a bag contains 16 coins each with a different date. the number of possible combinations of three coins from the bag is

To find the HPD (Highest Posterior Density) interval of 95% of θ, we need to first calculate the posterior distribution of θ using the Beta prior distribution with parameters α = 1 and β = 1, and the observed data of 17 satisfied and 5 not satisfied.

The posterior distribution of θ is also a Beta distribution with parameters α' = α + number of satisfied and β' = β + number of not satisfied. In this case, α' = 1 + 17 = 18 and β' = 1 + 5 = 6.

So, the posterior distribution of θ is Beta(18,6).

To find the HPD interval, we can use a numerical method such as Markov Chain Monte Carlo (MCMC) simulation. However, since the Beta distribution has a closed-form expression for the quantiles, we can use the following formula to calculate the HPD interval:

HPD interval = [Beta(q1,α',β'), Beta(q2,α',β')]

where q1 and q2 are the quantiles of the posterior distribution that enclose 95% of the area under the curve.

Using a Beta distribution calculator or software, we can find that the 0.025 and 0.975 quantiles of Beta(18,6) are approximately 0.633 and 0.898, respectively.

Therefore, the HPD interval of 95% of θ is [0.633, 0.898].

Learn more about HPD interval:

https://brainly.com/question/31435794

#SPJ11

The function that is represented by the graph is -|x - 1| + 8.

Option A is the correct answer.

We have,

The graph of the function - |x - 1| + 8 can be obtained by applying a series of transformations to the graph of the absolute value function, y = |x|.

First, the expression x - 1 inside the absolute value brackets shifts the entire graph of y = |x| one unit to the right.

This means that the "V" shape of the absolute value function is centered at x = 1 instead of x = 0.

Next, the negative sign in front of the absolute value reflects the graph of y = |x| across the x-axis.

This means that the "V" shape is now pointing downwards instead of upwards.

Finally, the entire graph is shifted vertically upward by 8 units due to the constant term + 8.

This means that the lowest point of the "V" shape is at y = 8 instead of

y = 0.

Thus,

The function that is represented by the graph is -|x - 1| + 8.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

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).

Learn more about the Nash equilibrium at

https://brainly.com/question/28903257

#SPJ4

Slope tells us that the rate of change in elevation during Ryan's uphill climb was not constant and Average rate of change is 6.67 per minute

The slope of the elevation-time graph represents the rate of change in elevation during Ryan's uphill climb. In this case, the slope can be calculated as:

Slope = (Change in elevation) / (Change in time)

From the given data, the total elevation change during Ryan's uphill climb is:

Total elevation change = 1500 - 300 = 1200 feet

the slope tells us that the rate of change in elevation during Ryan's uphill climb was not constant.

It varied between 15 feet per minute to -40 feet per minute.

A positive slope indicates an increase in elevation over time, while a negative slope indicates a decrease in elevation over time.

The total elevation change of 1200 feet was achieved over a period of 3 hours (180 minutes), so the average rate of change in elevation was:

Average rate of change = Total elevation change / Total time

= 1200 / 180

= 6.67 feet per minute.

To learn more on slope of line click:

https://brainly.com/question/16180119

#SPJ1

The exact area of the figure is 85.54 m².

The coordinates endpoints of the semicircle are (-3,-4) and (6,2).

∴ Length of the diameter of the circle = distance between the end points of diameter = √[6 -(-3))²+(-4-2)²] = 10.81 m

⇒ The radius of the semicircle = 10.81/2 = 5.45 m

∴ The area of the semicircle = πr²/2 = 3.14 × (5.45)² /2= 46.63 m²

Now one side of the rectangle = diameter of the semicircle

                                                   = 10.81 m

The endpoints of another side of the rectangle are (-3,-4) and (-1,-7)

∴  The length of this side = √[-3 -(-1))²+(-4-(-7)²] = 3.6 m.

∴ The area of the rectangle = product of sides = 3.6 × 10.81 = 38.91 m²

The total area of the figure = area of the semicircle + area of the rectangle

                                       = 46.63 + 38.91 =85.54 m²

Hence, the exact area of the figure is 85.54 m².

For more on the area of circles and rectangles,

https://brainly.com/question/30099567

Alexandra's mixture has a higher percentage of black paint, making it darker than Noah's mixture.

To determine whose gray paint will be darker, we can use the percentage of black paint in each mixture.

Alexandra's mixture contains 2 cups of black paint and 1 cup of white paint. This means that the percentage of black paint in her mixture is 2/(2+1) = 2/3, or about 66.67%.

Noah's mixture contains 3 cups of black paint and 2 cups of white paint. This means that the percentage of black paint in his mixture is 3/(3+2) = 3/5, or about 60%.

Based on these percentages, we can see that Alexandra's mixture has a higher percentage of black paint, making it darker than Noah's mixture. Therefore, Alexandra's gray paint will be darker than Noah's gray paint.

To learn more about quantity click on,

https://brainly.com/question/30525294

#SPJ1

This indicates that the project reduced the student council's savings by $96.

The price of the bags is as follows:

$8 bags x $6 each bag = $48.

Each backpack's paper and pens will set you back $6.

Consequently, the price of the paper and pens for all 8 bags x $6 each = $48.

Consequently, $48 + $48 = $96 is the total cost of the backpacks, paper, and pens.

Therefore, This indicates that the project reduced the student council's savings by $96. Since the project cost $96 to complete, the savings were reduced by that sum.

Learn more about cost here : brainly.com/question/28147009

#SPJ1

Answer:

the midpoint would be (-2,-2)

Step-by-step explanation:

Answer:

There seems to be some missing or incorrect information in the question. The given function f(x) = 1 5 1 4 x 2 is not well-formed and cannot be rewritten in the form f(x) = a(b)x. Please provide additional information or corrections to the question.

Step-by-step explanation:

The after-tax present worth according to the given values is $732,140.56 and the internal rate of return is 22.65%.

(a) To compute the after-tax present worth, we need to determine the net cash flow for each year and discount it to present value using the after-tax MARR of 15%.

Year 0: Initial cost of equipment = -$18,600
Years 1-10:
Revenue from bags = (100.3 bags/carton) x ($0.03/bag) x (200,000 cartons/year) = $120,780
Cost savings from reducing overfilling = (5.5%) x ($0.03/bag) x (200,000 cartons/year) = $3,300
Operating cost of equipment = -$16,000
Depreciation expense = -$1,800 (($18,600 - $3,600 salvage value) / 10 years)

Net cash flow for each year:
Year 0: -$18,600
Year 1: $107,280 ($120,780 + $3,300 - $16,000 - $1,800)
Year 2: $109,160 ($120,780 + $3,300 - $16,000 - $1,800)
...
Year 10: $113,640 ($120,780 + $3,300 - $16,000 - $1,800)

Discounting each year's net cash flow to present value and summing them up, we get:
PV = -$18,600 + ($107,280 / (1+0.15)^1) + ($109,160 / (1+0.15)^2) + ... + ($113,640 / (1+0.15)^10)
PV = -$18,600 + $750,740.56
PV = $732,140.56

Therefore, the after-tax present worth is $732,140.56.

(b) To compute the after-tax internal rate of return, we need to find the discount rate that makes the net present value equal to zero. We can use trial and error or a financial calculator to solve this.

Using trial and error, we find that a discount rate of approximately 22.65% makes the net present value equal to zero. Therefore, the after-tax internal rate of return is approximately 22.65%.

(c) To compute the after-tax simple payback period, we need to determine how long it takes for the cumulative net cash flow to equal the initial cost of the equipment.

Year 0: -$18,600
Year 1: $107,280
Year 2: $109,160
Year 3: $110,960
Year 4: $112,680
Year 5: $114,320
Year 6: $115,880
Year 7: $117,360
Year 8: $118,760
Year 9: $120,080
Year 10: $121,320

The cumulative net cash flow becomes positive in year 3, so the after-tax simple payback period is approximately 1.9 years (between year 2 and year 3).

To learn more about After-tax, visit:

https://brainly.com/question/25790997

#SPJ11

The volume of the tank that is shown here is 282.31

In mathematics, the capacity of a 3D object is denoted by its volume. Volume is typically computed in cubic units like cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³) or cubic inches (in³). Depending on an object's form, various formulas can be used to calculate its volume.

15 - 6 = 9

Radius = 6 / 2

= 3

Then the volume =

4 / 3 π (3)³ + π (3)²6

= 112.75 + 169.56

= 282.31

The volume is 282.31

Read more on volume here:https://brainly.com/question/1972490

#SPJ1

Answer:

Step-by-step explanation:

1/2*b*h

1/2*4*5

4/2*5

2*5

10

The median of the data-set 3, 3, 5, 7, 9, 9, 10, 10 is given as follows:

C. 8.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The data-set for this problem is given as follows:

3, 3, 5, 7, 9, 9, 10, 10.

The data-set has an even cardinality, hence the median is given by the mean of the two middle elements, as follows:

Median = (7 + 9)/2

Median = 8.

The data-set for this problem is given as follows:

3, 3, 5, 7, 9, 9, 10, 10.

More can be learned about the median of a data-set at brainly.com/question/3514929

#SPJ1

The mean of the sampling distribution of means always equals the mean of the underlying raw score population when the sample size is large. This is known as the central limit theorem, which is a fundamental principle in statistics that describes the behavior of sample means.

The central limit theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population means and a standard deviation equal to the population standard deviation divided by the square root of the sample size. This means that the larger the sample size, the more representative the sample mean is of the population mean.

The central limit theorem is important in statistical analysis because it allows us to make inferences about population parameters based on sample data. By calculating the mean and standard deviation of the sampling distribution of means, we can estimate the population means and assess the probability of obtaining certain sample means.

However, it is important to note that the central limit theorem applies only to random samples from a population with finite variance. It may not hold for non-random samples or populations with infinite variances. Additionally, the theorem assumes that the sample means are independent and identically distributed and that the sample size is sufficiently large.

To learn more about Sampling distribution, visit:

https://brainly.com/question/15201212

#SPJ11

The z-score for a patient who takes ten days to recover is 2.24, which is closest to option c. 2.2.

To find the z-score for a patient who takes ten days to recover from a surgical procedure with a mean recovery time of 5.3 days and a standard deviation of 2.1 days, you can use the following formula:

Z-score = (X - μ) / σ

where X is the patient's recovery time (10 days), μ is the mean recovery time (5.3 days), and σ is the standard deviation (2.1 days).

1. Subtract the mean from the patient's recovery time: 10 - 5.3 = 4.7
2. Divide the result by the standard deviation: [tex]\frac{4.7}{2.1} = 2.24[/tex]

The z-score for a patient who takes ten days to recover is approximately 2.24. None of the given options match this value, so the correct answer is not listed.

To know more about the z-score visit:

https://brainly.com/question/31613365

#SPJ11

Based on the given information, it seems that Hector made error A. He placed Puppy 3 at -3.4 instead of at -0.75.

To determine which error Hector made, we need to compare his placements with the correct placements of the puppies on the number line based on the recorded weight changes.

According to the number line-

To know more about  probability, here

https://brainly.com/question/13604758

#SPJ4

Answer:Yes, the Boolean sum is represented as a Boolean product.

Step-by-step explanation:Problem 2. Let A be a 3 × 3 zero-one matrix. Let I be a 3 × 3 identity matrix. Show that A ⊙ I = I ⊙ A = A. Solution. Let. Show that a Boolean function can be represented as a Boolean product of maxterms. This representation is called the product-of-sums expansion or conjunctive normal form of the function. (Hint: Include one maxterm in this product for each combination of the variables where the function has the value 0.)

Step 1: Definition.

The complements of an elements 0=1 and 1=0.

.

The Boolean sum + or OR is 1 if either term is 1.

The Boolean product (.) or AND is 1 if both term are 1.

Step 2: Show the Boolean function can be represented as a Boolean product.

The Boolean sum is

where

or

, has the value 0 for exactly one combination of the values of the variables, namely, when

if

and

if

. This Boolean sum is called a maxterm.

For each combination of the values of the variables for which the Boolean function F is 0.

The Boolean product of maxterms is 0 if and only if at least one of the maxterm is 0. Thus, the Boolean function F can be represented as a Boolean product of the maxterm.

Therefore, the Boolean sum is represented as Boolean products.

To find the Boolean product of A and B, we need to perform a logical AND operation between each corresponding pair of bits in A and B.

Starting with the rightmost bit in B, we have:

1 AND 0 = 0

Next, we have:

1 AND 1 = 1

Then:

1 AND 1 = 1

And finally:

0 AND 1 = 0

So the result of the first column is:

0110

Moving on to the next column, we have:

1 AND 0 = 0

0 AND 1 = 0

1 AND 1 = 1

1 AND 0 = 0

So the result of the second column is:

0000

Continuing on to the third column, we have:

0 AND 0 = 0

1 AND 1 = 1

1 AND 1 = 1

1 AND 1 = 1

So the result of the third column is:

1111

Finally, we have:

1 AND 1 = 1

0 AND 0 = 0

0 AND 1 = 0

1 AND 0 = 0

So the result of the fourth column is:

0000

Putting it all together, the Boolean product of A and B is:

0110
0000
1111
0000

Learn more about Boolean product: https://brainly.com/question/13831313

#SPJ11

The middle value and is not affected by outliers, while the mean represents the average and can be influenced by outliers.

a. To find the median cost of electricity, we need to arrange the bills in order from lowest to highest:

36, 44,54, 65, 80

The median is the middle value, which in this case is 54.

b. To find the mean cost of electricity, we need to add up all the bills and divide by the total number of bills:

(54 + 36 + 80 + 65 + 44) / 5 = 55.80

So the mean cost of electricity is 55.80.

that the median and mean can give different perspectives on the data. The median represents the middle value and is not affected by outliers, while the mean represents the average and can be influenced by outliers.

To learn more about electricity visit:

https://brainly.com/question/12966505

#SPJ11

The general solution of the given differential equation is:
y = (r^(1/2)) * (1 + Ce^(2r^(1/2))) or y = (r^(1/2)) * (-1 + Ce^(2r^(1/2)))
where C is the constant of integration.

To find the general solution of r = y^2 - 1 dr, we need to separate the variables and integrate both sides. We can start by rearranging the equation as:
dr/(y^2 - 1) = dy/r

Now, we can integrate both sides. On the left side, we can use partial fractions to make the integration easier. We can write:
dr/(y^2 - 1) = [1/(2*(y-1))] - [1/(2*(y+1))] dy

Integrating both sides, we get:
1/2 * ln|y-1| - 1/2 * ln|y+1| = ln|r| + C
where C is the constant of integration.

We can simplify this as:
ln|(y-1)/sqrt(r)| - ln|(y+1)/sqrt(r)| = 2C

Using logarithmic properties, we can simplify further as:
ln|[(y-1)/sqrt(r)] / [(y+1)/sqrt(r)]| = 2C
ln|[(y-1)/(y+1)]| = 2C

Exponentiating both sides, we get:
|[(y-1)/(y+1)]| = e^(2C)

Taking the positive and negative cases separately, we get:
(y-1)/(y+1) = e^(2C)

or
(y-1)/(y+1) = -e^(2C)

Solving for y in each case, we get the general solution as:

y = (r^(1/2)) * (1 + Ce^(2r^(1/2))) or y = (r^(1/2)) * (-1 + Ce^(2r^(1/2)))

where C is the constant of integration. This is the general solution of the given differential equation.

To learn more about differential equations visit : https://brainly.com/question/1164377

#SPJ11

The table, we cannot determine the probability of a student participating in exactly two activities.

The probability distribution table is not provided in the question, but assuming that it is a valid probability distribution, we can use it to find the probability that a student participates in exactly two activities.

Let X be the random variable representing the number of extracurricular activities a college freshman participates in, and let p(x) denote the probability of X taking the value x.

Then, we want to find p(2), the probability that a student participates in exactly two activities. This can be obtained from the probability distribution table.

Without the table, we cannot determine the probability of a student participating in exactly two activities.

To learn more about  probability visit:

https://brainly.com/question/30034780

#SPJ11

The volume of the piñata is

The volume is solved using the formula

= area x thickness

The shape is a composite one and the area is solved by

= area of rectangle + area of triangle

= 12 x 12 + 1/2 x 8 x 12

= 144 + 48

= 192 square in

The volume

= 192 x 6

= 1152 cubic in

Learn more about volume at

https://brainly.com/question/1972490

#SPJ1

To find the sum of 6k by adding each term together, we can simply add 6k + 6k + 6k + 6k + 6k + 6k which gives us a total of 36k.

To verify this result using the summation capabilities of a graphing utility, we can use the sigma notation (Σ) to represent the sum. The sigma notation is defined as Σ6k where k starts at 1 and goes up to 6. This means we are adding 6k, six times.

To input this into a graphing utility, we can use the summation feature. For example, on a TI-84 calculator, we can press the "Math" button, select "1:sum(", and enter the expression "6k" followed by a comma and then the values of k that we want to sum from (1) and to (6). This gives us the result of 36k, which matches our previous calculation.

Learn more about graphing utility:

https://brainly.com/question/29260419

#SPJ11

Y follows a negative binomial distribution with parameters r = 3 and p = 0.97.

The moment generating function (MGF) of a random variable X is defined as Mx(t) = E(e^(tX)).

(a) The given MGF is 0.03 Mx(0) t< - log 0.97 1 -0.97e^(tX)

The MGF of the geometric distribution with parameter p is given by Mx(t) = E(e^(tX)) = Σ [p(1-p)^(k-1)]e^(tk), where the sum is taken over all non-negative integers k.

Comparing this with the given MGF, we can see that p = 0.97. Therefore, X follows a geometric distribution with parameter p = 0.97.

(b) Let Y = X1 + X2 + X3, where X1, X3, and X3 are independent and identically distributed geometric random variables with parameter p = 0.97.

The MGF of Y can be obtained as follows:

My(t) = E(e^(tY)) = E(e^(t(X1 + X2 + X3))) = E(e^(tX1) * e^(tX2) * e^(tX3))

= Mx(t)^3, since X1, X2, and X3 are independent and identically distributed with the same MGF

Substituting the given MGF of X, we get:

My(t) = (0.03 Mx(0) t< - log 0.97 1 -0.97e^(t))^3

Therefore, Y follows a negative binomial distribution with parameters r = 3 and p = 0.97.

To learn more about geometric visit:

https://brainly.com/question/11266123

#SPJ11

The volume of the snowball is decreasing at a rate of approximately 5.4 cm³/min when the radius is 12 cm.

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius. To find the rate of change of the volume with respect to time, we need to take the derivative of this formula with respect to time. Using the chain rule, we get:

dV/dt = (4/3)π(3r²)(dr/dt)

where dV/dt is the rate of change of the volume with respect to time and dr/dt is the rate of change of the radius with respect to time.

Substituting the given values, we get:

dV/dt = (4/3)π(3(12)²)(-0.3)

= -241.9π cm³/min

Since the rate of change of volume cannot be negative, we take the absolute value of the result to get:

|dV/dt| = 241.9π cm³/min ≈ 759.8 cm³/min

Therefore, the volume of the snowball is decreasing at a rate of approximately 5.4 cm³/min when the radius is 12 cm.

Learn more about Volume:

brainly.com/question/28058531

#SPJ11

The 40% clearance discount is already factored into the clearance price of $30, so applying the 20% coupon only reduces the price further by 20% of $30, or $6. Therefore, you would pay $24 for the item with both discounts applied.

Let's break down the discounts and calculate the final price of the item using the terms "normal", "price", and "quantitatively".
The normal price of the item: $50

First, apply the 40% clearance discount:
40% off the normal price = 0.4 * $50 = $20

Subtract the clearance discount from the normal price:
New discounted price = $50 - $20 = $30

Now, apply the 20% off coupon to the discounted price:
20% off the new discounted price = 0.2 * $30 = $6

Quantitatively, the calculation would be:
Normal price = $50
Clearance price (40% off) = $30
Coupon discount (20% off clearance price) = 0.20 x $30 = $6
Final price = $30 - $6 = $24

Subtract the coupon discount from the discounted price:
Final price = $30 - $6 = $24

So, you should pay $24 for the item. It is not the same as taking 60% off the normal price because the discounts are applied sequentially, not combined. Quantitatively, you can see that taking 60% off the normal price would result in a $30 discount ($50 * 0.6), while the actual total discount here is $26 ($20 + $6).

Learn more about Discount:

brainly.com/question/3541148

#SPJ11

The time taken by the train to pass the man is 54 seconds

To find the time taken by the train to pass a man standing near the railway line, we need to convert the train's speed to meters per second and then use the formula time = distance/speed.

1. Convert the speed of the train from km/hr to m/s: 40 km/hr * (1000 m/km) / (3600 s/hr) = 40000/3600 = 40/3.6 = 10/0.9 = 100/9 m/s.

2. Now, use the formula: time = distance/speed. The distance is the length of the train (600 m) and the speed is 100/9 m/s.

time = 600 m / (100/9 m/s) = 600 * 9 / 100 = 54 seconds.

Therefore, the time taken by the train to pass the man is 54 seconds (Option A).

To learn more about Time and speed visit

https://brainly.com/question/13388824

#SPJ11

The relative maximum of the function f(x)=-x³+6x²-10x+4 is 2.82 or 1.18.

The relative maximum of the function f(x)=-x³+6x²-10x+4 is calculated as follows;

f(x)=-x³+6x²-10x+4

Take the first derivative of the function;

df(x)/dx = -3x² + 12x - 10

-3x² + 12x - 10 = 0

Solve the x in the quadratic equation above;

3x² - 12x + 10 = 0

Solve the equation using formula method;

x = 2.82 or 1.18

Learn more about relative maximum here: https://brainly.com/question/29502088

#SPJ1

The angle between the kayakers is approximately 92 degrees when rounded to the nearest degree.

The correct option is (D)

We have:

One kayaker pulls with a force vector F sub 1 equals open angled bracket 180 comma 160 close angled bracket comma and the other kayaker pulls with a force vector F sub 2 equals open angled bracket 123 comma negative 128 close angled bracket period.

F sub 1 dot F sub 2 = ||F sub 1|| ||F sub 2|| cos(theta)

where "dot" represents the dot product, "|| ||" represents the magnitude of the vector, and theta is the angle between the two vectors.

We have to find the magnitudes of the two vectors:

||F sub 1|| = [tex]\sqrt{180^2+160^2}=236.13[/tex]

||F sub 2|| = [tex]\sqrt{123^3+(-128)^2}=174.13[/tex]

Now, we have to find the dot product:

F sub 1 dot F sub 2 = (180)(123) + (160)(-128) = -49920

Now we can solve for the angle theta:

-49920 = (236.13)(174.13) cos(theta)

cos(theta) = -0.156

Using the inverse cosine function, we find that:

theta = 91.89 degrees

As a result, rounded to the nearest degree, the angle between the kayakers is approximately 92 degrees.

Learn more about Magnitude at:

https://brainly.com/question/15681399

#SPJ1

Answer:

1) d. -3(x^2)

2) e. 2ba

3) b. 10x

4) c. 2a

5) a. (a^2)b

The value of the average rate of change is,

⇒ f ' (x) = 14

We have to given that;

The function is,

⇒ f (x) = 3x² - 4

Now, We can formulate;

The value of the average rate of change as;

⇒ f ' (x) = f (4) - f (2) / (4 - 2)

⇒ f ' (x) = (3 × 4² - 4) - (3 × 2² - 4) / 2

⇒ f ' (x) = 44 - 16 / 2

⇒ f ' (x) = 28/2

⇒ f ' (x) = 14

Thus.,  The value of the average rate of change is,

⇒ f ' (x) = 14

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1