3 for a decimal expansion k.d1d2d3d4 ···, let (sn) be defined as in discussion 10.3. prove sn < k 1 for all n ∈ n. hint: 9 10 9 102 ··· 9 10n

The circumference of the football field is given as 264 meters.

Let's assume that the radius of the football field is "r" meters. We know that the circumference of a circle is given by the formula C=2πr, where C is the circumference and r is the radius.

Therefore, we have:

C = 2πr

264 = 2πr   (since C = 264 meters)

132 = πr

Now we can solve for the radius:

r = 132/π ≈ 42

Therefore, the radius of the football field is approximately 42 meters, rounded to the nearest whole number.

Learn more about radius here: brainly.com/question/19489828

#SPJ11

Step-by-step explanation:

mr barnes has aa higher lilac to rose ratio

I hope you help :)

Answer:

Mr Yen: 7:3

Mrs Barnes: 9:4

Therefore, Mrs Barnes has a higher lilac to rose ratio.

Step-by-step explanation:

Answer:

Yea you correct, you answer is right

The numbers in the G P are 40, 20, and 10. with

a = 40 and r = 1/2

The geometric progression (GP) is assumed to be

a, ar, and ar²

where

a + ar + ar² = 70

multiplying the two extreme terms by 4

4a and 4ar^2

multiplying  the geometric mean of the three terms by 5

5∛(a * ar * ar²) = 5ar

forming the arithmetic progression (AP)

4a, 5ar, 4ar² in A.P

solving the equations to find the values of a and r

a + ar + ar² = 70

a(1 + r + r²) = 70

From the A.P. condition (the average of the AP)

2(5ar) = 4a + 4ar²

10ar = 4a + 4ar²

4ar² - 10ar + 4a = 0

dividing both sides by 2a:

2r² - 5r + 2 = 0

factoring the quadratic equation

(2r - 1)(r - 2) = 0

Solving for r:

2r - 1 = 0 then r = 1/2

or

r - 2 = 0 then r = 2

solving for a

For r = 1/2

a(1 + 1/2 + 1/2²) = 70

a(7/4) = 70

a = 40

For r = 2:

a(1 + 2 + 2²) = 70

a(6) = 70

a = 11.667

Learn more about GP at

https://brainly.com/question/31345290

#SPJ1

The change-of-coordinates matrix from basis B to basis C is given by the matrix [3 -4; -1 1]. This matrix allows us to convert coordinates expressed with respect to basis B to coordinates expressed with respect to basis C.

The change-of-coordinates matrix from basis B to basis C can be determined by expressing the basis vectors of C in terms of the basis vectors of B. In this case, we are given B = {b1, b2} and C = {c1, c2}, where b1 = (1, 2), b2 = (-2, 1), c1 = (1, 1), and c2 = (2, -1). To find the change-of-coordinates matrix, we express c1 and c2 in terms of b1 and b2 and arrange the coefficients in a matrix. The first column of the change-of-coordinates matrix corresponds to the coefficients of b1 in terms of c1 and c2. To find these coefficients, we solve the equation c1 = x1 * b1 + x2 * b2, where x1 and x2 are the unknown coefficients. Using the given values, we have (1, 1) = x1 * (1, 2) + x2 * (-2, 1). Solving this system of equations, we get x1 = 3 and x2 = -1. Similarly, for the second column of the change-of-coordinates matrix, we solve the equation c2 = y1 * b1 + y2 * b2, where y1 and y2 are the unknown coefficients. Substituting the values, we have (2, -1) = y1 * (1, 2) + y2 * (-2, 1). Solving this system, we find y1 = -4 and y2 = 1.

Therefore, the change-of-coordinates matrix from basis B to basis C is:

[3  -4]

[-1  1]

Learn more about system of equations here: brainly.com/question/20067450

#SPJ11

Answer:

c. greater than 7

Step-by-step explanation:

Answer:

C. The answer is molecular motion.

Step-by-step explanation:

When a molecule moves it would heat up. Therefore, by moving it would heat up.

The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

To learn more about the explicit formula from the given link

https://brainly.com/question/9859279

#SPJ1

Step-by-step explanation:

\(\blue\star\)sn = 549

\(\blue\star\) d = 3

\(\blue\star\)56th term of Ap

\(\blue\star\)the sum of 32 tem

Answer:

y= -3x + 7:)

Step-by-step explanation:

Hope this helps!

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = - 12 + c ⇒ c = - 5 + 12 = 7

y = - 3x + 7 ← equation of line

The New Profit Function is P(x)=-2x^2+44x-42 and the  maximum profit of 200 dollars.

(Price * Units Sold = Revenue)

\(r(x)=(48-2x)x\)

Now we can write a function for profit.

\(P(x)=(48-2x)x-(4x+42)\)

\(48x-2x^2-4x-42\)

\(P(x)=-2x^2+44x-42\)

If you want to solve with out a graph, use vertex form equation:

-b/2a

-44/-4=11

\(-2(11)^2+44(11)-42=200.\)

After Pop it into the graph and we would find that she has to sell 11 wind chimes to gain the maximum profit of 200 dollars.

Hence , the New Profit Function is\(P(x)=-2x^2+44x-42\)and the  maximum profit of 200 dollars.

Learn more about Maxima at:

brainly.com/question/29502088

#SPJ1

The equation of the line that goes through the points (−3,−4) and (9,7) can be written in the form 5x - 12y = -75.

To find the equation:

The available points are (3,5) and (9,10).

The line's slope is given by:

\(\mathrm{m}=\frac{(10-5)}{[9-(-3)]}=\frac{5}{12}\)

The equation is as follows:

\(\begin{aligned}&y-5=\left(\frac{5}{12}\right)[\mathrm{x}-(-3)] \\&\mathrm{y}-5=\left(\frac{5}{12}\right)(\mathrm{x}+3)\end{aligned}\)

Solve it to obtain the equation:

\(\begin{aligned}&12 y-60=5 x+15 \\&5 x-12 y=-75\end{aligned}\)

Therefore, the equation is 5x - 12y = -75.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ4

The correct question is given below:
Find an equation of the line through the points (−3,5) and (9,10) and write it in standard form Ax+By=C, with A>0.

Answer:

51 Yards

Step-by-step explanation:

Each side is 36 yards. split the square in half(corner to corner) making two right triangle use the pythagorean theorem (\(A^{2}\) + \(B^{2}\) =\(C^{2}\) ) to solve.

\(36^{2}\)+\(36^{2}\)= \(C^{2}\)

1296+1296= 2592

√2592= 50.911

50.911 rounds up to 51

The length of each walkway would be,

⇒ 51 yards

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

We have to given that;

A school has a square courtyard and wants to create diagonal walkways.

Here, The length of each side of the courtyard is 36 yards.

Now, The length of each walkway would be,

⇒ √ 36² + 36²

⇒ √ 1296 + 1296

⇒ √ 2592

⇒ 50.91

⇒ 51 yards

Thus, The length of each walkway would be,

⇒ 51 yards

Learn more about the Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ2

Answer:

Step-by-step explanation:

Expanding the expression (g+h)(p+q-r) using the distributive property, we get:

(g+h)(p+q-r) = g(p+q-r) + h(p+q-r)

Now, applying the distributive property again, we can simplify this expression to:

(g+h)(p+q-r) = gp + gq - gr + hp + hq - hr

Therefore, the expression (g+h)(p+q-r) is equivalent to:

gp + gq - gr + hp + hq - hr

If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.

In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without  further information.  

Minimum score: 50

Lower quartile (Q1): 65

Median (Q2): 75

Upper quartile (Q3): 85

Maximum score: 95

Josh's score: 72

Using the steps outlined previously:

Q1 = 65, Q2 = 75, Q3 = 85

IQR = Q3 - Q1 = 85 - 65 = 20

Minimum score = 50, Maximum score = 95

Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:

Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.

Learn more about statistics at

https://brainly.com/question/22825309

#SPJ4

this is the correct answer

Answer:

x = 4

Step-by-step explanation:

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition y = 24 when x = 6 , then

24 = 6k ( divide both sides by 6 )

4 = k

y = 4x ← equation of proportion

When y = 16, then

16 = 4x ( divide both sides by 4 )

4 = x

Answer:

О  D.  \(\frac{5}{9}v - \frac{5}{9}\)

Step-by-step explanation:

\(\frac{2}{9}v - (-\frac{1}{3}v + \frac{5}{9})\\ The rule is:\\ - * - = +\\ - * + = -\\Then:\\\frac{1}{3} = \frac{3}{9}\\\\\\\)

\(= \frac{2}{9}v - (-\frac{3}{9}v + \frac{5}{9})\\\\ = \frac{2}{9}v + \frac{3}{9}v - \frac{5}{9}\\\\ = \frac{5}{9}v - \frac{5}{9}\)

Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Answer:

  (a)  see attached

Step-by-step explanation:

A table will represent a function if no input (x) values are repeated.

The offered tables can be evaluated as follows:

  (a) x-values {-4, -1, 1, 4}, no repeats. Is a function.

  (b) x-values {2, 2, 3, 3}, both values repeated

  (c) x-values {-5, -5, 5, 5}, both values repeated

  (d) x-values {2, 2, 7, 7}, both values repeated

Answer:

37.5

Step-by-step explanation:

18/48 = x/100

18 x 100 = 48 x x

1800 = 48x

1800/48 = x

x = 37.5

Based on the information given regarding the percentage, the correct option is 37.5%.

It should be noted that in order to calculate the percentage, the following should be done.

= 18/48 × 100

= 3/8 × 100

= 37.5%

Therefore, based on the information given, it can be seen that the answer is 37.5%.

Learn more about percentages on:

https://brainly.com/question/24304697

A sixth wind turbine will be placed near the intersections of the bisector. To find the location of the sixth wind turbine near the intersections of the bisector.

Start by identifying the bisector of the given intersections. The bisector is a line that divides the angle formed by the two intersections into two equal angles.Locate the midpoint of the bisector. This point will be equidistant from the two intersections.

From the midpoint, measure the desired distance to place the sixth wind turbine. This distance should be consistent with the placement of the other wind turbines. Mark the location of the sixth wind turbine at the measured distance from the midpoint along the bisector. This will ensure that it is equidistant from the two intersections.

To know more about intersections visit:

https://brainly.com/question/31274160

#SPJ11

The question pertains to the placement of a wind turbine near the intersection of the bisectors, setting a scenario of using principles of geometry and the application of translation and rotation in real life for maximum utilization of wind energy.

The placement of a wind turbine near the intersection of the bisectors involves understanding the principles of geometry. In order to understand this, one needs to understand bisectors, which are a line, ray, or segment that divides an angle or segment into two equal parts.

In the case of wind turbines, these might be placed near the intersections of the bisectors based on the consideration of maximum distribution of wind energy. The bisectors could be representing the ideal locations to capture the wind from all directions equally. This concept combines both principles of translation and rotation. The turbines rotate to generate power (rotational motion), and they may be laid out in a grid (translational symmetry) to efficiently capture wind energy.

It's a great example of how rotational motion and principles of geometry may be applied in real life, especially in the field of renewable energy resources. Therefore, this is a blend of geometry and physical science, with a practical application in engineering and environmental science.

https://brainly.com/question/28663444

#SPJ12

Answer:

Pepperoni placement caused the difference in customer ratings

Step-by-step explanation:

Random assignment of the pepperoni placement for each customer makes this study an experiment, so we can make causal conclusions.

Answer:

2

Step-by-step explanation:

The equation for a line is:

y=mx+b

Where m is the slope, b is the y-intercept, and x and y are the x and y coordinates.

The equation given to us is:

y=2x+3

Therefore 2 is the slope

The required two cords together is 5 1/8 yards long, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
We can add the two cords together in different ways:

2 6/8 yards = 22/8 yards

2 3/8 yards = 19/8 yards

Total length in eighths of a yard: 22/8 + 19/8 = 41/8 yards

Simplifying 41/8 yields 5 1/8 yards.

So the two cords together are either 4 19/36 yards or 5 1/8 yards long.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).

To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:

Step 1: Identify the system of inequalities in the given constraints

Step 2: Graph those inequalities

Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities

Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.

The given equation is C = 7x + 8y, and the constraints list is

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Graphing these inequalities and shading the region that satisfies the given inequalities.

So, from the graph,

the x-values that satisfy all the given inequalities are [6, ∞]

the y-values that satisfy all the given inequalities are [0, ∞]

So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y

Then,

C = 7(6) + 8(0) = 42 + 0 = 42

Thus, the minimum value of the given equation is 42.

Learn more about finding minimum value here:

https://brainly.com/question/10114820

#SPJ1

Disclaimer: The given question is incomplete. Here is the complete question.

Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Answer:

pythagorean theorem

c^2(hypotenuse)=a^2(adjacent)+b^2(opposite)

=6^2+4^2

36+16

c^2=52

\(c = \sqrt{52 } \)

c=7.21

sorry if its wrong...just giving it a try

Answer:

Actually people the answer is 7.2 to and here is proof

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

\(2(x+8)-4x=10x+4\\=>2x+16-4x=10x+4\\\)

Shifting the variable terms on left side gives :-

\(2x-4x-10x=4-16\\=>-12x=-12\\=>x=\frac{-12}{-12}=1\)

The value of x  in the equation will be; x = 1

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation 2(x+8)-4x=10x+4

Here, we need to solve for x as

2(x+8)-4x=10x+4

combine the like terms;

2x + 16 - 4x = 10x + 4

-2x -10x = 4 -16

-12x =-12

x = 1

Therefore, the solution will be as;

x = 1

Learn more about equations here;

brainly.com/question/25180086

#SPJ3

It will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.

By noon, half of the town's population, which is 3500/2 = 1750, has heard the rumor. This means that 1750 - 280 = 1470 people heard the rumor between 8AM and noon. Therefore, the number of people who have yet to hear the rumor is 3500 - 1750 = 1750.

To find out when 90% of the population will have heard the rumor, we can use the formula:

(people who have heard the rumor) / (total population) = 0.9

Solving for the number of people who need to hear the rumor, we get:

(0.9)(3500) = 3150

To find out how many people need to hear the rumor from noon onwards, we subtract the number of people who have already heard it:

3150 - 1750 = 1400

To find out how long it will take for 1400 more people to hear the rumor, we can use the ratio:

(number of people who hear the rumor per hour) / (total population) = (1400 / 1750)

Solving for the number of people who hear the rumor per hour, we get:

(number of people who hear the rumor per hour) = (1400 / 1750) * (1 / k)

where k is the number of hours it takes for 90% of the population to hear the rumor. Solving for k, we get:

k = (1400 / 1750) * (1 / (number of people who hear the rumor per hour))

Plugging in the value of 280 for the number of people who heard the rumor from 8AM to noon, we get:

\(k = (1400 / 1750) * (1 / ((1470 + 280) / 4))\)

k = 3.86

Therefore, it will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.

For more questions like Percentage visit the link below:

https://brainly.com/question/30077132

#SPJ11