Find the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis. y=0, y=√16−x2

The percentage that the flower has grown than expected is 50%.  

In Mathematics, the percentage is a figure or ratio that is stated as a fraction of 100 in mathematics. To calculate a percentage we need to divide the number by the whole and multiply it by 100.

Here we have

Marcello investigating plant growth

The flowers he planted were expected to grow two inches in one year.

This year there was more rainfall, so the flowers grew three inches.

which means the length of the flower should be 2 inches but it grows up to 3 inches i.e for 2 inches it grows an extra 1 inch

So, the percentage can be calculated as given below

=> \(\frac{1}{2} \times 100\) = 50%

Therefore,

The percentage that the flower has grown than expected is 50%.  

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Tippi Hendron, a researcher at a major university, was trying to explain to students what researchers mean by the term Random assignment. She stated that it involves randomly placing participants into the different groups of the experiments.

Random assignment is a technique for assigning participants in a sample to different treatment groups. The researcher employs a random number generator to assign individuals to treatment groups without bias, such that each participant has an equal probability of being assigned to any one group.

In a research study, the use of a random sample allows for the generalization of findings to the target population, while the use of random assignment ensures that a control group is available and that the difference in results between the two groups can be attributed to the manipulation of the independent variable rather than other extraneous variables that might impact the dependent variable.

The researcher ensures that individuals are randomly allocated to treatment groups during random assignment.

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Answer:

f(-3) = 6

Step-by-step explanation:

\(f(-3)=\frac{2}{3} (-3)+8=\frac{2(-3)}{3} +8=-\frac{6}{3}+8= -2+8=6\)

Hope this helps.

Answer:

f(x) = 6

Step-by-step explanation:

f(-3) means replace the x in f(x) with a -3, and replace every x in the equation with -3.

f(-3) = (2/3)x + 8

      = (2/3) (-3) + 8

      = (2 X -3)/3 + 8

      = -6/3   + 8

      = - 2 + 8

      = 6

Answer:

59.5 sales tax, 909.5 total

Step-by-step explanation:

850 x .07 = 59.5

850 + 59.5 = 909.5

Answer:

67% (rounded)

Step-by-step explanation:

Since there is 1-6,

There is 3,4,5,6 which is 4/6 chance being above 2.

2/3 = 66.6%  

Answer:1/36

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

a) x = 25 tickets

   y = 43.75 - Total cost

   a = admission cost

b/c) 1.25(25)+a=43.75

   31.25+a=43.75

   43.75-31.25=12.50 cost of admission

   12.50+31.25=43.75 total cost at the country fair.

(8,9) and (-2,4)

equation would be y = 1/2x+5

(do the work its a lot there can be videos found online)

nfadkjnbvjkn I'm busy i hope this helped

Answer:

d^-1(t)=t/70

Step-by-step explanation:

The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10

The proof of this statement is constructive, as it will provide a way to explicitly construct a positive integer which is equal to the sum of the positive integers not exceeding it.

To prove this, we will use the following formula:

Let n = the positive integer

Let S = the sum of the positive integers not exceeding n

n = 1 + 2 + ... +n-1 + n

S = 1 + 2 + ... +n-1

Therefore, n = S + n

For example, let n = 5. The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10. Therefore, 5 = 10 + 5, which is true. This proves that for any positive integer, n, it is equal to the sum of the positive integers not exceeding it.

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Answer:

StartFraction 5 Over 136 EndFraction

Step-by-step explanation:

The total number of books in Nadia's bookshelf is 10 + 2 + 5 = 17.

To calculate the probability, we multiply the probability of picking up a reference book (2 out of 17) by the probability of picking up a nonfiction book (5 out of 16, since one reference book has already been picked).

Probability = (2/17) * (5/16) = 10/272 = 5/136

Therefore, the correct answer is StartFraction 5 Over 136 EndFraction.

i hope i helped!

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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False. The Six Sigma DMAIC approach is one of many problem-solving methods that can be used, and is most appropriate when the problem is complex and the potential solutions are not immediately evident.

Six Sigma DMAIC (define, measure, analyze, improve, control) is a strategy used to improve processes and products. It is designed to help companies identify and eliminate defects and reduce variability in their processes. It is not the best way to attack all problems, as there are many other problem-solving methods, such as Design Thinking and Lean, that may be more suitable solution depending on the complexity of the problem.

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The probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%. The 15th percentile of the population is 2.57.

To find the probability that the sample mean will be between 8 and 14, we need to calculate the standard error of the mean (SEM) first. The SEM is the standard deviation of the sampling distribution of the mean, and it is given by the formula SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, σ = 12 and n = 75, so SEM = 12/√75 ≈ 1.386.

Next, we need to standardize the sample mean using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We do this by calculating the z-score for each endpoint of the interval:

z1 = (8 - 10) / 1.386 ≈ -1.441

z2 = (14 - 10) / 1.386 ≈ 2.882

We then use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. Alternatively, we can use the formula for the cumulative distribution function (CDF) of the standard normal distribution:

P(-1.441 < Z < 2.882) ≈ Φ(2.882) - Φ(-1.441) ≈ 0.985 - 0.204 ≈ 0.785

So, the probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%.

To find the 15th percentile of the population, we use the inverse of the CDF of the standard normal distribution. That is, we find the z-score that corresponds to a cumulative probability of 0.15:

Φ(z) = 0.15

z ≈ -1.036

Finally, we use the formula for the sample mean in terms of the standard normal distribution to find the corresponding value in the original units:

X = μ + z(σ/√n)

X = 10 + (-1.036)(12/√75)

X ≈ 2.57

Therefore, the 15th percentile of the population is 2.57

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d. Dummy coding. Categorical variables need to be converted into numerical variables to be used in regression analysis. Dummy coding involves creating binary variables for each category of the categorical variable.

For example, if the categorical variable is "color" with categories "red," "green," and "blue," dummy coding would involve creating three binary variables: "red" (0 or 1), "green" (0 or 1), and "blue" (0 or 1). These binary variables can then be used in the regression analysis. In conclusion, to use categorical variables in regression analysis, dummy coding is necessary.


In order to use categorical variables in a regression analysis, they must be converted into numerical values. This process is called dummy coding (also known as one-hot encoding). Dummy coding involves creating new binary variables (0 or 1) for each category of the categorical variable. This allows the regression model to incorporate the categorical data while maintaining its numerical nature.

To use categorical variables in a regression analysis, you must apply dummy coding to convert them into numerical values.

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The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

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A falling stone is at a certain instant 178 feet above the ground and 3 seconds later it is only 10 feet above the ground. The stone was dropped from a height of approximately 14.75 feet.

To find the height from which the stone was dropped, we can use the equations of motion.

Determine the time taken to fall from 178 feet to 10 feet.

The time taken can be calculated using the equation h = (1/2)\(gt^2\),

where h is the height, g is the acceleration due to gravity (approximately 32 ft/\(s^2\)), and t is the time.

Rearranging the equation,

we have t = \(\sqrt{((2h)/g)\). Substituting the values,

we get t = \(\sqrt{((2 * 168) / 32)\) ≈ 2.06 seconds.

Calculate the initial height.

Since the stone fell for 3 seconds after being at a height of 178 feet,

we subtract the time taken in step 1 from the given time.

Thus, the stone took 3 - 2.06 ≈ 0.94 seconds to fall from the initial height to 178 feet.

Using the equation h = (1/2)\(gt^2\) and substituting the values,

we get h = (1/2) ×32×\((0.94)^2\)≈ 14.75 feet.

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Answer:

If you are asking if y = 4x is proportional, the answer is yes.  It is linear and it goes through the origin.

Step-by-step explanation:

Answer:

6.5,5,3.5,2

Step-by-step explanation:

they want us to write it in repetition. thus, we can simplify

The results of the study examining the relationship between years spent smoking and attitudes toward quitting should show a negative relationship between these variables. This means that as the number of years spent smoking increases, participants' optimism for the success of a treatment program should decrease.

In the study, participants were asked to rate their optimism for the success of a treatment program, which serves as a proxy for their attitudes toward quitting. The variable being measured is the level of optimism, which can be quantified using a numerical rating scale or likert scale. The independent variable is the number of years spent smoking, which represents the duration of smoking behavior.

To determine the relationship between these variables, researchers would likely conduct statistical analyses, such as correlation or regression analysis. These analyses would examine the association between the number of years spent smoking and participants' optimism ratings. A negative relationship would be indicated by a statistically significant negative correlation coefficient or a negative regression coefficient.

The study's results should demonstrate that as the number of years spent smoking increases, participants' optimism for the success of a treatment program decreases. This suggests that individuals who have been smoking for a longer duration may be less hopeful about quitting successfully.

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The measurements are;

a. 4 inches = No

b. 15 inches = Yes

c. 23 inches = Yes

d. 5 inches =  Yes

e. 25 inches = Yes

f. 10 inches = Yes

Jose in this problem draws a triangle, ABC.

We know the length of two sides of the triangle:

AB = 10 inches

BC = 15 inches

The length of the third side in a generic triangle can be calculated using the cosine theorem:  

\(\alpha = \sqrt{b^2 + c^2 - 2bc cos \alpha }\)

where;

Looking at the formula, we observe that:

- The maximum value for  is obtained for α = 180 degrees, so that cos α = -1 .

In this case, the length of the missing side  (AC, in this case) is

\(AC = \sqrt{10^2 + 15^2 - 2*10*15 *-1 }\)

AC = 25 inches

- The minimum value for α is obtained for 180 degrees , for which cos α= 1;

\(AC = \sqrt{10^2 + 15^2 - 2*15*10*1}\)

AC = 5 inches

Hence, the length must be between 5 and 25 inches.

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The complete question:

Jose draws ABC. AB has a length of 10 inches and BC has a length of 15 inches.

Determine whether each measurement could be the length of AC.

Choose Yes or No for each measurement.

a. 4 inches Yes : No

b. 15 inches Yes : No

c. 23 inches Yes : No

d. 5 inches Yes : No

e. 25 inches Yes : No

f. 10 inches Yes : No

The solution of  the value is mathematically given as

√6 =2.449

This is further explained below.

Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.

As an example, both 3 and –3 are square roots of the number 9.

A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.

Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.

In conclusion,

√6 is not -4

because

√6 =2.449

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Answer: $34.50

Step-by-step explanation

If you multiply .75=3/4 x 10 it will will be 7.50 so 10x 3.45= 34.50 or 7.50 x 3.45= 25.875

25.875/.75 = $34.50

False; if A and B are invertible matrices, then (AB)^-1=B^-1A^-1C.

The statement is false because the order of the matrices matters when taking the inverse of their product. The correct formula for the inverse of the product of two invertible matrices A and B is (AB)^-1 = B^-1A^-1. To see why, we can use the definition of matrix inversion:

if A is an invertible n x n matrix, then its inverse A^-1 is the unique n x n matrix such that AA^-1 = A^-1A = I, where I is the n x n identity matrix.

Now, suppose A and B are invertible n x n matrices. To show that (AB)^-1 = B^-1A^-1, we need to verify that (AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I. Using matrix multiplication, we have:

(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I

and

(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IB = BB^-1 = I

Therefore, (AB)^-1 = B^-1A^-1, and the given statement (AB)^-1 = A^-1B^-1C is false.

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Therefore width = 10cm

                 height = 20cm

                 length = 20cm

given that

volume = 4,000\(cm^{3}\)

let height = h

    width = w

    length = l

width and length are equal

height = length = h

volume of box = height × width × height

             4000  = h × w × h

             4000 = \(h^{2}\)w

                  w = 4000/\(h^{2}\)

surface area(SA) = area of base + sum of area of each side

                           =  \(h^{2}\) + hw + hw + hw + hw

                           =  \(h^{2}\) + 4hw

substitute y = 4000/\(h^{2}\)

SA =  \(h^{2}\)  + 4x(4000/ \(h^{2}\) )

SA =  \(h^{2}\)  + 16000/h

Taking the derivative:

SA' = 2h - 16000/ \(h^{2}\)

making SA' = 0:

0 = 2h - 16000/ \(h^{2}\)

2h = 16000/ \(h^{2}\)

2\(h^{3}\) = 16000

\(h^{3}\) = 8000

h = 20 cm

w = 4000 /  \(h^{2}\)  = 4000 / 20² = 10 cm

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

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Answer:

The correct answer is 51%

The equation of the line graph in slope intercept form is gotten as;

y = x + 3

The general formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given straight line equation graph, we can see that the line crosses the x-intercept at x = -3 and crosses the y-intercept at y = 3. Thus;

When x = 0, y = 3

When y = 0, x = -3

Slope is gotten by using two points and their coordinates to get;

m = (3 - 0)/(0 - (-3))

m = 3/3

m = 1

Thus, the equation of the line is y = x + 3

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9514 1404 393

Answer:

  True

Step-by-step explanation:

We assume your equation is intended to be ...

  \(\sqrt{x+56} =x\)

The usual method of solution squares both sides, then solves the resulting quadratic.

  \(x+56=x^2\\\\x^2-x-56=0\\\\(x-8)(x+7)=0\longrightarrow x=\{-7,+8\}\)

Considering the initial problem, we require x ≥ 0, so the x=-7 solution is extraneous.

__

A graphical solution shows there is only one value of x that satisfies the equation. The other "solution" arises from considering the negative square root. It is introduced when the equation is squared.

Answer:

its c but I didn't really do any math it was kinda ez no cap but its just pi times 8 which Is bigger than 24 I think

Answer:

c

Step-by-step explanation:

8(3.14...) =

25.132.... >24

Answer : x = 4

Step-by-step explanation:

Area = 1/2 × base × height

Area= 200cm²

base = 5x

height = 5x

200cm² = 1/2 × base × height

200 = 1/2 × 5x × 5x

200 = 1/2 × 25x²

2( 200) = 25x²

400 = 25x²

16 = x²

4 = x

Answer:  " x = 4 " .

______________________________________

Step-by-step explanation:

______________________________________

The formula for the area of a triangle:

             Area, "A" = (1/2) * base * height;

          that is:   A = (1/2) * b * h ;

From our given problem and image/diagram:

    A = 200 cm² ;

          b = 5x ;

          h = 5x ;

We are asked to find the value for "x" ;

 A = (1/2) * b * h ;

Plug in our known values:

 200 cm² = (1/2) * 5x * 5x ;

Simplify:

 200 cm²  = (1/2)*(25x²) ;

 200 cm² = (12.5)x² ;

⇔  (12.5)x² = 200 cm² ;

Divide each side by:  " (12.5)" ;

     (12.5)x² / (12.5)  = (200 cm²)/(12.5) ;

to get:   x² = 16 ;

Take the positive square root of each side of the equation; to get the value for "x" ;

   ⁺ \(\sqrt{x^{2} } =\) ⁺ \(\sqrt{16}\) ;

to get:

  x = 4 .

________________________

Good luck to you in your academic endeavors!

________________________