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and that angle
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The answer is 2.33 standard deviations above the mean for a student to receive an A.

In order to curve the grades of the class in such a way that the top 9% would receive an A, the professor must use a normal distribution of grades. Normal distributions follow a bell-shaped curve in which the mean (or average score) is in the middle and the scores spread out symmetrically on either side.

The scores must be distributed such that the top 9% receive an A, and since the normal curve is symmetric, the top 9% would have to span two standard deviations above the mean in order for the student to receive an A.

Knowing this, we can use the 68-95-99.7 rule, which states that 68% of the data lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three. In order for the top 9% to lie within two standard deviations of the mean, 2.33 standard deviations are required for a student to receive an A.

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Therefore, the area of the surface generated by revolving the curve y = 1/6 x³ around the x-axis is `π/4[√5 + ln(2 + √5)]`.

To find the area of the surface generated by revolving the curve y = 1/6 x³ around the x-axis,

we can use the formula for the surface area of a solid of revolution given by:

`2π∫baf(x)√(1+(f′(x))^2)dx`

where `a` and `b` are the limits of integration, `f(x)` is the function being revolved, and `f′(x)` is its derivative.

Step-by-step solution

To start, we need to find `f′(x)`:`f(x) = (1/6)x³`

Differentiating both sides with respect to `x`:`f′(x) = (1/2)x²`

Now, we can plug `f(x)` and `f′(x)` into the formula for surface area:

`2π∫baf(x)√(1+(f′(x))^2)dx`

= `2π∫21/6x³√(1+(1/2x²)^2)dx`

We can simplify the integrand

`√(1+(1/2x²)^2)

= √(1+1/4x^4)

= √(4x^4+1)/2x²`

Substituting back:`

2π∫21/6x³√(1+(1/2x²)^2)dx`

=`2π∫21/6x³(√(4x^4+1)/2x²)dx`

=`π∫21x√(4x^4+1)dx`

Next, we can use a Trigonometric function.

Let `u = 2x²`,

so `du/dx = 4x`

and `x dx = du/4`.

Substituting:

`π∫21x√(4x^4+1)dx`

=`π/2∫21√(u^2+1)du`

=`π/2[(1/2)u√(u^2+1) + (1/4)ln(u + √(u^2+1))]_2^1`

=`π/2[(1/2)(2)√5 + (1/4)ln(2 + √5)]`

=`π/4[√5 + ln(2 + √5)]`

Therefore, the area of the surface generated by revolving the curve y = 1/6 x³ around the x-axis is `π/4[√5 + ln(2 + √5)]`.

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Answer:

1. Two points coplanar with the point D are the points A and B which are on the same plane, K, as the point D

2. Another name for the line P is a straight straight angle AEB

3. The intersection of line r and plane K is the point X

4. A point non-coplanar to the plane K is the point W

Step-by-step explanation:

1. Two points collinear to point D are point E and F.

2. Another name of line p is line AB

3. the intersection of line r and plane K is point X

4. Points W and Y are non-coplanar to plane K

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The general solution to the given differential equation, in powers of x, is y = C1 for x = 2 and y = C2 for x = -5.

The recurrence relation is y = C1 for x = 2 and y = C2 for x = -5. The guaranteed radius of convergence for the solution is infinite, as it does not involve any series expansions.

To find the general solution of the given differential equation, we can rewrite it in terms of y and its derivatives. Let's start by rearranging the equation:

(x^2 - 10)y' + 2xy' = 0

Factor out the common factor of y' from both terms:

y' (x^2 - 10 + 2x) = 0

Since y' cannot be zero (otherwise it would be a trivial solution), we have:

(x^2 - 10 + 2x) = 0

Simplifying the equation:

x^2 + 2x - 10 = 0

Now, we can solve this quadratic equation for x using the quadratic formula or factoring:

x^2 + 2x - 10 = (x - 2)(x + 5) = 0

So, we have two solutions: x - 2 = 0 and x + 5 = 0, which give x = 2 and x = -5.

Now, we can find the general solution by considering these two cases separately:

Case 1: x = 2

Substituting x = 2 into the original differential equation:

(2^2 - 10)y' + 2(2)y' = 0

(-6)y' + 4y' = 0

-2y' = 0

y' = 0

Integrating y' with respect to x, we obtain:

y = C1

where C1 is an arbitrary constant.

Case 2: x = -5

Substituting x = -5 into the original differential equation:

((-5)^2 - 10)y' + 2((-5)y') = 0

(15)y' - 10y' = 0

5y' = 0

y' = 0

Integrating y' with respect to x, we obtain:

y = C2

where C2 is an arbitrary constant.

Therefore, the general solution to the given differential equation is:

y = C1 for x = 2 and y = C2 for x = -5

The recurrence relation is y = C1 for x = 2 and y = C2 for x = -5, as there are no derivatives involved in the equation.

The guaranteed radius of convergence for the solution is infinite, as the solution is not in the form of a power series and does not involve any series expansions.

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The missing values represented by x and y are 8 and 20, that is

(x, y) = (8, 20)

The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight-line graph.

The ordered pairs simply mean for every value of x, there is a corresponding value of y.

The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row, for example, the pair is given as (-4, 14).

This means when x equals negative 4, y equals 14.

Where y = 16 + 0.5x

y = 16 + 0.5(-4)

y = 16 + (-2)

y = 16 - 2

y = 14

Therefore the first pair, just like the other four pairs all satisfy the equation.

Hence, looking at the options given, we can determine which satisfies the equation

(option 1) When x = 0

y = 16 + 0.5(0)

y = 16 + 0

y = 16

(0, 16)

(option 2) When x = 5

y = 16 + 0.5(5)

y = 16 + 2.5

y = 18.5

(5, 18.5)

(option 3) When x = 8

y = 16 + 0.5(8)

y = 16 + 4

y = 20

(8, 20)

From our calculations, the third option (8, 20) is the correct ordered pair that would fill in the missing values x and y.

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Answer:

Step-by-step explanation:

is that map testing

Answer:15)5760.1 6)78. 17)582.4 18)112

Step-by-step explanation:

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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Answer:

55m²

Step-by-step explanation:

So for the two small triangles, I did 10x3 =30  and divided by 2 to get 15

For the two big triangles, did 10x8 and got 80/2 =40

To find area of a triangle, it's: base x height, then divided by 2.

(Yes that's not a kite, but I cut it in half)

The sequence 8, 6, 4, 2, ... diverges. It is a divergent sequence.

Divergent sequence is defined as the sequence whose limit does not exists or is infinite.

Here,

The sequence given is,

8, 6, 4, 2,..

The common difference of the sequence, d = 6 - 8 = -2

nth term of the sequence, aₙ = a + (n - 1)d

aₙ = 8 + (n - 1) x -2

aₙ = 8 + 2n - 2

aₙ = 2n + 6

Taking the limit of the sequence,

L = \(\lim_{n \to \infty} a_n\)

L = \(\lim_{n \to \infty} (2n + 6)\)

We get the limit of the sequence as infinite. So, the sequence is a divergent sequence.

Hence,

The sequence 8, 6, 4, 2, ... diverges.

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Answer:

1

Step-by-step explanation:

V = pie x 7² x h

V = 3.14 ×7² x 10

V = 3.14 x 49 x 10

V = 3.14 x 490

V = 1538.6

If you add 2 it will make it 3077.2 and that goes over so 1

Hope this helps :)

Yes, and there are actually several methods to do so. One method to ensure congruency is to rotate and translate the triangle onto the other, which does not change the shape or size, only where it is. They perfectly match each other when rotated and translated, showing perfect congruency. Another way to ensure congruency is to find angle lengths/slope. Using the slope formula (rise/run), we can find both slopes (whch is the distance in this case) of each side length of both triangles. The angle lengths and slopes are equal to each other.

Mapping the triangle DEF onto triangle GHI gives the coinciding image so the length will be the same and thus it can prove congruency.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides.

As per the given graph,

Triangle GHI and triangle DEF are plotted.

If we map triangle DEF onto GHI since the length is the same and orientation will become the same so both triangles will coincide with each other.

And it is known that if the length of all sides of a triangle is the same then they will be called a congruent triangle.

Hence"Mapping the triangle DEF onto triangle GHI gives the coinciding image so the length will be the same and thus it can prove congruency".

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For the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

As given in the question,

Total number have to pick by a player in a lottery daily game is equal to 3

Numbers  from which player have to pick the three numbers is 0 to 9

Total numbers from which player have to pick the three numbers = 10

Given condition : Order of the number does not matter

Total number of choices to pick three numbers from 0 to 9

= ¹⁰C₃

= ( 10! ) / ( 10 - 3 )! (3!)

= 10! / 7! 3!

= ( 10 × 9 × 8 × 7! ) / ( 7!) ( 3 × 2 × 1 )

= 10 × 3 × 4

=120 choices

Therefore, for the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

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Answer:

A≈78.54in²

Step-by-step explanation:

Can I have brainliest pls?

\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)

Answer:

y  is the output and x  the input:-

y = x - 3

Step-by-step explanation:

Hope that helps :)

The solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

What are equations?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation \(\frac{4}{q}(q-10) = 8\) we can begin by simplifying the left side of the equation:

\(\frac{4}{q}(q-10) = 8\)

\(\Rightarrow \qquad 4(q-10) = 8q \text {multiply both sides by }q\)

\(\Rightarrow \qquad 4q - 40 &= 8q && \text{distribute }4 \\\\\Rightarrow \qquad -40 &= 4q && \text{subtract }4q\text{ from both sides} \\\\\Rightarrow \qquad -10 &= q && \text{divide both sides by }-4.\\\end{align*}\)

Therefore, the solution to the equation is q= -10. We can check our answer by plugging q= -10 back into the original equation:

\(\frac{4}{q}(q-10) &= 8 \\\\\\\Rightarrow \qquad \frac{4}{-10}(-10-10) &= 8 && \text{substitute }q=-10\\\\\\\Rightarrow \qquad -\frac{4}{5} \cdot (-20) &= 8 \\\\\\\Rightarrow \qquad 16 &= 8\end{align*}\)

Since the last equation is false, the solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.

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f(x) = x + 2

g(x) = x - 4

(g•x) =?

a. 2x - 2

b. x² – 8

c. x^2 - 2x -8

d. x^2 + 2x - 8

we have that

(g•x) =g(x)*f(x)

substitute

(x-4)*(x+2)

apply distributive property

x^2+2x-4x-8

x^2-2x-8

therefore

The 97% confidence interval for the proportion of left-handed people can be calculated using the following formula:

p ± z*(sqrt(p(1-p)/n))

where:

p is the sample proportion of left-handed people (13% in this case)

z is the z-score for the desired confidence level (97% in this case, with a z-score of 2.33)

n is the sample size (145 in this case)

So the calculation would be: p = 0.13

z = 2.33

n = 145p ± z*(sqrt(p(1-p)/n)) = 0.13 ± 2.33 * (sqrt(0.13 * (1 - 0.13) / 145))

The lower and upper bounds of the confidence interval can be calculated as follows:

Lower bound: 0.13 - 2.33 * (sqrt(0.13 * (1 - 0.13) / 145)) = 0.085

Upper bound: 0.13 + 2.33 * (sqrt(0.13 * (1 - 0.13) / 145)) = 0.175

So the 97% confidence interval for the proportion of left-handed people is (0.085, 0.175). This means that we can be 97% confident that the true proportion of left-handed people in the population is between 8.5% and 17.5%.

The 97% confidence interval for the proportion of left-handed people gives us a range of values within which we can be 97% confident that the true proportion of left-handed people in the population falls. In other words, if we were to repeatedly sample 145 people from the population and calculate the proportion of left-handed individuals in each sample, we would expect that the true proportion of left-handed people in the population would fall within the calculated confidence interval approximately 97% of the time.

The lower bound of the confidence interval represents the minimum value of the proportion of left-handed people that is consistent with the sample data, while the upper bound represents the maximum value. In this case, the lower bound of the confidence interval is 8.5% and the upper bound is 17.5%.

It is important to note that the confidence interval is not a prediction of the exact proportion of left-handed people in the population, but rather a range of values that is consistent with the sample data. The wider the confidence interval, the less precise our estimate of the true proportion is, while a narrow confidence interval indicates a more precise estimate.

In conclusion, the 97% confidence interval for the proportion of left-handed people in this case is (0.085, 0.175), which means that we can be 97% confident that the true proportion of left-handed people in the population falls within this range.

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1. To have 50, 4-ounce portions of green beans, we need to find how many pounds of fresh green beans should be bought.

Firstly, we'll need to find out how many ounces are needed to have a total of 50 portions of 4-ounces each.

50 portions of 4 ounces each = 50 × 4 = 200 ounces.

To find the total weight in ounces of the green beans that need to be purchased, we divide 200 by 0.85 (as 85% of fresh green beans are edible) as follows:

Total weight in ounces = 200/0.85 = 235.29 ounces.

1 pound is equal to 16 ounces, so to find the total weight in pounds of fresh green beans, we divide 235.29 by 16 as follows:

Total weight in pounds = 235.29/16 = 14.7 pounds.

Therefore, approximately 15 pounds of fresh green beans should be purchased.

2. We need to find out how much whole fish we need to buy to obtain 10 pounds of fish after it has been cleaned (with 40% yield).

We can solve for this using the formula: Yield% = (edible portion ÷ raw portion) × 100.

We can rearrange the formula as: Edible portion = (yield% ÷ 100) × raw portion

We need a 40% yield, so substituting the given values in the formula above, we get:

Edible portion = (40 ÷ 100) × Raw portion

Let's say Raw portion is R. We need 10 pounds of edible portion, so:

10 pounds = (40 ÷ 100) × R10 ÷ (40 ÷ 100) = R25 = R

Therefore, 25 pounds of whole fish should be purchased.

3. We are serving 60 people with half-pound strip sirloin, so we need to find how many pounds of sirloin should be brought in, assuming that 20% of it will be wasted after trimming.

Each serving requires a half-pound, so 60 people need a total of 60 × 0.5 = 30 pounds of sirloin.

To find out the total weight of sirloin that should be brought in, we can use the formula:

Total weight of sirloin = Required weight of sirloin ÷ (1 - Waste%)

Required weight of sirloin = 30 pounds

Waste% = 20% = 0.2

Substituting these values into the formula, we get:

Total weight of sirloin = 30 ÷ (1 - 0.2)= 30 ÷ 0.8= 37.5 pounds.

So, approximately 38 pounds of sirloin should be brought in.

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Given:

On a coordinate plane a line contains the point (2,6) and models a proportional relationship.

To find:

The points which are also on the line.

Solution:

The line models a proportional relationship.

\(y\propto x\)

\(y=kx\)            ...(i)

where, k is constant of proportionality.

Put x=2 and y=6 in the above equation.

\(6=k(2)\)

Divide both sides by 2.

\(\dfrac{6}{2}=k\)

\(k=3\)

Put k=3 in equation (i).

\(y=3x\)

We can say that the point whose y-coordinate is 3 times of its x-coordinate, are the point which are lie on the line.

For example: (1,3), (3,3), (-1,-3) etc.

So, the equation of line is \(y=3x\). All the points which satisfy this equation represents the points on the line.

0 is the outlier in this set of values is the answer.

To identify the outlier in a set of values, we need to look for a value that significantly deviates from the rest.

In the given set of values: 17, 21, 19, 10, 15, 19, 14, 0, 11, and 16, the outlier is the value that stands out the most.
To determine this, we can calculate the interquartile range (IQR).

The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the data set.

Any value that falls below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR can be considered an outlier.

Arranging the values in ascending order, we have: 0, 10, 11, 14, 15, 16, 17, 19, 19, 21.
The first quartile (Q1) is 11.5 and the third quartile (Q3) is 18.5. Therefore, the IQR is 7.
Using the formula, we find that Q1 - 1.5 * IQR is -5 and Q3 + 1.5 * IQR is 35.
Comparing these values with the data set, we can see that 0 is the only value that falls below Q1 - 1.5 * IQR.

Hence, 0 is the outlier in this set of values.

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Answer:

3393

Step-by-step explanation:

because 3395 -2 is 3393

Answer:

605

Step-by-step explanation:

2 tons = 4,000 lbs

4,000-3,395=605

Answer:

0 the bucket don't have black socks so you can't pick them

To solve the equation, we need to multiply both sides by 1/3. This will result in T = 6 hours. Therefore, it would take the turtle 6 hours to walk 2 miles.

The equation to find out how long it would take the turtle to walk 2 miles is: T = 2 / (1/3) Where T represents the time in hours.This equation is derived from the formula "distance = rate * time". In this case, the distance is 2 miles, the rate is 1/3 mile per hour, and the time, represented by T, is what we're trying to solve for.To solve the equation, we need to multiply both sides by 1/3. This will result in T = 6 hours. Therefore, it would take the turtle 6 hours to walk 2 miles.

A) Equation:Time = 2 miles ÷ (1/3 mile per hour) B) Solve equation:

Time = 2 miles ÷ (1/3 mile per hour)

Time = 2 miles × (3/1 mile per hour)

Time = 6 hours

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The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.

Total moves required are 7, as follows:

Three steps up as well as four steps right.

Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.

There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).

For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.

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Answer:

what?

Step-by-step explanation:

Outliers are sample values that lie very far away from the majority of the other sample values.

We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

It differs significantly from other observations in a sample values.

Outlier is a value that is distant from the majority of the values in a data set.

For a scatter plot, an outlier is the point or points that are farthest from the regression line.

For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.

Therefore, outliers are sample values that lie very far away from the majority of the other sample values.

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