Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0, and x = 2, about the y-axis.
V = ?

Answer:

I believe it is 39 percent

Step-by-step explanation:

25/64 is approximately 39

Answer:

39%

Step-by-step explanation:

question is:  25 is what percent of 64?

you can use this proportion:  is/of = x/100

is = 25

of = 64

what % = x

percent = always out of 100

25/64 = x/100

cross-multiply to get:

64x = 2500

x = 2500/64

x = 39

Answer:

400

Step-by-step explanation:

12 divided by .03 is 400

Answer:

1  7/12

Step-by-step explanation:

2 1/4 + 1 1/6 = 3 5/12 because 2 1/4 = 27/12 and 7/6 = 14/12

27/12 + 14/12 = 41/12 = 3 5/12

x  + 3 5/12 = 5

x =  5 - 3 5/12;   you can make 5 into 4 12/12

x = 1  7/12

Answer:

196π

Step-by-step explanation:

14^2=196

196×π

=196π

Answer:

-5, -16

Step-by-step explanation:

-5*-16=80

(-5)+(-16)=-21

Answer:

x=12

Step-by-step explanation:

(x-6)=6

x=12

Answer:

x = 0.5

Step-by-step explanation:

The given expression is :

4(x+2) = 10

Using commutative property at LHS.

4x+8 = 10

Subtract 8 from both sides.

4x+8-8 = 10-8

4x = 2

x = (1/2) = 0.5

So, the value of x is equal to 0.5 instead of 0. Hence, the given expression cannot be equal to 0.

The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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Performance relative to the whole class refers to an individual's academic achievement in comparison to the rest of their peers in a particular subject or course.

We describe performance relative to the whole class.

To do this, we'll be using the terms "average", "percentile rank", and "standard deviation".
Average:

Calculate the average performance of the whole class by adding all students' scores and then dividing by the number of students.

This will give you a baseline to compare individual performances against the class average.
Percentile Rank:

Determine the percentile rank of a student by calculating the percentage of students in the class who scored lower than them.

For example, if a student is in the 75th percentile, it means they performed better than 75% of the class.
Standard Deviation:

Calculate the standard deviation, which measures the spread of scores within the class.

A low standard deviation indicates that most students have similar performances, while a high standard deviation shows more variability in scores.
By considering these three factors, you can effectively describe a student's performance relative to the whole class. For example, you might say: "John scored above the class average, placing him in the 80th percentile with a moderate standard deviation, indicating that his performance is better than the majority of his classmates."

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Caroline saved $3. 84 on a discounted item that was marked down 15% off of the original price of the item. What was the original price of the item before the discount, the original price of the item was $4.52 before the discount.

Let the original price of the item be $x. The item was marked down by 15%, so the discounted price is 85% of the original price. This is equivalent to saying that the discounted price is 100% - 15% of the original price. Mathematically, we can write this as: 0.85x = discounted price

Since Caroline saved $3.84 on the discounted item, we can write an equation that equates the amount she paid for the item to the discounted price minus the amount she saved. Mathematically, we can write this as:

0.85x - 3.84 = amount paid

Solving for x (the original price) requires us to rearrange the equation to isolate x. Mathematically, we can write this as:

x = (amount paid + 3.84) / 0.85

Substituting in the given values gives: x = ($0.00 + $3.84) / 0.85 = $4.52

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We will prove the statement  \(n^n / 3^n < n!\)for n ≥ 6 by induction. The base case is n = 6, and we will assume the inequality holds for some k ≥ 6. Using the induction hypothesis, we will show that it also holds for k + 1. Thus, proving the statement for n ≥ 6.

Base case: For n = 6, we have 6⁶ / 3⁶ = 46656 / 729 ≈ 64. As 6! = 720, we can see that the statement holds for n = 6.

Inductive step: Assume that the inequality holds for some k ≥ 6, i.e.,

\(k^k / 3^k < k!.\) We need to show that it holds for k + 1 as well.

Starting with the left side of the inequality:

\((k + 1)^{k + 1} / 3^{k + 1} = (k + 1) * (k + 1)^k / 3 * 3^k\)

\(= (k + 1) * (k^k / 3^k) * (k + 1) / 3\)

Since k ≥ 6, we know that (k + 1) / 3 < 1. Therefore, we can write:

\((k + 1) * (k^k / 3^k) * (k + 1) / 3 < (k + 1) * (k^k / 3^k) * 1\)

\(= (k + 1) * (k^k / 3^k)\)

< (k + 1) * k!

= (k + 1)!

Thus, we have shown that if the inequality holds for k, then it also holds for k + 1. By the principle of mathematical induction, the statement

\(n^n / 3^n < n!\) is proven for all n ≥ 6.

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The probability that at most 2 out of 6 randomly sampled people from the city are unemployed is 0.8474, rounded to two decimal places.

To find the probability that at most 2 out of 6 randomly sampled people from the city are unemployed, we can use the binomial probability formula.

The formula for the probability of getting exactly x successes in n independent Bernoulli trials, each with a probability of success p, is:

\(P(X = x) = (nCx) * (p^x) * ((1-p)^{(n-x)})\)

In this case, the number of trials n is 6, the probability of success (unemployment) p is 0.12 (12% as a decimal), and we want to find the probability for at most 2 unemployed people, so we sum up the probabilities for x = 0, 1, and 2.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Let's calculate each probability:

\(P(X = 0) = (6C0) * (0.12^0) * (0.88^6) = 1 * 1 * 0.4177 = 0.4177\)

\(P(X = 1) = (6C1) * (0.12^1) * (0.88^5) = 6 * 0.12 * 0.4437 = 0.3197P(X = 2) = (6C2) * (0.12^2) * (0.88^4) = 15 * 0.0144 * 0.5153 = 0.1100\)

Now, let's calculate the cumulative probability:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4177 + 0.3197 + 0.1100 = 0.8474

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Answer:

the awnser should be. c

Step-by-step explanation:

because shes cutting them which divides them

Answer:

$18

Step-by-step explanation:

If she starts with $50 and has $32 left when she's done then. 50-32= 18

So she spent $18 on clothing.

These relative frequencies demonstrate the relationship between high blood pressure and exercise habits in the population under study. The data suggests that a higher proportion of individuals with high blood pressure engage in regular exercise compared to those without high blood pressure.

Based on the information given, the study could provide the following relative frequency table:

Exercise ≥ 90 mins/week  86%  32%

Exercise < 90 mins/week  14%   68%

The table shows the relative frequencies of exercise habits among the population based on whether they have high blood pressure or not.

The study reveals that 72% of the population has high blood pressure, so the remaining 28% does not have high blood pressure. Out of the group without high blood pressure, 32% exercise for at least 90 minutes per week, while the remaining 68% exercise less than 90 minutes per week.

Among those with high blood pressure, 86% exercise for at least 90 minutes per week, while 14% exercise less than 90 minutes per week.

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Answer:

The distance between the grocery store and the school is 4 miles.

Step-by-step explanation:

Given that each point is represented in rectangular form. The staight-line distance (\(d\)) between two points on a plane is given by the Pythagorean Theorem:

\(d =SF\cdot \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}\)

Where:

\(x_{A}\), \(x_{B}\) - Horizontal locations of points A and B, dimensionless.

\(y_{A}\), \(y_{B}\) - Vertical locations of points A and B, dimensionless.

\(SF\) - Scale factor, measured in miles.

If \(SF = 1\,mi\), \(A = (6, 4)\) and \(B = (6,8)\), the straight line distance is:

\(d = (1\,mi)\cdot \sqrt{(6-6)^{2}+(8-4)^{2}}\)

\(d = 4\,mi\)

The distance between the grocery store and the school is 4 miles.

The constant solutions of the differential equation y' = y^2 - 4y + 3 are y = 1 and y = 3. Any value of m can be a solution to the differential equation y" + 6y' - 7y = 0.

To find the values of c for which y = c is a constant solution of the differential equation y' = y^2 - 4y + 3, we need to substitute y = c into the equation and solve for c.

Plugging in y = c, we have c' = c^2 - 4c + 3. Simplifying, we get c' - c^2 + 4c - 3 = 0. Factoring the quadratic, we have (c - 1)(c - 3) = 0.

Therefore, the values of c that satisfy the equation are c = 1 and c = 3.

Hence, the correct answer is option (a) 1 and 3.



To find the values of m for which y = e^m is a solution of the differential equation y" + 6y' - 7y = 0, we need to substitute y = e^m into the equation and solve for m.

Substituting y = e^m, we get (e^m)'' + 6(e^m)' - 7e^m = 0. Differentiating twice, we have e^m + 6e^m - 7e^m = 0.

Simplifying, we get e^m - e^m = 0. This equation holds true for any value of m.

Therefore, any value of m can be a solution for the given differential equation.

Hence, the correct answer is option (c) none of the given.

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The best fitting regression model for the given data plot is  A.Quadratic

The curve-shaped graph of a quadratic function is known as a parabola. On the graph, it is either the highest or lowest point. You can imagine it as the parabola's endpoint.

It is a diagram that illustrates the connection between two or more values or objects. Linear simply implies straight. Straight-line graphs called linear graphs are used to show the relationship between two quantities.

A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope is called an exponential graph. i.e., it begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates.

The given curve is Quadratic as its graph is parabolic in nature.

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it is 1/6 that is the anwser

Answer:

answer: 3/4

Step-by-step explanation:

The length of the hypotenuse in this right-angled triangle =  6.98 cm².

The Pythagorean theorem states that the total of the squares on the legs of a right triangle equals the square upon that hypotenuse (the side opposite the right angle)—or, in popular algebraic notation, a2 + b2 = c2.

The basic formula for calculating the area of a triangle is the half square product of its base as well as height, i.e., A = 1/2 b h. This formula applies to all triangles, whether they are scalene triangles, isosceles triangles, or equilateral triangles.

Hypotenuse (c) = 8 cm

Base (b) = 3.9 cm

Length =

C² = (a² + b³)

a² = C² - b²

a = √((8)² - (3.9)²)

  = 6.98 cm²

The length of the hypotenuse in this right-angled triangle =  6.98 cm².

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Answer:

39200000

Step by step explanation is in the photo

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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Answer:

-42

Step-by-step explanation:

.

..

............

.....................

.......

Answer:

true

Step-by-step explanation:

cant make a triangle with only two lines

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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To sketch the two complete cycles of the sinusoidal function, we need to determine the amplitude, period, phase shift, and vertical shift of the function based on the given information.

The amplitude is the distance between the maximum and minimum values of the function, and is equal to (maximum value - minimum value)/2. In this case, the maximum temperature is 18°C and the minimum temperature is not given, so we'll assume it is 6°C (the average of the initial temperature of 12°C and the maximum temperature of 18°C). Therefore, the amplitude is (18 - 6)/2 = 6°C.

The period is the length of one complete cycle of the function, and is equal to the time it takes for the temperature to go through one complete cycle of heating and cooling. In this case, the time for one complete cycle is the time it takes for the temperature to go from the maximum of 18°C, to the minimum of 6°C, and back to the maximum of 18°C. From the given information, we know that the time for the first half of the cycle (heating) is 2 minutes, so the total time for one complete cycle is 2 x 2 = 4 minutes.

The phase shift is the horizontal shift of the function, and indicates how far the function is shifted to the left or right from its usual position. In this case, there is no phase shift, since the function starts at themaximum temperature of 18°C at time t = 2 minutes.

The vertical shift is the vertical displacement of the function, and indicates how far the function is shifted up or down from its usual position. In this case, the vertical shift is 6°C, since the average temperature of the liquid is 6°C higher than the minimum temperature of 6°C.

Putting all of this together, the sinusoidal function that describes the temperature of the liquid over time can be written as:

T(t) = 6 sin(πt/2) + 12

where T is the temperature of the liquid in degrees Celsius, t is the time in minutes, and the amplitude is 6, the period is 4, the phase shift is 0, and the vertical shift is 12.

To sketch two complete cycles of this function, we can use a graph with time on the x-axis and temperature on the y-axis. We can plot points for the maximum and minimum temperatures at t = 2, t = 3, t = 4, t = 5, t = 6, and t = 7 minutes, and then connect the points with a smooth curve to show the sinusoidal variation in temperature over time.

Here is a sketch of two complete cycles of the sinusoidal function:

     |         /\

 18  |      /   \

     |       /     \

     |___/       \______

            2 |      / \      / \

 15 |__/   \__/

    |          /     \

 12 |____/       \______

         2    4    6

The curve starts at the maximum temperature of 18°C at t = 2 minutes, decreases to the minimum temperature of 6°C at t = 4 minutes, increases back to the maximum temperature of 18°C at t = 6 minutes, and then completes another cycle by returning to the minimum temperature of 6°C at t = 8 minutes. The curve repeats this pattern over time, showing the sinusoidal variation in temperature as the liquid is heated and cooled repeatedly during the experiment.

The correct relationship between Student's t-distribution and the standard normal distribution is option B: as the sample size approaches infinity, the Student's t-distribution approaches the standard normal distribution.

The sample mean's estimation of the population mean is less precise and the sample mean's distribution is more erratic when the sample size is small. Because the distribution of t-values is more skewed as a result, the student's t-distribution has thicker tails than the traditional normal distribution.

The sample mean's distribution, however, narrows as sample size increases, making it a more precise reflection of the population mean. The student's t-distribution resembles the traditional normal distribution as a result of the narrowing of the t-value distribution.

For the ordinary normal distribution to accurately approximate the student's t-distribution in practice, a sample size of 30 or more is frequently thought to be sufficient.

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Correct question:

what is the relationship between student's t distribution and the standard normal distribution?

student's t will approach to standard normal distribution as the sample size approachs 0.

student's t will approach to standard normal distribution as the sample size approachs infinite

standard normal distribution will approach to student's t distribution as the sample size approachs 0

standard normal distribution will approach to student's t distribution as the sample size approachs infinite.