In which situation below would you want to use the Explicit Formula instead of the Recursive Formula

The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

The perimeter of a polygon is the sum of its, all the side lengths.

Given that, the dimension of a rectangle is given by, √50a³b² and √200a³

The perimeter of the rectangle is = 2(length + width)

Solving for the perimeter,

2(√50a³b²+√200a³)

= 2(5ab√2a+10a√2a)

= 10ab√2a+20a√2a

The student solved it as 30ab√2a,

Which is incorrect, because 'b' is not there in both the expressions, hence, we cannot add them.

Hence, The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

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if the rate of the current is 5 kilometers per hour, The rate of the boat in still water is 15 km/h.

The rate of the boat in still water is the rate of the boat when the current is not affecting its motion, so we can calculate the rate of the boat in still water by subtracting the rate of the current from the rate of the boat while moving downstream and adding the rate of the current to the rate of the boat while moving upstream. In this case, the rate of the boat while moving upstream is 8 km/h, and the rate of the boat while moving downstream is 20 km/h. Since the rate of the current is 5 km/h, we can subtract 5 km/h from 20 km/h to get the rate of the boat in still water, which is 15 km/h.

Rate of boat in still water = Rate of boat while moving downstream - Rate of current + Rate of boat while moving upstream

= 20 km/h - 5 km/h + 8 km/h

= 15 km/h

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Answer:

yellow

Step-by-step explanation:

i can only see one line, and infinitely many points are on it

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Answer:

8

Step-by-step explanation:

40:20

x:4

20/4 = 5

40/5 = 8

Answer:

find it using angles

Step-by-step explanation:

Angle ABC is a straight angle.

Angles ABD and DBC are right angles.

Angles CBE and DBE are acute angles.

Angle ABE is an obtuse angle.

Angles

The sum of the three angles in any triangle is always 180°.

a + b + c = 180°

Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.

Angles

In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?

a + b + c = 180°

Since b is a right angle, b = 90°.

The problem states that c = 40°.

Therefore, a + 90° + 40° = 180°

a + 130° = 180°

a + 130° − 130° = 180° − 130°

a = 50°

Angle a measures 50°.

Angles

Click on the figure that matches this description.

An obtuse angle

Question 1 of 8

This is an acute angle. It measures less than 90°. Try again

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°.

One of these figures is an obtuse angle. Try again.

An obtuse angle is larger then a right angle and smaller then a straight angle.

Angles

Click on the figure that matches this description.

An acute angle

Question 2 of 8

This is an acute angle. It measures less than 90°.

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°. Try again.

One of these figures is an acute angle. Try again.

An acute angle is smaller then a right angle.

Angles

Click on the figure that matches this description.

A right angle

Question 3 of 8

This is an acute angle. It measures less than 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.

This is an acute angle. It measures less than 90°. Try again.

A right angle looks like a square corner and measures 90°.

A right angle measures 90°.

Angles

There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.

Angles

Click on the correct answer.

Angle ABC is a right angle. If angle n is 40°, how large is angle m?

50°

140°

90°

60°

None of these

Question 4 of 8

90° − 40° = 50°

Angle m is 50°.

Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.

Angle ABC is 90°, and angle m is only part of this right angle. Try again.

Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.

One of these is size of angle m. Try again.

Since angle ABC is a straight angle, angle m + angle n = 90°.

Answer:

Step-by-step explanation: To solve this problem, we can use the following formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A is the total amount at the end of the period

P is the principal (initial investment)

r is the annual interest rate

n is the number of times the interest is compounded per year

t is the number of years

We can rearrange this formula to solve for r:

r = n * ((A/P)^(1/n*t) - 1)

We can plug in the values for A, P, and t for each year to solve for the annual interest rate:

Year 1:

r = n * ((4240.00/P)^(1/n*1) - 1)

r = 1 * ((4240.00/P)^(1/1) - 1)

r = (4240.00/P) - 1

r = 4240.00/P - 1

r = 4240.00 - P/P

r = 4240.00 - 1

r = 0.08

Year 2:

r = n * ((4494.40/P)^(1/n*2) - 1)

r = 1 * ((4494.40/P)^(1/2) - 1)

r = (4494.40/P)^(1/2) - 1

r = 4494.40/P - 1

r = 4494.40 - P/P

r = 4494.40 - 1

r = 0.08

Year 3:

r = n * ((4764.06/P)^(1/n*3) - 1)

r = 1 * ((4764.06/P)^(1/3) - 1)

r = (4764.06/P)^(1/3) - 1

r = 4764.06/P - 1

r = 4764.06 - P/P

r = 4764.06 - 1

r = 0.08

Since the annual interest rate is consistent at 0.08 for all three years, we can conclude that this is the annual rate of compound interest earned.

To solve for the principal, we can use the formula for compound interest again, this time solving for P:

P = A / (1 + r/n)^(n*t)

Plugging in the values for A, r, and t for each year, we get:

Year 1:

P = 4240.00 / (1 + 0.08/1)^(1*1)

P = 4240.00 / 1.08

P = 3925.93

Year 2:

P = 4494.40 / (1 + 0.08/1)^(1*2)

P = 4494.40 / 1.16

P = 3925.93

Year 3:

P = 4764.06 / (1 + 0.08/1)^(1*3)

P = 4764.06 / 1.24

P = 3925.93

Since the principal is consistent at $3925.93 for all three years, we can conclude that this is the amount Sima invested.

Answer:

[tex]5\sqrt{p} ^{11}[/tex]

x ≥ -26 / (6a - 15)  where a >5/2.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Given a equation, (3ax + 2)/ 3  -  (5x / 2) ≥  -8 where a > 5/2

solving for x in terms of a

ax + 2/3  - 5x/2  ≥ -8

x(6a - 15 )  ≥ -26

x ≥ -26 / (6a - 15)

since a is greater than 5/2 let a be 3 than the value of x ≥ -26/3.

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The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/0.47 or 0.53 to 0.47. So, correct answer is option(A).

Two-way frequency tables are powerful tools for examining relationships between categorical variables. The entries in the main part of the table are common frequencies. The entries in the "Total" row and "Total" column are limit frequencies. Relative frequencies are used when comparing different classes and classes to the entire data set. The relative frequencies in the body of the table is known as the conditional frequencies. We have a data on the table which decribe the preferred type of music (Rock, Pop and Hip Hop ) a surveyed by females and males as seen above table. We calculated the relative frequencies for each music type so that we should compare the data more reliably. Now, the relative frequency for males who prefer pop music = 10/19

= 0.53

the relative frequency for females who prefer pop music = 9/19 = 0.47

Based on the data collected, males are more likely to prefer pop music than females. The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/ 0.47 . So, required conditional relative frequency is 0.53/ 0.47 .

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Complete question:

The data on the table decribe the preferred type of muic a urveyed by 9th grader. Rock Pop Hip Hop Total Male 20 17 10 47 Female 16 28 9 53 Total 36 45 9 100 Compare the conditional relative frequencie of a male preferring pop muic to a female preferring pop muic. Round your anwer to two decimal place.

A) 0. 53 to 0. 47

B)0. 37 to 0. 62

C) 0. 36 to 0. 53

D) 0. 17 to 0. 28

Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.

Option D is the correct answer.

Net income is the amount remaining after deducting the expenses from the revenue collected.

We have,

Consider,

Amount collected after production of items = $400

Cost of production of the items = $250

Net income.

= Amount collected - Cost of production

= 400 - 250

= $150

Thus,

Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.

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Answer:

Matthew has 24 inches of green ribbon and 3/4 inch of yellow ribbon. How much ribbon does he have in all?

Kiki had 24 marbles. She put 3/4 of the marbles in a jar. How many marbles did she put in the jar?

There were 24 questions on a test. Three-fourths of the questions were science questions. How many questions were science questions?

Aisha baked 24 muffins. She gave 3/4 of the muffins to her friends. How many muffins does she have left?

Step-by-step explanation:

Answer:

Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?

Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?

Step - by - step explanation

2/3 × 18

Checking all options

Sarah mixed 18 ounces of orange juice with 23 ounce of pineapple juice. How many ounces of juice did she have in all?

Ounces of orange juice = 18

Ounces of pineapple juice = 23

Total ounces of juice = 18 + 23

= 41 ounces

A container held 18 ounces of water. Two-thirds of the water leaked out of the container. How many ounces of water were left in the container?

Total water in the container = 18

Water leaked out = 2/3

Ounces of water left = 18 - 2/3(18)

= 18 - 36/3

= 18 - 12

= 6

Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?

Total Number of coins = 18

Dimes = 2/3 of 18

Number of dimes = 2/3 × 18

= 36 / 3

= 12

Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?

Total quarters = 18

Quarters used for game = 2/3 × 18

= 2/3 × 18

= 36 / 3

= 12

The inequality is 7<x<31.

What is inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The third side of any triangle must be more than the difference between the other two sides.

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

Put them together.

7<x<31 (or) 31>x>7

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A polynomial function is a mathematical function defined by an expression that is a sum of terms, each of which is a product of a constant and a non-negative integer power of a variable. The term "polynomial" comes from the Greek word "polys," which means "many," and "nomos," which means "terms." Polynomial functions are distinguished by the degree of their highest-degree term, which is the largest exponent of the variable. For example, the polynomial function f(x) = x3 + 2x2 + x - 1 has a degree of 3 because the highest-degree term is x3.

Out of the four given options, only the functions f(x) = x3 + 2x2 + x - 1 and f(x) = x3 +1 are polynomial functions. The other two options, y = -2x3 + 5x – 4 - 4 and f(x) = V2x3 + 5, are not polynomial functions because they contain terms that are not of the form "constant times a non-negative integer power of a variable." The function y = -2x3 + 5x – 4 - 4 contains the term -4, which is not a product of a constant and a non-negative integer power of a variable, and the function f(x) = V2x3 + 5 contains the term V2x3, which is not a product of a constant and a non-negative integer power of a variable. Therefore, the correct answer is A and D.

The x-intercept of the function f is greater than the x-intercept of function g is the correct statement.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Setting y = 0 will provide the x-value at which the line crosses the x-axis, allowing us to find the x-intercept

Function g(x) is defined as:

g(x)=2+[tex]\sqrt[3]{3x+1}[/tex]

and f(x)=0

To find x-intercept let g(x)=0

So

2+[tex]\sqrt[3]{3x+1}[/tex]=0

[tex]\sqrt[3]{3x+1}[/tex]=-2

Taking cube on both sides we get

3x+1= -8

3x=-9

x=-3

The x-intercept of g(x) + -3, which is less than the x-intercept of function f(x), hence, the correct statement is:

The x-intercept of the function f is greater than the x-intercept of function g.

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Answer:

5.1

Step-by-step explanation:

When dividing or multiplying numbers, the answer should have the same amount of significant figures as the number in the problem with the least amount of sig figs.

In the problem 65.8 ÷ 13 ...

65.8 has 3 sig figs

13 has 2 sig figs

13 has THE LEAST AMOUNT OF SIGNIFICANT FIGURES

So, this means the answer must have the same number of sig figs as 13.

Let's round 5.0615384615 to TWO significant figures

the 6 in the number must be rounded up!

Final answer: 5.1

5.1 has  TWO sig figs like the number 13

keeping in mind that perpendicular lines have negative reciprocal slopes, and that line "k" has a slope of 1/3, then

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{1}\implies -3}}[/tex]

so for line "j" we're really looking for the equation of a line whose slope is -3 and that it passes through (1 , 4)

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 3}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-3x+3\implies {\Large \begin{array}{llll} y=-3x+7 \end{array}}[/tex]

Answer:

7,2,15

Step-by-step explanation:

In general, to find rational numbers that satisfy a given set of conditions, it is often helpful to first write an equation that relates the numbers to each other.

The three rational numbers are 7, 2 and 15

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

First Number= x

Second Number= x- 5

Third Number = 2x+ 1

so, the product of the three number be 210

x(x-5 )(2x+ 1)= 210

(x² -5x )(2x+ 1)= 210

2x³ + x² - 10x² - 5x= 210

2x³ -9x² -5x -210=0

On solving the equation we get only one real value 7 and other values are imaginary.

Then, the number are

x= 7

2-x-5 = 2

2x+1 = 15

Hence, the three rational numbers are 7, 2 and 15.

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59/40

The numerators don't line up. We require a connecting factor. Therefore, we multiply both denominators next. The next step is to multiply each numerator by the denominator of the other term.

As a result, we multiply 3 by 8 to get 24 and multiply  7 by 5 to get 35 and then 5 by 8 to get 40.

3/5=3*8/5*8 and 7/5= 7*5/8*5

We can add the numerators because our denominators are same.

24 + 35 = 59

As a result, we have the sum, which is

59/40

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Using the values provided and a derivative of the cone's volume formula, the result is 0.059 feet per minute.

In mathematics, the rate at which a function changes in relation to a variable.

A cone is a three-dimensional geometric structure that has a smooth transition from a flat base that is typically circular to the point at the top, which is also referred to as the apex or vertex.

The formula for cone volume is:

V=πr2h/3

yields the formula for cone volume:

dv/dt = 2r * h/3 * dr/dt dV/dt = 3 r=2 h=12

dr/dt = 0.059 feet per minute.

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Answer:

5000

Step-by-step explanation:

1000+0.8s < 5000

                                  subtract 1000 from both sides of the inequality

0.8s < 4000

                                  divide both sides by 0.8 to get the number of sales (s)

s <5000

The quadratic function x² + 4x - 5 is factorized to give

(x + 5) (x - 1)

The given quadratic function is x² + 4x - 5

The graph is plotted and the roots of the equation which is the x intercepts that is the points where the graph cuts the x axis is found to be points 1 and -5

Using points 1 and -5 the equation is sort as follows

for 1

x = 1

x - 1 = 0

for -5

x = -5

x + 5 = 0

bringing the solutions together

(x + 5) (x - 1)

The solution is (x + 5) (x - 1)

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The performance of a thermocouple is displayed in the scatterplot is

Explanatory variable: Temperature

Response variable: Voltage

Given that,

The performance of a thermocouple is displayed in the scatterplot below.

We have to find which of the following choices accurately identifies the explanatory and response variables for the scatterplot.

We know that,

Dots are used to indicate the values for two different numerical variables in a scatter plot (also known as a scatter chart or scatter graph). The positions of each dot on the horizontal and vertical axes represent the values of a single data point. To see how different variables relate to one another, utilize scatter plots.

Explanatory variable: Temperature

Response variable: Voltage

So, we can see the scatterplot in the picture.

Therefore, Explanatory variable: Temperature

Response variable: Voltage when the performance of a thermocouple is displayed in the scatterplot

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Answer:

Explanatory variable: Temperature

Response variable: Voltage

Step-by-step explanation:

Got it right on the test.

the percent increase in enrollment, and round to the nearest percent is 40%

Given that number of students enrolled in 2010= 2000

Given that number of students enrolled in 2018 = 2800

2800is more than 2000 so that means number of students enrollment is increasing.

increase = 2800-2000= 800

Percent increase is given by formula:

% increase = 800/2000*100= 40

which is approx 40%.

Hence final answer is that enrollment increases by 40%

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Answer:

Step-by-step explanation:

The hypotenuses(x) of the triangle whose legs are 12 cm and 16 cm is 20 cm.

As we know that in a right angled triangle there are base, perpendicular and hypotenuse. a hypotenuse is the longest side of a right triangle. In other words, the side opposite to the right angle is called the hypotenuse.

Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

By Pythagoras theorem, hypotenuse (x)  = √(a² + b²)

                                                                        =  √(16² + 12²)

                                                                        = 20 cm

Answer:

x= 30

Step-by-step explanation:

Angle E

E + F + G = 180

E + 60 + 90 = 180

E + 150 = 180

E = 180-150

E = 30

Angle E  is congruent to angle X so the measures must be the same

E = X = 30

X = 30

Answer:

[tex]E=30[/tex]

Step-by-step explanation:

[tex]E + F + G = 180\\E + 60 + 90 = 180\\E + 150 = 180 \\E= 180-150 = 30[/tex]

Hope this helps u :)

Answer:

1. Step by step explanation:- Since 120$ is obtained by reducing the price by 30% that is subtracting ORIGINAL COST from its 30%.

In order to obtain the Cost Price we shall add back the 30% to 120$ to obtain the Cost Price -

120+30%*120 = 120+36= 156 $ . (Ignore the currency. Answer remains unaffected )

2. Question is incomplete.

3. 48=2*2*2*2*3

4. Factorization of x^2-2x-35 is

=x^2-7x+5x-35         (-7x+5x= -2x)

=x(x-7)-5(x-7)            (Taking x common from the first () and 5 from the            second bracket)

=(x-5)(x-7)

Factors are 7 and 5.

5. 2.1*10^8

6. For this question it is to be assumed that -

    2x+7=-1

    Now normally solving the equation we get

   2x=-1-7

  => 2x= -8

  => x= -4

7. Multiples of 270 = 3*3*3*2*5

   Multiples of 84 = 2*2*3*7

  Common multiples = 2*3=6

8. First 5 terms can be obtained by putting (1,2,3,4,5) serially in the equation 8n+2

8*1+2=10, 8*2+2= 18, 8*3+2=26 , 8*4+2=34, 8*5+2= 42

We can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Two-Hypotheses:  

H0: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is not significantly less than the overall mean waiting time of 13 minutes.

Ha: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Test Statistic:  t = (11 - 13) / (8/√50) = -2.5  and the Critical Value Approach is: The critical value for a one-tailed test at alpha = 0.05 is 1.645. Since the test statistic (-2.5) is less than the critical value (1.645), we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes, and the   P-Value Approach:  The p-value for the one-tailed test is 0.0062. Since this p-value is less than alpha = 0.05, we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

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The statements which must be true is statement 4 which is  :-

  Point a is not necessarily the center of the circle that passes through points e, f, and g or the center of the circle that passes through points x, y, and z.

3 points uniquely define a circle. so points e,f and g uniquely defines a circle C1 and point x,y and z uniquely defines a circle C2.

The below figure shows the condition that 2 different circle C1 and C2  can have same center , point a and this conditon occurs when they are concentric circle so statement 1,2 is false as in these statement it is told that point a can be center of only one circle but point a can be center of more than 1 circles.

and it is also possible that these 2 different cirlce C1 and C2 can have different center which is 2 different circle ,so statement 3 is also false.

so only statement which must be correct statement is 4 as in this case point a might be center of circle C3 which is neither C1 or C2.

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Answer: C

Step-by-step explanation: because I am amazing

By the age of four, Adam knows that changing one's exterior characteristics  does not change one's gender. Adam has "acquired" or "learned" gender constancy.

Which of the three stages of gender constancy are you?

A child's developing sense of the permanency of being a boy or a girl, which happens in stages: gender identification, gender stability, and gender consistency. Gender constancy is similar to Piaget's concept of physical property conservation in that gender constancy relates to the awareness that gender is an invariant human property that is stable through time and superficial changes in appearance. It starts at the age of six or seven, when a youngster realizes that gender remains consistent across settings (e.g. if a man puts on a dress he is still a man).

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Answer:

The speed in yards per year is 60.8.

Step-by-step explanation:

To convert the speed from inches per day to yards per year, we need to first convert the speed to inches per year and then convert the units to yards per year.

First, we can convert the speed to inches per year by multiplying the speed by the number of days in a year:

Speed (inches/day) * Days per year = Speed (inches/year)

6 inches/day * 365 days/year = 2190 inches/year

Next, we can convert the units to yards per year by dividing the speed in inches per year by the number of inches per yard:

Speed (inches/year) / Inches per yard = Speed (yards/year)

2190 inches/year / 36 inches/yard = 60.8 yards/year

Rounding to the nearest 10th, we have:

60.8 yards/year ≈ 60.8 yards/year

Therefore, the speed in yards per year is 60.8.