Solve number 7 using combinations

The number of pieces of candy that will be left on day 4 would be 2, 560 candies .

The number of pieces of candy left on day 8 would be 66 candies .

To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:

= Number of starting candy x ( 1 - Percent given away ) ^ number of days

= 100, 000 x ( 1 - 60 % ) ⁴

= 100, 000 x 40 % ⁴

= 2, 560 candies

On Day 8, this would be:

= 100, 000 x ( 1 - 60 % ) ⁸

= 66 candies

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The question is:

How many pieces of candy will be left on day 4? On day 8?

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 12x + 300√x - 2500.

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x) is dP/dx = 12 + 300/2√x.

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold is dP/dx ÷ x = (12 + 300/2√x) ÷ x.

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201 is $16.62.

What do you mean by  profit function?

A profit function is a mathematical model that represents the profit made from selling a certain product or service as a function of the number of units sold. The profit function is calculated as the difference between the total revenue and the total cost of producing and selling the product.

Mathematically, if R(x) represents the total revenue from selling x units of a product and C(x) represents the total cost of producing and selling x units of the product, then the profit function can be represented as P(x) = R(x) - C(x).

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have:

P(x) = 14x - (2x - 300√x + 2500)

P(x) = 12x + 300√x - 2500

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x):

dP/dx = 12 + 300/2√x

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold.

dP/dx ÷ x = (12 + 300/2√x) ÷ x

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201:

P(201) = 12 * 201 + 300 * √201 - 2500 = $3347.09

Since we want the profit from the sale of one unit, we divide the profit by 201:

P(201) ÷ 201 = $16.62

So, the estimated profit from the sale of the 201st doll is $16.62.

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Answer:

A.

Step-by-step explanation:

Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])

The answer is not one of the given choices. The correct answer is 73.

To find the total number of individuals who took the quiz, we need to add up the frequency (f) for each score (x) and then take the sum:

5(6) + 4(5) + 3(5) + 2(3) + 1(2) = 30 + 20 + 15 + 6 + 2 = 73

Therefore, the answer is not one of the given choices. The correct answer is 73.

       Frequency distributions are portrayed as frequency tables or charts. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In the latter instance, the distribution is called a relative frequency distribution.

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The linear functions for this problem are classified as follows:

a. Parallel.

b. Neither parallel nor perpendicular.

c. Perpendicular.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

They are classified as parallel, perpendicular or neither according to their slopes as follows:

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Answer: The answer to your problem is choice b

Answer:

45

Step-by-step explanation:

Three possible rectangles of area 24 square inches are:

A rectangle with width 6 inches and length 4 inches

A rectangle with width 8 inches and length 3 inches

A rectangle with width 4 inches and length 6 inches

It should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.

In this case, W and L are variables and A is a constant.

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1. The amount of pizzas which the pizzeria must sell for employees to receive the bonus is 78.

2. The new number of pizzas sold is considered as percent increase of 20%.

The pizzeria sold 65 pizzas yesterday and the owner offers bonus if the number sold increases by 20% today. The number that must be sold, to receive a bonus is computed as follows:

= 65 pizza * (65 pizza * 20%)

= 65 pizza * 13 pizza

= 78 pizza.

It is a percent increase which is computed as follows. The formula for percentage increase is: ((Final value - Initial value)/Initial value * 100).

The Percent increase:

= (78 pizza - 65 pizza) / 65 pizza.

= 13 pizza / 65 pizza

= 0.2

= 20%

Full question "A local pizzeria sold 65 pizzas yesterday. (step 1) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. (Part 2) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work. Answer:"

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Answer:

The service tax paid was:

0.06 * RM180 = RM10.80

Step-by-step explanation:

To calculate the service tax paid by Mr. Lim, we need to first find the amount of the bill before the service tax was added.

Let's call the original bill amount "x".

After the 6% service tax was added, the total bill became x + (0.06 * x) = RM190.80.

So we can set up the equation:

x + (0.06 * x) = RM190.80

Expanding the right side of the equation:

x + (0.06 * x) = 190.80

Combining like terms:

1.06x = 190.80

Solving for x:

x = 180

So the original bill amount before the service tax was added was RM180.

The service tax paid was:

0.06 * RM180 = RM10.80

Answer:

Step-by-step explanation:

C. There is a moderate correlation between the scores and grades.

Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.

The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.

In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.

However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.

Answer:

each parking ticket costs $100 and each traffic violation costs $124.28.

Step-by-step explanation:

To find out the cost of each parking ticket and each traffic violation, we can set up two equations using the information given:

Let x be the cost of each parking ticket.

In the first month, 3 parking tickets cost 3x, and 14 traffic violations cost 14y.

The total cost for the first month is 2030, so we have:

3x + 14y = 2030

In the second month, 11 parking tickets cost 11x, and 11 traffic violations cost 11y.

The total cost for the second month is 2200, so we have:

11x + 11y = 2200

Now that we have two equations, we can use substitution to find the value of x and y.

From the first equation, we can solve for y:

y = (2030 - 3x) / 14

Substituting this expression for y into the second equation:

11x + 11((2030 - 3x) / 14) = 2200

Expanding the expression for y and simplifying the equation:

11x + 2030 - 33x / 14 = 2200

Multiplying both sides by 14:

154x + 28420 = 30800

Solving for x:

x = $100

So each parking ticket costs $100, and each traffic violation costs:

y = (2030 - 3x) / 14 = (2030 - 3 * 100) / 14 = (2030 - 300) / 14 = 1730 / 14 = $124.28

Therefore, each parking ticket costs $100 and each traffic violation costs $124.28.

Answer:

-727.41 dollars

Step-by-step explanation:

To find the cost of each parking ticket and each traffic violation, we can set up a system of two equations. Let's call the cost of a parking ticket "x" and the cost of a traffic violation "y".

For the first month:

3x + 14y = 2030

For the second month:

11x + 11y = 2200

We can solve for x and y using any method, such as substitution or elimination. For this problem, let's use substitution.

First, we'll solve for x in the first equation:

3x + 14y = 2030

3x = 2030 - 14y

x = (2030 - 14y) / 3

Next, we'll substitute this expression for x into the second equation:

11x + 11y = 2200

11((2030 - 14y) / 3) + 11y = 2200

2030 - 14y + 11y = 2200 * 3 / 11

2030 - 3y = 636

-3y = -1394

y = 464.67

Finally, we'll substitute this value of y back into the first equation to find x:

3x + 14y = 2030

3x + 14(464.67) = 2030

3x = 2030 - 6544.68

x = (2030 - 6544.68) / 3

x = -2180.23 / 3

x = -727.41

So each parking ticket costs approximately -727.41 dollars, and each traffic violation costs approximately 464.67 dollars. However, since these values are negative, it means the suspect has received a credit rather than being charged for these fees.

Answer:

96 stamps

Step-by-step explanation:

We know

Connor collected 80 stamps last year. This year he increased his collection by 20%.

80 stamps = 100%

100% + 20% = 120%

So, this year he collected 120% of the number of stamps from last year.

120% = 1.2

How many stamps are in his collection?

We take

80 times 1.2 = 96 stamps

So, there are 96 stamps in his collection.

Answer:

x(f)- this is the correct answer

The angles x and 3x - 12 are two vertical angles and the measure of the vertical angle x is equal to 48°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

We shall evaluate for the measure of x as follows:

x + x + 3x - 12 + 3x - 12 = 360° {sum of angles at a point}

2x + 6x - 24 = 360°

8x - 24 = 360°

8x = 360° + 24 {add 24 to both sides}

8x = 384°

x = 384°/8 {divide through by 8}

x = 48°

Therefore, since the angles x and 3x - 12 are two vertical angles we have derived the measure of the vertical angle x to be equal to 48°.

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Answer:

x = 42°

Step-by-step explanation:

Please here it is.

Answer:

Step-by-step explanation:

m=3-1/2-7= -2/5

c⇒ -2

y=mx+c

y=-2/5x-2

Answer:

{40.7,49.3}

Step-by-step explanation:

[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{80\%}=45\pm1.282\biggr(\frac{19}{\sqrt{32}}\biggr)\\ \\CI_{80\%}\approx45\pm 4.3\\\\CI_{80\%}=\{40.7,49.3\}[/tex]

Thus, we are 80% confident that the true sample mean amount spent is between $40.70 and $49.30

Based on the proceeds and effective rate, Wilson should take out the simple discount note, which has a higher proceeds of $5,005 and a higher effective rate of 9.9% compared to the simple interest note's proceeds of $5,995 and effective rate of 9.0%.

To compare the simple discount note and the simple interest note, we can calculate the proceeds and effective rates for each.

For the simple discount note, the interest is deducted upfront and the borrower receives the difference, or the proceeds. The interest on a $5,500 note at 6% for 18 months can be calculated as:

Interest = Principal × Rate × Time

Interest = $5,500 × 6% × 1.5 years

Interest = $495

The proceeds for the simple discount note can be calculated as:

Proceeds = Principal - Interest

Proceeds = $5,500 - $495

Proceeds = $5,005

The effective rate for the simple discount note can be calculated using the formula:

Effective Rate = Interest / Proceeds × 100%

Effective Rate = $495 / $5,005 × 100%

Effective Rate = 9.9%

For the simple interest note, the interest is calculated on the principal amount and added to the principal at the end of the term. The interest on a $5,500 note at 6% for 18 months can be calculated as:

Interest = Principal × Rate × Time

Interest = $5,500 × 6% × 1.5 years

Interest = $495

The total amount due at the end of the term for the simple interest note can be calculated as:

Total Due = Principal + Interest

Total Due = $5,500 + $495

Total Due = $5,995

The effective rate for the simple interest note can be calculated using the formula:

Effective Rate = Interest / Principal × 100%

Effective Rate = $495 / $5,500 × 100%

Effective Rate = 9.0%

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Answer:

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a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.

b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.

c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.

A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.

A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.

The current total world oil reserves, R = 2,090 billion barrels

Average decrease per year = 18 billion barrels

a) Linear equation for R is 2,090 - 18t

b) In 15 years, the total oil reserves = 2,090 - 18(15)

= 2,090 - 270

= 1,820

c) The constant rate of decrease = 18 billion barrels per year

The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).

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This student would receive 10 bag of popcorns.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;

Number of bag of popcorns = Cost of one bag of popcorn/Unit price

Substituting the given parameters into the mathematical expression above, we have the following;

Number of bag of popcorns = 5/0.50

Number of bag of popcorns = 10 bag of popcorns.

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The volume of the parallelopiped is 4

We have to solve this with the use of matrix system in math

PQ, PR, PS where

P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)

we have to find

Q - P

(-1, 6, 5) - (-3, 3, 2)

= (2, 3, 3)

R - P

R(-4, 2, 1) - (-3, 3, 2)

= ( -1 , -1, -1)

S - P

S(3, 1, 4) - (-3, 3, 2)

= (6 , -2, 2)

we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]

the determinant of the matrix is the volume

2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]

= -8 - 12 + 24

= 4

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The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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The sample variance and the standard deviation are 52.8 and 7.26

From the question, we have the following parameters that can be used in our computation:

23, 16, 5, 7, 11

Calculate the mean

Mean = (23 + 16 + 5 + 7 + 11)/5

Mean = 12.4

The standard deviation is

SD = √[Sum of (1 - Mean)²]/[N - 1]

So, we have

SD = √[(23 - 12.4)² + (16 - 12.4)² + (5 - 12.4)² + (7 - 12.4)² + (11 - 12.4)²]/[5 - 1]

This gives

SD = √211.2/4

So, we have

SD = √52.8

SD = 7.26

Hence, the standard deviation is 7.26

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 17160\\ P=\textit{original amount deposited}\dotfill & \pounds 11000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &16 \end{cases}[/tex]

[tex]17160 = 11000[1+(\frac{r}{100})(16)] \implies \cfrac{17160}{11000}=1+\cfrac{16r}{100}\implies \cfrac{39}{25}=1+\cfrac{4r}{25} \\\\\\ \cfrac{39}{25}=\cfrac{25+4r}{25}\implies 39=25+4r\implies 14=4r\implies \cfrac{14}{4}=r\implies \stackrel{\%\qquad }{\boxed{3.5=r}}[/tex]

The solution is Option D.

The difference in shopping from store and online is given by the equation D = $ 0.46

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 total cost of shopping in physical store be A

Let the total cost of shopping online be B

Now , the equations will be

The number of batteries = 2

The number of stereo = 1

The number of CDs = 3

The cost of buying 2 packs of batteries from store = 2 x ( 5.99 ) = $ 11.98

The cost of buying 1 stereo from store = 1 x ( 100 ) = $ 100.00

The cost of buying 3 CDs from store = 3 x ( 7.95 ) = $ 23.85

The total purchase cost without discount and sales tax = $ 135.83

The cost with 10 % discount = $ 122.247

The cost after 5 % sales tax = $ 128.35935

So , the total cost of shopping in store A = $ 128.35935

And ,

The cost of buying 2 packs of batteries online = 2 x ( 4.99 ) = $ 9.98

The cost of buying 1 stereo from online = 1 x ( 90 ) = $ 90.00

The cost of buying 3 CDs from online = 3 x ( 8.95 ) = $ 26.85

The total purchase cost without discount and sales tax = $ 126.83

The cost with $ 5 discount = $ 121.83

The shipping cost in online store = $ 121.83 + $ 6.99 =

So , the total cost of shopping in online store A = $ 128.82

Now , the difference in shopping from store and online is

D = $ 128.82 - $ 128.35935

On simplifying the equation , we get

D = $ 0.46

Hence , the equation is D = $ 0.46

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To make the concentration of 50% syrup,

she needs to add 0.5 lb of sugar.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

Emma has half a pound of sugar.

To make the concentration of 50% syrup:

Let n be the required amount.

In decimals, 50% is 0.5.

Applying the percentage formula;

we get,

[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]

Applying cross multiplication,

we get,

[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]

0.5 = 0.5(n + 0.5)

1 = n + 0.5

n = 1 - 0.5

n = 0.5 lb.

Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.

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1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

When the statistics students number = 2·x + 3, we have;

The number of students that study

The parameters given are;

Total number of students = 30

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

The Venn diagrams can be presented as follows;

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