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The distance across the lot, or the altitude of the trapezoid, is 60 feet.

Let's denote the length of the shorter base by x, and the length of the longer base by y. Then, we can use the formula for the area of a trapezoid:

Area = (x + y) * h / 2,

where h is the altitude (distance across the lot) and Area is given as 8,400 square feet.

We also know that the sum of the bases is 280 feet, so x + y = 280.

Now we can solve for h:

h = 2 x  Area / (x + y)

Substituting the given values, we get:

h = 2 x  8,400 / 280 = 60 feet.

Therefore, the distance across the lot, or the altitude of the trapezoid, is 60 feet.

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After 14 years, Bryn will owe £2,109.47, when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

Determine the annual interest rate: 28%

Convert the interest rate from a percentage to a decimal: 28% ÷ 100 = 0.28

Calculate the total interest owed over 14 years: £800 * 0.28 = £224

Calculate the new loan amount after the first year: £800 + £224 = £1024

Repeat steps 3 and 4 for each subsequent year, using the updated loan amount from the previous year instead of the original loan amount:

The amount owed by Bryn after 14 years can be calculated by multiplying the original loan amount by (1 + the annual interest rate) raised to the power of the number of years:

£800 * (1 + 0.28)¹⁴

= £800 * 1.28¹⁴

= £800 * 2.636849

= £2,109.47

So, Bryn will owe £2,109.47 after 14 years; when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

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Answer:

answer is (C).

Step-by-step explanation:

Substituting y = -x + 2 from the second inequality into the first inequality, we get:

z^2x + 1 < (-x + 2)z^2

Rearranging, we get:

z^2(x + 1) < (-x + 2)z^2 - 1

Dividing both sides by z^2, and noting that z^2 > 0, we get:

x + 1 < (-x + 2) - 1/z^2

Simplifying, we get:

2x < -1/z^2

x < -1/(2z^2)

Therefore, for any value of z, the solution set of the system is the set of all ordered pairs (x, y) where x < -1/(2z^2) and y < -x + 2.

Checking each of the answer choices:

   (-6, 3.5): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-6, -3): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-4, 3): In the solution set, since -4 is less than -1/(2z^2) for any value of z, and 3 is less than -(-4) + 2 = 6.

   (-4, 4): Not in the solution set, since -4 is not less than -1/(2z^2) for any value of z.

Therefore, the ordered pair included in the solution set is (-4, 3), and the answer is (C).

In the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

A sample space is a set of potential results from a random experiment.

The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results.

There are just two possible results when we toss a coin: either head or tail.

So, S = H, T, where H is the head and T is the tail, will be the sample space.

As a result, we are aware that there will be a total of 2n outcomes available if there are 'n' coins.

So, the coin has 2 outcomes which are H and T.

And the spinner has 8 outcomes which are 1 - 8.

Then, the sample space would be as follows:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

So, the sample space has a total of 16 elements.

Therefore, in the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

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Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 1500(1 + (0.04 × 5)) = 1800

A = $1,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 4% per year for 5 years is $1,800.00.

It is not differential at interval [-2,0].

What is the mean value theorem?

The mean value Theorem basically asserts that there is at least one place where the tangent to the arc is parallel to the secant through its ends for any given planar arc between two endpoints. One of the most significant findings from the serious analysis is this one.

Here, we have

Given: f(x) = [tex]\left \{ {{x^2-x, -2\leq x\leq -1} \atop {2x^2-3x-3, -1 < x\leq 0}} \right.[/tex]

We have to find that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.

We need to check the continuity at -1.

LHL: [tex]\lim_{n \to \ -1} x^2-x[/tex]

= (-1)² -(-1)

= 1 + 1 = 2

RHL:  [tex]\lim_{n \to \ -1} x^2-x[/tex]

= 2(-1)² - 3(-1) -3

= 2 + 3 - 3

= 2

f(-1) = 2

f(x) is continuous at x = -1

Now,

f'(x) = [tex]\left \{ {{2x-1, -2\leq x\leq -1} \atop {4x - 3, -1 < x\leq 0}} \right.[/tex]

LHL: [tex]\lim_{n \to \ -1} 2x - 1[/tex]

= 2(-1) - 1

= -3

RHL: [tex]\lim_{n \to \ -1} 4x - 3[/tex]

= 4(-1) - 3

= -7

∴ LHL ≠ RHL

It is not differential at interval [-2,0]

Hence, it is not differential at interval [-2,0].

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The events are Not Mutually Exclusive (Inclusive)

The concept of mutually exclusive events is based on the idea that two events cannot occur at the same time. In other words, the occurrence of one event means that the other event cannot happen.

In the case of the jersey example, the events "picking a purple jersey" and "picking a jersey with a number greater than five" are not mutually exclusive because it is possible to pick a jersey that satisfies both conditions (i.e., a purple jersey with a number greater than five).

On the other hand, if the events were mutually exclusive, it would mean that it is impossible for them to happen at the same time. For example, if we modified the scenario to have only yellow jerseys numbered one to five and purple jerseys numbered six to ten, then the events "picking a purple jersey" and "picking a jersey with a number greater than five" would be mutually exclusive, as no jersey can satisfy both conditions.

Therefore, in the original scenario where the bag contains six yellow jerseys numbered one to six and four purple jerseys numbered one to four, the events are not mutually exclusive (inclusive).

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24 cupcakes in 1 hour and 18 cupcakes in 3/4 hour (or 45 minutes) both have same rate of change.

The rate of change refers to the speed at which a variable or quantity changes over a given period of time. It is often expressed in terms of units per time, such as meters per second or dollars per year. The rate of change can be positive or negative, depending on whether the variable is increasing or decreasing.

A constant rate refers to a fixed or unchanging rate of change over time. In other words, it is a steady and consistent rate that does not fluctuate or vary. This term is commonly used in mathematics and finance to describe situations where a value or quantity changes at a constant rate over a given period of time.

Athena made 3 dozen cupcakes in 1 1/2 hours. To find the constant rate of change, we need to determine the number of cupcakes she made per hour.

1 dozen = 12 cupcakes

So, Athena made 3 dozen cupcakes = 3 x 12 = 36 cupcakes.

Constant rate of change = Cupcakes made / Time taken

Option 1: 24 cupcakes in 1 hour

Option 2: 18 cupcakes in 3/4 hour (or 45 minutes)

Both options represent the same constant rate of change as Athena's, which is 36 cupcakes per hour.

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The volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.

The volume of a cuboid also known as a rectangular prism can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of two rectangular prism observed and thus derive the volume of the solid figure by the sum of our results as follows:

Volume of larger cuboid = 5 ft x 4 ft x 4 ft = 80 ft³

Volume of smaller cuboid = 6 ft x 4 ft x ft = 72 ft³

Volume of solid figure = 80 ft³ + 72 ft³ = 152 ft³

Therefore, the volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.

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Answer:

2.5

Step-by-step explanation:

I took the test :)

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

The speed (cοmmοnly referred tο as v) οf an οbject is the magnitude οf the change οf its pοsitiοn οver time οr the magnitude οf the change οf its pοsitiοn per unit οf time; it is thus a scalar quantity.

The average speed οf an οbject in an interval οf time is the distance travelled by the οbject divided by the duratiοn οf the interval the instantaneοus speed is the limit οf the average speed as the duratiοn οf the time interval apprοaches zerο. Speed is nοt the same as velοcity.

Here,

The 216-fοοt length οf the car's skid marks is all that is presented tο us. The speed οf the car befοre the brakes were applied can be calculated using the fοrmula s = 24d(1/2), where s is the speed οf the car in miles per hοur (mph) and d is the length οf the skid marks in feet.

When we replace the specified value οf d, we οbtain:

=> s = 24√(216)

=> s = 24(14.6969)

=> s = 352.7256

Thus, the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

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A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his  trapezoid office.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given trapezoid , Base a = 10ft , Base b= 18ft and Height h = 18ft.

Now using area of trapezoid formula then,

=> Area A = [tex]\frac{a+b}{2}\times h[/tex] square unit.

=> A = [tex]\frac{10+18}{2}\times 18[/tex]

=> A = [tex]\frac{28}{2}\times 18[/tex]

=> A = [tex]14\times18[/tex]

=> A = 252 [tex]ft^2[/tex]

Hence A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his office.

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Answer:

The mean of the sample distribution of sample means will be equal to the population mean, which is 317 grams. The standard deviation of the sample distribution (also called the standard error) will be equal to the population standard deviation divided by the square root of the sample size:

standard error = 29 / sqrt(25) = 5.8

To find the weight at which the mean weight of 25 fruits will be greater than 5% of the time, we need to find the z-score that corresponds to the 95th percentile (since 5% of the time we want the mean weight to be greater than some value). Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 95th percentile is approximately 1.645.

Now we can use the formula for z-scores to find the weight at which the mean weight of 25 fruits will be greater than 5% of the time:

z = (x - mu) / se

where x is the weight we want to find, mu is the population mean (317 grams), and se is the standard error (5.8 grams).

Substituting the values we have:

1.645 = (x - 317) / 5.8

Solving for x, we get:

x = 317 + 1.645 * 5.8 = 326.5

Rounding to the nearest gram, we get that the mean weight of 25 fruits will be greater than 326 grams 5% of the time.

Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

If Lorna uses 7.2 cups of flour in 3 different baking recipes, and uses an equal amount of flour in each recipe, we can find the amount of flour she uses in each recipe by dividing the total amount of flour by the number of recipes:

Flour per recipe = Total flour / Number of recipes

Flour per recipe = 7.2 cups / 3 recipes

Flour per recipe = 2.4 cups per recipe

Therefore, Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

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The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

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The vertex of the graph of the given equation y = x² - x - 2 is calculated as: (1/2, -9/4).

To find the vertex of a parabolic function in the form of y = ax² + bx + c, we use the formula x = -b/2a to find the x-coordinate of the vertex.

In this case, the given equation is y = x² - x - 2, so a = 1, b = -1, and c = -2.

Using the formula, we have:

x = -b/2a = -(-1)/(2*1) = 1/2

To find the y-coordinate of the vertex, we substitute this value of x back into the original equation:

y = (1/2)² - (1/2) - 2 = -9/4

Therefore, the vertex of the equation, y = x² - x - 2, is: (1/2, -9/4).

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Answer:

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.Converting to a mixed number, they had 16 2/3 marbles altogether.

Applying the triangle proportionality theorem, the measure of side FD in the image is calculated as: FD = 13.6.

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Use the triangle proportionality theorem to find AB:

AB/BC = AE/ED

Substitute:

AB/12 = 6/9

AB = (12 * 6) / 9

AB = 8

Find CD using the Pythagorean theorem:

CD = √(AC² - AD²)

Substitute:

CD = √(20² - 15²)

CD = 13.2

Since ΔACD ~ ΔDFC, therefore their sides are proportional:

AC/FD= CD/FC

Substitute:

20/FD= 13.2/9

FD= (20 * 9) / 13.2

FD = 13.6

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If a survey is taken at a movie theater in Winterville. The first 225 people who entered the theater were asked about their favorite type of movie. The  true about this situation is: C. The population is the total number of people who go to the movie theater, and the sample is the first 225 people at the theater.

In this situation, the survey was taken of the first 225 people who entered the movie theater. Therefore, the sample is the group of 225 people who were surveyed. The population of interest is the total number of people who go to the movie theater, as these are the individuals who could potentially have a favorite type of movie.

However, it is not practical to survey every person who goes to the movie theater, so a sample of 225 people was taken from the population.

Therefore, option C is the correct answer.

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The equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

A mathematical assertion that proves the equality of two mathematical expressions is what an equation in algebra means.

For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the 'equal' sign separating them.

So, we know that the machine charges:

11.9%

Then, the equation that will tell the total charge would be:

Let Y represents the total charge and x be the value of coins.

Then, the equation would be:

Y = x/100 * 11.9

Therefore, the equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

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Correct question:

Many grocery stores have machines that will give you cash for your change but charge a fee. Coinstar machines charge an average fee of 11.9% of your coins' value. Write an equation that models the total fee you pay (y) based on the value of your coins (x) if you use a Coinstar machine.

The probability of taking salmon packet  is 5/12.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here Total number of packets = 18

Then the cat eat all tune . Number of tune packets = 6.

Then remaining packet= 18-6 = 12

Now number of salmon packet = 5.

Then probability that it will be salmon is,

=> P = Number of salmon packet/ Total number of remaining packet.

=> P = 5/12.

Hence the probability of taking salmon packet in fraction is 5/12.

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Answer:

Step-by-step explanation:

(x-5)^2 +5=49

(x-5)(x-5)+5=49

x^2-10x+25+5=49

x^2-10x-19 -  quadratic formula

2[tex]\sqrt{11}[/tex]+5 and -2[tex]\sqrt{11}[/tex]+5

Step-by-step explanation:

(x-5)² + 5 =49

(x-5)(x-5) + 5 = 49

(x² - 5x -5x + 25) + 5 = 49

x² - 10x + 25 + 5 = 49

x² - 10x + 30 =49

x² - 10x = 19

x² - 10x - 19 = 0( USING QÜÃDRATÏC FØRMÛLÂ)

2√11 +5 / -2√11 + 5

~~KIM~~

Answer:

Step-by-step explanation:

Given a total expense of $175 for 4 tickets and an included parking fee of $25, you want an equation for the cost of a ticket, and the solution to that equation.

The total cost is the sum of the items that contribute to that total. Here, the 175 total cost is the sum of 25 and the price of 4 tickets. If we let 't' represent the price of a ticket, we can describe this relation by ...

   175 = 25 + 4t . . . . . . equation for the cost of a ticket

This is a 2-step linear equation. The two steps to the solution are ...

  Step 1: isolate the variable term by subtracting the constant

     175 -25 = 25 -25 +4t

     150 = 4t

  Step 2: find the value of the variable by dividing by its coefficient

     150/4 = 4t/4

     37.50 = t

This tells us the cost of a ticket is $37.50.

__

Additional comment

"Write an equation that can be used ..." covers a lot of territory. It is simplest to interpret it to mean "describe the given relationships using one or more equations." You are expected to know how costs are added based on your life experience: the total you pay is the sum of the costs of the individual items.

We could write the equation as ...

  t + t + t + t + 25 = 175

Some cashiers will add every item separately like this. Others will enter the price once and tell how many times that price is part of the total:

  4t +25 = 175

Multiplication was invented for the purpose of simplifying repeated addition.

The amount of the Pilipino pesos that we are going to obtain here is 59220.

Direct proportionality is a mathematical relationship between two variables, where an increase in one variable is accompanied by a corresponding increase in the other variable, and a decrease in one variable is accompanied by a corresponding decrease in the other variable. In other words, if two variables are directly proportional, they change in the same direction at the same rate.

Let the Philippines pesos be P and the US dollars be D

P α D

P = kD

k = P/D

k = 44391.90/1050

k = 42.3

Then;

P = 42.3 * 1400

P = 59220

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If the manager of a home economics stores considering the pricing a new model of digital cameras. The maximum revenue is $78,000.

To find the price that will maximize monthly value, we need to determine the price that will give us the highest revenue. Revenue is given by the formula:

Revenue = Price x Quantity

Let's let x be the number of times the price is decreased by $20 from $900. Then the price of the camera would be:

Price = 900 - 20x

And the quantity sold would be:

Quantity = 70 + 5x

So the revenue would be:

Revenue = (900 - 20x)(70 + 5x)

Expanding this expression gives:

Revenue = 63000 + 1300x - 100x^2

To maximize this quadratic function, we need to find the x-value that corresponds to the vertex of the parabola. The x-value of the vertex is given by:

x = -b/2a

where a = -100, b = 1300, and c = 63000. Substituting these values gives:

x = -1300/(2(-100)) = 6.5

Since we can't decrease the price by a fractional amount, we'll round this down to 6, which means we'll decrease the price by $120. So the price of the camera that maximizes monthly revenue is:

Price = 900 - 20(6) = $780

And the quantity sold at this price is:

Quantity = 70 + 5(6) = 100

So the maximum revenue is:

Revenue = 780(100) = $78,000.

Therefore the revenue is $78,000.

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Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

Answer:

The value for theta is 16.7 degrees and that of alpha is 73.3 degrees.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.

To find alpha, we can take the inverse tangent of both sides of the equation:

tan α = 10/3

tan⁻¹(tan α) = tan⁻¹(10/3)

α = tan⁻¹(10/3)

Using a calculator, we get:

α ≈ 73.3 degrees (rounded to one decimal place)

Therefore, the value of alpha is approximately 73.3 degrees.

To find theta, we can take the inverse tangent of both sides of the equation:

tan θ = 3/10

tan⁻¹(tan θ) = tan⁻¹(3/10)

θ = tan⁻¹(3/10)

Using a calculator, we get:

θ ≈ 16.7 degrees (rounded to one decimal place)

Therefore, the value of theta is approximately 16.7 degrees.\

Step-by-step explanation:

As the sample size increases, the t distribution becomes narrower and closer to a normal distribution.

The t statistic for the larger sample size is larger than the t statistic for the smaller sample size, indicating stronger evidence against the null hypothesis.

To calculate the estimated standard error for the larger sample size of n=89:

sM = √(sample variance / sample size)

sM = √(39.7 / 89)

sM= 0.6527

To calculate the t statistic for the larger sample size:

t = (sample mean - population mean) / sM = (16.9 - 16) / 0.6527

t = 1.375

The probability of getting the t statistic or something more extreme for the sample size of n=35 can be found by using the t distribution with degrees of freedom (df) = 34 (n-1). Using the Distributions tool and the given t statistic of 0.85, we find that the probability is approximately 0.2.

The probability of getting the t statistic or something more extreme for the sample size of n=89 can be found by using the t distribution with df=88. Using the Distributions tool and the calculated t statistic of 1.375, we find that the probability is approximately 0.085.

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