1 point
Officer Cooter spent half of the money in his wallet going to the movies. After the movies, he found 6 dollars in the dryer while doing his laundry
and put it in his wallet. How much money did he start with in his wallet if he ended with 16 dollars?
Choose the equation from the following list and solve.
16 = 2 + 6
16 = -6
16 = +6
16 = 2r - 6
Officer Cooter started with $ type your answer...
in his wallet
​

The probability that a randomly selected student is not majoring in nursing, criminal justice, or business technology is 0.7.

Probability is the study of random events and their outcomes. It is the likelihood that something will occur under given conditions. Probability is expressed as a number between 0 and 1, with 0 representing an impossibility and 1 representing a certainty. Probability theory provides the tools to calculate the likelihood of a given event, and can be used to make decisions when faced with uncertainty. Probability is a useful tool in many fields, including science, finance, medicine, and gaming.

This is an example of a theoretical probability, since it is based on theoretical data rather than actual observations. Theoretical probability is calculated by taking the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of students who are not majoring in nursing, criminal justice, or business technology, and the total number of possible outcomes is the total number of students.

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Answer:

Step-by-step explanation:

4\(x^{4}\)-x²+3 / x =  

So, we need to think about this problem as either what we have to multiply x by to get the equation, and do long division

= 4x³- x + \(\frac{3}{x}\)

The binomial theorem expansion is solved and

a) ( 3x² + y )² = 9x⁴ + 6x²y + y⁴

b) ( 5x⁴+2y⁵ )⁴ = 625x¹⁶ + 1000x¹²y⁵ + 600x⁸y¹⁰ + 160x⁴y¹⁵ + 16y²⁰

c) ( x³ + 4y² )⁵ = x¹⁵ + 20x¹²y² + 160x⁹y⁴ + 640x⁶y⁶ + 1280x³y⁸ + 1024y¹⁰

d) ( x - 2y )⁶ = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶

e) The coefficient of x³y⁴ in the expansion of (2x + 5y²)⁵ = 2000

Given data ,

The binomial expansion is given by the formula:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

a)

Let the binomial expansion be represented as A

A = ( 3x² + y )²

Using the binomial theorem:

(3x² + y)² = C(2, 0) * (3x²)² * y^0 + C(2, 1) * (3x²)^(2-1) * y^1 + C(2, 2) * (3x²)^(2-2) * y^2

A = 9x⁴ + 6x²y + y⁴

b)

B = ( 5x⁴+2y⁵ )⁴

Using the binomial theorem:

(5x^4 + 2y^5)^4 = C(4, 0) * (5x^4)^4 * (2y^5)^0 + C(4, 1) * (5x^4)^(4-1) * (2y^5)^1 + C(4, 2) * (5x^4)^(4-2) * (2y^5)^2 + C(4, 3) * (5x^4)^(4-3) * (2y^5)^3 + C(4, 4) * (5x^4)^(4-4) * (2y^5)^4

B = 625x¹⁶ + 1000x¹²y⁵ + 600x⁸y¹⁰ + 160x⁴y¹⁵ + 16y²⁰

c)

C = ( x³ + 4y² )⁵

Using the binomial theorem:

(x³ + 4y²)^5 = C(5, 0) * (x³)^5 * (4y²)^0 + C(5, 1) * (x³)^(5-1) * (4y²)^1 + C(5, 2) * (x³)^(5-2) * (4y²)^2 + C(5, 3) * (x³)^(5-3) * (4y²)^3 + C(5, 4) * (x³)^(5-4) * (4y²)^4 + C(5, 5) * (x³)^(5-5) * (4y²)^5

C = x¹⁵ + 20x¹²y² + 160x⁹y⁴ + 640x⁶y⁶ + 1280x³y⁸ + 1024y¹⁰

d)

D = ( x - 2y )⁶

Using the binomial theorem:

(x-2y)^6 = C(6, 0) * x^6 * (-2y)^0 + C(6, 1) * x^(6-1) * (-2y)^1 + C(6, 2) * x^(6-2) * (-2y)^2 + C(6, 3) * x^(6-3) * (-2y)^3 + C(6, 4) * x^(6-4) * (-2y)^4 + C(6, 5) * x^(6-5) * (-2y)^5 + C(6, 6) * x^(6-6) * (-2y)^6

D = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶

e)

E = (2x + 5y²)⁵

The coefficient is 5C2 ( 2 )³ ( 5 )² = 2000

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\(\Large\maltese\underline{\textsf{A. What is Asked}}\)

What is the value of a in the equation 3a+b=54, if b=9?

\(\Large\maltese\underline{\textsf{B. This problem has been solved!}}\)

Put in 9 for b.

\(\bf{3a+9=54}\) | subtract 9 on both sides

\(\bf{3a=45}\) | divide the entire equation by 3

\(\bf{a=15}\)

\(\cline{1-2}\)

\(\bf{Result:}\)

       \(\bf{\bigcirc 15}\)

\(\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}\)

Answer:

a = 15

Step-by-step explanation:

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

Answer:

$300

Step-by-step explanation:

First, you subtract 475 and 175.

Which equals 300. That means that you saved $300.

Answer:$300

Step-by-step explanation:

475 (base price) - 175 (sale price)

=300 (saved price)

Among the given sets of vectors, the sets that can be bases for ℝ³ are (a) (2, 0, 0), (4, 4, 0), (6, 6, 6) and (b) (3, 1, -3), (6, 3, 3), (9, 2, 4). The correct options are (a) and (b).

In order for a set of vectors to form a basis for ℝ³, they must satisfy two conditions: (1) The vectors must span ℝ³, meaning that any vector in ℝ³ can be expressed as a linear combination of the given vectors, and (2) the vectors must be linearly independent, meaning that no vector in the set can be expressed as a linear combination of the other vectors.

(a) (2, 0, 0), (4, 4, 0), (6, 6, 6): These vectors span ℝ³ since any vector in ℝ³ can be expressed as a combination of the form a(2, 0, 0) + b(4, 4, 0) + c(6, 6, 6). They are also linearly independent, as no vector in the set can be expressed as a linear combination of the others. Therefore, this set forms a basis for ℝ³.

(b) (3, 1, -3), (6, 3, 3), (9, 2, 4): These vectors also span ℝ³ and are linearly independent, satisfying the conditions for a basis in ℝ³.

(c) (4, -3, 5), (8, 4, 3), (0, -10, 7): These vectors do not span ℝ³ since they lie in a two-dimensional subspace. Therefore, they cannot form a basis for ℝ³.

(d) (4, 5, 6), (4, 15, -3), (0, 10, -9): These vectors do not span ℝ³ either since they also lie in a two-dimensional subspace. Hence, they cannot form a basis for ℝ³.

In conclusion, the correct options for sets of vectors that form bases for ℝ³ are (a) and (b)

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Answer:

1. The Positive Integers - Natural Numbers

2. An Ordering of Quantities Separated by Commas - Sequence

3. The Sum of The Terms of an Associated Sequence - Series

4. One of The Individual Quantities of a Sequence - Term of a Sequence

5. A Formula That Yields The Value of a Term When That Term is Substituted In It - General Term of a Sequence

6. A Series That Has a Common Difference Between Terms - Arithmetic Series

7. A Series That Has a Common Ratio Between Terms Sequence - Geometric Series

8. A Sequence in Which Each Successive Terms Changes Sign - Alternating Sequence

Series are sum of terms of sequences. The names of each of the items specified are specified below.

Sequence is an ordering of numerical or mathematical quantities separated by commas, and series is sum of terms of sequences if addition is defined for those terms.

For the considered definitions, their names are given as:

1. the positive integers : It is called Natural Numbers. Example: 4 is a natural number.

2. an ordering of quantities separated by commas: Sequence

Example: 2,4,6...

3. the sum of the terms of an associated sequence: Series

Example: 2 + 4 + 6 + ...

4. one of the individual quantities of a sequence term of a sequence: Term

5. a formula that yields the value of a term when that term is substituted in it: general term of a sequence

6. a series that has a common difference between terms: Arithmetic series

7. a series that has a common ratio between terms: Geometric series

8. a sequence in which each successive terms changes sign: Alternating sequence

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Answer:

x= 2 y= -2

(2, -2)

I hope this helps you!

The solutions to the equation is

The value of x = 2

The value of y = -2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be A

The value of A is

2x + 3y = -2   be equation (1)

Let the second equation be B

The value of B is

3x - 6y = 18   be equation (2)

Now , on simplifying the equation , we get

Multiply equation (1) by 3 , we get

6x + 9y = -6   be equation (3)

Multiply equation (2) by 2 , we get

6x - 12y = 36   be equation (4)

Subtracting equations (3) and equation (4) , we get

21y = -42

Divide by 21 on both sides of the equation , we get

y = -2

Substitute the value of y in equation (1) , we get

2x + 3 ( -2 ) = -2

2x - 6 = -2

Adding 6 on both sides of the equation , we get

2x = 4

Divide by 2 on both sides of the equation , we get

x = 2

Therefore , the value of x and y is 2 and -2 respectively

Hence , the solutions to the equations is x = 2 and y = -2

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Answer:

6 minutes

Step-by-step explanation:

The copy machine can print 720 copies every 6 minutes. which is determined by the ratio of printing.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that the copy machine can print 480 copies every 4 minutes.

Let time would be x when copy machine can print 720 copies

According to the given question, we can write the ratio as

480 copies : 4 minutes = 720 copies : x minutes

⇒ 480 / 4 = 720 / x

⇒ 120 = 720 / x

Apply the cross-multiplication operation,

⇒ x = 720 / 120

Apply the division operation,

⇒ x = 6

Therefore, the copy machine can print 720 copies every 6 minutes.

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Answer:

what do you need help with?

Step-by-step explanation:

❤️

Answer:

A. -2 + 12 -2 ^ 3 + 2 ^ 0 * 3

= 10 - 2 ^ 3 + 2 ^ 0 * 3

= 10 - 8 + 1

= 3

B. 9 ^ (1/2)(25) - 8 + 2 + 3 ^ 2

= 9 ^ (1/2)(25) - 6 + 9

= 3 ^ 25 + 3

= 3 ^ 25 + 3

= 847288609446

C. 1/2 * 3/5 * (2 ^ 3 - 6) + 1/5

= 1/2 * 3/5 * 2 + 1/5

= 3/5 + 1/5

= 4/5

Answer:

Step-by-step explanation:

A.

B.

C.

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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It rained approximately 4.47 inches on Tuesday.

The meaning of SUBTRACT is to take away by or as if by deducting. How to use subtract in a sentence.

On Monday, it rained 4(1/2) inches.

On Tuesday, it rained 0.03 inches less than on Monday.

To find out how much it rained on Tuesday, we need to subtract 0.03 inches from the rainfall on Monday.

4(1/2) inches - 0.03 inches = 4.5 inches - 0.03 inches = 4.47 inches

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Answer:

C. 56°

Step-by-step explanation:

mXTW=180°-(mSTX+mUTW)

mSTX=mUTW=180°-118°=62°

mXTW=180°-2*62°=180°-124°=56°

Option C. 56°

Answer:

its 56. sorry for late answer

Step-by-step explanation:

person above me is right

By substituting the limits of integration and solving the definite integral, the volume of the solid is approximately 3.57 cubic units.

What is integration ?

Integration is a fundamental concept in calculus that deals with the problem of finding the total change in a quantity over a given interval. It is the reverse process of differentiation, which deals with finding the rate of change of a quantity.

We can think of slicing the solid into thin horizontal slices, each parallel to the y = 0 plane. The cross-section of each slice with the elliptic cylinder will be an ellipse. The area of each ellipse can be calculated using the formula for the area of an ellipse, which is πab, where a and b are the semi-major and semi-minor axes of the ellipse.

The semi-major axis of the ellipse is 2, and the semi-minor axis is √(4 - 4x^2) = √(4(1 - x^2)) = 2√(1 - x^2). So the area of each slice is A(x) = π(2)(2√(1 - x^2)) = 4π√(1 - x^2)

The height of each slice is dy = dz = dx, since the slices are parallel to the y = 0 plane and the height of each slice is equal to the change in y or z between two consecutive slices.

So, the volume of the solid is ,

∫ (4π√(1-x^2)) dx from x = -1/2 to x = 1/2

By substituting the limits of integration and solving the definite integral, the volume of the solid is approximately 3.57 cubic units.

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Answer:

-1/2  

Step-by-step explanation:

first point is 1,-4

second point is 5,-6

Slope is  y2-y1/x2-x1

-6 - -4 / 5 - 1

-2/ 4

-1/2

It will take 22 years and 3 months to get the present value of $12,000 invested at 2.3% compounded monthly to get to $20,000 (future value).

The period that it will take the present value to reach a certain future value can be determined using an online finance calculator with the following parameters for periodic compounding.

I/Y (Interest per year) = 2.3%

PV (Present Value) = $12,000

PMT (Periodic Payment) = $0

FV (Future Value) = $20,000

Results:

N = 266.773

266.73 months = 22 years and 3 months (266.73 ÷ 12)

Total Interest = $8,000.00

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The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now,the radius line from one corner point to the centre will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now,from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

Answer:

A, B, D

Step-by-step explanation:

Answer:

Answer C

Step-by-step explanation:

This is because acute triangles have angles that are under 90 degrees and Option A would be true to what you are trying to make false and B & D are false because they have angles that go over 90 degrees.

The other statements that provide contradiction to the given expression are option (B) and (C).

An elementary polygon having three sides and three vertices is a triangle. There are three internal angles since it has three sides. An acute angle is one that ranges in measurement from 0° to 90°. A form of triangle called an acute triangle has acute angles at each of its three internal angles.

In the option (A),

the three angles could be 30°, 30°, and 30°.

These angles contradict the basic property of triangle.

Which is sum of all the triangles are 180°.

In the option (B),

the three angles could be 30°, 60°, and 90°.

The above angles hold the property of an acute triangle.

In the option (C),

The three angles could be 30°, 70°, and 80°.

The above angles also hold the property of an acute triangle.

In the option (D),

The three angles could be 30°, 30°, and 120°.

Angle 120° greater than 90°.

This statement contradicts the basic property of an acute triangle.

Therefore, the other statements that provide contradiction to the given expression are option (B) and (C).

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Answer:

Left most and the one u selected

Step-by-step explanation:

7p-4p+15 = 3p+15

3(p+5) = 3p + 3 * 5 = 3p + 15

2p-p+15 = p+15

3(p+15) = 3p+45

if correct, pls mark 5 star, thanks, and brainliest!

1 and 2.

7p - 4p + 15

3p + 15

3 (p + 5)

(3 • p) + (3 • 5)

3p + 15

I hope this helps let me know if you need any more help :)

The probability of an increase in house sales and no increase in house sales will occur in the next 6 months is 0.09.

The event that an increase in house sales and no increase in house sales will occur in the next 6 months are:

1) The probability of house sales to increase in the next 6 months is estimated to be 0.25, then the probability of no increase is 0.75.

2) The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89,

then the probability that interest rates will go up is 0.89 - 0.25

= 0.64.

3) The probability of an increase in house sales and no increase in interest rates

= Probability of increase in house sales * Probability of no increase in interest rates

= 0.25 * (1 - 0.64)

= 0.25 * 0.36

= 0.09

Therefore, the probability of an increase in house sales and no increase in house sales will occur in the next 6 months is 0.09.

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Answer:

03

Step-by-step explanation:

03

Answer:
20.02

If this help please set brainliest.

Explain:

If you increase the number 14 by 43%, you would get
14 + (14 * 43%) = 14 + 6.02 = 20.02.

On solving the provided question, we can say that by permutation 26 possible letters  x  10 possible digits  = 260 possible plates

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of

26 possible letters  x  10 possible digits  =

26 x 10   =

260 possible plates

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The roots of the given equation is real and equal.

Given , 5\(x^{2} \\\) - 10x+ k=0

The quadratic equation is b² - 4ac = 0

Here, a= 5, b= -10, c= k

substitute in b² - 4ac = 0

(-10)² - 4 * 5* k =0

100 - 20k =0 , let this be equation (1)

100 = 20k

k = \(\frac{100}{20}\)

k = 5.

now, substitute  k= 5 in equation (1)

100 -20k = 0

100 - 20*5 = 0

100 - 100 = 0

Therefore, the given equation is real and equal .

The correct question is 5x² - 10x + k =0

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Answer:

y= -2/5x+16

y=-3/10x+33/2

–π/2 is the exact value of arcsine (-1).

The six main inverse trigonometric functions include arcsin. It is the sine function's inverse trigonometric function. The mathematical symbol for arcsin, commonly known as inverse sine, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the reciprocal function of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions arccos, arcsin, arctan, arcsec, arccsc, and arccot to calculate angles. Arcsin x calculates the angle that corresponds to the right-angled triangle's perpendicular to hypotenuse ratio. We shall examine the idea of arcsin in this article and determine its formula. We'll also talk about the domain and range.

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Answer:

No

Step-by-step explanation:

These are NOT equivalent. If you expand the 2nd expression you get 27+23k which is close, but not the same.

At 95% confidence-level, the true difference between the mean amount of caffeine in the two brands of coffee jars is between -0.3641 mg/jar and 6.3641 mg/jar.

Sample size of Brand I coffee jars (n₁) = 15

Mean of the sample of Brand I coffee jars (x₁-bar) = 80

Standard deviation of the sample of Brand I coffee jars (s₁) = 5S

ample size of Brand II coffee jars (n₂) = 12

Mean of the sample of Brand II coffee jars (x₂-bar) = 77

Standard deviation of the sample of Brand II coffee jars (s₂) = 6

To construct a 95% confidence interval for the difference between the mean amounts of caffeine in one-pound jars of these two brands of coffee, we use the formula given below:

CI = (x₁-bar - x₂-bar) ± tα/2 * SE where

CI = Confidence Interval

x₁-bar = Sample mean of Brand I coffee jars

x₂-bar = Sample mean of Brand II coffee jars

s₁ = Standard deviation of the sample of Brand I coffee jars

s₂ = Standard deviation of the sample of Brand II coffee jars

n₁ = Sample size of Brand I coffee jars

n₂ = Sample size of Brand II coffee jars

SE = Standard Error of the difference between mean

s= √(s1^2/n1 + s2^2/n2)tα/2

 = t-score for 95% confidence interval with (n1+n2-2) degrees of freedom

  = t0.025

Here, the degrees of freedom = (15+12-2)

                                                  = 25 degrees of freedom

Using the t-distribution table for 25 degrees of freedom at a 95% confidence level, we get t0.025 as 2.0592.

Substituting the values in the formula, we get,

SE = √(s₁²/n₁ + s₂²/n₂)

    = √(5²/15 + 6²/12)

    = √(25/15 + 36/12)

     = √(5/3 + 3)

      = √(8/3)

      = 1.6325CI

      = (80 - 77) ± 2.0592 * 1.6325

      = 3 ± 3.3641

The 95% Confidence interval for the difference between the mean amounts of caffeine in one-pound jars of these two brands of coffee is (3-3.3641, 3+3.3641) or (-0.3641, 6.3641) mg/jar.

At 95% confidence level, we can conclude that the true difference between the mean amount of caffeine in the two brands of coffee jars is between -0.3641 mg/jar and 6.3641 mg/jar.

This means the difference between the mean amount of caffeine in the two brands of coffee jars is statistically significant and we can reject the null hypothesis.

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