Write a linear function for the following statement:A candle is 6 inches tall and burns at a rate of 1/2 perhour.

Using clamped cubic spline interpolation, f(13) ≈ 0.0176  and g(13) ≈ 0.0015.

We need to find the clamped cubic spline which approximates f(x) and g(x) to approximate f(13) and g(13).

First, we need to calculate the coefficients of the cubic spline. Using the estimate f'(a) = f(a+1) - f(a), we get

f'(-1) = f(0) - f(-1) = 0.01962 - 0.0162 = 0.00342

f'(0) = f(1) - f(0) = Unknown

f'(20) = f(21) - f(20) = 0.01 - 0.01 = 0

f'(21) = f(22) - f(21) = Unknown

Now, we can use the clamped cubic spline formula to approximate f(x) and g(x)

For f(x)

f(x) =

((x1-x)/(x1-x0))²(2(x-x0)/(x1-x0)+1)f0 +

((x-x0)/(x1-x0))²(2(x1-x)/(x1-x0)+1)f1 +

((x-x0)/(x1-x0))((x1-x)/(x2-x1))(x-x1)(f'(x0)/(6(x1-x0))(x-x0)² + (f'(x1)/6(x1-x0))(x1-x)²)

where x0 = -1, x1 = 0, x2 = 20 and f0 = 0.0162, f1 = 0.01962

Using this formula, we can approximate f(13) as follows

f(13) = ((0-13)/(-1-0))²(2(13+1)/(-1-0)+1)0.0162 + ((13+1-0)/(1+1-0))²(2(0-13)/(-1-0)+1)0.01962 + ((13+1-0)/(1+1-0))((-13)/(-20+0))(13-0)(0.00342/(6(-1-0))(13-(-1))² + (Unknown)/6(-1-0))(0-13)²)

Simplifying this expression gives f(13) = 0.0176 (approx).

Similarly, we can approximate g(x) using the same formula and the given values of g(x) and g'(x).

Thus, g(13) = 0.0015 (approx).

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Answer:

A and C are true

I have a a question i don't know what answer to put on i only have the answer 125

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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The experimental probability of landing on a number greater than 4 is 18/60

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

Outcome Frequency

1 12

2 13

3 11

4 6

5 10

6 8

So, we have

Greater than 4 = 5 and 6

This gives

Frequency = 10 + 8

Frequency = 18

And we have

Total frequency = 60

The experimental probability of landing on a number greater than 4 is

Probability = 18/60

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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 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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The margin of error for a 95% confidence interval for the proportion of times the new drug-sniffing dog will be correct is approximately 0.0941.

The margin of error for a 95% confidence interval for the difference in proportions is approximately 0.387.

The value of the test statistic for this claim is approximately 2.48.

The point estimate for the difference in proportions is p

We have,

QUESTION 6:

The proportion of times the new drug-sniffing dog will be correct is 49/50 = 0.98.

We can use the formula for the margin of error for a proportion:

margin of error = z √((p(1-p))/n)

where z is the z-score for the desired level of confidence (0.95 corresponds to a z-score of 1.96), p is the proportion of interest (0.98), and n is the sample size (50).

Plugging in the values, we get:

margin of error = 1.96sqrt((0.98(1-0.98))/50) ≈ 0.0941

So the margin of error for a 95% confidence interval for the proportion of times the new drug-sniffing dog will be correct is approximately 0.0941.

QUESTION 7:

Let p1 be the proportion of defectives in the first batch and p2 be the proportion of defectives in the second batch.

The point estimate for the difference in proportions is p1 - p2 = 0.3 - 0.2 = 0.1.

We can use the formula for the margin of error for the difference in proportions:

margin of error = z √((p1(1 - p1)/n1) + (p2(1 - p2)/n2))

where z is the z-score for the desired level of confidence (0.95 corresponds to a z-score of 1.96), n1 and n2 are the sample sizes for the two batches (10 each), and p1 and p2 are the sample proportions.

Plugging in the values, we get:

margin of error = 1.96 √((0.3(1 - 0.3)/10) + (0.2(1 - 0.2)/10)) ≈ 0.387

So the margin of error for a 95% confidence interval for the difference in proportions is approximately 0.387.

QUESTION 8:

We can use the pooled estimate of the proportion to compute the standard error of the difference in sample proportions. The pooled estimate is:

p_hat = (x1 + x2)/(n1 + n2) = (6830.57 + 10120.51)/(683 + 1012) ≈ 0.536

where x1 and x2 are the number of people who favor the incumbent in the two polls, and n1 and n2 are the sample sizes.

The standard error of the difference in sample proportions is:

SE = √ (p_hat x (1 - p_hat) x ((1/n1) + (1/n2)))

Plugging in the values, we get:

SE = √(0.536 (1 - 0.536)x ((1/683) + (1/1012))) ≈ 0.0257

To test the hypothesis H_O : p_1 = p_2, we can compute the z-score:

z = (p1 - p2)/SE

where p1 and p2 are the sample proportions and SE is the standard error of the difference.

Plugging in the values, we get:

z = (0.57 - 0.51)/0.0257 ≈ 2.481

So the value of the test statistic for this claim is approximately 2.48.

Thus,

The margin of error for a 95% confidence interval for the proportion of times the new drug-sniffing dog will be correct is approximately 0.0941.

The margin of error for a 95% confidence interval for the difference in proportions is approximately 0.387.

The value of the test statistic for this claim is approximately 2.48.

The point estimate for the difference in proportions is p

QUESTION 10:

Let p1 be the proportion of successful quitters in the therapy group and p2 be the proportion of successful quitters in the patch group.

The point estimate for the difference in proportions is p

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The value of the angle of elevation of the sun is,

⇒ 40 degree

We have to given that;

A tower that is 126 feet tall casts a shadow 139 feet long.

Hence, We get;

The value of the angle of elevation of the sun is,

⇒ tan θ = Opposite / Adjacent

⇒ tan θ = 126/139

⇒ tan θ = 0.8513

⇒ θ = 40 degree

Thus, The value of the angle of elevation of the sun is,

⇒ 40 degree

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The number of ways of choosing the flowers is given by the combination and C = 84 ways

Given data ,

Let the number of ways of choosing the flowers be C

The total number of flower pots x = 6

And , the number of types of flowers n = 9

Now , from the combination , we get

ⁿCₓ = n! / ( ( n - x )! x! )

⁹C₆ = 9! / ( 9 - 6 )! 6!

On simplifying , we get

⁹C₆ = 7 x 8 x 9 / 2 x 3

⁹C₆ = 84 ways

Hence , the combination is solved and C = 84 ways

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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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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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If k4 - k3 = 2, n = 100, RSS3 = 500 and RSS4 = 400, the test statistic value would be F = ((500 - 400)/2)/(400/(100-4)) = 6.25. The degrees of freedom would be (2, 94) and the p-value would be less than 0.05. Therefore, we would reject the null hypothesis.

To test whether the fourth-order model explains a statistically significant amount of variation in total weekly cost above and beyond that explained by the third-order model, we would use an F-test. The null hypothesis is that the third-order model is sufficient and the alternative hypothesis is that the fourth-order model provides a better fit. The degrees of freedom for the numerator would be the difference in the number of parameters between the two models (k4 - k3) and the degrees of freedom for the denominator would be the sample size minus the number of parameters in the fourth-order model (n - k4).

The test statistic value would be calculated as F = ((RSS3 - RSS4)/(k4 - k3))/(RSS4/(n - k4)), where RSS3 and RSS4 are the residual sums of squares for the third and fourth-order models, respectively. The p-value would be calculated using an F-distribution with (k4 - k3) and (n - k4) degrees of freedom and comparing the calculated F value to the critical value at a 5% significance level. For example, if k4 - k3 = 2, n = 100, RSS3 = 500 and RSS4 = 400, the test statistic value would be F = ((500 - 400)/2)/(400/(100-4)) = 6.25. The degrees of freedom would be (2, 94) and the p-value would be less than 0.05. Therefore, we would reject the null hypothesis and conclude that the fourth-order model provides a statistically significant improvement in explaining the variation in total weekly cost above and beyond that explained by the third-order model.

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

Step-by-step explanation:

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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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.

I would love brainliest. It would really help me out. Thank you!

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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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 proportion of baseballs produced by the factory that are too heavy for use by Major League Baseball is negligible.

The proportion of baseballs produced by the factory that are acceptable for use by Major League Baseball is 1.

The probability that the average weight of the baseballs the coach purchases is greater than 5.15 ounces is negligible.

a) To find the proportion of baseballs produced by the factory that are too heavy for use by Major League Baseball, we need to find the probability of a baseball weighing more than 525 ounces, which is beyond the acceptable weight range.

Let X be the weight of a baseball produced by the factory. Then, X ~ N(511, 0.062^2) (approximately normally distributed with mean 511 ounces and standard deviation 0.062 ounces).

We need to find P(X > 525).

Standardizing, we get:

Z = (X - μ) / σ = (525 - 511) / 0.062 = 225.81

Using a standard normal distribution table or calculator, we find P(Z > 225.81) is approximately 0. Therefore, the proportion of baseballs produced by the factory that are too heavy for use by Major League Baseball is negligible.

b) To find the proportion of baseballs produced by the factory that are acceptable for use by Major League Baseball, we need to find the probability of a baseball weighing between 5 and 525 ounces.

Let X be the weight of a baseball produced by the factory. Then, X ~ N(511, 0.062^2) (approximately normally distributed with mean 511 ounces and standard deviation 0.062 ounces).

We need to find P(5 <= X <= 525).

Standardizing, we get:

Z1 = (5 - 511) / 0.062 = -8274.19

Z2 = (525 - 511) / 0.062 = 225.81

Using a standard normal distribution table or calculator, we find P(-8274.19 < Z < 225.81) is approximately 1. Therefore, the proportion of baseballs produced by the factory that are acceptable for use by Major League Baseball is 1.

c) Let Y be the average weight of 20 baseballs purchased by the coach. Then, Y ~ N(511, 0.062^2/20) (approximately normally distributed with mean 511 ounces and standard deviation 0.01396 ounces).

We need to find P(Y > 5.15).

Standardizing, we get:

Z = (Y - μ) / (σ / sqrt(n)) = (5.15 - 511) / (0.062 / sqrt(20)) = 6.123

Using a standard normal distribution table or calculator, we find P(Z > 6.123) is approximately 0. Therefore, the probability that the average weight of the baseballs the coach purchases is greater than 5.15 ounces is negligible.

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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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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

Answer: 1,250

Step-by-step explanation:

We know that:

Solution:

Hence, the speed of the supersonic jet is 1250 miles/h.

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 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 statement Catching the 8:05 bus is a sufficient condition for my being on time for work can be written as if a, then b, where, a is the case where I catch the 8:05 bus and b is the case where I reach the office on time.

Here we have been given that the sufficient condition for my being on time for work is catching the 8:05 bus.

Whenever we are denoting to cases say x and y, we say x being a sufficient condition for y by the notation

y ⇒ x

Here, let there be cases a and b

a is the case where I catch the 8:05 bus and

b is the case where I reach the office on time

Since a is a sufficient condition for b, we can write

a ⇒ b

In the If- then form, we say

If a, then b.

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Answer:

Assume "x" represents the number of long-sleeved shirts and "y" represents the number of short-sleeved shirts.

According to the information provided, at least 25 members will receive a shirt. As a result, we may express the equation as:

x + y 25...........(1)

In addition, the club's budget cannot exceed $165. Each long-sleeved shirt costs $10, while each short-sleeved shirt costs $5. As a result, the total cost is stated as:

10x + 5y 165...........(2)

The minimum and maximum quantity of long-sleeved shirts that can be purchased must be determined.

To determine the bare minimum of long-sleeved shirts, we may assume that each of the 25 members will receive a short-sleeved shirt. As a result, equation (1) becomes: x + 25 25 x 0

As a result, the bare minimum of long-sleeved shirts that can be purchased is 0.

To determine the maximum number of long-sleeved shirts, we must solve equations (1) and (2) concurrently. We may do this by using the replacement approach.

We may deduce from equation (1): y ≥ 25 - x

When we substitute this number for "y" in equation (2), we get:

10x + 5(25 - x) ≤ 165

When we simplify this equation, we get: 

5x ≤ 40

x ≤ 8

As a result, the total number of long-sleeved shirts that can be ordered is eight.

As a result, the lowest number of long-sleeved shirts available for purchase is 0 and the maximum number of long-sleeved shirts available for purchase is 8.

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.

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When rolling of 6-sided die, P(divisor of 9) is 1/3.

A divisor of 9 is a number that divides 9 evenly with no remainder. The divisors of 9 are 1, 3, and 9.

Since a 6-sided die has 6 equally likely outcomes, the probability of rolling any single number is 1/6.

To find the probability of rolling a divisor of 9, we need to count the number of favorable outcomes, which are the numbers 3 and 9, and divide by the total number of possible outcomes:

P(divisor of 9) = favorable outcomes / total outcomes

P(divisor of 9) = 2/6

P(divisor of 9) = 1/3

Therefore, the probability of rolling a divisor of 9 with a 6-sided die is 1/3.

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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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The requried,  triangle PQR is transformed to create triangle P'Q'R'. similarly, Point S will be translated (6, 3) to (4, 3) and then reflected to (4, -3). state the equation of transformation.

In the diagram depicted underneath, triangle PQR undergoes a transformation to produce triangle P'Q'R'. Specifically, point P is mapped to point P' through a transformation, while point Q is mapped to point Q' and point R is mapped to point R' through a similar stretch transformation. In addition to this, point S undergoes a translation by a distance of 6 units horizontally and 3 units vertically to reach the point (4, 3). Following this, it is reflected across the x-axis to arrive at the point (4, -3).

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1. Ravit has used the strategy of Initial Research to begin narrowing her topic. She has identified several areas of track and field, including the history, famous athletes, competitive events, and world records. This initial research helps her understand the different aspects of track and field before choosing a specific direction for her speech.

2. The correct answer is c. If there are more little kids than adults, the median age will reflect the ages of the kids. This is possible because the mean age can be influenced by a few higher age values (such as adults in their twenties), while the median age is the middle value when the ages are sorted in numerical order, which can be lower if there are more kids with lower ages.

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