to solve one cube = 4 minutes = 240 seconds

Time taken by Michael to solve 5 cubes = 12 minutes

Time taken by Michael to solve 1 cube = [tex]\frac{12}{5}[/tex] minutes = 144 seconds

Since one solves the cube alone, they do it individually,

For the first 12 minutes,  Michael solves 5 cubes and Jeremy solves 3 cubes ([tex]\frac{12}{3}[/tex])

Then, to solve 2 or more cubes Michael takes 288 seconds

And if Michael and Jeremy each solve one cube it takes them 144 seconds and 240 seconds respectively.

Therefore, the second situation is responsible for solving in the least time which comes out to be 12 minutes + 4 minutes (240 seconds) is 16 minutes.

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The change in the perimeter is:

= 36m

The side lengths of a triangle are 3 meters,4 meters, and 5 meters.

We have to find the perimeter of the triangle.

Now,

Perimeter of a triangle is sum of all sides.

We have the side's length are:

[tex]P_1[/tex] = 3 + 4 + 5 = 12 meters.

Now, In the second case we have to multiplied the side length by 4.

Side's length are:

3 = 3 × 4 = 12

4 = 4 × 4 = 16

5 = 4 × 5 = 20

Perimeter of a triangle is sum of all sides.

[tex]P_2[/tex] = 12 + 16 + 20

[tex]P_2[/tex] = 48 meters

Now, the change in the perimeter is:

[tex]P_2 - P_1[/tex] = 48 - 12 = 36m

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Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160).

1) Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160). Alternative hypothesis: The mean height of top-rated roller coasters is not 160 feet (Ha: u ≠ 160). The claim is the null hypothesis.

2) Sample mean = (325+188+306+107+208+167+105+78+140+232+230+170+170+205+305+135+200+200+100+223+135+195+80+90+120+210+82+161+245+88+70+116+121+146+149+124)/36 = 164.97 feet. The test statistic z = (x - μ) / (σ / √n) = (164.97 - 160) / (71.6 / √36) = 1.21.

3) The p-value is the probability of observing a test statistic as extreme as the one computed from the sample, assuming the null hypothesis is true. Using a standard normal distribution table, the p-value is 0.1131.

4) At α = 0.05, the p-value (0.1131) is greater than a. Therefore, we fail to reject the null hypothesis.

5) Based on the statistical analysis, we do not have sufficient evidence to reject the claim that the mean height of top-rated roller coasters is 160 feet.

6) Hypothesis testing is a statistical method used to make decisions based on the analysis of sample data. It is used to determine whether a claim or hypothesis about a population is supported by the evidence provided by the sample data.

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The estimated probability that the golfer will hit at least 4 times in his next 10 attempts is approximately 40%. So correct option is B.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It involves quantifying the chance or likelihood of an event happening, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to happen.

Probability is often used in real-world situations to predict the likelihood of future events, make informed decisions, and understand patterns in data. It has many applications in various fields such as finance, physics, biology, and engineering.

To simulate the situation, we can use the table of random numbers to generate 10 digits, and count the number of times a digit is less than or equal to 3, which represents a hit for the golfer.

Using the table, we get the following sequence of digits:

26 53 48 69 55 23 44 72 89 55

Counting the number of hits, we get 4 hits out of 10 attempts. Therefore, the estimated probability that the golfer will hit at least 4 times in his next 10 attempts is approximately 40%.

So, the answer is B. Possible answer: 40%.

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Answer:

Step-by-step explanation:

I do believe you should most definitly add units

Hence, the rectangular prism has a surface area of 272 square centimetres.

For instance, by multiplying the length and breadth of a rectangle, the area of the shape can be determined. Pi (roughly 3.14), multiplied by the square root of the radius, can be used to get a circle's area. Calculating the size of numerous forms and figures, including triangles, circles, squares, and polygons, involves the usage of area, a key topic in geometry. The size of a piece of land, a building's floor area, or the surface of such an object are just a few examples of the many real-world uses for it.

given

We must add up the areas of all six faces of a rectangular prism in order to determine its surface area.

In this instance, the dimensions are as follows: width (w), length (l), and height (h), all in centimetres.

You can compute the surface area (A) as follows:

A = lw + lh + lw

Inputting the values provided yields:

A is equal to 2 (4 x 4 cm) + 2 (4 x 15 cm) + 2. (4 cm x 15 cm)

[tex]A=32 cm^2 + 120 cm^2 + 120 cm^2[/tex]

A = 272 cm²

Hence, the rectangular prism has a surface area of 272 square centimetres.

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Answer: Part A is (-9, 13) Part B is (9, 13)

Step-by-step explanation:

The formula C6*D6 can be found in the cell E6. Option A is the correct answer.

A spreadsheet cell is a square region in a grid that can hold text, numbers, or formulas as well as other types of data. A unique cell address, which comprises of a column letter and a row number, is used to identify each cell. For instance, cell C4 is the cell in the third column and fourth row, and cell A1 is the top-left cell in the spreadsheet. Users can enter data, format cells, and use formulas to conduct calculations on the cells in a spreadsheet, among other tasks.

The formula C6*D6 can be found in the cell E6. Option A is the correct answer.

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If the base of an isosceles triangle is 50 cm and the length of one of its legs is 65 cm, the height of the isosceles triangle is 60 cm.

To find the height of the isosceles triangle, we need to use the Pythagorean theorem and the properties of isosceles triangles.

First, we draw a diagram of the triangle and label the known values. We know that the base is 50 cm and one of the legs is 65 cm. Since the triangle is isosceles, the other leg is also 65 cm.

Next, we can draw a perpendicular line from the top vertex to the base, which represents the height of the triangle. We can label this height as "h".

Now, we have a right triangle with a base of 50 cm, a hypotenuse of 65 cm, and a height of "h". We can use the Pythagorean theorem to find the value of "h":

h² + 25² = 65²

h² + 625 = 4225

h² = 3600

h = 60

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Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

its 12.67 because like look at it this way

Using Ariana's method to  work out 135 ÷  12 1/2 without a calculator will gives us:  54/5 or 10.8.

Ariana's method for division involves breaking down the divisor into a more manageable fraction and adjusting the dividend accordingly. Here's how we can use this method to solve 135 ÷ 12 1/2 without a calculator:

Step 1: Rewrite the mixed number as an improper fraction:

12 1/2 = 25/2

Step 2: Determine the reciprocal of the fraction:

25/2 → 2/25 (reciprocal)

Step 3: Rewrite the division problem as multiplication by the reciprocal:

135 ÷ 12 1/2 = 135 x 2/25

Step 4: Simplify the expression:

135 x 2/25 = (27 x 5) x 2/25 = 54/5

Therefore, 135 ÷ 12 1/2 = 54/5 or 10.8 when rounded to one decimal place.

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Skewness measures the magnitude, degree, and direction of asymmetry in a distribution. It is an important tool for describing and understanding the shape of data distributions.

Skewness is a measure of the asymmetry of a distribution. It is a statistical measure that indicates the degree to which a distribution deviates from the symmetry of a normal distribution. Skewness can be either positive or negative, or it can be zero, indicating no skewness.

Magnitude, The magnitude of skewness is determined by the degree of asymmetry in the distribution. The larger the magnitude of skewness, the more asymmetrical the distribution is. A small magnitude indicates a distribution that is close to symmetric.

Degree, The degree of skewness is the extent to which the distribution deviates from symmetry. Positive skewness indicates a distribution with a longer right tail than left, while negative skewness indicates a distribution with a longer left tail than right.

Direction, The direction of skewness is the direction of the longer tail of the distribution. If the tail is to the right, the distribution is positively skewed, and if the tail is to the left, the distribution is negatively skewed.

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The probability of not getting a purple after turning the spinner would be = 0.75

To calculate the probability of the given sample;

= possible outcome/sample space

where;

possible outcome = 3

sample space = 4

Probability = 3/4 = 0.75

Therefore, the probability of not getting a purple colour would be = 0.75

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Naya earns a total of $98538.30 in the 5th year

Naya starts with a salary of $85,000 per year, and her salary increases by 3% each year.

So, her salary in year 5 will be:

Salary = Initial salary * (1 + rate)^5

So, we have

Salary = 85000* (1 + 3%)^5

Evaluate

Salary = 98538.30

Hence, the 5th year earnings is 98538.30

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Here are the general steps for using the u-substitution method to evaluate a definite integral:

1. Identify a part of the integrand that looks like the derivative of another function.

This is usually denoted as u, and u should be a function that is easy to integrate.

2. Replace the selected part of the integrand with u. In other words, substitute u for the expression inside the integral.

3. Take the derivative of u with respect to the variable of integration, and then multiply by dx to obtain du.

4. Replace dx with the expression in terms of du, using the relationship you found in step 3.

5. Rewrite the entire integral in terms of u and du, and simplify as much as possible.

6. Evaluate the integral using u and the limits of integration. Replace u with the original expression, and then evaluate the expression at the upper and lower limits of integration.

7. Substitute the values obtained in step 6 into the original equation to get the final answer.

The u-substitution method is a powerful technique for evaluating definite integrals.

The general idea behind the u-substitution method is to replace a complicated expression inside the integral with a simpler expression, which is equal to the original expression.

Here are the general steps for using the u-substitution method to evaluate a definite integral:

Let's take an example to illustrate these steps:

Evaluate the definite integral ∫[tex](2x + 1)^(3/2) dx from x = 1 to x = 2.[/tex]

Let u = 2x + 1.

Replace 2x + 1 with u in the integral to get ∫[tex]u^{3/2} dx.[/tex]

Take the derivative of u with respect to x to get du/dx = 2, and then multiply by dx to obtain du = 2dx.

Replace dx with 1/2 du.

Rewrite the entire integral in terms of u and du to get ∫[tex]u^{3/2} (1/2) du.[/tex]

Evaluate the integral using u and the limits of integration to get (2/5) [tex]u^{5/2}[/tex] from 3 to 5.

Substitute the values obtained in step 6 into the original equation to get the final answer, which is[tex](2/5) [(5^{5/2}- 3^{5/2}].[/tex]

Therefore, the value of the definite integral ∫[tex](2x + 1)^{3/2}[/tex]dx from x = 1 to x = 2 is approximately 6.243.

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Answer: Luis will spend a total of $22,868.48 on his lease.

Step-by-step explanation: To calculate the total cost of Luis's lease, we need to multiply the monthly cost by the number of months in the lease:

Total cost = monthly cost x number of months

The number of months in 4 years is 4 x 12 = 48 months.

Therefore, the total cost of Luis's lease is:

Total cost = $475.86/month x 48 months

Total cost = $22,868.48

So Luis will spend a total of $22,868.48 on his lease.