Which of the following sets of numbers could represent the three sides of a triangle? { 7 , 10 , 18 } {7,10,18} { 6 , 19 , 25 } {6,19,25} { 11 , 17 , 26 } {11,17,26} { 8 , 16 , 24 } {8,16,24}

To construct a matrix with the required property (a), (d) & (e) are possible to construct the matrix. (b), (c) are not possible to construct the matrix.

(a) It is possible to construct a matrix with the given properties as follows:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The columns of this matrix span the column space, and the vector (-1,0,1) spans the nullspace.

(b) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the nullspace are different. The column space is a subspace of [tex]R^3[/tex], whereas the nullspace is a subspace of[tex]R^1[/tex].

(c) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the left nullspace are different. The column space is a subspace of[tex]R^3[/tex], whereas the left nullspace is a subspace of [tex]R^2[/tex].

(d) It is possible to construct a matrix with the given properties as follows:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The rows of this matrix span the row space, and the vector (1,0,3,2) spans the nullspace.

(e) It is possible to construct a matrix with the given properties as follows:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The rows of this matrix span the row space, and the vector (-3,1) spans the left nullspace.

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The explicit rule for sequence 3200,1600,800, 400,... is aₙ = 3200(1/2)⁽ⁿ⁻¹⁾, the explicit rule for sequence 12, 84, 588, 4116, .. is aₙ = 12(7)⁽ⁿ⁻¹⁾, the explicit rule for sequence 1395, 465, 155, 51.67,... is aₙ = 1395(1/3)⁽ⁿ⁻¹⁾.

The common ratio in this geometric sequence is 1/2. Thus, the explicit rule for this sequence is given by

aₙ = 3200(1/2)⁽ⁿ⁻¹⁾

where aₙ represents the nth term of the sequence.

This sequence appears to be a geometric sequence where the common ratio is 7. Thus, the explicit rule for this sequence is

aₙ = 12(7)⁽ⁿ⁻¹⁾

where aₙ represents the nth term of the sequence.

This sequence appears to be a geometric sequence where the common ratio is 1/3. Thus, the explicit rule for this sequence is

aₙ = 1395(1/3)⁽ⁿ⁻¹⁾.

where aₙ represents the nth term of the sequence.

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Answer:

64

Step-by-step explanation:

the total must be 60×4 =240

subtract the miles already given and that us your answer. You could also make an equation. (64+53+59+x)/4=

The formula for standard error that applies to this problem is SE = sqrt[p(1-p)/n], where SE represents the standard error, p represents the probability of success, and n represents the sample size. In this case, N represents the population size, but it is not necessary for calculating the standard error.

Substituting the values given in the problem, we have:

SE = sqrt[0.45(1-0.45)/44] = 0.0717 (rounded to four decimal places)

Therefore, the standard error for this problem is 0.0717. This value represents the degree of variability or uncertainty in the sample proportion, or the degree to which the sample proportion is likely to deviate from the true population proportion. A larger sample size or a more extreme probability of success (closer to 0 or 1) would result in a smaller standard error, indicating greater precision in the estimate of the population proportion.

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The consumers' surplus if the market price is set at $9/disc is $2,167.2.

The consumer's surplus is calculated from the quantity demanded as shown below;

-0.01x² − 0.1x + 51 = 9

-0.01x² - 0.1x + 42

solve the quadratic equation using formula method as follows;

x = -70 or 60

So we take only the positive quantity demanded.

Integrate the function from 0 to 60;

∫-0.01x² − 0.1x + 51 = [-0.0033x³ - 0.05x² + 51x]

= [-0.0033(60)³ - 0.05(60)² + 51(60)] - [-0.0033(0)³ - 0.5(0)² + 51(0)]

= -712.8 - 180 + 3,060

= $2,167.2

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The distance form point A to point B is 333 feet.

An angle of depression is the measure of an angle formed when an object is viewed below the horizontal plane by an observer.

In the given question, let the distance from point A to the base of the lighthouse be represented by x, and that of B to the base of the lighthouse as y.

So that to determine x, we have;

Tan θ = opposite/ adjacent

Tan 15 = 115/ x

x = 115/ 0.2680

  = 429.1045

x = 429.1045 feet

To determine y, we have;

Tan θ = opposite/ adjacent

Tan 50 = 115/ y

y = 115/ 1.1918

  = 96.492y

y =  96.4927 feet

The distance from point A to point B = x - y

                             = 429.1045 - 96.4927

                             = 332.6118

The distance from point A to point B is 333 feet.

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Answer:

do this solve in calc (a+1)^2+(a+3)^2=(a+5)^2

Since the arrival times are independent and uniformly distributed, the probability that a single person arrives in the first hour is 1/10^6. Therefore, the number of people N that arrive in the first hour follows a binomial distribution with parameters n=10^6 and p=1/10^6.

The probability that exactly i people arrive in the first hour is then given by the binomial probability mass function:

P{N=i} = (10^6 choose i) * (1/10^6)^i * (1 - 1/10^6)^(10^6 - i)

Using the normal approximation to the binomial distribution, we can approximate this probability as:

P{N=i} ≈ φ((i+0.5 - np) / sqrt(np(1-p)))

where φ is the standard normal probability density function. Plugging in the values of n=10^6 and p=1/10^6, we get:

P{N=i} ≈ φ((i+0.5 - 1) / sqrt(1*0.999999)) = φ(i - 0.5)

Therefore, an approximation for P{N=i} is given by the standard normal density function evaluated at i-0.5.

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Answer: The answer is 2 and 3 or B and C which ever way you want it.

The reason its 2and3 is because you can see its 60 degree angle.

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The reason its 3 also is because they are all congruent and its the only other right answer that fits.

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Hence, The answer is 2 and 3 or B and C.

Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions if you want.

The probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.

Assuming that each participant has an equal chance of preferring any of the four coffee brands and that their preferences are independent of each other, we can model the preference of each participant as a Bernoulli random variable with probability p of preferring Simply Significant Coffee.

Then, the probability of the first 2 participants preferring Simply Significant Coffee and the remaining 13 participants preferring one of the other coffee brands can be calculated as follows:

P(2 participants prefer Simply Significant and 13 prefer other brands) = P(Simply Significant)^2 * P(other brands)^13

where P(Simply Significant) is the probability of a participant preferring Simply Significant Coffee and P(other brands) is the probability of a participant preferring one of the other brands, which is 1/3 since there are three other brands besides Simply Significant.

Using the binomial probability formula, we can calculate P(Simply Significant) as follows:

P(Simply Significant) = C(15,2) * (1/4)^2 * (3/4)^13

where C(15,2) is the number of ways to choose 2 participants out of 15.

Plugging in the values, we get:

P(Simply Significant) = 105 * (1/16) * (0.3164) ≈ 0.0392

Therefore, the probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.

Note that this assumes that participants are choosing at random and are not influenced by factors such as the order in which the coffees are presented or any other external factors that could affect their preferences.

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The correct answer is B. Max: 29, Min: 27

To find the absolute maximum and minimum values of the function f(x) = x³ + 3x² – 9x + 27 on the interval [0,2], we need to first find the critical points and then evaluate the function at these points and at the endpoints of the interval.

Taking the derivative of the function, we get:

f'(x) = 3x² + 6x - 9

Setting this equal to zero and solving for x, we get:

x = -1 or x = 3/2

We need to check these critical points and the endpoints of the interval [0,2] to find the absolute maximum and minimum values.

f(0) = 27

f(2) = 37

f(-1) = 22

f(3/2) = 54.25

Comparing these values, we see that the absolute maximum value is 54.25 and the absolute minimum value is 22. Therefore, the correct answer is B. Max: 29, Min: 27

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The time for which plane B will take to refuel plane A is equals to 10 minutes. The two points who satisfy the equation, y = x + 1, are (0, 1), (-1,0). The two points who satisfy the equation, y = -x + 21, are (0,21), (21,0).

We have a fuel left in Plane A = 1 ton

fuel left in Plane B = 21 tons

Fuel transfer rate = 1 ton per minute

In order that for them to have the same amount of fuel, We add up the fuel left in Plane A and Plane B = 21 + 1 = 22 tons. This implies each plane will have fuel of 11 tons. Time that plane B will take to refuel plane A until both planes have the same amount of fuel is calculated by : Plane B will transfer 10 tons of fuel to A.

Plan A has a total of 11 tons. Since, the transfer rate = 1 ton per minute

=> 1 ton will transfer in 1 minute

So, 10 tons fuel will need 10 minutes. Hence, required time value is 10 minutes. Now, The equation for quantity of fuel with respect to time in plane A is, y = x + 1 --(1). If x = 0 => y = 1

and y = 0 => x = -1. So, (0, 1) and (-1,0).

The equation for quantity of fuel with respect to time in plane B is, y = -x + 21 --(2). For it, x = 0 => y = 21 and y= 0 => x = 21. Hence, two points that satisfy the equation(1) and equation(2) are (0, 1), (-1,0) and (0,21), (21,0) respectively.

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The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].

The probability of a success in one Bernoulli trial is given by p, and the probability of a failure is q = 1 - p.

(a) The probability of no successes is (1-p)^n.

(b) The probability of at least one success is 1 minus the probability of no successes, which is 1 - (1-p)^n.

(c) The probability of at most one success is the sum of the probabilities of 0 and 1 successes, which is (1-p)^n + np(1-p)^(n-1).

(d) The probability of at least two successes is 1 minus the probability of 0 or 1 success, which is 1 - [(1-p)^n + np(1-p)^(n-1)].

(e) The probability of no failures is the same as the probability of n successes, which is p^n.

(f) The probability of at least one failure is 1 minus the probability of no failures, which is 1 - p^n.

(g) The probability of at most one failure is the sum of the probabilities of 0 and 1 failures, which is p^n + nqp^(n-1).

(h) The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].

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The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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Answer:

Step-by-step explanation:

(x - 2)²/16 - (y - 1)²/4 = 1

(x - 2)² - 4(y - 1)² = 16

x² + 4 - 4x - 4(y² + 1 - 2y) = 16

x² + 4 - 4x - 4y² - 4 + 8y = 16

x² - 4x + 8y - 4y² = 16

x² - 4x = 16  ,  -4y² + 8y = 16

x(x - 4) = 16  ,  4y(-y + 2) = 16

x = 16, x = 20,  y = 4, y = -14

The probability that at most 2 columns will fail is 0.98.

This is a binomial distribution problem, where the number of trials n = 16, the probability of success (a column failing) p = 0.05, and we want to find the probability of at most 2 columns failing.

To solve this, we need to calculate the probability of 0, 1, or 2 columns failing and add them up.

P(at most 2 columns failing) = P(0 columns failing) + P(1 column failing) + P(2 columns failing)

P(0 columns failing) = (n choose 0) * p^0 * (1-p)^(n-0) = (16 choose 0) * 0.05^0 * 0.95^16 = 0.45

P(1 column failing) = (n choose 1) * p^1 * (1-p)^(n-1) = (16 choose 1) * 0.05^1 * 0.95^15 = 0.38

P(2 columns failing) = (n choose 2) * p^2 * (1-p)^(n-2) = (16 choose 2) * 0.05^2 * 0.95^14 = 0.15

P(at most 2 columns failing) = 0.45 + 0.38 + 0.15 = 0.98

Therefore, the probability that at most 2 columns will fail is 0.98.

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The correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.

Given is a dot plots show the distribution of heights, in inches, for third grade girls in two classrooms.

The dot plot of class 1 is uneven and that of class 2 is even.

So, the center of the graph will be calculated by mean and that of class 2 by median.

Hence. the correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.

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To calculate the percentage of the 250 ha paddock that can be sowed with 12.560 kg of wheat seed, we first need to determine how much seed is needed per hectare and this will give the answer 0.063%.

Given that the showing rate is 79.62 kg/ha, we can divide the total seed amount by the showing rate to get the number of hectares that can be sown with the given amount of seed:

12.560 kg / 79.62 kg/ha = 0.1576 ha

This means that 0.1576 hectares of land can be sown with 12.560 kg of wheat seed.

To calculate the percentage of the 250 ha paddock that can be sown, we can divide the sown land area by the total paddock area and then multiply by 100:

0.1576 ha / 250 ha x 100% = 0.063%

Therefore, you can sow approximately 0.063% of the 250 ha paddock with 12.560 kg of wheat seed, assuming a showing rate of 79.62 kg/ha.

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The correct statement regarding the end behavior of the graph is given as follows:

C. As x approaches positive infinity, D(x) approaches negative infinity.

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

For this problem, the function is a quadratic function with negative leading coefficient, meaning that it will approach negative infinity when x approaches negative infinity and when x approaches positive infinity.

This means that the correct option is given by option C.

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Answer: A. 10.2

Step-by-step explanation: For this problem we have to create a second right triangle to find the length. You can apply the pythagorean theorem which continues to 10^2+2^2=c^2 which would get us 104. Then find the root of 104 which is equal to 10.2

Answer:

To find the height of the box, we need to use the formula for volume of a box: Volume = length x breadth x height

Given the values for length and breadth, we can substitute them into the formula and solve for height: 140 = 7 x 5 x height

Simplifying the equation, we get: 140 = 35 x height

Dividing both sides by 35, we get: height = 4

Therefore, the height of the box is 4 cm

Answer:

1414 tickets, in explanation

Hope this helps!

Step-by-step explanation:

1 ticket = $9.50

? tickets = $13,433

13,433 ÷ 9.50 = 1414

9.50 × 1414 = 13,433

1 ticket × 1414 = ? tickets

? tickets = 1414 tickets

We first need to clarify a few terms and the question itself. It seems like you are asking about a codeword in polynomial form and finding the third circular shift of the codeword. Let's express the codeword in polynomial form:

Let u(x) be the original polynomial codeword, and let n = 4. Based on the information provided, assuming that q(x) = u(x)n(x) = u(x)(1 + x^4).

To find the third circular shift of the codeword, follow these steps:

1. Express the original codeword u(x) in polynomial form, for example, u(x) = a_0 + a_1x + a_2x^2 + a_3x^3 (where a_i are coefficients).
2. Perform the first circular shift by moving the last term to the front: a_3x^3 + a_0 + a_1x + a_2x^2.
3. Perform the second circular shift: a_2x^2 + a_3x^3 + a_0 + a_1x.
4. Perform the third circular shift: a_1x + a_2x^2 + a_3x^3 + a_0.

The third circular shift of the codeword u(x) is given by the polynomial a_1x + a_2x^2 + a_3x^3 + a_0.

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The effects of the interest rate in each situation are given as follows:

The interest rate is the percentage by which an amount of money increases over a period of time.

For lower interest rate, loans or purchases are desired, as the person can pay back the loan after some time without a high additional tax.

For higher interest rates, investments are desired, as the balance of the investment should increase fast. Purchases, on the other hand, should be avoided with higher interest, as there will be a high tax for paying the purchase in installments.

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All Trigonometric Expressions:

a. ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx = ∫2sin³θ cos²θ dθ

b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]= ∫tan²θ sec²θ dθ

c. ∫x√(5x + 50)/(x + 118)dx = ∫(5tan²θ – 25)tanθ sec³θ dθ

d. ∫(19 – 50x)/(119 – 5x² + 50x)dx = -2∫dθ/(25tan²θ + 94)

a. The integral ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx, we can use the substitution x = (2/5)sinθ. This gives dx = (2/5)cosθ dθ and 5x² – 2 = 5(2/5 sinθ)² – 2 = 2cos²θ. Substituting these expressions into the integral, we get:

∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx  

= ∫2sin³θ cos²θ dθ

b. For the integral ∫x²dx/(4x² + 6), we can use the substitution x = tanθ. This gives dx = sec²θ dθ and 4x² + 6 = 4tan²θ + 6 = 2sec²θ. Substituting these expressions into the integral, we get:

∫x²dx/(4x² + 6) = ∫tan²θ sec²θ dθ

c. For the integral ∫x√(5x + 50)/(x + 118)dx, we can use the substitution

x + 25 = 5tan²θ.

This gives x = 5tan²θ – 25 and dx = 10tanθ sec²θ dθ, and

5x + 50 = 25sec²θ. Substituting these expressions into the integral, we get:

∫x√(5x + 50)/(x + 118)dx

= ∫(5tan²θ – 25)tanθ sec³θ dθ

d. For the integral:

∫(19 – 50x)/(119 – 5x² + 50x)dx,

we can use the substitution

5x – 5 = √(50x – 5)tanθ.

This gives x = (1/10)[(tanθ)² + 1] and

dx = (1/5)(tanθ sec²θ) dθ, and 119 – 5x² + 50x

= (25tan²θ + 94)².

Substituting these expressions into the integral, we get:

∫(19 – 50x)/(119 – 5x² + 50x)dx

= -2∫dθ/(25tan²θ + 94)

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Correct Question:

For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.

a. ∫5x * ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx

b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]

c. ∫x√(5x + 50)/(x + 118)dx

d. ∫(19 – 50x)/(119 – 5x² + 50x)dx

The probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.

To solve this problem, we will use the Poisson probability distribution formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where:

P(X = k) is the probability of getting k events in a specific time interval

e is Euler's number (approximately equal to 2.71828)

λ is the average rate of events per interval (also known as the Poisson parameter)

k is the number of events we want to calculate the probability for

k! is the factorial of k (i.e., k! = k x (k-1) x (k-2) x ... x 2 x 1)

In this problem, we are given that the rate of calls to a customer service center follows a Poisson process with a rate of 1 call every 3 minutes. Therefore, the average rate of calls per minute (i.e., λ) is:

λ = 1 call / 3 minutes = 1/3 calls per minute

Now, we want to find the probability of receiving more than 5 calls during the next 15 minutes. We can use the Poisson formula to calculate this probability as follows:

P(X > 5) = 1 - P(X ≤ 5)

= 1 - ∑(k=0 to 5) [e^(-λ) * λ^k / k!]

= 1 - [(e^(-λ) * λ^0 / 0!) + (e^(-λ) * λ^1 / 1!) + ... + (e^(-λ) * λ^5 / 5!)]

Substituting λ = 1/3 and simplifying the equation, we get:

P(X > 5) = 1 - [(e^(-1/3) * 1^0 / 0!) + (e^(-1/3) * 1^1 / 1!) + ... + (e^(-1/3) * 1^5 / 5!)]

≈ 0.0322

Therefore, the probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.

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The slope of the line is 4/5.

Option C is the correct answer.

We have,

The slope of the line that passes through the points (3, -1) and (-2, -5) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the coordinates, we get:

slope = (-5 - (-1)) / (-2 - 3) = -4 / (-5) = 4/5

Therefore,

The slope of the line is 4/5.

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The probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

We are given that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean of [tex]$\mu = 16.9$[/tex] and standard deviation of [tex]$\sigma = 3.3$[/tex]. We need to find the probability that in a given week the airline will lose less than 20 suitcases.

Let X be the number of suitcases lost in a week. Then we need to find P(X < 20).

Using the Z-score formula, we can standardize the variable X as:

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

Substituting the given values, we get:

[tex]Z=\frac{20-16.9}{3.3}=0.91[/tex]

Now, we need to find the probability that Z is less than 0.91. We can use a standard normal distribution table or calculator to find this probability, which is approximately 0.8186.

Therefore, the probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

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The given statement, "You can infer statistical significance from a 95% CI. "A 95% CI gives you information about the precision of the association." and "A study with a small sample will have a wider 95% CI." are true and "A 95% CI gives you information about the precision of the association, but not the strength of the association." is false.

The statement You can infer statistical significance from a 95% CI is true, as it is a measure of the precision of the association between two variables.

A 95% CI will be wider for a study with a smaller sample size, but this does not necessarily indicate a weaker association. In other words, the width of a 95% CI does not indicate the strength of the association, and so the statement that A 95% CI gives you information about the precision of the association, but not the strength of the association is false.

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Full Question ;

Identify the true and false statements about 95% confidence intervals.

- You can infer statistical significance from a 95% CI.

- A 95% CI gives you information about the precision of the association.

- A study with a small sample will have a wider 95% CI.

-A 95% CI gives you information about the strength of the association.

Answer:

If the mean amount of money that students from the university spend on a first date is $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.

Step-by-step explanation: