Write expressions that the cash register can use to determine the tax and the total for any item

In the binomial expansion of (2 + 3x)ⁿ, the value of n = 22/5

Binomial expansion is the expansion of the binomial (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ where ⁿCₓaˣbⁿ⁻ˣ is the general term and x = 0 to n

Since we require the expansion of  (2 + 3x)ⁿ, comparing it with the binomial expansion equation above  (a + b)ⁿ.

So, a = 2 and b = 3x

So, the binomial expansion is (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3x)ⁿ⁻ˣ

= ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ

So, the general term of  (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ and the coefficient term is ⁿCₓ2ˣ(3ⁿ⁻ˣ)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15. Then

For the x³ term, xⁿ⁻ˣ = x³

⇒ n - x = 3

⇒ x =n - 3

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₃2ⁿ⁻ˣ(3³) =

Also, for the x⁴ term, xⁿ⁻ˣ = x³

⇒ n - x = 4

⇒ x =n - 4

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15, we have that

ⁿCₙ₋₃2ⁿ⁻ˣ(3³)/ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴) = 8/15

ⁿCₙ₋₃/(ⁿCₙ₋₄ × 3)= 8/15

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/15 × 3

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/5

n!/(n - 3)![n - (n - 3)]!  ÷ n!/(n - 4)![n - (n - 4)]! = 8/5

n!/(n - 3)![n - n + 3)]!  ÷ n!/(n - 4)![n - n + 4)]! = 8/5

n!/(n - 3)!3!  ÷ n!/(n - 4)!4! = 8/5

n!/3!(n - 3)! ÷ n!/4!(n - 4)(n - 3)! = 8/5

n!/3!(n - 3)! × 4!(n - 4)(n - 3)!/n! = 8/5

4!/3! × (n - 4) = 8/5

4 × 3!/3! × (n - 4) = 8/5

4(n - 4) = 8/5

Dividing through by 4, we have

(n - 4) = 8/(5 × 4)

(n - 4) = 2/5

Cross-multiplying, we have

5(n - 4) = 2

Expanding the brackets, we have

5n - 20 = 2

5n = 20 + 2

5n = 22

n = 22/5

So, the value of n = 22/5

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Answer:

120/4=30

Step-by-step explanation:

I you can figure out how much b has then divide it by 4

Answer:

G6

Step-by-step explanation:

Answer:

f[g(1)]=6.

Explanation:

Given f(n) and g(n) defined below:

First, we evaluate g(1):

Therefore:

Therefore, f[g(1)]=6.

Answer:

302 cm2

Step-by-step explanation:

A brainiest, rating, or thanks would be appreciated!

Have a great day, and let me know if you need more help

:)

Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

A Type II error, in the context of hypothesis testing, occurs when the null hypothesis (H₀) is not rejected even though it is false. In other words, it's the failure to reject a false null hypothesis.

In this scenario, the null hypothesis states that the complaint rate is 8%, and the alternative hypothesis (Hₐ) states that the complaint rate is less than 8%.

A Type II error would occur if the chef believes that the complaint rate is not less than 8% (failing to reject the null hypothesis), when in fact it is less than 8% (the alternative hypothesis is true).

Consequences of a Type II error in this context:

The consequence of a Type II error would be that the chef continues to use the new gluten-free recipe for the topping even though the actual complaint rate is less than 8%.

This means that the chef would miss out on an opportunity to improve the recipe and potentially satisfy more customers.

In this case, the chef might continue to experience a significant number of unsatisfied customers who might have been pleased with an improved recipe.

This could lead to negative customer reviews, loss of customer loyalty, and a potential negative impact on the restaurant's reputation and business.

To summarize:

Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%.

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers, potentially harming the restaurant's reputation and business.

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A Type II error in this scenario would occur if the chef wrongly assumes the complaint rate is less than 8%, leading to continued use of the disliked recipe and unsatisfied customers.

In this context, a Type II error in the chef's hypothesis test would occur if the chef believes the complaint rate for the new gluten-free recipe is less than 8%, when in fact, it is not. That means the chef is under the false impression that the customers are more satisfied with the new recipe than they truly are. The consequence would be that the chef continues to use the new recipe, despite a higher complaint rate. This would lead to a significant number of unsatisfied customers because the recipe is not meeting their taste preferences as much as the chef thinks. This could subsequently affect the restaurant's reputation and customer loyalty.

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Answer:

9

Step-by-step explanation:

.9 is bigger than 5 so we can round 8 up to 9

Answer: Midpoint (xM, yM)  =  (4, 5)

Answer:

21kg

Step-by-step explanation:

We will do this.

11x - 12 = 7x

11x - 4x = 7x

4x = 12

4x/4 = 12/4

x = 3

3 x 7 = 21

Laura weighs 21 kg.

For this problem, we need to convert the radius of the ball from centimeters to inches.

This is done by dividing the radius by 2.54:

Assuming that both balls are spheres, their volumes are:

The ball with a radius of 7.5 inches has the most volume in cubic inches.

there are 27,132 different ways to choose 13 donuts out of 19 varieties.

This problem involves selecting 13 donuts out of 19 different varieties, without regard to order. This is a combination problem, and the number of combinations of n objects taken r at a time is given by the formula:

n! / (r!(n-r)!)

Using this formula, we can find the number of ways to choose 13 donuts out of 19:

19! / (13!(19-13)!) = 19! / (13!6!) = 27,132

what is combination?

Combination refers to the mathematical concept of choosing a subset of objects from a larger set, where the order of selection is not considered. In other words, combination is a way of selecting items from a group without any regard to the order in which the items are arranged.

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SOLUTION :

a² = hypo² - base²

a² = 13² - 12²

a² = 169 - 144 = 25

a = √25

a = 5 units.

________________________________

HOPE IT HELPS

Answer:

\(\huge{\boxed{\sf{ -20i^{2} + 48i - 16}}}\)

Step-by-step explanation:

( 8 - 4i ) ( 5i - 2 )

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

⇒\(8 ( 5i - 2 ) - 4i ( 5i - 2 )\)

⇒\(40i - 16 - 20i^{2} + 8i\)

Combine like terms.

Like terms are those which have the same base.

⇒\(- 20i^{2} +40i+ 8i - 16\)

⇒\(-20i^{2} + 48i - 16\)

Hope I helped!

Best regards!

~TheAnimeGirl

Answer:

y = 0

Step-by-step explanation:

The line y = 0 is cutting your triangle in half with perfect symmetry.

The equation that describes the line of symmetry in the figure given is: y = 0.

A line of symmetry can be described as an imaginary line that divides a shape or figure into two equal halves, where each is a mirror image of the other.

The triangle given will be divided into two equal halves by a line of symmetry that runs through the horizontal axis (x-axis).

Equation of the horizontal axis is expressed as y = 0.

Therefore, the equation that describes the line of symmetry in the figure given is: y = 0.

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Using multiplication principle of counting,

There are 160 ways to select your dinner choice if you need to pick one menu item from each category.

We have,

To determine the total number of ways to select a dinner choice, we need to use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m × n ways to do both things.

Using this principle, we can find the total number of ways to select a dinner choice as follows:

Number of ways to select an appetizer = 4

Number of ways to select a main course = 5

Number of ways to select a dessert = 8

Using the multiplication principle of counting, the total number of ways to select a dinner choice is:

= 4 × 5 × 8

= 160

Therefore,

There are 160 ways to select your dinner choice if you need to pick one menu item from each category.

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Answer:

B

I hope this helps :) !

Answer:

the length of a chord that contains the center of the circle

Step-by-step explanation:

The approximate mean for the given data set is 27.6, rounded to one decimal place.

To approximate the mean for the given data set, we can calculate the weighted average of the class midpoints, where each midpoint is multiplied by its corresponding frequency.

The class midpoints can be obtained by taking the average of the lower and upper class limits.

For the given data set, the class midpoints would be:

Midpoint of 0-8: (0 + 8) / 2 = 4

Midpoint of 9-17: (9 + 17) / 2 = 13

Midpoint of 18-26: (18 + 26) / 2 = 22

Midpoint of 27-35: (27 + 35) / 2 = 31

Midpoint of 36-44: (36 + 44) / 2 = 40

Midpoint of 45-53: (45 + 53) / 2 = 49

Next, we calculate the weighted average by multiplying each midpoint by its corresponding frequency, and then dividing the sum of these products by the total frequency.

Using the given frequencies, the weighted average would be:

(2 * 4 + 12 * 13 + 5 * 22 + 12 * 31 + 14 * 40 + 5 * 49) / (2 + 12 + 5 + 12 + 14 + 5) = 27.6

Therefore, the approximate mean for the given data set is 27.6, rounded to one decimal place.

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Answer:c

Step-by-step explanation:

Answer:

B.

3m - 11 = 2m + 9

Amount Maddie earns = m = $20

Step-by-step explanation:

Let

Amount Maddie earns = m

Amount Lauren earns = 3m - 11

Amount Shannon earns = 2m + 9

If Lauren and Shannon both earned the same amount of money, how much money, m, did Maddie earn?

Amount Lauren earns = Amount Shannon earns

3m - 11 = 2m + 9

Collect like terms

3m - 2m = 9 + 11

m = 20

Amount Maddie earns = m = $20

B.

3m - 11 = 2m + 9

Answer:

True

True

False

Step-by-step explanation:

Answer:

his distance from home is increasing between 1 minute and 4 minute

Step-by-step explanation:

stays constant between 5 and 10 then decreases from 10 to 15

Answer:

Complex and imaginary number

Step-by-step explanation:

First, let's write the number\(-16.2i\) in the form of \(a+bi\).

\(0+ (-17)i\)

Since \(-16.2i\) can be written in the form of \(a + bi\), where \(a\) and \(b\) are real numbers, it is a complex number.

Also, since \(a=0\), it is also an imaginary number.

\(-16.2i\) is complex and imaginary.

There are 4 integers between 20 and 30 that have a prime factorization with exactly 3 factors that are not necessarily unique.

To find the integers with a prime factorization having exactly 3 factors, we need to look for numbers that can be expressed as the product of two distinct prime numbers.

Step 1: Identify the prime numbers between 20 and 30. The prime numbers in this range are 23, 29.
Step 2: Determine all possible pairs of distinct prime numbers. In this case, we have only one pair: (23, 29).
Step 3: Calculate the products of these pairs. The products of (23, 29) are 667 and 667.
Step 4: Count the integers between 20 and 30 that match these products. We have two integers that match, which are 21 and 27.
Step 5: Check if these integers have exactly 3 factors. The factors of 21 are 1, 3, 7, and 21 (a total of 4 factors), so it does not meet the criteria. The factors of 27 are 1, 3, 9, and 27 (a total of 4 factors), so it also does not meet the criteria.

Therefore, there are no integers between 20 and 30 with a prime factorization having exactly 3 factors that are not necessarily unique.

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Answer:

a) 3x + ky = 8

ky = 8 - 3x

x – 2ky = 5

x - 2(8 - 3x) = 5

x - 16 + 6x = 5

7x = 21

x = 3 (shown)

b) x-2ky = 5

sub x = 3, y = 1/2

3-2k(1/2) = 5

-2k = 2

k = -1

0.529 is the probability that a student does not have a college degree.

From the information given, we know that:

The formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Let A be the event of not having a college degree, and B be the event of being married. We want to find P(A).

Using these values, we can calculate:

P(college degree and B) = (1/2) * (400/850) = 0.235

P(A and B) = 310/850 - 0.235 = 0.07

Finally, we can calculate P(A) using the formula for total probability:

P(A) = 1 - P(college degree)

= 1 - (400/850)

= 0.529

Therefore, the probability that a student does not have a college degree is 0.529.

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If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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The area of the section of the truncated pyramid by the plane that passes through the middle of the height parallel to the bases is (49/3) cm2.

The area of a section of a truncated pyramid by the plane that passes through the middle of the height parallel to the bases can be calculated using the formula: (1/2)(a+b)l where a and b are the bases and l is the slant height.
Given that the bases have areas of 98 cm2 and 2 cm2. Let a and b be the larger and smaller bases, respectively. Then, we have:
a + b = 98 + 2
a + b = 100
Since the height is perpendicular to the bases and passes through the center of the truncated pyramid, it also bisects the slant height. Therefore, the slant height can be calculated using the Pythagorean theorem as follows:
l² = h² + [(a - b)/2]²
l² = (h² + (a/2 - b/2)²) + (a/2 + b/2)²
l² = h² + (a/2)² - ab/2 + (b/2)² + (a/2)² + ab + (b/2)²
l² = h² + (5/4)a² + (5/4)b²
l² = h² + (5/4)(a² + b²)
The height of the truncated pyramid can be calculated using the similar triangles formed by the truncated pyramid and the smaller pyramid that is cut off from the top. Let x be the height of the smaller pyramid. Then, we have:
x/(h + x) = 2/7
7x = 2h + 2x
5x = 2h
x = (2/5)h
Substituting this into the formula for the slant height, we have:
l² = h² + (5/4)a² + (5/4)b²
l² = h² + (5/4)(98² + 2²)
l² = h² + (24500/2)
l² = h² + 12250
Finally, substituting the expressions for the area and slant height into the formula for the section of the truncated pyramid, we have:
(1/2)(a+b)l
(1/2)(98+2)√12250
(1/2)(100)√12250
50√12250
(50/2)√(5²⋅7⁴/2)
25√(5²⋅7²⋅2)
25⋅7√(10/2)
175√5
Therefore, the area of the section of the truncated pyramid by the plane that passes through the middle of the height parallel to the bases is (49/3) cm2.

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Answer:

D 70,000

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

simple if you know how to multiply cuz thats all you doing anyway.

anyways you Welcome.