(a) How many forks should Kathy plan to
have if she expects there will be 20
guests? Show how you arrived at your
answer.

The amount of metal needed to make a can is 78.5.

The surface area of a cylinder is the sum of the areas of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

Surface area = 2πr² + 2πrh

where r is the radius of the circular base, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.

The first term in the formula, 2πr², represents the area of both circular bases. The second term, 2πrh, represents the area of the curved surface of the cylinder.

The surface area of the can can be calculated as,

Area = 2πrl

Area = 2π( 2.5 x 5)

Area = 78.5 inches²

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Answer:

The formula for the volume of the cylinder is =²ℎ, which is equivalent to =²ℎ, where is the radius of the cylinder, is the diameter of the cylinder, and ℎ is the height of the cylinder. Therefore, the correct answer is d. V=pix^2.

Step-by-step explanation:

The experimental probability that the coin will land tails up on the next flip is given as follows:

p = 9/26.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the experimental probability that the coin will land tails up on the next flip is given as follows:

p = 18/52 = 9/26.

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Answer:

The product of 5 and an odd number will end in a 5.

For x = 0, 1, 2, 3,....., 5(2x + 1) = 10x + 5

So, four days of the week have an even number of letters. { Monday (6 letters), Tuesday (7 letters), Friday (6 letters), Sunday (6 letters)

An even number is one that can be divided by two and leaves a residue of zero. Even numbers include 2, 4, 6, 8, 10, and so on. Even numbers are ones that can be split into two equal parts, but odd numbers cannot be divided into two equal parts.  Odd numbers are those that cannot be equally divided by two.

It cannot be equally split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers.

The days of the week with an even number of letters are:

Monday (6 letters)

Tuesday (7 letters)

Friday (6 letters)

Sunday (6 letters)

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The null hypothesis and conclude that the average number of months looking for jobs after graduation is different for GMU and University of Alaska students with 95% confidence.

H0: The average number of months looking for jobs after graduation is the same for GMU and University of Alaska students. Ha: The average number of months looking for jobs after graduation is different for GMU and University of Alaska students.

alpha = 0.05

df = ngmu + nua - 2 = 198 (degrees of freedom)

t* = t(0.025, 198) = 1.972 (from t-distribution table)

SE = sqrt[(sgmu^2/ngmu) + (sua^2/nua)] = sqrt[(2.1^2/100) + (2.3^2/100)] = 0.324

tobt = (xgmu - xua) / SE = (3.6 - 2.7) / 0.324 = 2.77

Since tobt (2.77) > t* (1.972), we reject the null hypothesis and conclude that the average number of months looking for jobs after graduation is different for GMU and University of Alaska students with 95% confidence.

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The angle at which the brace meets the wall is approximately 56.51 degrees.

To calculate the angle at which the brace meets the wall at a construction site, we can use the right triangle trigonometry. Here, the brace is the hypotenuse of a right-angled triangle, with the distance from the wall to the lower end of the brace being one of the legs. We will use these terms: construction, brace, and angle in our explanation.

Step 1: Identify the given measurements
- Length of the brace (hypotenuse) = 9.6 m
- Distance from the wall to the lower end of the brace (adjacent leg) = 5.3 m

Step 2: Use the cosine function to find the angle
cos(angle) = adjacent leg / hypotenuse
cos(angle) = 5.3 m / 9.6 m

Step 3: Calculate the angle using the inverse cosine function
angle = cos^(-1)(5.3 m / 9.6 m)

Step 4: Find the angle using a calculator
angle ≈ cos^(-1)(0.5521) ≈ 56.51°

So, at the construction site, the angle at which the brace meets the wall is approximately 56.51 degrees.

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This suggests that the Poisson distribution may not be a good tool for predicting the actual results in this case.

To find the Poisson probabilities, we first need to find the mean number of homicides per city-year:

Mean = total number of homicides / total number of city-years

Mean = 77/280

Mean = 0.275

a. P(0) = e^(-0.275)*0.275^0 / 0!

P(0) = 0.7597

b. P(1) = e^(-0.275)*0.275^1 / 1!

P(1) = 0.2089

c. P(2) = e^(-0.275)*0.275^2 / 2!

P(2) = 0.0286

d. P(3) = e^(-0.275)*0.275^3 / 3!

P(3) = 0.0025

e. P(4) = e^(-0.275)*0.275^4 / 4!

P(4) = 0.0002

To compare the actual results to the expected Poisson probabilities, we can calculate the expected number of city-years for each number of homicides using the Poisson mean of 0.275:

Expected number of city-years with 0 homicides:

E(0) = 280 * P(0)

E(0) = 213.12

Expected number of city-years with 1 homicide:

E(1) = 280 * P(1)

E(1) = 58.64

Expected number of city-years with 2 homicides:

E(2) = 280 * P(2)

E(2) = 8.13

Expected number of city-years with 3 homicides:

E(3) = 280 * P(3)

E(3) = 0.71

Expected number of city-years with 4 homicides:

E(4) = 280 * P(4)

E(4) = 0.05

We can see that the actual results do not match the expected results very closely. For example, there were 213 city-years with 0 homicides, but the expected number was 213.12. Similarly, there were 8 city-years with 2 homicides, but the expected number was only 8.13. This suggests that the Poisson distribution may not be a good tool for predicting the actual results in this case.

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On solving this trigonometry, we find that (a) sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{13}{5}[/tex] and (b) tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{12}{5}[/tex]

(a) To find the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that sec(x) = [tex]\frac{1}{cos}[/tex](x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:

a² + b² = c²

a² + 12² = 13²

a² = 169 - 144

a = √25

a = 5

So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹  [tex]\frac{12}{13}[/tex]) by looking at the adjacent/hypotenuse ratio in this triangle:

cos(sin⁻¹ [tex]\frac{12}{13}[/tex]) =  [tex]\frac{5}{13}[/tex]

Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ [tex]\frac{12}{13}[/tex])

                                            = 1/[tex]\frac{5}{13}[/tex]

                                            = [tex]\frac{13}{5}[/tex].

So the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{13}{5}[/tex].

(b) To find the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.

Then sin(sin⁻¹ [tex]\frac{12}{13}[/tex])=  [tex]\frac{12}{13}[/tex] and cos  [tex]\frac{12}{13}[/tex]) = [tex]\frac{5}{13}[/tex]  , so

tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = sin(sin⁻¹ [tex]\frac{12}{13}[/tex])/cos(sin⁻¹[tex]\frac{12}{13}[/tex])

                        = [tex]\frac{12}{13}[/tex] / [tex]\frac{5}{3}[/tex]

                        = [tex]\frac{12}{5}[/tex]

So the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{12}{5}[/tex].

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The balance of this account be at the end of 2 years is $3,276.075.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]A(2) = 3000(1 + \frac{0.045}{1})^{1 \times 2}\\\\A(2) = 3000(1.045)^{2}[/tex]

Future value, A(2) = $3,276.075

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The answer for the following inequality expressed in interval notation is (-77/3, infinity)

To solve the inequality 2x - 75 < 5x + 2,

we need to isolate the variable x on one side of the inequality sign.

Starting with 2x - 75 < 5x + 2:

Subtracting 2x from both sides:
-75 < 3x + 2

Subtracting 2 from both sides:
-77 < 3x

Dividing both sides by 3 (and flipping the inequality sign because we are dividing by a negative number):
x > -77/3

So the solution to the inequality is x > -77/3.

Expressing this in interval notation, we have:

(-77/3, infinity)

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Answer:

To find the dimensions of the actual painting, we need to use the scale factor of 4:1. This means that the actual dimensions of the painting are four times larger than the scaled dimensions.

Let's start with the width of the actual painting:

8 inches (scaled width) × 4 = 32 inches (actual width)

Now, let's find the height of the actual painting:

10 inches (scaled height) × 4 = 40 inches (actual height)

Therefore, the dimensions of the actual painting are 32 inches by 40 inches.

Answer:

The answer is 1.) 13/85

Step-by-step explanation:

Triangle MCT is a right triangle because angle T = 90°

So to find the sine of an angle, you need the opposite of that angle/hypotenuse.

Since M is at the beginning of the triangle, MCT is at the top. C is in the middle, so it is at the end, and t is the right angle. That makes MC the hypotenuse because it is the longest side of the triangle, and TM would be the opposite angle.

To find sine, you need the opposite/hypotenuse. So the answer is 13/85.

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The 6 criteria are Internal consistency, Contextual consistency, Intelligibility, Mathematical plausibility, Historical plausibility and Replicability.

According to Eleanor Robson's interpretation of Plimpton 322, she lists six criteria for interpreting ancient mathematical texts. These six criteria are as follows:
1. Internal consistency: The mathematical text should be internally consistent and coherent in its logic.
2. Contextual consistency: The mathematical text should be consistent with the historical and cultural context in which it was written.
3. Intelligibility: The mathematical text should be understandable and intelligible to the intended audience.
4. Mathematical plausibility: The mathematical content of the text should be mathematically plausible and in line with known mathematical principles.
5. Historical plausibility: The mathematical text should be historically plausible and fit within the known historical context.
6. Replicability: The mathematical text should be replicable, meaning that other mathematicians should be able to reproduce the calculations and results presented in the text.

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The linear function for the given statement is y = (-1/2)x + 6.

To write a linear function for the statement "A candle is 6 inches tall and burns at a rate of 1/2 inch per hour," we will need to use the slope-intercept form of a linear function, which is y = mx + b. In this case, y represents the remaining height of the candle, m represents the rate of burning, x represents time in hours, and b represents the initial height of the candle.

Step 1: Identify the initial height (b). The candle is 6 inches tall, so b = 6.

Step 2: Identify the rate of burning (m). The candle burns at a rate of 1/2 inch per hour, so m = -1/2 (negative because the height decreases as time passes).

Step 3: Write the linear function using the slope-intercept form y = mx + b. Substitute the values of m and b:
y = (-1/2)x + 6

Thus, we can state that the linear function for the given statement is:

y = (-1/2)x + 6.

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The probability is approximately 0.0549 or 5.49%. So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.

To answer your question, we'll use the concept of probability. In this case, we want to find the probability that all three randomly selected homes in the Quail Creek area have a security system.

1. First, determine the probability that the first home has a security system:
There are 5 homes with security systems out of 14 total homes, so the probability is 5/14.

2. Next, determine the probability that the second home also has a security system:
Since one home with a security system has been "selected," there are now 4 homes with security systems out of the remaining 13 homes. So, the probability is 4/13.

3. Finally, determine the probability that the third home has a security system:
Since two homes with security systems have been "selected," there are 3 homes with security systems left out of the remaining 12 homes. So, the probability is 3/12, which simplifies to 1/4.

4. Multiply the probabilities from steps 1, 2, and 3 to get the probability that all three selected homes have a security system:
(5/14) * (4/13) * (1/4) = 20/364.

5. Round your answer to 4 decimal places:
The probability is approximately 0.0549 or 5.49%.

So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.

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Answer:

Let x be the length of Danika's old running route in miles.

Then, her new running route can be represented by x + 4, since it is 4 miles longer than her old route.

Step-by-step explanation:

The points of inflection are (0, 3π), (π, 4π), and (2π, 9π).

To find the maximum/minimum and inflection points of the function y = 5 sin x + 3x, we need to take the first and second derivatives of the function with respect to x, and then find the critical points and points of inflection by setting these derivatives equal to zero.

First derivative:

y' = 5 cos x + 3

Setting y' = 0 to find critical points:

5 cos x + 3 = 0

cos x = -3/5

Using a calculator or reference table, we can find the two values of x between 0 and 2π that satisfy this equation: x ≈ 2.300 and x ≈ 3.840.

Second derivative:

y'' = -5 sin x

At x = 2.300, y'' < 0, so we have a local maximum.

At x = 3.840, y'' > 0, so we have a local

To check whether these are global maxima/minima, we need to examine the behavior of the function near the endpoints of the interval 0 < x < 2π.

When x = 0, y = 0 + 0 = 0.

When x = 2π, y = 5 sin (2π) + 6π = 6π, since sin(2π) = 0.

So the function is increasing on the interval [0, 2.300], reaches a local maximum at x = 2.300, is decreasing on the interval [2.300, 3.840], reaches a local minimum at x = 3.840, and then is increasing on the interval [3.840, 2π]. Therefore, the maximum value of the function occurs at x = 2π, where y = 6π, and the minimum value of the function occurs at x = 3.840, where y ≈ 1.221.

To find the points of inflection, we set y'' = 0:

-5 sin x = 0

This equation is satisfied when x = 0, π, and 2π. We can use the second derivative test to determine whether these are points of inflection or not.

At x = 0, y'' = 0, so we need to examine the behavior of the function near x = 0.

When x is close to 0 from the right, y is positive and increasing, so we have a point of inflection at x = 0.

At x = π, y'' = 0, so we need to examine the behavior of the function near x = π.

When x is close to π from the left, y is negative and decreasing, so we have a point of inflection at x = π.

At x = 2π, y'' = 0, so we need to examine the behavior of the function near x = 2π.

When x is close to 2π from the right, y is positive and increasing, so we have a point of inflection at x = 2π.

Therefore, the points of inflection are (0, 3π), (π, 4π), and (2π, 9π).

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To find the average number of bits required to encode this source using a Huffman code, we need to first construct the Huffman code for the given probabilities. The Huffman code assigns shorter codes to more probable values and longer codes to less probable values. We can start by listing the probabilities in descending order:

0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1

Next, we group the two least probable values and assign them a code of 0. We then repeat this process, grouping the next two least probable values and assigning them a code of 10. We continue until we have assigned codes to all values:

7: 0
1: 1000
2: 1001
3: 1010
4: 1011
5: 110
6: 111

We can see that the average number of bits required to encode this source using the Huffman code is:

(0.2 x 1) + (0.1 x 4) + (0.1 x 4) + (0.15 x 4) + (0.15 x 4) + (0.15 x 3) + (0.2 x 3) = 2.771 bits

Therefore, the correct answer is b) 2.771 bits.
To find the average number of bits required to encode this source using a Huffman code, follow these steps:

1. Arrange the probabilities in descending order: 0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1.

2. Build the Huffman tree:
- Combine the two smallest probabilities (0.1 and 0.1) into a single node with a probability of 0.2.
- Combine the next two smallest probabilities (0.15 and 0.15) into a single node with a probability of 0.3.
- Combine the next smallest probability (0.2) with the previously created 0.2 nodes to create a node with a probability of 0.4.
- Combine the remaining 0.3 and 0.4 nodes to create the root node with a probability of 0.7.

3. Assign binary codes to each value based on the Huffman tree:
- Value 1: 111
- Value 2: 110
- Value 3: 101
- Value 4: 100
- Value 5: 011
- Value 6: 010
- Value 7: 00

4. Calculate the average number of bits required to encode the source using the assigned binary codes and their probabilities:
- (3 * 0.1) + (3 * 0.1) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (2 * 0.2) = 0.9 + 0.9 + 1.35 + 1.35 + 0.4 = 2.771 bits

So, the average number of bits required to encode this source using a Huffman code is 2.771 bits, which corresponds to option (b).

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Answer:

6.03

Step-by-step explanation:

In math terms, we can model the area left when cutting a circle out of a triangle as subtracting the area of a circle inscribed in a triangle.

There was only one side length of the triangle given (its base), so we can assume that it is an isosceles triangle with the given height.

To find the radius of the triangle, we can use the formula:

r = (A / s)

where r is the radius of the inscribed circle, A is the area of the triangle, and s is the semiperimeter (half-perimeter) of the triangle.

Finding the area of the triangle:

A = (1/2) * b * h

A = (1/2) * 6 * 5

A = 15

Finding the length of the congruent sides of the triangle:

[tex]a^2 + b^2 = c^2[/tex]

[tex]c^2 = 5^2 + 3^2[/tex]

[tex]c^2 = 34[/tex]

[tex]c \approx 5.83[/tex]

Finding the semiperimeter:

s = (side1 + side2 + side3) / 2

s = (5.83 + 5.83 + 6) / 2

s ≈ 8.83

Plugging these values into the radius formula:

r = A / s

r = 15 / 8.83

r ≈ 1.69

From here, we can get the area of the circle cutout:

A(circle) = πr²

A(circle) = π(1.69)²

A(circle) ≈ 8.97

Finally, we can get the leftover area by subtracting the area of the circle from the area of the triangle:

A = A(triangle) - A(circle)

A = 15 - 8.97

A = 6.03

The Independent Variables for a 2x2, factorial, between subjects ANOVA are the two IVs, each of which has two levels. The conditions (levels) for each IV are completely related. There are four cells in total, and each participant has a score in each of the four cells.

In a 2x2 factorial, between-subjects ANOVA, there are two Independent Variables (IVs), each with two levels. The IVs are factors that the researcher manipulates to examine their effect on the Dependent Variable (DV). The four cells represent the unique combinations of the two IVs, and each participant is assigned to only one cell, where they receive a score on the DV. The conditions (levels) of each IV are completely related, meaning they are fully crossed with each other, resulting in a balanced design.

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B. The data shows a positive, linear association.

To determine the association between height and weight of the ten boys, we will first observe the data points provided. We can compare the increase or decrease in height with the corresponding increase or decrease in weight to identify a pattern.

Here's a list of height and weight pairs:
(60, 125), (63, 139), (65, 155), (61, 136), (70, 170), (55, 108), (58, 116), (61, 139), (64, 129), (57, 121)

Upon observing these pairs, we can see that as height increases, weight generally increases as well. For example, when height increases from 55 inches to 70 inches, weight increases from 108 pounds to 170 pounds. This pattern can also be seen in other data pairs.

This means that there is a direct relationship between the height and weight of the boys, where taller boys tend to weigh more, and shorter boys tend to weigh less.

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The time it would take to run 625,000 miles depends on several factors such as the speed at which one is running and how often they take breaks.

Assuming a constant speed of 6 miles per hour, which is a moderate running pace, it would take approximately 104,166.67 hours or 4,340.28 days or 11.89 years to run 625,000 miles without taking any breaks. However, in reality, one would need to take breaks for rest and recovery, so the actual time it would take to cover this distance would be longer.

Assuming a constant speed of 6 miles per hour, it would take approximately 104,166.67 hours to run 625,000 miles without taking any breaks. This equates to 4,340.28 days or 11.89 years. However, in reality, taking breaks for rest and recovery is necessary, so the actual time it would take to cover this distance would be longer.

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The rationalizable strategies for two law partners sharing a firm equally in revenue are s1'=s2'=1/(1-b) which is a Nash equilibrium, and if they agree to work the same amount, they should choose s'=4/(2+b) to maximize net revenue.

To find the rationalizable strategies, we first need to find the best response of each player to the other's strategy. The best response of player 1 to player 2's strategy s2 is given by:

s1 = argmax u1(s1, s2)

Taking the derivative of u1 with respect to s1 and setting it equal to zero, we get:

4(1 + bs2) - 2s1 = 0

Solving for s1, we get:

s1 = 2(1 + bs2)

Similarly, the best response of player 2 to player 1's strategy s1 is given by:

s2 = 2(1 + bs1)

Using the rationalizability criterion, we delete any strategy that is not the best response to some other strategy. We repeat this process until no further strategies can be deleted. In this case, we see that the only strategies that survive this process are those where s1 = s2 = 1/(1-b). Therefore, these are rationalizable strategies.

To check if this is a Nash equilibrium, we need to verify that neither player has an incentive to deviate from this strategy. If both players play s1 = s2 = 1/(1-b), the revenue of the firm is 4(2/(1-b) + b/(1-b)²)².

If player 1 deviates and chooses a higher effort level, the revenue of the firm decreases because player 2 will choose a lower effort level in response.

Therefore, player 1 has no incentive to deviate. Similarly, player 2 has no incentive to deviate. Therefore, (s1', s2') = (1/(1-b), 1/(1-b)) is a Nash equilibrium.

If the partners agree to work the same amount, they should choose the effort level that maximizes the revenue net of total effort costs. The total effort cost is given by s², and the net revenue is given by:

R = 4(s + bs²)² - 2s²

Taking the derivative of R with respect to s and setting it equal to zero, we get:

8s(1 + bs²) - 4s² = 0

Solving for s, we get:

s' = 4/(2 + b)

This is greater than the rationalizable effort level of s1' = s2' = 1/(1-b).

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The surface area is 2302.8 sq. ft.

The surface area of a given object implies the sum or total area of all its individual surfaces.

In the given question, the object has trapezoidal and rectangular surfaces. So that;

i. area of the trapezoidal surface = 1/2(a + b)h

                                      = 1/2 (10 + 34) 24.7

                                      = 1/2(44)24.7

                                      = 22*24.7

                                      = 543.4

area of the trapezoidal surface is 543.4 sq. ft.

ii. area of rectangular surface 1 = length x width

                                              = 10 x 19

                                              = 190 sq. ft.

iii. area of rectangular surface 2 = length x width

                                                   = 19 x 27

                                                   = 513

The surface area of the object = (2*543.4) + 190 + (2*513)

                                                   = 2302.8

The surface area of the object is 2302.8 sq. ft.

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The answers are explained in the solution.

Given is a circle F,

The central angle = ∠GFH

The semicircle = arc GJI

The major arc = arc GJH

Since, the measure of semicircle is 180°, therefore,

The semicircle = arc GJI = 180°

We know that the measure of arc intercepted by the central angle is equal to the measure of the central angle.

Therefore, ∠GFH = 125°

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Answer:

There is enough sufficient evidence to support the claim.

Step-by-step explanation:

There is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method. The conclusion is that utilizing the new CAI training approach, it takes much less time on average to obtain a basic driving license than it does using the conventional method.

To determine if the new license training method using computer aided instruction (CAI) performs differently than the traditional method, we need to conduct a hypothesis test. Let's define the null and alternative hypotheses as follows:

Null hypothesis (H0): The mean time to receive a basic driving license using the new CAI training method is equal to the mean time using the traditional method, i.e., μ = 99.

Alternative hypothesis (Ha): The mean time to receive a basic driving license using the new CAI training method is different from the mean time using the traditional method, i.e., μ ≠ 99.

We are given that the sample size is 260, the sample mean is 98, and the population standard deviation is 7. We can use a z-test to test the hypothesis since the sample size is large (n > 30).

The test statistic can be calculated as:

z = (x - μ) / (σ / √n) = (98 - 99) / (7 / √260) = -2.475

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

The corresponding p-value for a two-tailed test is 0.013, which is less than the level of significance of 0.1. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method.

In other words, the mean time to receive a basic driving license using the new CAI training method is significantly different from the mean time using the traditional method.

Learn more about hypothesis at https://brainly.com/question/14747545

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Answer:  We will see that the function is f(x) = 0.559*ln(x)

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

3x - y + 1 =0

d/dx (3x) - dy/dx + d/dx (1) = 0

dy/dx = 3

y = x2 + 4x - 16

dy/dx = 2x + 4

Hence

2x + 4 = 3

x= 3-4/2 = -1/2

at x = -1/2y = (-1/2)2 + 4 (-1/2) - 16 = 1/4 -2 -16

y = -71/4

so the point p (-1/2, -71/4)

equation of tangent

y - (-71/4) = 3 (x-(-1/2))

y + 71/4 = 3 ( x + 1/2)

3x - y = 71/4 - 3/2 = 71-6/4 = 65/4

12x - 4y = 65.

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Hi, I'm glad to help you with this question. To determine if the normal distribution gives a reasonable approximation using the given data, we need to calculate the mean and standard deviation. Here are the steps:

1. Calculate the mean (average): Add all the data points together and divide by the number of data points.
(71+42+77+84+46+93+94+63+82+88+57+32+79+67+68+83+60+65+58+70) / 20 = 1380 / 20 = 69

Mean = 69

2. Calculate the standard deviation: First, find the difference between each data point and the mean, square the differences, and then find the average of those squared differences. Finally, take the square root of that average.
a. Differences from the mean: (-2, 27, 8, 15, -23, 24, 25, -6, 13, 19, -12, -37, 10, -2, -1, 14, -9, -4, -11, 1)
b. Squared differences: (4, 729, 64, 225, 529, 576, 625, 36, 169, 361, 144, 1369, 100, 4, 1, 196, 81, 16, 121, 1)
c. Average of squared differences: (4520) / 20 = 226
d. Square root of the average: √226 ≈ 15.03

Standard Deviation ≈ 15.03

Now that we have the mean (69) and the standard deviation (15.03), you can compare these values to the distribution line that you draw through the data by eye. If the distribution line follows a bell-shaped curve with the mean at the center and the data points spread around it following the standard deviation, then the normal distribution provides a reasonable approximation for this data set.

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Standard deviation:https://brainly.com/question/475676