I need help on these probability questions.

The correct answer is 3. There is no statistically significant evidence that the average course grade differs between courses taught asynchronously online and courses taught online with synchronous remote meetings.

The correct answer is 3. There is no statistically significant evidence that the average course grade differs between courses taught asynchronously online and courses taught online with synchronous remote meetings. This is because the p-value (0.094) is greater than the level of significance (0.05), which means we cannot reject the null hypothesis that the average course grades are the same in both types of courses. .

Therefore, we conclude that there is not enough evidence to support a difference in average course grades between the two types of courses.

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The calculated area of the kite is 1340.1 square units

Given that

BE = 21

BC = 32

Start by calculating EC using pythagoras theorem

So, we have

EC^2 = 32^2 - 21^2

EC^2 = 583

So, we have

EC = 24.15

Calculate ED using

tan(35) = 24.15/ED

So, we have

ED = 24.15/tan(35)

Evaluate

ED = 34.49

The area of the kite is then calculated as

Area = BD * EC

So, we have

Area = (21 + 34.49) * 24.15

Evaluate

Area = 1340.1

Hence, the area is 1340.1

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The 40th percentile for X is approximately  67.98. To find the 40th percentile for X, we need to use a standard normal distribution table or calculator.

We first need to standardize the random variable X by subtracting the mean and dividing by the standard deviation:

z = (X - mean) / standard deviation
z = (X - 70) / 8

We can then find the z-score corresponding to the 40th percentile, which is -0.253:

z = invNorm(0.4)
z = -0.253

Using this z-score and the formula for standardizing a random variable, we can solve for X:

z = (X - 70) / 8
-0.253 = (X - 70) / 8
-2.024 = X - 70
X = 67.976

Therefore, the 40th percentile for X is approximately 67.98.

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If a constraint is in a surplus, then it is not necessary to buy additional labor time. If a constraint is in a slack, then buying additional labor time may be beneficial.

Linear programming is a mathematical technique used to optimize a set of variables subject to a set of constraints. When solving a linear programming problem, it is important to consider the constraints in order to determine the optimal solution. In the context of buying additional labor time, we need to consider the constraints in terms of surplus and slack.

If a constraint is in a surplus, meaning that the resources required for that constraint are greater than or equal to the actual resources available, then it is not necessary to buy additional labor time. This is because the constraint is already being met, and buying additional labor time would be an unnecessary expense. In this case, it would be more efficient to focus on optimizing other variables.

On the other hand, if a constraint is in a slack, meaning that the resources required for that constraint are less than or equal to the actual resources available, then buying additional labor time may be beneficial. This is because the constraint is not being fully utilized, and buying additional labor time could help to increase the efficiency of the process. However, it is important to consider the cost of buying additional labor time and weigh it against the potential benefits.

In summary, when deciding whether or not to buy additional labor time in a linear programming problem, it is important to consider the constraints in terms of surplus and slack. If a constraint is in a surplus, it is not necessary to buy additional labor time, whereas if a constraint is in a slack, buying additional labor time may be beneficial but the cost must also be considered. Additionally, content loaded linear programming can be used to incorporate various factors, such as production capacity and demand, into the decision-making process.
Question 1: Should you buy additional labor time if a constraint is in a "surplus" (greater or equal to)?

Answer: No, you should not buy additional labor time if a constraint is in a surplus. In the context of content-loaded linear programming, a surplus indicates that the constraint's resources are already more than enough to meet the requirement. Additional labor time would not be beneficial, as it would lead to higher costs without providing any improvement in the solution.

Question 2: Should you buy additional labor time if a constraint is in a "slack" (less than or equal to)?

Answer: It depends on the specific situation. In content-loaded linear programming, a constraint with slack means that there is still some unused capacity in the constraint. You should analyze the potential benefits and costs of adding additional labor time. If adding labor time will lead to an increase in profit, efficiency, or overall improvement of the solution, then it may be worth considering. However, if the additional labor time would not result in any significant benefits or would lead to higher costs without a substantial return on investment, then it is not recommended to buy additional labor time.

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The correct expression which can be used to find AC is,

⇒ 7.8 (cos 23°)

We have to given that;

A triangle ABC shown in figure.

Now, We can formulate;

cos 23° = AC / AB

cos 23° = AC / 7.8

AC = 7.8 (cos 23°)

Thus, The correct expression which can be used to find AC is,

⇒ 7.8 (cos 23°)

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When f(x)=4x+3 and g(x)=x^2-x+1, the value of f(x) + g(x) is x^2 + 3x + 4.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It shtbe noted that to get the sum of f(x) and g(x), we merely add the two functions:

f(x) + g(x) = (4x + 3) + (x^2 - x + 1)

Then, it is possible to simplify this expression by combining terms having the same coefficients:

f(x) + g(x) = x^2 + 3x + 4

In conclusion, f(x) + g(x) = x^2 + 3x + 4.

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Let f(x)=4x+3 and g(x)=x^2-x+1    f(x) + g(x)

Answer:

2 rays: Two examples of rays are AB and AC, both emanating from a common endpoint A and extending infinitely in opposite directions.

2 line segments: Two examples of line segments are AB and CD, both of which have two endpoints and a finite length.

2 lines (not including the parallel lines): Two examples of lines are AB and CD, which intersect at a point E.

2 sets of parallel lines: Two examples of sets of parallel lines are AB and CD, and EF and GH, where AB and CD are parallel to each other, and EF and GH are parallel to each other.

2 acute angles (not incl. the ones in the As): Two examples of acute angles are ∠BAC and ∠EFG, both of which measure less than 90 degrees.

2 obtuse angles (not incl. the ones in the As): Two examples of obtuse angles are ∠PQR and ∠XYZ, both of which measure greater than 90 degrees.

2 right angles (not incl. the ones in the As): Two examples of right angles are ∠ABC and ∠EFG, both of which measure 90 degrees.

2 clear examples of supplementary angles: Two examples of supplementary angles are ∠ABC and ∠DEF, and ∠PQR and ∠RST, where the sum of the angles in each pair is 180 degrees.

2 clear examples of complementary angles: Two examples of complementary angles are ∠ABC and ∠PQR, and ∠DEF and ∠RST, where the sum of the angles in each pair is 90 degrees.

2 clear examples of more than two angles on a line that add up to 180°: Two examples of sets of angles on a line that add up to 180 degrees are ∠ABC, ∠BCD, and ∠CDE, and ∠PQR, ∠QRS, and ∠RST.

2 right triangles: Two examples of right triangles are ΔABC and ΔPQR, where ∠CAB and ∠QRP are right angles.

2 acute triangles: Two examples of acute triangles are ΔDEF and ΔGHI, where all angles are acute.

The sum of the measures of angles within each triangle:

In ΔABC, the sum of the measures of the angles is 180 degrees, where ∠A measures 90 degrees, and ∠B and ∠C measure 45 degrees each.

In ΔPQR, the sum of the measures of the angles is 180 degrees, where ∠P and ∠R measure 90 degrees each, and ∠Q measures 0 degrees.

In ΔDEF, the sum of the measures of the angles is 180 degrees, where all angles are acute, and ∠D, ∠E, and ∠F measure 60 degrees each.

In ΔGHI, the sum of the measures of the angles is 180 degrees, where all angles are acute, and ∠G, ∠H, and ∠I measure 40 degrees each.

In ΔJKL, the sum of the measures of the angles is 180 degrees, where ∠K measures 90 degrees, and ∠J and ∠L measure 45 degrees each.

In ΔMNO, the sum of the measures of the angles is 180 degrees, where ∠O measures 90 degrees, and ∠M and ∠N measure 45 degrees each.

In the context of ideal gas behavior, the most ideal conditions for the parameters pressure (P), temperature (T), and number of moles (n) depend on the specific situation or application. However, I can provide general insights for each parameter.

1. Low pressure (P): Ideal gas behavior is best approximated when the pressure is low. This is because the gas molecules have more space to move around, minimizing their interactions with each other and making their behavior more predictable.

2. High temperature (T): Ideal gas behavior is more accurate at higher temperatures because the gas molecules have more kinetic energy. This allows them to move more freely, reducing the influence of intermolecular forces that can deviate the gas from ideal behavior.

3. High number of moles (n): Having a high number of moles means there are more gas molecules present. This generally improves the accuracy of ideal gas predictions because the behavior of individual molecules tends to average out, leading to more predictable and consistent results.

Considering these factors, the most ideal conditions for P, T, and n are low pressure, high temperature, and high number of moles, respectively. This corresponds to the option: low P, high T, and high n.

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To recognize linear equations write them in Ax = b form, Gaussian elimination, check in raw-echelon for all coefficients in zero, and if it exists its a contradiction and inconsistent.

To easily recognize when a system of linear equations is inconsistent, you can follow these steps:

1. Write the system of linear equations in the form Ax = b, where A is the matrix of coefficients, x is the vector of variables, and b is the constant vector.

2. Perform Gaussian elimination or row reduction on the augmented matrix [A | b] to obtain the row-echelon form.

3. Check for any row in the row-echelon form where all the coefficients of the variables are zero, but the constant term is nonzero (i.e., 0x + 0y + ... + 0z = k, where k ≠ 0).

4. If such a row exists, then the system of linear equations is inconsistent because it represents a contradiction (e.g., 0 = k, where k ≠ 0).

If no such row is found, then the system is either consistent and has a unique solution or consistent and has infinitely many solutions, depending on the number of free variables.

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Approximately 95% of the engineering students spend between 150 and 270 minutes studying each day.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

150 and 270 minutes are within two standard deviations of the mean, as:

Hence the percentage is given as follows:

95%.

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a. The statement that the dot product is the only possible inner product in Rn is false. While the dot product is one example of an inner product, there are other inner products that can be defined in Rn. b. True. The projection is zero. c. The statement that it is possible to construct an inner product in the continuous function space using a definite integral is true

a. False. The dot product is a common inner product in Rn, but there are other inner products that can be defined. Also, the vectors (1,2,1) and (1,-1,1) are not orthonormal because their dot product is not zero and their magnitudes are not equal to 1.

b. True. The projection of a vector onto another vector is zero if they are orthogonal. Mathematically, proj_v1(v2) = 0 if (v1, v2) = 0, where (v1, v2) represents the inner product of vectors v1 and v2.

c. True. It is possible to construct an inner product in the continuous function space using a definite integral. One such inner product is defined as (f, g) = ∫_a^b f(x)g(x) dx, where f and g are continuous functions on the interval [a, b], and a and b are real numbers.

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The correct confidence interval for the mean lifetime of this type of battery is (114.56, 125.64).

Explanation:
We know that the sample size n is 50, the sample mean x is 120.1, and the population standard deviation is 20. We want to construct a 99% confidence interval for the mean lifetime of this type of battery.

The formula for the confidence interval is:

x ± z*(σ/√n)

where x is the sample mean,  is the population standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level.
   
For a 99% confidence interval, the z-score is 2.576 (using a z-score table or calculator).    
   
Plugging in the values, we get:

120.1 ± 2.576*(20/√50)

= (114.56, 125.64)

Therefore, the confidence interval for the mean lifetime of this type of battery is (114.56, 125.64) with 99% confidence.
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The statement that is true about the dilation is AB/BC = AD/DE

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

This means that

So, we have

AB/BC = AD/DE

This represents option (b)

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The value of angle s is determined as 22.5 ⁰.

The value of angle s is calculated by applying intersecting chord theorem as shown below;

The missing arc angle is calculated as;

arc LI = 360 - (125 + 95)

arc LI = 140⁰

The value of angle s is calculated as follows;

∠s = ¹/₂ (arc LI - arc KI) (intersecting chord theorem)

∠s =  ¹/₂ ( 140 - 95 )

∠s =  ¹/₂ ( 45 )

∠s = 22.5 ⁰

Thus, the value of the missing angle s (tangent angle) is determined by applying intersecting chord theorem.

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The transformations of the exponential function are given as follows:

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

Hence the transformations of the exponential function are given as follows:

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The one less function is defined as a function that accepts an integer argument and returns an integer value, which is one less than the input argument. For example, if the input is 7, the function returns 6, and if the input is 44, the function returns 43.

To define a function named "one less" that receives an int argument and returns an int that is one less than the value of the argument, you can write:

```
def oneless(num: int) -> int:
   return num - 1
```

This function takes an integer argument "num" and returns the result of subtracting 1 from it. So if you call the function with the argument 7, it will return 6, and if you call it with argument 44, it will return 43.
The oneless function is defined as a function that accepts an integer argument and returns an integer value, which is one less than the input argument. For example, if the input is 7, the function returns 6, and if the input is 44, the function returns 43.

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The probability of the spinner first not landing on green, spun again, and then landing on green is P ( A ) = 0.2475

Given data ,

Let the probability of the spinner first not landing on green, spun again, and then landing on green is P ( A )

Now , the probability that spinner landing on green = 0.45

And , the probability that spinner not landing on green = 0.55

So , P ( A ) = probability that spinner landing on green x probability that spinner not landing on green

P ( A ) = 0.45 x 0.55

P ( A ) = 0.2475

Hence , the probability is 0.2475

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True.

A number c is an eigenvalue of a matrix A if and only if the equation (A - cI)v = 0 has a non-zero solution, which can be rewritten as (A - cI)v = 0v. This means that v is a non-zero eigenvector of A corresponding to the eigenvalue c.

A number c is an eigenvalue of a matrix A if and only if the equation (A - cI)v = 0 has a non-zero solution, which can be rewritten as (A - cI)v = 0v. This means that v is a non-zero eigenvector of A corresponding to the eigenvalue c.

If we multiply both sides of the equation (A - cI)v = 0 by -1, we get (cI - A)v = 0. This means that v is a non-zero solution to the homogeneous equation (cI - A)v = 0.

Therefore, we can say that a number c is an eigenvalue of A if and only if the equation (A - cI)v = 0 has a non-zero solution or equivalently if and only if (cI - A)v = 0 has a nontrivial solution.

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Therefore, the vector form of the quadratic equation y = x² + 8x + 15 is y = (x + 4)² + 14.

To convert the standard form of a quadratic equation, y = ax² + bx + c, into vertex form, we need to complete the square.

First, let's factor the quadratic coefficient a out of the first two terms:

y = x² + 8x + 15

y = 1(x² + 8x) + 15

To complete the square, we need to add and subtract (b/2)² inside the parentheses:

y = 1(x² + 8x + 16 - 16) + 15

Notice that we added and subtracted 16 inside the parentheses, which is equal to (8/2)². We can now write the first three terms as a perfect square:

y = 1(x + 4)² - 1 + 15

Simplifying the constant terms, we get:

y = (x + 4)² + 14

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Answer: 2.1 is the answer

so you change 1 1/2 to a decimal then it becomes 1.5 then multiply by 1.4 and that equals 2.1

Answer:

The Correct answer is 21/10 or 2.1

Step-by-step explanation:

1.4×1½

7/5×3/2

21/10=2.1

The number line has been plotted below.

             -2 1/4                                      5/2

 < _____⊥____________________⊥___________>    

         -3    °  -2       -1       0       1        2  °      3

We know that,

A number line is a visual representation of numbers placed in a straight line. It is a tool used in mathematics to illustrate the concept of magnitude and order of numbers. The line is usually drawn horizontally, with zero placed in the middle and positive numbers to the right and negative numbers to the left.

The distance between the numbers on the line represents their magnitude or difference. Number lines are commonly used to teach students about basic arithmetic, fractions, decimals, and other mathematical concepts.

             -2 1/4                                      5/2

 < _____⊥____________________⊥___________>    

         -3    °  -2       -1       0       1        2  °      3

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A new golf instructional expert claims her students can hit their drivers an average of 300 yards, but the LPGA doubts this accuracy.

After taking a random sample of 45 students, the LPGA found an average distance of 285 yards with a standard deviation of 25 yards. To examine the expert's claim with a 5% error margin, you would perform a hypothesis test. If the test result falls within the 5% error margin, you would fail to reject the expert's claim.

However, if the result falls outside the 5% error margin, you would reject the claim and conclude that the students do not hit an average of 300 yards.

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Based on the given information, a journalist conducted a survey of a random sample of 900 adults in the United States, and 60 percent of them are in favor of increasing the minimum hourly wage.

The margin of error is given as 2.7 percentage points.
To determine the level of confidence, we need to use the margin of error and the sample size. The formula for margin of error is:
Margin of error = z * (standard deviation / sqrt(sample size))
where z is the z-score for the desired level of confidence, standard deviation is the estimated standard deviation of the population (which we don't know), and sqrt(sample size) is the square root of the sample size.
Since we don't know the standard deviation of the population, we can use the conservative estimate of 0.5 as the estimated proportion (since we don't know if the true proportion is closer to 0 or 1).
Using this information, we can solve for the z-score:
2.7 = z * (0.5 / sqrt(900))
2.7 = z * 0.0167
z = 2.7 / 0.0167
z = 161.68
Looking up this z-score in a standard normal distribution table, we can see that it corresponds to a level of confidence of 99.0%. Therefore, the closest answer choice is 99.0%.

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. With a margin of error of 2.7 percentage points, the closest level of confidence is approximately 95.0%.
To determine this, you can use the following steps:
1. Identify the sample proportion (p) and sample size (n): p = 0.60, n = 900.
2. Calculate the standard error (SE): SE = sqrt[p(1-p)/n] = sqrt[0.60(0.40)/900] ≈ 0.016.
3. Determine the margin of error (MOE): MOE = 2.7% = 0.027.
4. Divide the MOE by the SE: 0.027/0.016 ≈ 1.69.
5. Look up the value in a Z-table or use a calculator to find the corresponding confidence level: Z = 1.69 corresponds to approximately 95.0% confidence level.

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The probability that Steve will get a nine on the next card he is dealt is 4/47.  Steve and Cathy are playing a card game with a standard deck of 52 playing cards. After Cathy is dealt an ace and a four and Steve is dealt a jack, there are 49 cards left in the deck. Out of the remaining cards, there are three aces.

If Steve gets an ace on the next card he is dealt, he will win. The probability of this happening is 3/49, as there are three aces left in the deck out of a total of 49 cards remaining.

After Steve gets a two and Cathy gets a five, there are now 47 cards left in the deck. The probability of Steve getting a nine on the next card he is dealt is 4/47, as there are four nines left in the deck out of a total of 47 cards remaining.

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Answer: Therefore, (10ab)^2(2a^4b^3)/4a^5b simplifies to 50a^6b^4.

Step-by-step explanation: To simplify the expression, we can first expand the square of (10ab)^2, which gives us:

(10ab)^2 = 10^2 * a^2 * b^2 = 100a^2b^2

Substituting this into the expression gives:

(100a^2b^2)(2a^4b^3)/4a^5b

Simplifying the numerical factors, we get:

(50a^2b^2)(a^4b^3)/a^5b

Now we can cancel out common factors in the numerator and denominator:

(50)(a^2)(b^2)(a^4)(b^3)/(a^5)(b)

= (50a^2b^2)(a^4b^2)

= 50a^6b^4

Therefore, (10ab)^2(2a^4b^3)/4a^5b simplifies to 50a^6b^4.

The 90% confidence interval for the population mean an annual number of reported larceny cases in small communities in Connecticut is (127.2, 152.8). The margin of error is half the width of the interval, which is (152.8 - 140) / 2 = 6.4 cases per year.

To find a 90% confidence interval for the population mean an annual number of reported larceny cases in small communities, we will use the following formula:

CI = x ± Z * (σ/√n)

Where:
CI = Confidence interval
x = Sample mean (average number of reported larceny cases, which is 140)
Z = Z-score for 90% confidence level (which is 1.645, as found in Z-score tables)
σ = Population standard deviation (43 cases per year)
n = Sample size (45 small communities)

Step 1: Calculate the standard error:
Standard Error (SE) = σ/√n = 43/√45 ≈ 6.41

Step 2: Calculate the margin of error:
Margin of Error (ME) = Z * SE = 1.645 * 6.41 ≈ 10.55

Step 3: Calculate the confidence interval:
Lower Limit: x - ME = 140 - 10.55 ≈ 129.45
Upper Limit: x + ME = 140 + 10.55 ≈ 150.55
CI = 140 ± 1.645 * (43/√45)
CI = 140 ± 12.8
CI = (127.2, 152.8)

Therefore, the 90% confidence interval for the population means the annual number of reported larceny cases in small communities is approximately (129.45, 150.55), and the margin of error is approximately 10.55 cases.

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The given angles are complementary and the value of x is 15°

As per the shown figure, the given angles have a common side and vertex.

Here, the pairing of angles sums up to 90° then they are called complementary angles.

As we know that complementary angles are defined as when the sum of two angles adds up to 90°.

As per the given figure,

∠2x° + ∠(3x+15)° = 90°

2x + 3x + 15 = 90

5x = 90 - 15

5x = 75

x = 75/5

x = 15°

Thus, the given angles are complementary and the value of x is 15°.

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The standard deviation of the possible outcomes is approximately 15.24 hours.

To calculate the standard deviation of the possible outcomes, we first need to find the mean or expected value of the work hours. We can do this by multiplying each work hour by its corresponding probability, and then summing up the results:

Expected value = (0.3 x 45) + (0.2 x 40) + (0.4 x 25) + (0.1 x 12) = 30.3

Next, we need to find the variance of the possible outcomes. The variance is the average of the squared deviations of each outcome from the expected value. We can calculate the variance using the formula:

Variance = (sum of (x - mean)^2 * probability)

where x is the work hours and the sum is taken over all possible outcomes.

Variance = (0.3 x (45 - 30.3)^2) + (0.2 x (40 - 30.3)^2) + (0.4 x (25 - 30.3)^2) + (0.1 x (12 - 30.3)^2) = 231.87

Finally, we can calculate the standard deviation as the square root of the variance:

Standard deviation = sqrt(231.87) = 15.24

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The ball will strike the ground approximately 3.71 seconds after it is thrown.

To determine when the ball will strike the ground, we need to find the value of t when h = 0.

So we need to solve the equation:

h = -16t² + 220

0 = -16t² + 220

16t² = 220

t² = 220/16

t² = 13.75

Taking the square root of both sides, we get:

t = ± √13.75

Since time cannot be negative, we take the positive root:

t = √13.75

t ≈ 3.71 seconds (rounded to two decimal places)

Therefore, the ball will strike the ground approximately 3.71 seconds after it is thrown.

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