What key features do the functions f(x) = 3x and g of x equals the square root of the x minus 3 end root have in common?
a) Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
b) Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
d) Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions have a y-intercept in common.
d) Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions increase over the interval (–3, 0).

The quarts of water needed for 9 quarts of grape juice is 18 quarts of water .

The amount of grape juice needed for 15 / 4 quarts of water is 1 7/8.

The amount of water needed for 100 quarts is  66 2/3 quarts.

The amount of grape juice needed for 100 quarts is 33 1/3 quarts.

The first step is to determine the ratio between the ingredients needed for sparking grape juice.

Ratio of sparking water to grape juice - 1 1/2 : 2/4

When expressed in its simplest form, the ratio becomes - 1 1/2 : 1.2

This means that there are twice the amount of water is needed for 1 quart of grape juice.

Quarts of sparking water needed for 9 quarts of grape juice = 9 x 2 = 18 quarts of sparking water

Grape juice needed for 15/4 quarts of sparking water = 15 / 4 ÷ 2

15 / 4 x 1/2 = 15 / 8 = 1 7/8

Let a represent the quarts of grape juice that would be used to make 100 quarts of punch.

Let a represent the quarts of sparking water that would be used to make 100 quarts of punch.

a + 2a = 100

3a = 100

a = 100 / 3

a = 33 1/3

Quarts of sparking water needed = 100 - 331/3 = 66 2/3 quarts

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The volume of 11 gallons is 50 litres.

The volume of 40 litres is 8.8 litres.

The capacity of the tank in gallons is 26.7 gallons

The graph of a proportional relationship is always a straight line through the origin.

Therefore, the graph is a relationship between the variables volumes in litres and gallons. The litres is on the y axis while the gallons is on the x axis.

Hence, let's use the graph to convert the volumes.

11 gallons = 50 litres

40 litres = 8.8 litres

A tank has a volume of 120, 000 cm cube.

1 litre  = 1000 cm³

The capacity of the tank in gallons can be found as follows:

1000 cm³ = 1 litres

120,000 cm³= ?

volume in litres = 120,000 / 1000

volume in litres = 120 litres

From the graph,

36 litres = 8 gallons

120 litres = ?

cross multiply

volume in gallons = 120 × 8  / 36

volume in gallons = 960 / 36

volume in gallons = 26.6666666667

Therefore, the capacity of the tank in gallons is 26.7 gallons

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Answer:

  a) 50 L

  b) 8.8 gal

  c) 26.4 gal

Step-by-step explanation:

Given a graph showing the relationship between (imperial) gallons and litres, you want equivalents for 11 gallons, 50 litres, and 120000 cm³.

You have correctly read the graph, which tells you 11 gallons is about 50 litres.

You have correctly read the graph, which tells you 40 litres is about 8.8 gallons.

You are told that 1000 cm³ is 1 litre, so 120,000 cm³ will be 120 litres.

You notice this is 3 times the volume of the previous question:

  120 L = 3×(40 L) = 3×(8.8 gal) = 26.4 gal

120000 cm³ is about 26.4 gallons.

__

Additional comment

A more precise conversion of 120000 cm³ is 26.3963097959... gallons. The decimal has a very long repeat.

ANSWER

EXPLANATION

We want to expand the given expression using binomial expansion:

(a) In summation notation, binomial expansion is written as:

where:

Therefore, the summation notation for the expansion is:

(b) Now, we want to expand the expression. To do this, find each term taking k to go from 0 to 4, find the sum of the terms, and simplify.

That is:

Therefore, in simplified form, the expanded expression is:

Answer: 2

Step-by-step explanation:

The equation of the sphere in standard form is (x - 3)² + (y + 1)² + (z - 3)² = 45. Its center is (3, -1, 3) and the radius is √45.

To express the equation of the sphere in standard form, we need to complete the square for each variable term. Starting with the given equation, we group the x, y, and z terms together:

x² + y² + z² + 6x - 2y - 6z = 17

Now, we complete the square for each variable. For the x-terms, we add (6/2)² = 9 to both sides, for the y-terms, we add (-2/2)² = 1 to both sides, and for the z-terms, we add (-6/2)² = 9 to both sides:

x² + 6x + 9 + y² - 2y + 1 + z² - 6z + 9 = 17 + 9 + 1 + 9

This simplifies to:

(x + 3)² + (y - 1)² + (z - 3)² = 45

Now we have the equation in standard form, where the squared terms represent the radius of the sphere centered at the point (x, y, z). Therefore, the center of the sphere is (-3, 1, -3), and the radius is the square root of 45.

In conclusion, the equation of the sphere in standard form is (x - 3)² + (y + 1)² + (z - 3)² = 45. The center of the sphere is (3, -1, 3), and its radius is √45.

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Answer:

P = 1.5x.

Step-by-step explanation:

Let the length of each side of the first triangle be x, then

Perimeter of this triangle

= 2x + 1.5x

= 3.5x.

So perimeter of smaller triangle is:

P = 1/2 * 3.5x

P = 1,.5x.

The measure m<D is 26

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

m<ABE = 52

<EBD = <CBD

Now,

<ABE + <EBD + <DBC = 180 (linear pair)

52 + 2<EBD = 180

2<EBD = 128

<EBD = 128/2

<EBD = 64

Now, In ΔDEB using angle sum property

<DEB + <EDB + <DBE = 180

90+ <EDB + 64=180

<EDB = 26

Hence, the measure of <D is 26 degree.

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Answer:

Step-by-step explanation:

y =  3x - 4

x = 0,  y = 3*0 - 4

          y = -4

(0 , -4)

x = 1 ,    y = 3*1 - 4

            y = 3 - 4

            y = -1

(1 , -1)

x = 2  , y = 3*2 - 4

           y = 6 - 4

           y = 2

(2 , 2)

Now mark these points (0 , -4) , (1 , -1) & (2 , 2) in the graph and join the points

P(8, 3 < X < 9) = 0.5. So, option (D) is correct.

A uniformly distributed continuous random variable is defined by the density function f(x) = 0 on the interval [8, 10]. So, we have to find P(8, 3 < X < 9).

We know that a uniformly distributed continuous random variable is defined as

f(x) = 1 / (b - a) for a ≤ x ≤ b

Where,b - a is the interval on which the distribution is defined.

P(a ≤ X ≤ b) = ∫f(x) dx over a to b

Now, as given, f(x) = 0 on [8,10].

Therefore, we can say, P(8 ≤ X ≤ 10) = ∫ f(x) dx over 8 to 10= ∫0 dx over 8 to 10= 0

Thus, P(8, 3 < X < 9) = P(X ≤ 9) - P(X ≤ 3)P(3 < X < 9) = 0 - 0 = 0

Hence, the correct answer is 0.5. Thus, we have P(8, 3 < X < 9) = 0.5. So, option (D) is correct.

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The polynomial expression x³ + 9x² - 16x - 144 can be factored as (x + 9)(x² - x - 16) with a remainder of -288 when divided by the linear expression x + 9.

To determine the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9, we can use synthetic division (SD) to divide the polynomial expression by the linear expression.

The polynomial expression can be rewritten as:

x³ + 9x² - 16x - 144 = (x + 9)(x² - x - 16)

Using synthetic division, we divide the polynomial expression by x + 9:

 -9  |   1   9   -16   -144

       ---------------------

          1   0    -16   -288

The result of the division is 1x² + 0x - 16 with a remainder of -288.

Therefore, the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9 is that the polynomial expression can be factored as (x + 9)(x² - x - 16) with a remainder of -288.

This means that the polynomial expression can be written as the product of the linear expression x + 9 and the quadratic expression x² - x - 16. The remainder -288 indicates that there is no perfect division, and there is a leftover term of -288.

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The after-tax present worth according to the given values is $732,140.56 and the internal rate of return is 22.65%.

(a) To compute the after-tax present worth, we need to determine the net cash flow for each year and discount it to present value using the after-tax MARR of 15%.

Year 0: Initial cost of equipment = -$18,600
Years 1-10:
Revenue from bags = (100.3 bags/carton) x ($0.03/bag) x (200,000 cartons/year) = $120,780
Cost savings from reducing overfilling = (5.5%) x ($0.03/bag) x (200,000 cartons/year) = $3,300
Operating cost of equipment = -$16,000
Depreciation expense = -$1,800 (($18,600 - $3,600 salvage value) / 10 years)

Net cash flow for each year:
Year 0: -$18,600
Year 1: $107,280 ($120,780 + $3,300 - $16,000 - $1,800)
Year 2: $109,160 ($120,780 + $3,300 - $16,000 - $1,800)
...
Year 10: $113,640 ($120,780 + $3,300 - $16,000 - $1,800)

Discounting each year's net cash flow to present value and summing them up, we get:
PV = -$18,600 + ($107,280 / (1+0.15)^1) + ($109,160 / (1+0.15)^2) + ... + ($113,640 / (1+0.15)^10)
PV = -$18,600 + $750,740.56
PV = $732,140.56

Therefore, the after-tax present worth is $732,140.56.

(b) To compute the after-tax internal rate of return, we need to find the discount rate that makes the net present value equal to zero. We can use trial and error or a financial calculator to solve this.

Using trial and error, we find that a discount rate of approximately 22.65% makes the net present value equal to zero. Therefore, the after-tax internal rate of return is approximately 22.65%.

(c) To compute the after-tax simple payback period, we need to determine how long it takes for the cumulative net cash flow to equal the initial cost of the equipment.

Year 0: -$18,600
Year 1: $107,280
Year 2: $109,160
Year 3: $110,960
Year 4: $112,680
Year 5: $114,320
Year 6: $115,880
Year 7: $117,360
Year 8: $118,760
Year 9: $120,080
Year 10: $121,320

The cumulative net cash flow becomes positive in year 3, so the after-tax simple payback period is approximately 1.9 years (between year 2 and year 3).

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From the information given, the towline must be completely released to enable it to get to the maximum height. This problem is a trigonometry problem because it involves a solution that looks like a right-angled triangle.

In order to determine the maximum height of the parasailer, the length of the rope or towline must be established.

If the length and the height are known, the angle of elevation can be determined using the SOHCAHTOA rule.

SOH - Sine is Opposite over Hypotenuse

CAH - Cosine is Adjacent Over Hypotenus; while

TOA - Tangent is Opposite over Adjacent.

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There were 2200 visitors in the zoo by the end of Wednesday.

Step 1: Start with the given information that there were 2000 visitors in the zoo on Tuesday.

Step 2: Calculate the increase in visitor count on Wednesday by finding 10% of the Tuesday's count.

10% of 2000 = (10/100) * 2000 = 200

Step 3: Add the increase to the Tuesday count to find the total number of visitors by the end of Wednesday.

2000 + 200 = 2200

Therefore, by the end of Wednesday, there were 2200 visitors in the zoo.

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Answer:

1 is >

2 is >

I think this is right, you may need to confirm this

Step-by-step explanation:

2x²+3x=20

2x²+3x=20

(√2x)²+2(√2x)(3/2√2)+(3/2√2)²-(3/2√2)²=20

(√2x+3/2√2)²=20+9/8

(√2x+3/2√2)²= 169/8

(√2x+3/2√2)= ±13/2√2

√2x=10/2√2 or -16/2√2

x= 10/4 or -16/4

x= 5/2 or -4

The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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Answer:

the basic family of this right- angled triangle is generally 6 , 8 , 10.

this units have been derived from 3, 4, 5 by multiplying each unit by 2.

So, the answer to the length of one of its legs can either be 6 units or 8 units.

HOPE THIS HELPS.

The given distribution satisfies both conditions for a probability distribution, we can conclude that it is a probability distribution.

To determine whether the given distribution is a probability distribution, we need to check if the sum of all probabilities is equal to 1 and if all probabilities are non-negative.

Let's calculate the sum of all probabilities:

Sum of probabilities = 0.42 + 0.34 + 0.18 + 0.06 = 1

The sum of all probabilities is equal to 1, which satisfies the first condition for a probability distribution.

Now, let's check if all probabilities are non-negative:

All probabilities are greater than or equal to 0, which satisfies the second condition for a probability distribution.

Therefore, since the given distribution satisfies both conditions for a probability distribution, we can conclude that it is a probability distribution.

In summary, the distribution is a probability distribution.

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The closing price of the stock is 131.82 dollars.

A stock is an equity or share that represents the ownership of a fraction of a issuing corporation.If someone holds a stock more than 50% that person decides or in charge of most of the things in that co-corporation.

According to the given question The value of a stock opens at 130.48 on monday.

Given it change throughout the day as follow: -0.47, +2.89 , +3 .39 , -4. 47.

∴ The closing price of the stock will be

130.40 + ( -0.47 +2.89  +3 .39  -4. 47 )

= 130.48 + 1.34.

= 131.82 dollars.

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The production level that will maximize profit is approximately 122 units.  

How can we determine the production level that will maximize profit given the cost function and the demand function?

To find the production level that maximizes profit, we can calculate the profit function by subtracting the cost function from the revenue function. By determining the vertex of the resulting quadratic equation, we can identify the production level (x-coordinate of the vertex) at which profit is maximized.

To find the production level that will maximize profit, we need to determine the point where the cost function and the demand function intersect. The profit function can be calculated by subtracting the cost function from the revenue function (which is the product of the demand function and the production level).

Given:

Cost function: C(x) = 1700 - 7x (where x represents the production level) Demand function: p(x) = 1700 - 7x (where p(x) represents the price per unit)

To calculate the profit function, we subtract the cost function from the revenue function:

Profit function: P(x) = x * p(x) - C(x)

Now we substitute the given functions: P(x) = x * (1700 - 7x) - (1700 - 7x)

Simplifying further:

\(P(x) = 1700x - 7x^2 - 1700 + 7x\\ P(x) = -7x^2 + 1707x - 1700\)

To find the production level that maximizes profit, we need to determine the vertex of the quadratic equation P(x). The x-coordinate of the vertex represents the production level at which profit is maximized.

To find the x-coordinate of the vertex, we can use the formula  \(x =\frac{-b}{2a}\), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -7, b = 1707, and c = -1700. Substituting these values into the formula:

\(x=\frac{1707}{2*(-7)}\)

\(x=\frac{1707}{-14}\)

x ≈ 122.36

Rounding to the nearest whole number, the production level that will maximize profit is approximately 122 units.

Therefore, the production level that will maximize profit is approximately 122 units.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

the 50th integer in the list is 31245.

To find the 50th integer in the list of positive five-digit integers that use each of the digits 1, 2, 3, 4, and 5 exactly once, we can determine the pattern of the list and then find the corresponding number.

Since the digits 1, 2, 3, 4, and 5 can be arranged in 5! = 120 different ways, there are 120 five-digit integers that can be formed. To determine the 50th integer, we need to find the number at the halfway point of the list.

To organize the list, we can consider the first digit:

- The first digit can be any of the five numbers (1, 2, 3, 4, or 5).

- For each choice of the first digit, the remaining four digits can be arranged in 4! = 24 different ways.

So, there are 5 * 24 = 120 different arrangements, forming the entire list.

To find the 50th integer, we divide 50 by 24 and round up to the nearest whole number:

50 / 24 ≈ 2.0833

Rounding up, we get 3.

Therefore, the 50th integer in the list is formed by choosing the third digit for the first position. We then arrange the remaining four digits in ascending order, resulting in the number 31245.

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For a function f(x), its average rate of change on an interval [a, b] is given by what's called the "difference quotient",

\(\dfrac{f(b)-f(a)}{b-a}\)

and is basically the ratio of the difference in values of f(x) at the endpoints to the difference in the endpoints themselves.

I assume the 6 intervals below each table correspond to each table immediately above them.

From the first table, we get the following average rates of change (after arranging the intervals from left to right):

• [-3, -2] : (f(-2) - f(-3)) / (-2 - (-3)) = (7 - 12)/1 = -5

• [-2, -1] : (f(-1) - f(-2)) / (-1 - (-2)) = (4 - 7)/1 = -3

• [-1, 0] : (f(0) - f(-1)) / (0 - (-1)) = (3 - 4)/1 = -1

• [0, 1] : (f(1) - f(0)) / (1 - 0) = (4 - 3)/1 = 1

• [1, 2] : (f(2) - f(1)) / (2 - 1) = (7 - 4)/1 = 3

• [2, 3] : (f(3) - f(2)) / (3 - 2) = (12 - 7)/1 = 5

Just do the same for the other two tables. Note that each listed interval has length 1, so practically, each average rate of change over [a, b] is exactly f(b) - f(a).

For parts (c) and (d):

• (c) You'll notice that each of the average rates of change are odd numbers …

• (d) … but they're not necessarily all the same size, and they follow slightly different patterns.

Answer:

what's the question

Step-by-step explanation:

I don't see a questions ton

Answer:

C. q = -24

Step-by-step explanation:

q + 12 = -12

q= -12- 12

q= -24

\(q=-24\)

Let's solve your equation step-by-step.

\(q+12=-12\)

Step 1: Subtract 12 from both sides.

\(q+12-12=-12-12\)

\(q=-24\)

Answer:

q=−24

I hope this help you :)

Answer:

\(100.00 \div 6 \)

The probability that the youngest member of the group sits in the seat closest to the door 1 / 6

Given that, a group of 6 friends of varying ages meets at a coffee shop and sits in a circle, we need to find the probability that the youngest member of the group sits in the seat closest to the door,

So, the probability = favorable outcomes / total outcomes

Here, the favorable outcome = 1

The total outcomes = 1, 2, 3, 4, 5, 6 = 6

So, the probability = 1/6 = 1/2

Hence, the probability that the youngest member of the group sits in the seat closest to the door 1 / 6

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a) The halogen that exists in the liquid state at room temperature is called bromine.

b) Four more element descriptions are explained.

The halogen that exists in the liquid state at room temperature is called bromine. The electron arrangement is related to the organization of elements in the periodic table as the elements are arranged in the order of increasing atomic numbers and the similar electronic configuration of elements is shown in the same vertical column.

Four more element descriptions are:

- Oxygen: It is a nonmetallic element that is essential for respiration and combustion, and exists in the atmosphere as a diatomic molecule.
- Gold: It is a transition metal that is highly valued for its rarity and beauty, and is used in jewelry and currency.
- Chlorine: It is a halogen that is a greenish-yellow gas at room temperature, and is used as a disinfectant and bleaching agent.
- Carbon: It is a nonmetallic element that is the basis of organic chemistry and is found in all living organisms, as well as in coal and diamonds.

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The option i.e. not true about the square is the first option.

In the square, all 4 sides does have an equal length. Also, it should have parallel sides. Moreover, it should be treated as a rectangle. However, it does not contain any right-angle since it contains four right angles. It is a plane figure that contains four equal,  straight sides.

Therefore, the first option is correct.

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The test statistic for this test is 3.09.

To calculate the test statistic for this test, we need to use the formula:

t = \((\bar x - \mu) / (s /\sqrt n)\)

where:

\(\bar x\) = the sample mean difference (after - before)

\(\mu\) = the population mean difference (assumed to be 0 if the test preparation course has no effect)

s = the standard deviation of the differences

n = the sample size (in this case, 30)

Plugging in the values given in the problem, we get:

t = \((6 - 0) / (10 / \sqrt 30)\) = 3.09

To determine whether a test preparation course improves scores on the ACT test, we can use a paired samples t-test.

This test compares the mean difference between two related groups (in this case, the pre- and post-test scores of the same students) to the expected difference under the null hypothesis that there is no change in scores.

The test statistic for a paired samples t-test is given by:

t = (mean difference - hypothesized difference) / (standard error of the difference)

The mean difference is the average difference between the two groups, the hypothesized difference is the expected difference under the null hypothesis (which is 0 in this case), and the standard error of the difference is the standard deviation of the differences divided by the square root of the sample size.

The mean difference is 6 points, the hypothesized difference is 0, and the standard deviation of the differences is 10 points.

Since there are 30 students in the sample, the standard error of the difference is:

SE =\(10 / \sqrt{(30)\)

= 1.83

Substituting these values into the formula for the test statistic, we get:

t = (6 - 0) / 1.83 = 3.28

The test statistic for this test is therefore 3.28.

To determine whether this test statistic is statistically significant, we would need to compare it to the critical value of t for 29 degrees of freedom (since there are 30 students in the sample and we are estimating one parameter, the mean difference).

The critical value for a two-tailed test at a significance level of 0.05 is approximately 2.045.

The test statistic (3.28) is greater than the critical value (2.045), we can conclude that the difference in scores between the pre- and post-test is statistically significant at a significance level of 0.05.

The test preparation course did indeed improve scores on the ACT test. It's important to note that this is just a single study and that further research would be needed to confirm these results.

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