A rocket is launched in the air. Its height in feet is given by ℎ ( � ) = − 16 � 2 + 144 � h(t)=−16t 2 +144t where � t represents the time in seconds after launch. What is the rocket’s greatest height?

The translated function can be written as:

g(x) =   |(1/2)*x - 5/2| + 3

For a function f(x), we define a translation of N units as:

g(x) = f(x + N)

Where:

Then a translation of one unit to the right is:

g(x) = f(x - 1)

For our function:

f(x) = | (1/2)*x - 2| + 3

We will have:

g(x) = |(1/2)*(x - 1) - 2| + 3

      =  |(1/2)*x - 5/2| + 3

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Answer:

There is a 2.56% chance that you would need to ask four people before finding someone who prefers a salad for lunch.

Answer:

Step-by-step explanation:

Use PEMDAS order

Parenthesis

Exponents

Mult/Div whichever is first

Add/Sub whichever is first

Special Because the division is there Do above the line and below first, dividing will be last

Substitute

[tex]\frac{2(5) - 3(5-3)}{3-1}[/tex]

[tex]\frac{2(5)-3(2)}{2}[/tex]

[tex]\frac{10-6}{2}[/tex]

[tex]\frac{4}{2}[/tex]

2

2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n  Following the resolution of the question

The cube root of a number is a value that, when multiplied by itself three times, returns the original value.

Let r1, r2, and r3 be the three integer roots of x3 + x + 4 (2 2016n) = 0.

According to Vieta's formulae, we have:

r1 + r2 + r3 = 0 r1r2 + r1r3 + r2r3 = r1r2r3 = r1r2r3 = 2 2016n - 4

Because r1, r2, and r3 are integers, their product r1r2r3 is an integer as well. As a result, 2 2016n - 4 must be an integer. That is, 2016n must be an integer plus 2/2n.

Because 2016 is divisible by 25, we may write 2016n as (25)n = 2(5n). As a result, 2/2n can be condensed to 2(1-n).

Thus, 2016n = k + 2(1-n), where k is an integer. That is, 2016n is congruent to 2(1-n) modulo 1.

We see that 2 is a primitive root modulo 31, which indicates that every integer close to 31 may be written as a power of 2 modulo 31. Specifically, 230 1 (mod 31), so 215 1 (mod 31).

We have 2016 0 (mod 2), 9 (mod 31), and 6 (mod 7), since 2016 = 25 32 7. As a result, 2016n = 0 (mod 2), 1 (mod 31), and 1 (mod 7).

We analyse three possible scenarios:

Case 1 consists of 2016n 0 (mod 2) and 2016n 1 (mod 7).

2016n 1 (mod 31) in this situation because 2016n 1 (mod 7) indicates that 2016n 1, 9, 15, or 23 (mod 31) and 2016n is even. As a result, 2016n 1 (mod 31) and 2016n 1 (mod 7).

2016n 1 (mod 217) is the sole possibility.

Case number two: 2016n 1 (mod 31) and 2016n 1 (mod 7).

2016n 1 (mod 217) because 2016n 1 (mod 31) indicates that 2016n 1, 15, or 16 (mod 217), and 2016n 1 (mod 7). As a result, the sole option is 2016n 1 (mod 217).

Cases 3 and 4: 2016n 1 (mod 31) and 2016n 2 (mod 7).

2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n.

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The possible values of α are:

-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)

-2(504ⁿ - 1) - 2

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Let the three integer roots of the given cubic equation be denoted by p, q and r, so we have:

x³ + αx + 4 - (2 × 2016ⁿ) = (x - p)(x - q)(x - r)

Expanding the right-hand side and equating coefficients with the left-hand side, we get:

p + q + r = 0

pq + qr + rp = α

pqr = 2 × 2016ⁿ - 4 = 4(504ⁿ - 1)

Since p, q, and r are integers, their sum is also an integer, which means that they must have the same parity (i.e., they are either all even or all odd). Moreover, since their product is even, at least one of them must be even. Therefore, we have two cases to consider:

Case 1: p, q, and r are all even

In this case, we can write p = 2m, q = 2n, and r = 2k, where m, n, and k are integers. Substituting these into the equations above, we get:

m + n + k = 0

4mn + 4nk + 4km = α/2

8mnk = 4(504ⁿ - 1)

Since m + n + k = 0, we have k = -(m + n). Substituting this into the second equation, we get:

-4mn - 4nm - 4n² = α/2

-8mn - 8n² = α

Substituting the expression for 8mnk from the third equation, we get:

-2(504ⁿ - 1) - 2n² = α

Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer.

Case 2: p, q, and r are all odd

In this case, we can write p = 2m + 1, q = 2n + 1, and r = 2k + 1, where m, n, and k are integers. Substituting these into the equations above, we get:

m + n + k = -1

4mn + 4nk + 4km = α

8mnk + 2(m + n + k) = 4(504ⁿ - 1)

Since m + n + k = -1, we have k = -(m + n + 1). Substituting this into the second equation, we get:

-4mn - 4nm - 4n² - 4m - 4n - 4 = α/2

-8mn - 8n² - 8m - 8n - 8 = α

Substituting the expression for 8mnk from the third equation, we get:

-2(504ⁿ - 1) - 2n² - 2(m + n + 1) = α

Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n² - 2(m + n + 1), where m, n, and k are integers such that m + n + k = -1.

In summary, the possible values of α are:

-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)

-2(504ⁿ - 1) - 2

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Answer:

Set your calculator to degree mode.

4) MU = √(28^2 - 17^2) = √495 = 3√55

= 22.2

sin(U) = 17/28, so U = 37.4°

E = 90° - 37.4° = 52.6°

5) tan(24°) = RT/28

RT = 28tan(24°) = 12.5

cos(24°) = 28/AT

AT•cos(24°) = 28

AT = 28/cos(24°) = 30.6

T = 90° - 24° = 66°

Required factors of the given expression is (7-10x) and (5x-4).

What is factor?

A number or algebraic expression that divides another number or expression evenly—that is, without a remainder is called factor. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression with only two factors (that is, itself and 1), is called a prime number; A positive integer or an algebraic expression that has more than two factors is called a complex number. The prime factors of a number or algebraic expression are those factors that are prime factors. According to the Fundamental Theorem of Arithmetic, any integer greater than 1 can be uniquely expressed as the product of its prime factors, except for the order in which the prime factors are written; for example, 60 can be written as a product of 2·2·3·5.

Given expression is

[tex]2(2x-1)^{2} + 2(3-6x)(4x-7) - 4 {x}^{2} + 1 - 6 {x}^{2} - 25x + 11[/tex]

We are Simplifying,

2(2x-1)² + 2(3-6x)(4x-7) - 4x² + 1 - 6 x² - 25x + 11

= 2( 4x²-4x+1)+2(12x-21-24x²+42x)-4x²+1-6x²-25x+11

= 8x²-8x+2+24x-42-48x²+84x-4x²+1-6x²-25x+11

= -50x²+75x-28

= -(50x²-75x+28)

= -[50x²-(50+25)x+28]

= -1[5x(10x-7)-4(10x-7)]

= -(10x-7)(5x-4)

= (7-10x) (5x-4)

Required factors of the given expression are (7-10x) and (5x-4)

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The limit of the given expression when we put the values of n and k is: γ = 0

We want to find the limit of the function as n tends to infinity:

lim n → ∞ [tex]\lim_{n \to \infty} \Sigma \frac{1}{k} - In (n)[/tex] for k = 1

n → ∞ simply means that n is approaching zero. Thus, we can simplify our expression when we put the limit for n to get:

1/k - 1

At k = 1, we have:

(1/1) - 1  = 0

Thus, γ = 0

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Answer:

Step-by-step explanation: 0.21

Answer:

Answer:

Step-by-step explanation:

Answer:

B. 8 fish

Step-by-step explanation:

Prism Formula = b × h (base × height)

b: 4 ft. ×2 ft.

h: 3 ft.

4 × 2 = 8 ft.

8 × 3 = 24 ft. of water.

Since 3 ft. of water is required for each fish, we will divide.

24 ÷ 3 = 8 fish.

Therefore, Mandy can fit 8 fish in her tank.

After answering the presented question, we may conclude that  expressions As a result, Sarah will have E61,600 left over from her loan after purchasing 8 limos.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

a) Sarah can buy 8 limousines because:

600,000 / 67,300 = 8.91

Because she cannot purchase a fraction of a limousine, the maximum number of limos she may purchase is eight.

b) To determine how much of the loan is left over, deduct the total cost of the limos from the loan amount:

8 x 67,300 = 538,400

600,000 - 538,400 = 61,600

As a result, Sarah will have E61,600 left over from her loan after purchasing 8 limos.

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The measure of the vertical angle m∠4 is equal to 29°, the equation that (3x - 8)° + 29° = 180° can be used to solve for x, which is equal to 53

The angles m∠4 and m∠2 are vertical angles as they are opposite on the intersecting lines, and they are equal so;

m∠4 = 29°

(3x - 8)° + 29° = 180° {sum of angles on a straight line}

3x + 21 = 180

3x = 180 - 21 {collect like terms}

3x = 159°

x = 159/3 {divide through by 3}

x = 53

Therefore, the measure of the vertical angle m∠4 is equal to 29°, the equation that (3x - 8)° + 29° = 180° can be used to solve for x, which is equal to 53

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The area of triangle PQR is approximately 23.07 square units.

To find the area of the triangle PQR, we can use the cross product of two of its sides and then compute half of the magnitude of the cross product vector.

First, let's find the vectors representing the sides PQ and PR:

PQ = Q - P = (2 - 4, 6 - 3, 0 - 3) = (-2, 3, -3)

PR = R - P = (4 - 4, -5 - 3, -3 - 3) = (0, -8, -6)

Now, let's compute the cross product of these two vectors:

PQ × PR = [(-2)(-6) - (3)(-8), (-3)(-8) - (-3)(0), (-2)(-8) - (3)(0)] = [12 + 24, 24, 16] = [36, 24, 16]

Now, we need to find the magnitude of this cross product vector:

|| PQ × PR || = √(36² + 24² + 16²) = √(1296 + 576 + 256) = √2128 ≈ 46.14

Finally, the area of triangle PQR is half the magnitude of the cross product:

Area = 0.5 * || PQ × PR || ≈ 0.5 * 46.14 ≈ 23.07

So, the area of triangle PQR is approximately 23.07 square units.

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Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.

Rent or a car payment are examples of monthly costs that are fixed expenses. On the other hand, a variable expense is one that can vary from month to month, like food or entertainment. Variable expenses demand greater flexibility in budgeting because the cost can change, but fixed expenses are often easier to prepare for because the amount is constant.

Given that, cost of tuition fee is $9,600 for the first year.

Now, Mateo's parents will pay for one-third of the tuition thus:

1/3 x $9,600 = $3,200

From the saving the money used is $1500 thus the remining cost is:

$9,600 - $3,200 - $1,500 = $4,900

For 12 months in a year we have:

$4,900 / 12 = $408.33

Hence, Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.

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Answer:

117.2

Step-by-step explanation:

P=a+b+a2+b2=50+15+502+152≈117.20153

AABC is similar to AGED with a scale factor of 22.5/48, which means that the width of the cart is proportional to the height, with a ratio of 30:22.5.

Since AABC and Matured are comparative, their relating points are equivalent, and their comparing sides are corresponding.

By definition, point An in AABC is equivalent to point An in Matured, as they are both right points. Likewise, point E in Matured is equivalent to point C in AABC, as they are both vertical points. At long last, point B in AABC is equivalent to point D in Matured, as they are both correlative points to point An and E, separately.

To demonstrate the sides are relative, we can utilize the proportions of comparing sides:

Stomach muscle/AG = BC/ED = AC/Promotion

Subbing the given qualities, we get:

Stomach muscle/48 = BC/36 = AC/x

where x is the length of the truck.

Tackling for x, we get:

x = AC * 36/BC

x = 30 * 36/48

x = 22.5 inches

In this way, AABC is like Matured with a scale variable of 22.5/48, and that implies that the width of the truck is relative to the level, with a proportion of 30:22.5.

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Answer:

18 minutes

Step-by-step explanation:

3 hours = 180 minutes (60*3)

You therefore have 180 minutes to visit 10 exhibits.

180/10=18

Assuming you spent the same amount of time at each exhibit, you would spend 18 minutes at each exhibit.

I hope this helps!

With a common ratio of 1.25, the percent change is 25%.

This indicates a relative increase or decrease of 25% from the initial value.

The percent change is a measure of the relative change in a value expressed as a percentage.

To calculate the percent change with a common ratio of 1.25, we can use the formula:

Percent Change = (Common Ratio - 1) [tex]\times[/tex]  100.

Percent Change = (Common Ratio - 1) [tex]\times[/tex]  100.

In this case, the common ratio is 1.25.

Substituting this value into the formula, we have:

Percent Change = (1.25 - 1 )[tex]\times[/tex] 100

[tex]= 0.25 \times 100[/tex]

= 25%.

The percent change, in this case, is 25%.

To understand the meaning of this percent change, consider an initial value of 100.

If we increase this value by 25%, the new value would be 125. Conversely, if we decrease the initial value by 25%, the new value would be 75.

Therefore, a percent change of 25% indicates a relative increase or decrease of 25% from the initial value.

It is important to note that the percent change is a measure of relative change and does not take into account the magnitude of the values.

In this case, a common ratio of 1.25 signifies a 25% increase or decrease, regardless of the specific values involved.

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The largest difference is between Olivia's score for level 1 and level 2, which is 34.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The largest difference between a player's score for level 1 and their score for level 2 can be found by subtracting their level 2 score from their level 1 score, and taking the absolute value of that difference.

For Edele: |(-4) - 27| = 31

For Zachary: |12 - (-5)| = 17

For Olivia: |-25 - 9| = 34

For Dominic: |16 - (-7)| = 23

Therefore, the largest difference is between Olivia's score for level 1 and level 2, which is 34.

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Answer:

x > - 31/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x > −31/2

For the deviation between each data value and the mean in column 3, there are around 1320.511 squared deviations in all.

To find the sum of the squared deviations in column 3, add up all the values in that column.

x x − x (x − x)²

50 50 − 40.545 (9.455)² = 89.397

28 28 − 40.545 (-12.545)² = 157.377

37 37 − 40.545 (-3.545)² = 12.567

30 30 − 40.545 (-10.545)² = 111.197

58 58 − 40.545 (17.455)² = 304.677

38 38 − 40.545 (-2.545)² = 6.477

39 39 − 40.545 (-1.545)² = 2.387

59 59 − 40.545 (18.455)² = 340.587

47 47 − 40.545 (6.455)² = 41.667

34 34 − 40.545 (-6.545)² = 42.837

26 26 − 40.545 (-14.545)² = 211.557

To find the sum of the squared deviations, add up the values in column 3:

x − x² = 89.397 + 157.377 + 12.567 + 111.197 + 304.677 + 6.477 + 2.387 + 340.587 + 41.667 + 42.837 + 211.557 = 1320.511

Rounded to three decimal places:

x − x² ≈ 1320.511

Therefore, the sum of the squared deviations in column 3 is approximately 1320.511.

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Carla is on track to get the correct answer.

Carla has set up the equations to find the slopes of CD, and DE correctly. But in contrast to Jonah she has also chosen to find the slopes of two adjacent sides. Since the question is to determine if the sides are perpendicular, we have to check if the pairs of adjacent sides are perpendicular. So we need to find the slopes of pairs of adjacent sides. So Carla is on right track.

Jonah also has set up the equations to find the slopes of CD and EF, correctly. But these two sides are non adjacent. And so comparing them does not given any information about whether adjacent sides are perpendicular. So Jonah is not on right track.

How do you find if the sides of a quadrilateral are perpendicular?

The question is really asking, if the adjacent sides of the quadrilateral are perpendicular. First we need to find, the slopes of pairs of adjacent sides. Then we need to find if the direction vectors corresponding to the slopes are perpendicular. to find this we can multiply the slopes. if the product is -1, then the vectors are perpendicular or else they are not.

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Answer:

s = 10

Step-by-step explanation:

using the cosine ratio with 45° on lower right of right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{10\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

s × [tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

s = 10

[tex]\boxed{\sf B.\,23x + 62}.[/tex]

[tex]\sf 5(4x + 12) + 3x + 2[/tex]

[tex]\sf (5)(4x)+(5)(12) + 3x + 2\\ \\20x+60 + 3x + 2[/tex]

[tex]\sf 20x+ 3x + 2+60 \\ \\\boxed{\sf 23x + 62} \Longrightarrow Final\,answer.[/tex]

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Solving equations is a process that involves a lot mathematical simplification. That's why I suggest you take a look at these answers to learn more about simplifying:  

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The total amount of interest earned on the account is $1049.15.

Simple interest is interest that is just based on the principal. It does not account for any interest accrued in prior periods and is determined as a percentage of the principal. If your principal is $1,000 and your yearly interest rate is 5%, for instance, you would make $50 in simple interest after a year ($1,000 0.05).

Contrarily, compound interest is calculated on the principal amount in addition to any prior quarters' interest. This means that interest is calculated on the new amount after the principal and interest earned during each period have been added.

The compound interest is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Rearranging for P we have:

[tex]P = A / (1 + r/n)^{(nt)}[/tex]

Substituting the value of r = 3.2%, n = 2 and t = 6 we have:

[tex]P = 6049.15 / (1 + 0.032/2)^{(2*6)}[/tex]

P = 5000

Here, P is the initial balance.

Now, for interest we have:

I = A - P

Substituting the values:

I = $6049.15 - $5000

I = $1049.15

Hence, the total amount of interest earned on the account is $1049.15.

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Answer:

336 square centimeters

Step-by-step explanation:

The area of a triangle is given by the formula:

A = (1/2)bh, where b is the base and h is the height.

The original triangle has a base of 7 cm and a height of 6 cm, so its area is:

A = (1/2)(7 cm)(6 cm) = 21 cm^2

When the triangle is dilated by a scale factor of 4, all of its dimensions are multiplied by 4. So the new base is 4 times the original base (28 cm) and the new height is 4 times the original height (24 cm).

The area of the new triangle is:

A' = (1/2)(28 cm)(24 cm) = 336 cm^2

Therefore, the area of the new triangle is 336 square centimeters.

Hope this helps^^

Answer:

13

Step-by-step explanation:

2(5) + 3(3 - 5) + (3)^2

10 + (9 - 15) + 9

19 - 6 = 13

Answer:

If Team A had 5 points less than Team B, and Team B had 15 more points than Team C, then Team A had 10 more points than Team C. If Team D had 15 more points than Team A, then Team D had 25 more points than Team C. Therefore, the order of finish from first to last would be Team D, Team B, Team A, and Team C.

According to the given data the length of a [tex]90^{0}[/tex] arc is [tex]\pi /2[/tex] or approximately [tex]1.57[/tex] feet.

In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.

According to the given information:

The length of a [tex]90^{0}[/tex] arc in a circle with radius [tex]1[/tex] foot can be calculated using the formula:

Length of arc = (angle/[tex]360[/tex]) x [tex]2\pi r[/tex]

where angle is the central angle of the arc in degrees, r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant approximately equal to [tex]3.14159[/tex].

Substituting the given values, we have:

Length of arc = ([tex]90/360[/tex]) x [tex]2\pi(1 ft)[/tex]

Length of arc = [tex](1/4)[/tex] x [tex]2\pi ft[/tex]

Length of arc = [tex]\pi /2 ft[/tex]

Therefore, the length of the [tex]90^{0}[/tex] arc is [tex]\pi /2 feet[/tex] or approximately [tex]1.57 feet[/tex]

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the length of the 90° arc is π/4 feet or approximately 0.785 feet

What is arc of circle?

In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.

The formula for the length of an arc is:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.

In this case, θ = 90° and r = 1 ft, so we have:

L = (90/360) × 2π(1) = (1/4) × π = π/4

Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).

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The t-value is given as follows:

t = 1.82.

The equation for the t-value is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 86.3, \mu = 83.5, s = 7.2, n = 22[/tex]

Hence the t-value is given as follows:

[tex]t = \frac{86.3 - 83.5}{\frac{7.5}{\sqrt{22}}}[/tex]

t = 1.82.

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