Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ), y = sec(θ), (1,√2)

suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. So, the number of people selected from the public for a research is known as a sample.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.

For the given details the correct matching will be:

Parameter - 17 hrs per week

Population - All high-school-aged teens in the US

Statistic - 14.4 hours per week

Sample - 15 students

Population is everything that is taken into account for an experiment since parameters reflect population characteristics and statistics state sample parameters.

The number of people selected from the public for a research is known as a sample.

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Answer:

3(5/3c+p)

Step-by-step explanation:

5c+3p=3(5/3c+p)

A graph when plotted, we get a straight line and it is called linear graph. Linear graph is a graph of linear function.

Domain refers to all the possible input values, it is the values in the x-axis of the graph. A range means all the output values, when each domain is used in a function. It is the y-axis values.

To determine the domain identify all the X- coordinates in the linear function graph. To determine the range, identify all Y-coordinates in the functions graph. The domain and range are usually represented as a set of values.

If the domain have values from 0-6, it is represented as {0<x<4}

If the range is values between -1 to 10, then it is represented as {-1<x<10}.

Lets consider the linear function y= 3x, the domain is between 0 and 10, and range above are,

Function  y= 3x

Domain  0    1      2    3     4     5       6        7         8        9        10

Range    0     3     6     9    12    15      18     21        24      27      30

So domain is the X-coordinates, and range the Y-coordinates.

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The equation of g(x), after the translations, is given as follows:

g(x) = x² + 8x + 14.

There are four translation rules that can be applied to a function, and they are listed as follows:

The parent function for this problem is given as follows:

f(x) = x².

The translations, along with their effects, are given as follows:

Hence the function g(x) is defined as follows:

g(x) = (x + 4)² - 2

g(x) = x² + 8x + 16 - 2

g(x) = x² + 8x + 14.

Which is in the standard form as is desired for this problem.

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If a quadratic equation  ax² + bx + c = 0, has equal roots , then the value of b , is : (a) ± 2√ac

The general form of a quadratic equation is;

ax² + bx + c = 0

The quadratic formula used to solve this quadratic equation is;

x = [-b ± √(b² - 4ac)]/2a

The quadratic equation ax² + bx + c = 0 has equal roots if its discriminant b² - 4ac = 0.

Thus;

b² = 4ac

b =  ±√4ac

b =  ±2√ac

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Answer:

3rd choice

a rotation of 90° counterclockwise about the origin and a translation down 1 unit

Step-by-step explanation:

This is just asking you what operations you need to perform to get figure N from figure M. Such a set of operations is called a transformation.

In this case we see that to get figure N we have to rotate figure M 90° in a counterclockwise direction. That would be the first transformation

From the choices you can eliminate the first two choices which deal only with clockwise rotation

Translation transformation is one where the figure is shifted horizontally or vertically

All we have to do is figure out if, after 90° counterclockwise rotation of M whether it was shifted 1 unit up or 1 unit down

Look at the point (-3, 1) in figure M.

When a figure is rotated 90° counterclockwise, each if its original coordinates (x, y) become new coordinates (-y, x)

In other words the coordinates are interchanged in the transformed figure and the sign of the new x-coordinate is changed from the original y value

So (-3, 1) should become (-1, -3)

But in figure N, that point has become (-1, -4) which is (-1, -3-1). This indicates the figure has been shifted down which corresponds to a translation down by 1 unit

Answer: 3rd choice

a rotation of 90° counterclockwise about the origin and a translation down 1 unit

The two images I have attached may help you understand better. First one is just the rotation of M. Second one is the rotated figure shifted down which results in figure N

1 is the only number that is neither prime nor composite number. 1 is the only factor of 1. One is the only number that has only 1 factor.

Explore factors using illustrations and interactive example

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The right answer is: Z requires that you know the population standard deviation, which can be erroneous.

The standard deviation calculates how much the data vary from the mean value. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. But the second is obviously more dispersed. It expresses the deviation of each observed value from the mean.

given

Both distributions must meet a number of requirements in order to be used. The prerequisites that must be met in order to execute a hypothesis test for employing a z-distribution are: The population has a normal distribution. We are aware of the population standard deviation.

The scope of the sample is broad.

The prerequisites that must be met in order to conduct a hypothesis test for employing a t-distribution are:

The population has a normal distribution. The chosen sample was chosen at random.

Use the t-distribution to conduct the test for the population mean in cases where the population standard deviation is unknown and the sample standard deviation must be computed.

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Answer:

Two billion, seven hundred forty million, two hundred fifty-three thousand, five hundred thirty-five is the right answer...

The shaded area between three mutually tangent circles of radii 5, 6, and 9 cm is 0.23 cm².

The three circles are mutually tangent which means that the distance between the centers of any two circles is equal to the sum of the radii of those circles.

Let's call the center of the largest circle C1, the center of the middle circle C2, and the center of the smallest circle C3.

Therefore, the distance between C1 and C2 is 9 cm + 6 cm = 15 cm, the distance between C2 and C3 is 6 cm + 5 cm = 11 cm and the distance between C1 and C3 is 9 cm + 5 cm = 14 cm. So semi-perimeter is

s = ( 15+11+14)/ 2 = 40/2 = 20

Area of triangle C1C2C3 is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A = \sqrt{20 (20-15)(20-11)(20-14)}[/tex]

A ≈ 73.48 cm²

Now we can use the area of a sector formula which is

(n/360)πr²

where n is degree subtended by the sector, to find the shaded area.

Area of the sector of C1 = (cos⁻¹(7.5/14)/360)π9² = 40.72 cm²

Area of the sector of C2 = (cos⁻¹(5.5/15)/360)π6² = 21.52 cm²

Area of the sector of C3 = (cos⁻¹(7/11)/360)π5² = 11.01 cm²

The shaded area enclosed between the circles is the sum of the above three area of sector subtracted from the area of triangle C1C2C3:

Shaded area = 73.48 - 40.72 -21.52 - 11.01 = 0.23 cm²

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Mean is NOT a value in the 5-number summary among the given options..

In descriptive studies or during the first exploration of a big data set, a five-number summary is very helpful. The maximum and lowest values, the median, the lower and upper quartiles, and the most extreme values in the data set make up a summary.

Comparisons may be made between five summaries of numbers. We shall see that two sets with comparable means and standard deviations may have summaries of five numbers that are substantially different. A normal probability plot, often known as a box and whiskers graph, can be used to quickly compare two five-number summaries.

5-number summary consists of : Min, Q₁, Median, Q₃, and Max

Thus, mean is not a value in the 5-number summary

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The complete question is as follows:

Answer:

Hence, 1 divided by 2 is 0.5. So, the correct answer is “0.5”

plse mark me as a brainalist

The required distance from the base of the lighthouse to the sailboat is 11 feet.

Let x be the distance from the base of the lighthouse to the sailboat.

We know that the angle of depression is 6° and the height of the observer is 104 ft. We can use the tangent function to find the ratio of the opposite side (x) to the adjacent side (104 ft).

tan(6°) = x / 104

To find x, we can multiply both sides by 104:

x = 104 × tan(6°)

x = 104 × 0.10510

x = 10.9308

x ≈ 11

The value of x ≈ 11 is the distance from the base of the lighthouse to the sailboat.

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Answer:

The value of b in the equation x^2+bx+c=0 can be found using the quadratic formula. The quadratic formula states that the roots of the equation are given by:

x = (-b ± √(b^2 - 4ac))/2a

Where a = 1, since the coefficient of x^2 is 1, b = b and c = c.

Step-by-step explanation:

Given that the roots of the equation are -4 and 2, we can substitute these values for x into the equation and solve for b.

For the first root of -4, we get:

1x^2 + bx + c = (1)(-4)^2 + b(-4) + c = 0

This simplifies to:

16 - 4b + c = 0

For the second root of 2, we get:

1x^2 + bx + c = (1)(2)^2 + b(2) + c = 0

This simplifies to:

4 + 2b + c = 0

Now we have two equations with two unknowns, we can use the substitution method to find the value of b.

By equating the two equation we get:

16 - 4b + c = 4 + 2b + c

We can simplify it as:

12 - 2b = 0

therefore b = 6

In summary, the value of b in the equation x^2+bx+c=0 is 6 when the roots of the equation are -4 and 2.

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4 and 2 have only one polynomial, which is [tex]x^2-6x+8[/tex]

If a polynomial has two real zeros, then it will be a Quadratic polynomial. A quadratic polynomial is a polynomial that has a degree of two. Zeros of a Quadratic polynomial can be found by two methods, 1. Splitting the middle term 2. Quadratic formula. In this question, zeros are given for this we will use the reverse of splitting the middle term.

4 and 2 are two zeros of a polynomial. It can be represented as:

[tex]x=4\\x=2[/tex]

therefore,

[tex]x-4=0\\x-2=0[/tex]

The Above Linear polynomials are a simplified form of a quadratic polynomial. When multiplying both equations, we get:

[tex](x-4)(x-2)=0[/tex]

[tex]=x^2-2x-4x+8[/tex]

[tex]=x^2-6x+8[/tex]

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Answer:

x = 19.425

Step-by-step explanation:

x = (asin(B)) / (sin(B))

x = (21sin(61∘)) / (sin(71∘))

x = 19.425 cm

a) The mean and the standard deviation of the proportion of 50 randomly-selected songs that are Beatles songs are given as follows:

b) The probability that more than 30% of the 50 songs are Beatles songs is given as follows: 0.2594 = 25.94%.

c) The mean and the standard deviation of the proportion of 40 randomly-selected songs that are Beatles songs are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For item a, the sample size and the proportion are given as follows:

n = 50, p = 0.26.

Hence the mean and the standard error are given as follows:

(using the third bullet point, about the Central Limit Theorem).

The probability that the proportion is above 30% is one subtracted by the p-value of Z when X = 0.3, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (0.3 - 0.26)/0.062

Z = 0.645.

Z = 0.645 has a p-value of 0.7406.

(halfway between Z = 0.64 and Z = 0.65 on the z-table appended at the end of the answer).

1 - 0.7406 = 0.2594 = 25.94%.

For item c, the sample size and the proportion are given as follows:

n = 40, p = 0.33.

Hence the mean and the standard error are given as follows:

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The value of x which makes ΔABC congruent to ΔDEF is 12.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

ΔABC is congruent to ΔDEF

This means,

∠A = ∠D ____(1)

∠B = ∠E ____(2)

∠C = ∠F _____(3)

Now,

From (1),

42 = 4x - 6

42 + 6 = 4x

48 = 4x

x = 48/4

x = 12

From (2),

7x + 10 = 94

7x = 94 - 10

7x = 84

x = 12

Thus,

The value of x is 12.

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Therefore , the required probability is therefore 1/151200, which is the answer to the probability problem.

The probability that a happening will happen or that the proposition is true is determined by a field of mathematics known as probability theory. A probability is a number between 0 and 1, where 1 represents certainty and 0 roughly represents the likelihood that an event will occur. A probability is a numerical expression of a certain event's likelihood or chance of happening. The percentages 0% - 100% and 0 to 1 can also be used to express probabilities. the percentage of times in an ideal collection of equally likely alternatives that an event occurs compared to all possible outcomes.

Here,

The six numbers can only be chosen in one way if the order chosen must match my phone number.

In 10P6 methods, six random digits from a possible total of ten can be chosen.

So the necessary probability is equal to 1/P. (10,6).

Alternative: Probability = 1/151200

The required probability is therefore 1/151200, which is the answer to the probability problem.

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Therefore , the solution of the given problem of ratio comes out to be 2:3 for the following cylinder and sphere.

An order pair of values "a" and "b" can be expressed with the straightforward formula "a / b," with "b" must be no bigger than zero. A ratio is created by adding two ratios together. In the event when there was only one guy and three women, the proportion might be shown as 1:3. 1/4 of the group are guys, and 3/4 are girls. A part can be a statistic, a portion of a thing's volume, or a division among two or more things.

Here,

Here, a sphere is engraved within a cylinder of height h=2r.

Sphere volume =>

4/3πr³.

and Cylinder Volume =πr²h = πr²(2r) = πr³

Volume of the sphere divided by the volume of the cylinder is equal to or greater than

=>4πr³/ 3×2πr³

=>2:3

Therefore , the solution of the given problem of ratio comes out to be 2:3 for the following cylinder and sphere.

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both the equation both equations are similar and they may or may not be equivalent.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Given equation (2d) / (d/r1) + (d/r2)

and (r1t1 + r2t2) / (t1 +t2)

Taking LCM: 2d/(dr2) (dr1) / r1r2

The product 2r1r2/ r1+r2

So both the equation equations are similar and they may or may not be equivalent.

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On solving the provided question, we can say that integral  =  [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt  =   [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.

integral

Curves, x = t³ or,

 = 3t²

y = t⁴ or,

  = 4t³  

Now, the line integral along C will be:

→  =  [tex]\int\limits^a_b \,[/tex]√(3t²)² + (4t³)² dt

            =  [tex]\int\limits^a_b \,[/tex]√9t⁴ + 16t⁶ dt

            =  [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt

           =  [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt

            =  [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt

            =   [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)

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The relationship between p(a), p(b) and p(a > b) is that p(a) + p(b) - p(a > b) = 1, meaning the probability of having at least one of the two types of cards is equal to the sum of the individual probabilities minus the probability of having both.

A. No, it could not be the case that p(a > b) = 0.5. This is because

p(a) + p(b) = 1,

so p(a > b) = 1 - p(a) - p(b)

= 1 - 0.6 - 0.4

= -0.1, which is not a valid probability.

B. The probability that the selected student has at least one of these two types of cards is

p(a) + p(b) - p(a > b)

= 0.6 + 0.4 - 0.3

= 0.7.

C. The probability that the selected student has neither type of card is 1 - (p(a) + p(b) - p(a > b))

= 1 - 0.7

= 0.3.

D. The relationships among p(a), p(b), and p(a > b) can be summarized by the equation p(a) + p(b) - p(a > b) = 1. This equation states that the probability of having atleast one type of card is equal to the sum of the probabilities of having a Visa card and a Mastercard minus the probability of having both types of card.

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The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.

z1 = (8181-7676)/55 = 1.89

z2 = (8686-7676)/55 = 3.04

Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.

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Length of the person's shadow is 3.75 feet.

Consider triangle as shown, segment DE represent the person standing, A represent the location of light, 22 feet away from ground, BC. The shadow's length would be the length of CE.

In triangle ABC and triangle DEC, ∠C is common, and ∠CBA = ∠CED = 90°. So by AA criterion, the triangles are similar. Thus

BC/ CE = AB/ DE

(BE + CE)/CE = AB/ DE

1 + BE/CE = AB/ DE

1 + 10/CE = 22/6

10/CE = 16/6 = 8/3

CE = (10 × 3)/8

CE = 3.75

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According to the formula of area of rectangle, the smallest perimeter possible to enclose this area is 60 and the length is 24 and the breadth is 6.

The general formula to calculate the area of rectangle is written as

A = l x b

And the perimeter of rectangle is written as.

P = 2(l + b)

Where l refers the length of the rectangle and b refers the breadth of the rectangle.

Here we know that the four-sided rectangular pen with an area of 144 square feet.

So, here we have to substitute the value of the formula, then we get,

=> l x b = 144

=> b = 144/l --------------------(1).

Here we have to substitute this one on the perimeter then we get,

=> 2(l + b) = 30

=> 2(144/l + l) = 30

=> 144/l + l = 15

=> l² - 15l + 144 = 0

When we factorize this one then we get the value of l as 24.

Then the value of the width is calculated as,

=> l = 144/ b

=> b = 144/24

=> 6

Then the perimeter us calculated as,

=> P = 2(24 + 6)

=> P = 60.

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The curvature of the curve r(t) = (9t, t², t³) at the point (9, 1, 1) is (3/ 800)√(91/ 94).

The curvature of a curve at a given point is a measure of how much the curve is bending at that point. In order to find the curvature of a curve, we need to first find the unit tangent vector, the unit normal vector, and the unit binormal vector at the point in question.

Given r(t) = (9t, t², t³) at the point (9, 1, 1). Thus t = 1 at (9, 1, 1).

The unit tangent vector at the point (9, 1, 1) is given by the derivative of r(t) with respect to t, evaluated at t = 1

r'(t) = (9, 2t, 3t²)

so T(t) = r'(1) = (9, 2, 3)

The magnitude of T(1) = √(9² + 2² + 3²) = √(94)

The unit tangent vector at (9, 1, 1) is T(1) = (9/√(94), 2/√(94), 3/√(94))

The unit normal vector, N(1), is given by the derivative of T(1) with respect to t, evaluated at t = 1

T'(t) = (0, 2, 6t)

T'(1) = (0, 2, 6)

The magnitude of T'(1) = √(0² + 2² + 6²) = √(40)

The unit normal vector at (9, 1, 1) is N(1) = (0, 2/√(40), 6/√(40))

The unit binormal vector, B(1), is given by the cross product of T(1) and N(1)

B(1) = T(1) × N(1)

= (18/√(40×94), 6/√(40×94), -54/√(40×94))

|B| = (3/2)√(91/ 235)

Finally, the curvature, k, at the point (9, 1, 1) is given by the magnitude of T'(1)

[tex]k = \frac{|B|}{|T|^3}[/tex]

k = (3/2)√(91/ 235)/ (√40)³ = (3/ 800)√(91/ 94)

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The estimated amount of paint needed for the grain silo is 103.61 m².

The cylinder and the conical lid are the two components that make up the figure. As a result, we solve for the total surface area of the cylinder and the cone and add.

TSA for cylinder = 2πr (h + r), for h = 6.2 m and r = 1.7 m.

= 2π * 1.7 (6.2 + 1.7)

= 84.38

TSA for cone = πr (l + r), for l = slant height = 1.9 m and r = 1.7,

resulting in a value = π * 1.7 (1.9 + 1.7) = 19.23

TSA for the cone plus TSA for the cylinder equals how much paint is needed.

how much paint needed = 84.38 + 19.23

how much paint needed = 103.61 m²

The volume of paint to be used depends on the thickness of the painting.

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So, the coach could have participated in at least 14 handshakes.

The total number of handshakes is the sum of the handshakes between gymnasts from different teams and the handshakes between gymnasts from the same team and the coach.

The coach shakes hands with each gymnast from her own team, so the number of handshakes between the coach and gymnasts is equal to the number of gymnasts on the team.

Let's assume the number of gymnasts on a team is x. And the number of teams is y. So the number of handshakes between gymnasts from different teams is x*(x-1)*y/2.

Given the total number of handshakes is 281, we know that:

x*(x-1)*y/2 + x = 281

In order to get the minimum number of handshakes the coach could have participated in, we can assume the maximum number of gymnasts on a team, which is x = 14.

So the equation becomes:

1413y/2 + 14 = 281

So we can find the value of y by solving this equation:

y = (281-14)/(13/2) = 17

Therefore, with x = 14 and y = 17, the minimum number of handshakes the coach could have participated in is 14, which is the number of gymnasts on the team.

So the coach could have participated in at least 14 handshakes.

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