(q24) Find the volume of the solid obtained by rotating the region bounded by y = x and y = x^2 about the line x = - 3.

The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater is correct.

In this situation, the population refers to the entire group of individuals that are of interest to the survey. In this case, the population is the total number of people who go to the movie theater. The sample, on the other hand, refers to a subset of the population that is actually observed and surveyed. In this case, the sample is the first 150 people who entered the theater and were asked about their favorite type of movie.

It is important to note that the sample should be representative of the population in order to draw valid conclusions from the survey. This means that the individuals in the sample should be selected in a way that reflects the characteristics of the population as a whole.

In summary, the population in this situation is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater who were asked about their favorite type of movie.

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If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the normal distribution properties to find the percentage of IQ scores between 85 and 130.

Specifically, we can standardize the scores and use a normal distribution table or calculator to find the area under the curve between the z-scores corresponding to 85 and 130.To find the percentage of IQ scores between 85 and 130, we first need to standardize the scores by subtracting the mean and dividing by the standard deviation. This gives:

z1 = (85 - 100) / 15 = -1.00

z2 = (130 - 100) / 15 = 2.00

We can then use a normal distribution table or calculator to find the area under the curve between these two z-scores. For example, using a standard normal distribution table, we can find that the area to the left of z = -1.00 is 0.1587 and the area to the left of z = 2.00 is 0.9772. Therefore, the area between these two z-scores is:

0.9772 - 0.1587 = 0.8185

This means that approximately 81.85% of IQ scores are between 85 and 130. Alternatively, we can use a normal distribution calculator to find the same result. For example, using an online calculator, we can input the mean (100), standard deviation (15), and the lower and upper limits (85 and 130) and obtain a probability of 0.8185, or 81.85%.

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sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine

We can use the sum-to-product formula for sine to show that sin(55°) + sin(5°) = sin(65°). The formula is:

sin A + sin B = 2 sin[(A + B)/2] cos[(A - B)/2]

Substituting A = 55° and B = 5°, we get:

sin(55°) + sin(5°) = 2 sin[(55° + 5°)/2] cos[(55° - 5°)/2]

Simplifying, we get:

sin(55°) + sin(5°) = 2 sin(30°) cos(25°)

We know that sin(30°) = 1/2 and cos(25°) = sin(90° - 25°), so we can substitute these into the expression:

sin(55°) + sin(5°) =  sin(90° - 25°)

We also know that sin(90° - 25°) = sin(65°), so we can substitute this into the expression:

sin(55°) + sin(5°) = sin(65°)

Therefore, sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine.

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Given question is incomplete, the complete question is below

Show that sin(55°) + sin(5°) = sin(65°)

use a sum-to-product formula for sine and simplify

To determine which method can be used to prove the similarity of the given triangles, use SAS, SSS, and AA.

To determine which method can be used to prove the similarity of the given triangles, let's briefly discuss each method:

a) SAS~ (Side-Angle-Side Similarity): If two sides of a triangle are proportional to two sides of another triangle, and their included angles are congruent, then the triangles are similar.

b) SSS~ (Side-Side-Side Similarity): If all three sides of a triangle are proportional to the corresponding sides of another triangle, then the triangles are similar.

c) AA~ (Angle-Angle Similarity): If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.

Unfortunately, I cannot see the given triangles in your question, but based on the provided information, you can use these explanations to determine which method (SAS~, SSS~, or AA~) can be used to prove their similarity. If none of these methods apply, then similarity cannot be proved for the triangles.

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Answer:

[tex]f(x) = -5(x -1)^{2} +6[/tex]

Step-by-step explanation:

[tex]f(x) = a(x - h)^{2} + k[/tex] is the standard form of a quadratic, so the fourth option [tex]f(x) = -5(x -1)^{2} +6[/tex] is in standard dorm

Georg's percent error is 4.30%.

The predicted value is 24 bags, and the actual value is 23 bags.

To find the percent error, we need to find the absolute value of the difference between the predicted value and the actual value, divide that by the predicted value, and multiply by 100 to get a percentage.

percent error = |(predicted value - actual value) / actual value| x 100%

Substituting the given values, we get:

percent error = |(24 - 23) / 23| x 100%

percent error = |1 / 23| x 100%

percent error = 4.3478%

Therefore, Georg's percent error is 4.30%.

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Answer:

About 17%.

Step-by-step explanation:

A dozen is 12.

2 out of 12 are cracked.

2 / 12 = 0.16666666666

That equals about 16.7%.

Your problem doesn't say which place to round to but this seems kind of basic so I'd write "about 17%."

The stem-and-leaf plot is a data visualization tool that provides a quick way to see the distribution of a set of data.

The given data represents the number of letters in the mailboxes of 10 houses. To construct a stem-and-leaf plot, we group the data by their tens digit and display them as stems on the left side of the plot, and the ones digit is shown as leaves on the right side of the plot. For the given data, the stem-and-leaf plot is:

 2 | 2

 4 | 4 5

 5 | 7 8

 7 | 0 1

 8 |

10 | 0 2

11 |

12 | 3

13 |

16 |

The plot shows that the majority of houses have between 4 and 13 letters in their mailboxes, with the most common numbers of letters being 7, 8, and 10. The plot also shows that there are two outliers: one house with only 2 letters and another with 16 letters in its mailbox.

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Integrating the concentration between 0 and 4, we can see that the correct option is A.

We know that the concentration is given by the quadratic equataion:

c(t) = 2t(4 - t)

To find the cardiatic output for the time interval [0,4 ], we need to integrate over that interval, we will get:

[tex]\int\limits^4_0 {2t*(4 - t)} \, dt = [-(2/3)t^3 + 4t^2 + C]^4_0[/tex]

Where C is the constant of integration.

Evaluating that in the given interval, we will get:

[ -(2/3)*4³ + 4*4² - 0] = 21.33

Then we can see that the correct option is A.

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The t-value needed to develop the 95% confidence interval for the population mean SAT score is: t = 2.009

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

To find the t-value needed to develop the 95% confidence interval for the population mean SAT score, we can use the following formula:

t = (x - μ) / (s / √(n))

where:

x = sample mean (1300)

μ = population mean (unknown)

s = sample standard deviation (200)

n = sample size (49)

To find the t-value, we need to find the margin of error (ME) first:

ME = t* (s / √(n))

We know that for a 95% confidence interval, the critical value of t is 2.009 (from t-distribution table or calculator) with 48 degrees of freedom

(df = n-1).

Therefore, the t-value needed to develop the 95% confidence interval for the population mean SAT score is:

t = 2.009.

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The volume of the piece of cheese is 252 cubic centimeters (cm³).

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length. It is a type of quadrilateral, a polygon with four sides. The length of the sides that are parallel to each other is called the base, and the length of the sides that are perpendicular to the base is called the height.

The volume of a rectangular pyramid is given by the formula:

V = (1/3) * base area * height

The base area of the wedge is 4 cm * 9 cm = 36 cm².

Substituting the given values into the formula, we have:

V = (1/3) * 36 cm² * 21 cm = 252 cm³

Therefore, the volume of the piece of cheese is 252 cubic centimeters (cm³).

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The value of x is 16 for the desired values of y and z.

If x varies directly with the square of y and inversely with the cube root of z, then we can write:

[tex]x = k * y^2 / z^{(1/3)[/tex]

where k is a constant of variation.

To find the value of k, we can use the given information that x=6 when y=2 and z=8:

[tex]6 = k * 2^2 / 8^{(1/3)[/tex]

Simplifying this equation:

6 = k * 4 / 2

k = 3

Now we can use this value of k to find x when y=4 and z=27:

[tex]x = 3 * 4^2 / 27^{(1/3)[/tex]

Simplifying this expression:

x = 3 * 16 / 3

x = 16

Therefore, when y=4 and z=27, x is equal to 16.

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The value of x if the triangle is equilateral is x = -16 and  x = -10

An equilateral triangle is a regular polygon with all three sides of equal length.  It is also equiangular, meaning that all three internal angles are congruent to each other and are each 60 degrees

If the triangle is equilateral therefore

5x + 16 = 4x and 5x + 16 = 3x - 4

5x -4x = -16

x = -16

Also, in equation 2

Also, 5x -  3x =-4 -16

2x = -20

therefore,

x = -10

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The correlation coefficient indicative of the weakest linear relationship is option (c) -0.05. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

Correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship. Therefore, a correlation coefficient closer to 0 indicates a weaker linear relationship. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

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The area of the surface obtained by rotating the curve x = 6e^(2y) from y = 0 to y = 6 about the y-axis is approximately 1337.47 square units.

We can use the formula for surface area obtained by rotating a curve about the y-axis:

SA = 2π∫a^b f(x)√(1+(dy/dx)^2) dx

In this case, the curve is x = 6e^(2y) and we want to rotate it from y = 0 to y = 6. So, we have:

f(x) = 6e^(2y)

dy/dx = (1/2)(1/x) = (1/2e^(2y))

(1 + (dy/dx)^2) = 1 + (1/4e^(4y))

Substituting these values into the formula, we get:

SA = 2π∫0^6 6e^(2y)√(1+(1/4e^(4y))) dy

This integral is difficult to solve analytically, so we can use numerical methods to approximate the value. Using a numerical integration method, we get:

SA ≈ 1337.47

Therefore, the area of the surface obtained by rotating the curve x = 6e^(2y) from y = 0 to y = 6 about the y-axis is approximately 1337.47 square units.

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The area of the triangular parcel of land is approximately 305,682.4 square feet.

We can use Heron's formula to find the area of a triangular parcel of land. This formula states that the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c)/2
Using the lengths of the sides given in the problem, we can calculate the semi-perimeter:
s = (860 + 820 + 1038)/2 = 1759
Then we can plug this value into Heron's formula to find the area:
Area = √(1759(1759-860)(1759-820)(1759-1038))
Area = √(1759×899×939×721)
Area = √(93587715844)
Area = 305682.4 square feet (rounded to the nearest tenth)
Therefore, the area of the triangular parcel of land is approximately 305,682.4 square feet.

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The price would lead to a shortage in the market is $8.

We know that,

When the amount required exceeds the amount supplied at the going rate, there is a shortage.

Three factors primarily contribute to shortages: rising demand, falling supply, and government action.

According to the given data

At $8, there would be a shortage because there is a greater demand than there are available items.

At $8, there is a shortfall of 4 units because only 10 are available while 14 are needed.

Thus,

The price is of $8 lead the shortage.

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To find the critical points of a function, we need to determine the points at which the gradient of the function is zero or undefined.

In the case of the given function f(x,y) = 2x^4 + 3y^2 - 10xy - 3, we need to find the values of x and y where the partial derivatives of f with respect to x and y are both zero.

After taking the partial derivatives of the function with respect to x and y, we got two equations.

We solved these equations simultaneously to obtain the values of x and y at which the partial derivatives of f are both zero. The obtained values of x and y are the critical points of the function.

In this case, we got two critical points ( √(25/12), (25/12)√(3/5)), (- √(25/12), -(25/12)√(3/5)).

To check whether these critical points are maximum, minimum, or saddle points, we can use the second derivative test.

We can evaluate the second partial derivatives of f and plug in the values of x and y for each critical point to determine the nature of the critical points.
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Answer: 45

Step-by-step explanation:

Let's call the number of students in the yearbook club "x". Since the drama club has 12 more students, the number of students in the drama club would be "x+12".

We know that the total number of students in both clubs is 78, so we can set up an equation:

x + (x+12) = 78

Simplifying the equation:

2x + 12 = 78

Subtracting 12 from both sides:

2x = 66

Dividing both sides by 2:

x = 33

So there are 33 students in the yearbook club.

To find the number of students in the drama club, we can substitute x = 33 into the equation we set up earlier:

x + 12 = 33 + 12 = 45

Therefore, there are 45 students in the drama club.

Answer:

year book club= 33 people

drama club = 45 people

Step-by-step explanation:

78 students in total

drama : year book

x+12 x

x+12+x=78

2x+12=78

2x=66

x=33

year book= 33

drama= 45

The standard form equation of the ellipse is 24(x + 6)^2 + 5(y + 3)^2 = 600

Since the center of the ellipse is at the point (-6, -3), we can write the standard form equation of the ellipse as:

((x + 6)/a)^2 + ((y + 3)/b)^2 = 1

where "a" and "b" are the lengths of the semi-major and semi-minor axes, respectively.

The distance between the center (-6, -3) and the vertices (-6, -13) or (-6, 7) is 10, which is equal to 2a. So, a = 5.

The distance between the foci (-6, -4) and (-6, -2) is 2, which is equal to 2c (where c is the distance between the center and the foci). So, c = 1.

Using the relationship between a, b, and c in an ellipse (a^2 = b^2 + c^2), we can solve for b:

5^2 = b^2 + 1^2

25 - 1 = b^2

b = sqrt(24)

Therefore, the standard form equation of the ellipse is:

((x + 6)/5)^2 + ((y + 3)/sqrt(24))^2 = 1

Simplifying, we get:

24(x + 6)^2 + 5(y + 3)^2 = 600

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Answer:

22

Step-by-step explanation:

whats ur question

The value of tan(A) is equal to 3/4.

Option B is the correct answer.

We have,

To find the tangent of angle A, we can use the formula for tangent in a right triangle, which is given by:

tan(A) = opposite/adjacent

In this case,

Side a is the length of the side opposite to angle A, and side b is the length of the side adjacent to angle A.

Given that b = 12 and a = 9, we can substitute these values into the formula:

tan(A) = a/b = 9/12 = 3/4

Therefore,

The value of tan(A) is equal to 3/4.

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The probability of drawing three cards from a deck of 52 cards one at a time without replacement and having all three cards be diamonds is 0.0026, or approximately 0.26%.

To calculate this probability, we can use the formula for conditional probability. The probability of drawing the first diamond is 13/52, since there are 13 diamonds in the deck. Once the first diamond has been drawn, there are 12 diamonds left out of 51 cards. So the probability of drawing a second diamond, given that the first card was a diamond, is 12/51. Finally, once two diamonds have been drawn, there are 11 diamonds left out of 50 cards. So the probability of drawing a third diamond, given that the first two cards were diamonds, is 11/50. Multiplying these three probabilities together gives us the probability of drawing three diamonds in a row, which is approximately 0.0026.

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The dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

To estimate the true mean April 2023 retail whole milk price with a margin of error of $0.10 and 95% confidence, a dairy farmer can use the sample size formula for estimating population means. The formula is:
n = (Z² × σ²) / E²
where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and E is the margin of error.
For a 95% confidence level, the z-score (Z) is 1.96. The standard deviation (σ) of milk prices is $0.60, and the margin of error (E) is $0.10. Plugging these values into the formula, we get:
n = (1.96² × 0.60²) / 0.10²
n = (3.8416 × 0.36) / 0.01
n ≈ 138.56
Since the sample size must be a whole number, we round up to the nearest whole number to ensure the desired level of accuracy. Therefore, the dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.

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The quadratic equation of the graph is:

x² - 4x = 0

The quadratic equation of a quadratic graph can be found by check the points where the curve cuts or intersect the x-axis. These two x values can then be used to form the quadratic equation.

Looking at the graph, you will notice that the graph cuts the x-axis at points x = 0 and x = 4 (Check the red circles in the attached image). We will then form the equation the x values as follow:

x = 0 and x = 4

x - 0 = 0 and x - 4 = 0

Combining them and simplifying:

(x - 0)(x - 4) = 0

x(x - 4) = 0

x² - 4x = 0

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Answer:

We know that P(AB) = P(A) + P(B) - P(A∪B), where P(A∪B) represents the probability that at least one of the events A or B will occur.

To calculate P(A∪B), we can use the formula P(A∪B) = P(A) + P(B) - P(AB), which follows from the addition rule of probability.

Substituting with the given values, we have:

P(A∪B) = P(A) + P(B) - P(AB)

P(A∪B) = 3/4 + 1/2 - 7/8

P(A∪B) = 6/8 + 4/8 - 7/8

P(A∪B) = 3/8

Now, we can calculate P(AB) using the first formula:

P(AB) = P(A) + P(B) - P(A∪B)

P(AB) = 3/4 + 1/2 - 3/8

P(AB) = 6/8 + 4/8 - 3/8

P(AB) = 7/8

Therefore, the correct answer is option b) 7/8.

Step-by-step explanation:

Answer:

  A.  2.60944

Step-by-step explanation:

You want the slope of the function f(x) = e^x +5^x at x=0.

The derivative is ...

  f'(x) = e^x +ln(5)·5^x

At x=0, this is ...

  f'(0) = e^0 +ln(5)·5^0 = 1 +ln(5)

  f'(0) ≈ 2.60944

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The straight line distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

The sheehan lake (point A) is at 2000 m .

The small lake ( point B) is at 3700 m .

Distance between the two lake can be calculated by finding the difference between lakes .

To find the distance between sheehan lake and small lake = point B - point A .

Distance =  3700 - 2000

Distance = 1700 m .

The distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

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The question is incomplete the complete question is :