PLEASE HELPP!!
Given the Following hexagon
Calculate the missing angles.

The number of four-digit numbers that are divisible by both 12 and 20 but are not divisible by 16, obtained by finding the least common multiples of 12 and 20 are 150. the correct option is therefore option (D)

(D) 150

The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of the integers.

The numbers 12, and 20 are divisible by 4, therefore, numbers that are divisible by 12 and 20 are also divisible by 4. Therefore, the number of four-digit numbers that are divisible by 4 are found as follows;

The number of 4 digit positive numbers between 1000 to 9999 are 9000 four-digit positive numbers.

The number of multiples of 4 between 1000 and 9999, includes the first number 1004 and the last number 9996

The number of four-digit positive integers that are divisible by 4 therefore is; (9996 - 1004)/4 + 1 = 2250

The least common multiple of 4, 12 and 20 is 60, therefore;

The number of four digit numbers that are divisible by 60 are can be found as follows;

The first number is 1020, the last number is 9960

Therefore, the number of 4 digit numbers that are divisible by 60 are;

(9960 - 1020)/60 + 1 = 150

The number of 4 digit numbers that are divisible by 12 and 20 but is not divisible by 16 is divisible by 4 and 15 that have a least common multiple of 60

The number of four-digit numbers that are divisible by 4 and 15 is also divisible by 60, therefore, the number of 4 digit numbers that are divisible by 4 and 15 are also 150

Therefore, the number of four-digit numbers that are divisible by 12 and 20 but are not divisible by 16 is 150.

The correct option is; (D) 150

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In a video store, a DVD that sells for $15 is marked 10% off. The amount of discount is $1.50.

If the DVD is marked 10% off, it means the price of the DVD has been reduced by 10% of its original price.

To calculate the amount of the discount, we need to find 10% of the original price. We can do this by multiplying the original price by 10% written as a decimal:

10% as a decimal = 0.10

Amount of discount = 0.10 x $15 = $1.50

Therefore, the amount of the discount on the DVD is $1.50.

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My end of the year balance is $2,142.45.

If the amount that is deposited is compounded bi-annually, it means that both the amount deposited and the interest earned, increases in value twice in a year. This is because bi-annually means twice in a year. An amount that is compounded grows at an exponential rate at each compounding date.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

2000 x (1 + 0.035)^(2 x 1)

2000 x (1.035)^2 = $2,142.45

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With a sample of 9 tables, the probability that diners would spend fewer than 100 minutes at their table during dinner is [tex]0.8413[/tex], or around [tex]84.13[/tex] percent.

The ratio of beneficial results to all beneficial results in the population is a common way to define probability.

Probability has many uses in both analysis and gaming. Probability is used in sectors of real life and business where making predictions is important. The utilisation of probabilistic principles was necessary for forecasting market prices and cricket team performance.

With the values from the problem substituted, we obtain,

[tex]z = (100 - 97) / (18/\sqrt{9} ) = 1[/tex]

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score less than [tex]1[/tex] is [tex]0.8413[/tex].

Therefore tables is [tex]0.8413[/tex] or approximately [tex]84.13[/tex]%.

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The number of ways choosing an even number using factorial can occur is 6! or 720.

Describe a factorial.

In mathematics, a factorial is a function that is applied to a non-negative integer, represented by the exclamation mark (!) symbol. The result of applying the factorial function to a number n, written as n!, is the product of  integers from 1 to n.

For example, 4! is equal to 4 x 3 x 2 x 1, which equals 24.

Now,

Given number are 1,2,3,4,5,6,7,8,9,10,11,12

from these numbers even numbers are 2,4,6,8,10,12

total even numbers=6

then, number of ways of selecting a even number=6! or 6*5*4*3*2*1

=720

Hence,

          The number of ways choosing an even number using factorial can occur is 6! or 720.

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Joe charges more per acre than Chris. Joe charges $20 per acre and Chris charges $30 per acre.
 

Starting a lawn mowing business can be a profitable and rewarding venture if you have the right tools, skills, and strategies in place.Research your local area to determine the demand for lawn mowing services, the competition, and the going rate for services. This will help you determine whether starting a lawn mowing business is a viable option in your area.Create a business plan that outlines your goals, target market, services, pricing, and marketing strategies. This will help you stay organized and focused as you launch and grow your business.Check with your local government to find out what licenses and permits you need to start a lawn mowing business in your area.Therefore,from the given information Joe charges more per acre.

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Answer= [tex]50cm^{2}[/tex]

The function which represents the inverse of the function f(x)=[tex]x^2[/tex]+5 is [tex]f^{(-1)(x)}[/tex] = ±[tex]\sqrt{(x - 5)}[/tex].

To find the inverse of a function, we can follow the steps:

Step 1: Replace f(x) with y. So we have:

y = [tex]x^2[/tex] + 5

Step 2: Swap x and y in the equation obtained in step 1:

x = [tex]y^2[/tex] + 5

Step 3: Solve for y in the equation obtained in step 2:

x - 5 = [tex]y^2[/tex]

y = ±[tex]\sqrt{(x - 5)}[/tex]

Note that we need to include both the positive and negative square roots to get the complete inverse function. Therefore, the inverse function of f(x) = [tex]x^2[/tex] + 5 is:

[tex]f^{(-1)(x)}[/tex] = ±[tex]\sqrt{(x - 5)}[/tex]

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Simple Interest(SI) is calculated as $288,000 where principal is $200,000, interest rate is 18% and type is 8 year.

The Simple Interest (S.I.) formula is a way to figure out how much interest will pay on a given principle sum of money. It is the cost of borrowing that is computed using the original principle amount alone and a constant interest rate.

Formula of Simple Interest is,

[tex]SI = \frac{P*R*T}{100}\ or\ Simply\ write\ SI = P*R*T[/tex]

[tex]Where, P = Principal,\\R= Rate\ of\ Interest\\T = Time\ Period[/tex]

⇒  [tex]SI = \frac{20000*18*8}{100}\ or\ SI = 200000*0.18*8[/tex]

⇒ [tex]SI = \$\ 288000[/tex]

Simple Interest(SI) is calculated as $288,000 where principal is $200000, interest rate is 18% and type is 8 year.

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1. Simple Interest = 288000

2. Interest = 135

3. Total amount to be paid = $408

4. PV or present value = $18348.62

5. r = 51%

7. Amount invested in 18% is $3,685.714

8. 48 930.00.

9. EAR = 14.4%

10. 26.8% per year

12. ~P13439

13. SI = 288000

15.  the account balance today if interest is 10 % compounded quarterly.

1. Formula of simple interest is,

SI = P*R*T/100 or

Simply write SI = P*R*T

Where,

P = Principal

R = Rate of interest

T = Time period

SI = 20000*18*8/100 or

SI = 200000*0.18*8

SI = 288000

2. Interest = Principal*Interest

             rate*time

Principal = 2000

Interest rate = 10%

Time = January 30, 2001 to September 2001

Interest = 135

(2000*10%*243/360)

Assume 360 days in a year in days counting include the day counting start from and exclude the day counting ends on.

3. Total Interest 3 Years = 300*12%*3 = 108

Total Amount Repaid = 300 + 108 = $408

Total amount to be paid = 300+(300*12%*3)

=$408

4. Given , we need to find the present worth of $20,000 at 12% interest rate per year which is due at the end of 9 months.

Therefore, FV i.e , future value = $20,000

i = rate of interest per year = 12% = 0.12

t or Time =9 months = 9/12 year ( in terms of years)

We know , FV = PV + PV * r * t

=> 20000 = P + P * (0.12) * (9/12)

PV or present value = 18348.62 = $18348.62

5. FV = Principal (1 + rate of interest per period * number of interest period)

Equation-1:

650,000 = Principal (1 + rate of interest per period * 90 days / 360 days)

650,000 = Principal (1 + 0.25 rate of interest per period)

Principal = 650,000 / (1 + 0.25 rate of interest per period)

Equation-2:

600,000 = Principal (1 + rate of interest per period * 30 days / 360 days)

600,000 = Principal (1 + 0.08 rate of interest per period)

Principal = 600,000 / (1 + 0.08 rate of interest per period)

Equating the equations we get:

650,000 / (1 + 0.25r) = 600,000 / (1 + 0.08r)

650,000 (1 + 0.08r) = 600,000 (1 + 0.25r)

650,000 + 52,000r = 600,000 + 150,000r

50,000 = 98,000r

r = 51%

7. Annual return from 18% = 3 * (Annual return from 16%)

Let Investment made in 18% = K

Return from 16% = P620 is less than triple the yearly income from 18%, at P620.

(20,000 - K) * 16% = [3 * (K* 18%)] - 620

3,200 - 0.16K = 0.54 K - 620

2,580 = 0.70 K

K = $3,685.714

So, Amount invested in 18% is $3,685.714

9. EMR = effective monthly rate

EMR = EAR/12

12*EMR = EAR

EAR = 12*EMR

The EMR is given to be 1.2% = 0.012, so the EAR is,

EAR = 12*EMR

EAR = 12*(0.012)

EAR = 0.144

EAR = 14.4%

10. No.

It's [tex]1.02^{12}[/tex] =~ 1.268

26.8% per year

12. [tex]F=A(1+3\%)^{10}[/tex]

A = P10,000

[tex]F=10,000(1+3\%)^{10}[/tex]

~P13439

According to the final value formula of compound interest.

13. Formula of simple interest is,

SI = P*R*T/100 or

Simply write SI = P*R*T

Where,

P = Principal

R = Rate of interest

T = Time period

SI = 20000*18*8/100 or

SI = 200000*0.18*8

SI = 288000

15.

An engineer established a savings account three years ago with a P 200,000 opening deposit.

Three months later, he removed P50,000, and six months after that, P50,000 more.

He made an investment of P100,000 and a withdrawal of P150,000 six months later last year.

If interest is compounded quarterly at 10%, find the amount of the account right now.

The table has been attached.

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The populations from which the samples are selected must not be equal variances, which is not consistent with assumptions for the independent-measures ANOVA.

Therefore, option A is the correct answer.

Independent-measures ANOVA Assumptions for the independent-measures ANOVA are listed below.

The one which is not consistent with the independent-measures ANOVA is described below:

The populations from which the samples are selected must have equal variances.

The populations from which samples are selected must be normal, especially as sample sizes decrease.

The observations within each sample must be independent.

The populations from which samples are selected must be normal, especially as sample sizes increase.

ANOVA is a statistical method that compares three or more groups' means to determine whether the differences are significant.

Independent Measures ANOVA (also known as One-Way ANOVA) compares the means of three or more unrelated groups to determine whether there are any significant differences.

When dealing with Independent Measures ANOVA, the following assumptions must be met:

Assumptions for the Independent-Measures ANOVA:

Independence: Observations in each group should be independent from one another.

Normally Distributed Populations:

Each group's scores should come from a normally distributed population.

Homogeneity of Variance: Each group's variance should be similar.

Mean Equality: Each group's means should be equal.

The above-mentioned assumptions are consistent with independent-measures ANOVA.

However, the populations from which the samples are selected must not be equal variances, which is not consistent with assumptions for the independent-measures ANOVA.

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The terminal point P(x,y)=(-23) can be located on the coordinate plane at the point (-23, -23).

The terminal point P(x,y)=(-23) can be visualized on a coordinate plane. To calculate the x- and y-coordinates of this point, we must first understand the definition of a terminal point. A terminal point is a point that marks the end of a line.

In this case, the terminal point P is the end of a line with coordinates (x, y) = (-23).

To calculate the x-coordinate of this point, we can simply look at the first number in the coordinate pair. In this case, the x-coordinate of P is -23.

To calculate the y-coordinate of this point, we must look at the second number in the coordinate pair. In this case, the y-coordinate of P is also -23.

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Answer:

She saw the letter K, and other letters Are X and Y

Step-by-step explanation:

The function f(x) = 3x + 3 - x is neither even nor odd.

The y-axis of the function k's graph is symmetric. This is apparent because, if we reflect any point on the graph across the y-axis, we will obtain a second point on the graph. For purposes of formal definition, the function k is even since k(-x) = k(x) for every x within the range of k.

If the function f(x) = 3x + 3 - x fits the requirements for even or odd functions, we may determine whether it is even, odd, or neither.

Being symmetric around the y-axis means that an even function has f(-x) = f(x) for every x falling inside its domain.

An odd function is symmetric around the origin, which means that for any x falling within the domain of f, f(-x) = -f(x).

We evaluate f(-x) and f(x) to see if they are equivalent in order to determine whether f(x) is even:

f(x) = 3x + 3 - x = 2x + 3 while f(-x) = 3x + 3 - x = -2x + 3

The function f(x) is not even since f(-x) is not equal to f(x).

We assess f(-x) and -f(x) and see if they are equivalent to determine whether f(x) is odd:

F(x) = -3(x) + 3(x) - (x) = -2x + 3 F(x) = -(3x + 3(x) - x) = -2x - 3

The function f(x) is not weird since f(-x) does not equate to -f(x).

The function f(x) = 3x + 3 - x is therefore neither even nor odd.

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Answer:

20)  y = 3/4x + 3 1/2

21)  Parallel: y = 3/4 x - 2 3/4

Perpendicular: y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

20)

y = mx + b

y = __x + ___  We need to find the slope that the y-intercept. We are given the slope 3/4.  We will you the x and y values from the point (2,5) to find the y intercept. Use 5 for y and 2 for x

y = mx + b

5 = 2(3/4) + b

5 = 3/2 + b  Subtract 3/2 from both sides

5 - 3/2 = 3/2 -3/2 +b

[tex]\frac{10}{2}[/tex] - [tex]\frac{3}{2}[/tex] = b

[tex]\frac{7}{2}[/tex] or 3 [tex]\frac{1}{2}[/tex]

y = 3/4x + 3 1/2

21)

Parallel slopes are equal so the slope will be 3/4.  Now we will use the x and y values from the point (5,1) to find the y-intercept.  We will use 1for y and 5 for x

y = mx + b

1 = 5(3/4) +b

1 = 15/4 + b  Subtract 15/4 from both sides.

[tex]\frac{4}{4}[/tex] - [tex]\frac{15}{4}[/tex] = [tex]\frac{15}{4}[/tex] - [tex]\frac{15}{4}[/tex] + b

[tex]\frac{-11}{4}[/tex] or - 2 [tex]\frac{3}{4}[/tex]

y = 3/4 x - 2 3/4

Perpendicular slopes or the opposite reciprocals.  So the slope of the reciprocal equations would be [tex]\frac{-4}{3}[/tex]. We would still use the x and y values from the point (5,1)

1 = -4/3(5) + b

1 = [tex]\frac{-20}{3}[/tex] + b  Add 20/3 to both sides

[tex]\frac{3}{3}[/tex] + [tex]\frac{20}{3}[/tex] = [tex]\frac{-20}{3}[/tex] + [tex]\frac{20}3}[/tex] + b

[tex]\frac{23}{3}[/tex] or 7 2/3

y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]

Helping in the name of Jesus.

Answer:

7.16  (in meters)

Step-by-step explanation:

Notice the drawing.
The total height from the ground is given by h+1.5

To find h you need to use the right triangle, since you need the opposite side,

[tex]h=7sin(54)[/tex]

so total height is
[tex]H=1.5+7sin(54)[/tex]

be carefull your calculator is set to DEGREES

the answer is:

H = 7.16m rounded to nearest hundredth

Answer:

x = 3.1 Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

3.1 rounded to the nearest tenth

Step-by-step explanation:

Using Sine Rule;

Sin A / a = Sin B / b = Sin C / c

Which is also as Sin M / m = Sin N / n = Sin P / p

Working with M and N;

Sin 15 / x = Sin 90 / 12

Sin 15 / x = 1 / 12 (cross multiply)

Making x the subject of the formula

x = 12 * Sin 15 = 3.10 = 3.1 rounded to the nearest tenth

It should be noted that the number of hours slept will have to be plotted on the x-axis.

Also, the number of mistakes that was made will be plotted on the y-axis.

Each point on the scatterplot will represent one participant in the study.

It should be noted that to illustrate the two variables given in Table 1, we can create a scatterplot using R code.

In this case the number of hours slept will have to be plotted on the x-axis, and the number of mistakes made will be plotted on the y-axis.

Looking at the scatter plot, we can see that there is a general trend that more hours of sleep are associated with fewer mistakes made.

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Answer:

To find AC, you use the tangent ratio, which is opposite over adjacent.

So, tan 27° = 12/AC.

AC = 23.551

To find AB, use the sine function, or opposite over hypotenuse.

So, sin 27° = 12/AB

AB = 26.432

Answer:

Let's call the salary of the governor of state B "x".

According to the problem, the governor of state A earns $49,070 more than the governor of state B. So the salary of the governor of state A can be expressed as "x + 49,070".

We also know that the total of their salaries is $291,120, so we can set up an equation:

x + (x + 49,070) = 291,120

Simplifying the equation, we can combine like terms:

2x + 49,070 = 291,120

Subtracting 49,070 from both sides:

2x = 242,050

Dividing by 2:

x = 121,025

So the salary of the governor of state B is $121,025.

To find the salary of the governor of state A, we can use the expression we came up with earlier:

x + 49,070

121,025 + 49,070 = 170,095

So the salary of the governor of state A is $170,095.

Therefore , the solution of the given problem of equation comes out to be it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces b + 7, in contrast to another algorithm, which can evaluate data from y + 7, divides 12 through two components, and produces y + 7.

Here,

The formula Hayden created is:

=> 470/h = 3008

We must separate h on one side of the equation in order to solve for it. By increasing both parts of the equation by h, we can achieve this:

=> 470 = 3008h

Then, to get h on its own, split the two sides of the equation by 3008:

=> h = 470/3008

By dividing the numerator and denominator by their 2 largest common factor, we can simplify this fraction:

=> h = 235/1504

Therefore, it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

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The value of x in this isosceles triangle is equal to: D. 50.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

In isosceles triangle ABC, side DE intersects its congruent sides and is parallel to side AB. Therefore, there are two sides that are congruent (equal) and as such we have;

(54 - 2x)° = (3x + 4)°

3x - 2x = 54 - 4

x = 50

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Answer: well f(x) equeals a funtction

your x is a given so all you have to do is plug in the given (X) to the equation given f(x)=x/2

Step-by-step explanation:

example for the first slot:

F(x)=-4

      ——

         2

Answer:

Below

Step-by-step explanation:

Here is how to do the first one....the others are similar

f(x) = x/2       when x = -4,     f(-4) = -4/2 = -2    (just put the number in for 'x')

                 when x = - 2 ,   f(-2) =  -2/2 = -1

              when x = 0 ,     0 /2 = 0

           when x = 1 ,        1/2 = 1/2

        when x = 6 ,         6/ 2 = 3

So the answers across the bottom for the first one are

    -2     -1     0    1/2     3

I think you can do the rest.....just put the number value in for 'x' in the equation....

C is Correct

C. Variety is the characteristic of big data that is referred to in the following statement: "Data also comes in all types, forms and granularity, both structured and unstructured."What is big data?Big data is a term used to describe vast, intricate data sets that cannot be processed or analyzed using conventional data processing tools. It is a term used to describe large amounts of structured, unstructured, and semi-structured data that cannot be processed using conventional processing methods. It is characterized by volume, speed, and complexity, and it necessitates new technologies, procedures, and strategies to manage, store, and analyze it.There are four essential characteristics of big data: volume, velocity, variety, and veracity, referred to as the four Vs. The different characteristics of big data are:Variety: Big data comes in all types, forms, and granularity, both structured and unstructured. It may include everything from text, images, and video to social media and IoT data. It can be a challenge to store, manage, and analyze data of such variety. Therefore, organizations must use tools and techniques that can handle all kinds of data.Velocity: The pace at which data is created and generated is referred to as velocity. In real-time, big data is collected and handled. The quicker you can process the data, the more valuable it becomes. Stream processing, complex event processing (CEP), and real-time analytics tools are examples of technologies that can handle high-velocity data.Volume: Big data is characterized by a large volume of data. Every day, we produce a tremendous amount of data that needs to be stored, processed, and analyzed. The huge data sets can make data analysis and management challenging.Veracity: The precision, relevance, and dependability of the data are referred to as veracity. Before processing and analyzing, big data must be checked for errors and inconsistencies. Quality checks and data cleansing procedures should be implemented to maintain data accuracy and reliability.

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Answer:

df= 6g-10

Step-by-step explanation:

[tex]\frac{df+10}{6}[/tex]= g

df+10= 6g

df= 6g-10

Optiοn C represents a prοpοrtiοnal relatiοnship . The values οf all the given values are prοpοrtiοnal tο each οther i.e, 1/3.

A prοpοrtiοnal relatiοnship is a mathematical relatiοnship between twο variables where the ratiο οf the twο variables is cοnstant. In οther wοrds, if we have twο variables x and y, they are said tο have a prοpοrtiοnal relatiοnship if the ratiο οf x tο y is always the same, regardless οf the values οf x and y.

This can be expressed mathematically as:

x/y = k

where k is a cοnstant called the prοpοrtiοnality cοnstant. This means that as x increases, y will increase prοpοrtiοnally, and as x decreases, y will decrease prοpοrtiοnally.

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Answer:          1

Step-by-step explanation:

i cant

The minimum Marissa should spend on eggs to use all of her chard leaves while keeping the recipe in the correct proportion is $3.40.

To use 10 chard leaves, the recipe calls for 6 eggs. Let's find out how many eggs we need to use 25 chard leaves in the same proportion:

10 chard leaves / 6 eggs = 25 chard leaves / x eggs

where x is the number of eggs needed.

Cross-multiplying, we get:

10 chard leaves * x eggs = 6 eggs * 25 chard leaves

Simplifying, we get:

x = (6 eggs * 25 chard leaves) / 10 chard leaves

x = 15 eggs

So, Marissa needs 15 eggs to use 25 chard leaves in the recipe.

Now, let's find out the cheapest way to buy 15 eggs. She can buy either a dozen eggs for $3.20 or a half-dozen eggs for $1.70. Since a dozen contains 12 eggs and a half-dozen contains 6 eggs, she can either buy:

1 dozen + 3 individual eggs = 15 eggs for $3.20 + $0.24 = $3.44

2 half-dozens = 12 eggs for $3.40

Therefore, the minimum Marissa should spend on eggs to use all of her chard leaves while keeping the recipe in the correct proportion is $3.40.

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The estimated area of the sidewalk that is getting wet is 706.5 square feet

The area of the sidewalk that is getting wet can be estimated by using the formula for the area of a circle: A = πr2, where "r" is the radius of the circle, which in this case is 15 feet. (A = π(152) = 706.5).

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

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Answer:

Let, price paid by adults be x and children be y.

then,

5x+4y=78----(1)

3x+6y=63----(2)

Solving both we get

x=12,y=4.5

So adult pays £12 and child pays £4.5

1. Vertical Shift: f(x) + 1 = 2(1/3)ˣ + 2, 2. Horizontal shift: f(x - 2) = 2(1/3)ˣ⁻² + 1, 3. Vertical stretch/compression: 3f(x) = 6(1/3)ˣ + 3, 4. Horizontal stretch/compression: f(2x) = 2(1/3)²ˣ + 1.

In two-dimensional geometry, a translation can be described as moving a point or a shape horizontally, vertically, or diagonally. To translate a shape, we can move each of its points by the same vector. For example, to translate a square 3 units to the right and 2 units up, we can move each of its four vertices 3 units to the right and 2 units up.

In three-dimensional geometry, a translation can be described as moving an object in the x, y, or z direction. To translate an object, we can move each of its points by the same vector. For example, to translate a cube 2 units in the x-direction, 3 units in the y-direction, and 4 units in the z-direction, we can move each of its eight vertices by the vector (2, 3, 4).

The function f(x) = 2(1/3)ˣ + 1 can be transformed using different techniques, such as shifting, stretching, or reflecting. Here are some possible transformations:

Vertical shift: Adding a constant to the function shifts the entire graph vertically. For example, adding 1 to f(x) shifts the graph up by 1 unit. The new function is:

f(x) + 1 = 2(1/3)ˣ + 2

Horizontal shift: Adding or subtracting a constant to the input variable x shifts the graph horizontally. For example, replacing x with x - 2 shifts the graph to the right by 2 units. The new function is:

f(x - 2) = 2(1/3)ˣ⁻² + 1

Vertical stretch/compression: Multiplying the function by a constant stretches or compresses the graph vertically. For example, multiplying f(x) by 3 stretches the graph vertically by a factor of 3. The new function is:

3f(x) = 6(1/3)ˣ + 3

Horizontal stretch/compression: Multiplying or dividing the input variable x by a constant stretches or compresses the graph horizontally. For example, replacing x with 2x stretches the graph horizontally by a factor of 1/2. The new function is:

f(2x) = 2(1/3)²ˣ + 1

These are some of the possible transformations of the function f(x) = 2(1/3)^x + 1. By applying one or more of these transformations, we can obtain a new function that represents a shifted, stretched, or reflected version of the original function.

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