if dydx=ysec2x and y = 5 when x = 0, then y =

The probability that a student's test score is over 90 is approximately 0.1587 or 15.87%.

To find this probability, follow these steps:

1. Identify the given values:
  Mean (µ) = 65
  Standard deviation (σ) = 20
  Target score (X) = 90

2. Calculate the z-score:
  Z = (X - µ) / σ
  Z = (90 - 65) / 20
  Z = 25 / 20
  Z = 1.25

3. Use a standard normal (Z) table or calculator to find the probability associated with the z-score:
  P(Z > 1.25) ≈ 0.211

4. However, the Z table gives the probability of values less than the z-score, so we need to find the probability of values greater than the z-score:
  P(Z > 1.25) = 1 - P(Z ≤ 1.25)
  P(Z > 1.25) = 1 - 0.211 ≈ 0.1587

So, the probability that a student's test score is over 90 is approximately 0.1587 or 15.87%.

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The prediction interval is then calculated as follows as: ±0.0196.

The prediction interval for the length of life of a horse can be calculated using the following formula:

Prediction interval = ±1.96 * standard error

here the standard error is the standard deviation of the sampling distribution of the estimate.

The standard error can be estimated using the formula:

Standard error = √[(1/n) * sum((estimate - y[tex])^2[/tex]]

here n is the sample size, estimate is the sample mean, and y is the true population mean.

In this case, the sample size is n = 2, the estimate is x = 2, and y = 18.89.01087.

Substituting these values into the formula, we get:

Standard error = √[(1/2) * (2 - 18.89.01087[tex])^2[/tex]]

= √[(1/2) * (2 - 18.89.01087)]]  ]][tex])^2[/tex]]

= √[0.5 * (2 - 18.89.01087)[tex])^2[/tex]]

= √[0.5 * 0.02087[tex])^2[/tex]]

= √0.5 * 0.001156

= 0.001156

The standard error is approximately 0.001156.

The prediction interval is then calculated as follows:

Prediction interval = ±1.96 * standard error

= ±1.96 * 0.001156

= ±0.0196

Rounding to the nearest hundredth, the prediction interval is approximately 0.02.  

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The appropriate limits of integration for finding the area between the functions defined by x = −1 and x = − y^3 − 3y^2 are y = -2 and y = 0.

To find the limits of integration, we need to determine the intersection points of the given functions. Equating x = −1 and x = − y^3 − 3y^2, we get:

−1 = − y^3 − 3y^2

Rearranging and simplifying, we get:

y^3 + 3y^2 - 1 = 0

We can solve this cubic equation to get the three roots, but we are only interested in the real root between y = -2 and y = 0. We can use numerical methods or a graphing calculator to find that the real root is approximately -1.7549.

Therefore, the appropriate limits of integration for finding the area between the given functions are y = -2 and y = 0. The integral to find the area is:

A = ∫^0_-2 [(− y^3 − 3y^2) + 1] dy

Simplifying and evaluating the integral, we get:

A = 49/12.

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The probability that Blaine earns more than $10,100 in 50 days is approximately:

P(X > $10,100) ≈ 1 - 0.7136 ≈ 0.2864 or 28.64%.

To calculate the probability that Blaine earns more than $10,100 after 50 days, we need to use the Central Limit Theorem, assuming that Blaine's daily earnings follow a normal distribution.

The Central Limit Theorem states that the sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the shape of the original distribution.

Given that Blaine's average earnings per day is $200 with a standard deviation of $25, we can calculate the mean and standard deviation for the sum of his earnings over 50 days:

Mean of 50-day earnings = 50 * $200 = $10,000

Standard deviation of 50-day earnings = √(50) * $25 ≈ $176.78

Now, we want to find the probability that Blaine earns more than $10,100 in 50 days. We can convert this into a standard normal distribution by standardizing the value using the z-score formula:

z = (x - μ) / σ

Where:

x is the value we want to standardize (in this case, $10,100)

μ is the mean of the distribution (in this case, $10,000)

σ is the standard deviation of the distribution (in this case, approximately $176.78)

z = ($10,100 - $10,000) / $176.78 ≈ 0.564

Next, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 0.564. The probability of earning more than $10,100 can be calculated as:

P(X > $10,100) = 1 - P(X ≤ $10,100)

= 1 - P(Z ≤ 0.564)

Using a standard normal distribution table or a calculator, we can find that P(Z ≤ 0.564) is approximately 0.7136.

Therefore, the probability that Blaine earns more than $10,100 in 50 days is approximately:

P(X > $10,100) ≈ 1 - 0.7136 ≈ 0.2864 or 28.64%.

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The calculated value of x from the frequency table is 21

From the question, we have the following parameters that can be used in our computation:

Number of points 0 1 2 3 4

Frequency  13 17 8 X 11

The mean is calculated as

Mean = Sum/Count

So, we have

Mean = (0 * 13 + 1 * 17 + 2 * 8 + 3x + 4 * 11)/(13 + 17 + 8 + x + 11)

The mean is given as 2

So, we have

(0 * 13 + 1 * 17 + 2 * 8 + 3x + 4 * 11)/(13 + 17 + 8 + x + 11) = 2

Solving for x, we have

(77+ 3x )/(49 + x) = 2

So, we have

77 + 3x = 2(49 + x)

Evaluate

x = 21

Hence, the value of x from the frequency table is 21

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Answer:

5 × 2 = 10

Step-by-step explanation:

5 + 5 = 10

or

2 + 2 + 2 + 2 + 2 = 10

The calculated coordinates of point B on the line AC is (-5/11, -19/11)

From the question, we have the following parameters that can be used in our computation:

A (-5,-4)  

C (5,1)

Also, we have

m : n = 5 : 6

The coordinates of point B are calculated using

B = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

B = 1/(5 + 6) * (5 * 5 + 6 * -5, 5 * 1 + 6 * -4)

Evaluate

B = (-5/11, -19/11)

Hence, the coordinates of point B on line AC is (-5/11, -19/11)

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Question

What are the coordinates of point B on line AC such that the ratio of AB to AC is 5:6

A (-5,-4) to C (5,1)

(4a) The value of arc BD is determined as 140⁰.

(4b) The value of arc ADC is determined as 200⁰.

(4c) The value of angle ADC is determined as 80⁰.

(4d) The value of angle BCD is determined as 110⁰.

(4e) The value of arc AC is determined as 160⁰.

(5a) The value of angle BCA is determined as 123⁰.

(5b) The length of AB is 17.32 units.

The value of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

question 4a.

arc BD = 2 x m∠BAD ( interior angles of intersecting secants)

arc BD = 2 x 70⁰

arc BD = 140⁰

Question 4b.

arc ADC = 2 x m∠ABC ( interior angles of intersecting secants)

arc ADC = 2 x 100⁰

arc ADC = 200⁰

Question 4c.

angle ADC = 180 - 100 (opposite angles of a cyclic quadrilateral are complementary)

angle ADC = 80⁰

Question 4d.

angle BCD =  180 - 70 (opposite angles of a cyclic quadrilateral are complementary)

angle BCD = 110⁰

Question 4e.

Arc AC = 360 - arc ADC (sum of angles in a circle)

Arc AC = 360 - 200⁰

Arc AC = 160⁰

Question 5a.

angle BCA = ¹/₂ ( (360 - 57 ) - 57 ) (exterior angles of intersecting secants)

angle BCA = ¹/₂ ( 303 - 57 )

angle BCA = 123⁰

Question 5b.

The length of AB is calculated by applying Pythagoras theorem as follows;

AC² = AB² +  BC²

AB² = AC² - BC²

AB² = 20² - 10²

AB² = 300

AB = √ ( 300 )

AB = 17.32 units

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The probability that a randomly selected park with newly updated picnic tables is a rural park is 2/7 .The probability is approximately 0.286 or 28.6%.

To find the probability that a randomly selected park with newly updated picnic tables is a rural park, we need to use conditional probability. We know the number of urban parks (30) and rural parks (18), as well as the number of urban parks updated with new picnic tables (10) and rural parks updated with new picnic tables (4).

Let's define the events:

A: Park is rural

B: Park is updated with new picnic tables

We want to find P(A|B), which represents the probability that the park is rural given that it is updated with new picnic tables.

Using the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

P(A ∩ B) represents the probability of both events A and B occurring. In this case, it is the probability that a park is both rural and updated with new picnic tables. From the information given, we know that 4 rural parks were updated with new picnic tables, so P(A ∩ B) = 4.

P(B) represents the probability of event B occurring, which is the probability that a park is updated with new picnic tables. This is the sum of the urban and rural parks that were updated, which is 10 + 4 = 14.

Now we can calculate P(A|B):

P(A|B) = P(A ∩ B) / P(B) = 4 / 14 = 2/7

Therefore, the probability that a randomly selected park with newly updated picnic tables is a rural park is 2/7.

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the domain of the vector function is the intersection of the domains of the component functions, which is:

(-2, 3) U (3, ∞)

To find the domain of the vector function, we need to consider the domains of the component functions. In particular, we need to make sure that the denominators in the component functions are not zero and the arguments of the logarithmic functions are positive.

For the x-component, we have:

t+2 ≠ 0

which gives t ≠ -2.

For the y-component, there are no restrictions on the domain of sin(t).

For the z-component, we have:

9-t^2 > 0

which gives -3 < t < 3.

Note that we exclude the value t = -2 from the domain because it makes the x-component undefined. We express the final answer in interval notation as (-2, 3) U (3, ∞).

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Answer:

The system "y < 6 and y > 6" has no solutions.

This is because the inequality "y < 6" means that y must be less than 6, while the inequality "y > 6" means that y must be greater than 6. There is no number that can be less than 6 and greater than 6 at the same time, so there are no solutions to this system.

The Sistine Chapel is a rectangular building with a length of 40.9 meters and an area of 548.06 square meters. To calculate the width of the building, we need to divide the area by the length.

To find the width of the Sistine Chapel, we can use the formula for the area of a rectangle: Area = Length × Width. In this case, we know the length is 40.9 meters and the area is 548.06 square meters.

Rearranging the formula, we can solve for the width by dividing the area by the length: Width = Area ÷ Length. Substituting the given values, we get Width = 548.06 ÷ 40.9 = 13.4 meters. Therefore, the width of the Sistine Chapel is approximately 13.4 meters.

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Answer:

-786000

Step-by-step explanation:

Answer:

-786000

Step-by-step explanation:

Use PEMDAS. Multiplication comes first and when deciding which multiplication to use go from left to right. First you multiply 1455 by -786, then you multiply 455 by 786. Then you get two values: -1143630 and 357630 which you add together.

1455 x -786 + 455 x 786:

1455 x -786 = -1143630

455 x 786 = 357630

-1143630 + 357630 = -786000

Answer:

0.05

Step-by-step explanation:

5%=5/100

5/100=5÷100

5÷100=0.05

The focus is located approximately 0.69 ft from the vertex. Rounded to two decimal places, the answer is (a) 0.52 ft.

The general equation for a vertical parabola in standard form is given by:

y = (1/4p)x^2

where p is the distance from the vertex to the focus.

In this case, the vertex is located at (0, 0) and the opening is 6 ft wide, which means that the parabola opens downwards. Therefore, the equation of the parabola is:

y = -(25/9)x^2

Comparing this with the standard form of the equation, we get:

4p = -25/9

Solving for p, we get:

p = -25/36

Since the focus is located at a distance of p from the vertex along the axis of symmetry, the focus is located at:

f = |p| = 25/36 ≈ 0.69 ft

Therefore, the focus is located approximately 0.69 ft from the vertex. Rounded to two decimal places, the answer is (a) 0.52 ft.

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while the statement may be generally true for most compound meter time signatures, there are exceptions where the top number may not be 6, 9, or 12.

This statement is not entirely accurate. While it is true that compound meter time signatures have a top number that is typically a multiple of three (e.g., 6, 9, or 12), it is not always the case.

For example, a compound meter time signature of 3/4 is possible, where the top number is not a multiple of three but the time signature is still compound because it is divided into three beats per measure and each beat is divided into three equal parts (eighth note triplets).

Another example is 2/4 time signature in compound duple meter, where the top number is not a multiple of three but the beats are still divided into three equal parts (eighth note triplets).

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The standard form of the equation of the hyperbola is ((x - 6)^2 / 9) - ((y - 0)^2 / 27) = 1 or equivalently ((x - 6)^2 / (3^2)) - ((y - 0)^2 / (3sqrt(3))^2) = 1.

Since the foci of the hyperbola lie on the x-axis, we know that the transverse axis is horizontal. The center of the hyperbola is the midpoint between the vertices, which is ((3+9)/2, 0) = (6, 0). The distance between the center and each vertex is a = (9-3)/2 = 3, and the distance between the center and each focus is c = 12/2 = 6. The distance between each focus and vertex is b, where b^2 = c^2 - a^2 = 36 - 9 = 27, so b = sqrt(27) = 3sqrt(3).

Therefore, the standard form of the equation of the hyperbola is:

((x - 6)^2 / 9) - ((y - 0)^2 / 27) = 1

or equivalently:

((x - 6)^2 / (3^2)) - ((y - 0)^2 / (3sqrt(3))^2) = 1

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Answer:

The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis. The slope and the intercept define the linear relationship between two variables, and can be used to estimate an average rate of change.

Some real life examples of slope include:

Intellectually gifted people score in the top 1 - 2percent on a standard IQ test.

From the question, we have the following parameters that can be used in our computation:

IQ of intellectual gifted people

The general rule is that

People with intellectuals are usually ranked high and the range is usually small

Next, we test the options

A. 10

The top 10% has a high range

B. 5-10

The top 10% omits people in top 5%

C. 5

The top 5% has a high range

D. 1-2

This has a small range and it is the highest

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Answer:

a=14.9

Step-by-step explanation:

first tan25=0.4663076582

so 32tan(25)=a

32*0.4663076582=a

a=14.921845061 or

a=14.9√√√√√√√√√√√√√

i hope it will help you

To write the parametric equations x = 2sin(θ), y = 9cos(θ), 0 ≤ θ ≤ π in cartesian form, we can use the trigonometric identity cos^2(θ) + sin^2(θ) = 1.

First, we solve for sin(θ) in terms of x:

x = 2sin(θ)
sin(θ) = x/2

Next, we solve for cos(θ) in terms of y:

y = 9cos(θ)
cos(θ) = y/9

Using these expressions for sin(θ) and cos(θ), we can substitute them into the identity above to get:

(cos(θ))^2 + (sin(θ))^2 = 1
(y/9)^2 + (x/2)^2 = 1
y^2/81 + x^2/4 = 1

Thus, the cartesian form of the parametric equations is:

y^2/81 + x^2/4 = 1, with x ≥ 0.

Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables. When necessary, more than one parameter can be used.

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Answer:

Step-by-step explanation:

(1)This equation does not properly represent the depth in relation to time and is not appropriate for this scenario.

(2)This equation does not accurately model the depth of the water as it does not account for time-dependent changes.

(3)The depth will fluctuate between 5 feet below the surface and 14 feet below the surface, with a period of 2π hours.

(4) The depth of the water at the marker, depending on the specific amplitude and vertical shift derived.

The equation for the depth of the water at the marker depends on the given options (1), (2), (3), and (4). Let's analyze each option:

(1) d = 5cos(t) + 9

This equation suggests that the depth of the water varies with time following a cosine function. The amplitude of the cosine function is 5, and the vertical shift is 9. However, the variable used in the cosine function is "t" instead of "t/2π," which implies that one complete cycle occurs over 2π hours.

(2) d = 9cos(1) + 5

In this equation, the cosine function does not depend on time. It uses a constant value of 1 inside the function. Consequently, the depth of the water remains constant at 14 feet (9 + 5).

(3) d = 9sin(t) + 5

This equation suggests that the depth of the water varies with time following a sine function. The amplitude of the sine function is 9, and the vertical shift is 5. This equation appropriately models the depth of the water at the marker, considering the sinusoidal nature of t.

This equation is similar to option (3) but with a different amplitude and vertical shift. The amplitude is 5, and the vertical shift is 9. This equation also correctly represents the depth of the water at the marker, with the depth fluctuating between 4 feet below the surface and 14 feet below the surface, with a period of 2π hours.

In conclusion, options (3) and (4) are both suitable equations for the depth of the water at the marker.

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The determinant of the matrix, using the method of expansion by cofactors would be -75.

The formula for the determinant of the matrix is :

= a 11 x C 11 - a 12 x C12 + a 13 x C 13

The a's are in the first row and the Cs are the cofactors that correspond to them.

These cofactors are:

| 5 6 |

| -3 1 |

C11 = (5 x 1) - (6 x -3)

= 5 + 18

= 23

| 4 6 |

| 2 1 |

C12 = (4 x 1) - (6 x 2)

= 4 - 12

= - 8

| 4 5 |

| 2 -3 |

C13 = (4 x -3) - (5 x 2)

= -12 - 10

= -22

The determinant is therefore:

= -3 x 23 - 2 x ( - 8 ) + 1 x (- 22)

= - 69 + 16 - 22

= - 75

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The probability that the binomial experiment results in fewer than 9 successes is approximately 0.1391.

The binomial experiment with probability of success p = 0.68 and n = 11 trials can be modeled by a binomial distribution. We want to find the probability of getting fewer than 9 successes, which can be written as:

P(X < 9)

where X is the number of successes in 11 trials. To calculate this probability, we can use the binomial cumulative distribution function with parameters n = 11 and p = 0.68:

P(X < 9) = F(8; n = 11, p = 0.68)

Using a binomial distribution table or a calculator, we can find that F(8; n = 11, p = 0.68) = 0.1391 (rounded to four decimal places).

Therefore, the probability that the binomial experiment results in fewer than 9 successes is approximately 0.1391.

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The solution is the frequency is 6.000-6.049  3 and 6.350-6.399 are 1.

Option C is the correct answer.

Given:

The table of the frequency distribution of the weights​ (in grams) of​ pre-1964 quarters is given.

Required:

Find the correct histogram from the given histogram.

Explanation:

We can observe from the given histogram that the frequency from 6.150-6.199 to 6.200-6.249 is decreasing. In histogram B it is increasing So option B is not the correct answer.

In histograms A and C we will observe that the frequency is 6.000-6.049

3 and 6.350-6.399 are 1.

But by observation in histogram A it is not correct.

It is correct in histogram C.

Final Answer:

Option C is the correct answer.

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complete question:

The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?

If the median of a normal distribution is known, it can be said that the mean of the distribution is also equal to the median. This is because the normal distribution is symmetric, with the median and mean at the center of the curve.

For a normal distribution, the mean and median are equal, so if the median is known, then the mean is also known. In a normal distribution, the median represents the point where exactly half of the data falls below and half falls above that point. Since the mean is also the point where the data balances out, meaning the sum of the values above the mean is equal to the sum of the values below the mean, it is also equal to the median. Therefore, if the median of a normal distribution curve is known, we can conclude that the mean is also equal to that value.

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The surface area of the portion of the paraboloid z = 25 − x^2 − y^2 in the first octant is approximately 150.94 square units.

The first octant is the portion of the coordinate system where all three coordinates are positive. In this case, we are interested in the portion of the paraboloid z = 25 − x^2 − y^2 that lies in the first octant.

To find the surface area, we need to integrate the surface area element over the portion of the surface we are interested in. The surface area element for a surface z = f(x, y) is given by:

d S = sqrt(1 + (f x)^2 + (f y)^2) d A

where f x and f y are the partial derivatives of f with respect to x and y, respectively, and d A is an element of area on the x y-plane. In this case, f(x, y) = 25 − x^2 − y^2, so we have:

f x = −2x

f y = −2y

Therefore, the surface area element becomes:

d S = sqrt(1 + 4x^2 + 4y^2) d A

To integrate over the portion of the surface in the first octant, we need to set up the limits of integration. Since we are only interested in the first octant, we have:

0 ≤ x ≤ sqrt(25 − y^2)

0 ≤ y ≤ sqrt(25)

Therefore, the surface area is given by:

S = ∫∫d S = ∫0^sqrt(25) ∫0^sqrt(25−y^2) sqrt(1 + 4x^2 + 4y^2) dx d y

This integral is not easy to evaluate analytically, so we can use numerical methods to approximate the value. Using a numerical integration method such as Simpson's rule with a step size of 0.1, we get:

S ≈ 150.94

Therefore, the surface area of the portion of the paraboloid z = 25 − x^2 − y^2 in the first octant is approximately 150.94 square units.

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Answer:

AAS

Step-by-step explanation:

For 2 triangles to be congruent, they must meet 1 of the following relative to each other:

These two triangles share 2 of the same angles and 1 of the same sides.

Therefore, they meet the AAS criteria.

The required possible value of U is approximately 74.3°.

In triangle TUV, we know that u = 9.6 cm, t = 6 cm, and ∠T = 143°. To find all possible values of ∠U, we can use the law of cosines, which states that:

c² = a² + b² − 2ab cos(C)

where c is the side opposite angle C, and a and b are the other two sides.

Here, we have to find angle U, which is opposite side u.

Therefore, we can rearrange the law of cosines to solve for cos(U):

cos(U) = (a² + b² - c²) / 2ab

Substituting the given values, we get:

cos(U) = (6² + 9.6² - 2(6)(9.6) cos(143°)) / (2(6)(9.6))

cos(U) = 0.267

Taking the inverse cosine of both sides, we get:

U = cos⁻¹(0.267)

U ≈ 74.3° or U ≈ 285.7°

Since the sum of the angles in a triangle is 180°, we know that U must be less than 143°.

Therefore, the only possible value of U is approximately 74.3°.

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