algebra Expression •x minus x​

The answers to the questions are:

This defined as the total number of points that a person has been able to cover at a given period. It is calculated by taking the time and the speed of takeoff into consideration. The speed that a person used and the time it took them to get to their destination is what is used to calculate distance

The time it takes for sunlight to reach is given as

distance/speed

778000000000/300000000

=2593.33 * 60

= 43.22 minutes

The formula for distance is given as speed * time

speed = 15km/hr

time = 1 hour

The distance = 15 * 1

= 15 km/hr

If the time is 2*1/2

the distance = 15 / 2.5

= 6 km

Expressed as a fraction we have the following

0.37 = 37/100

0.086 = 86/1000

Raed more on distance here:

https://brainly.com/question/17273444

#SPJ1

Missing data:

Viewer's Age Group  Excellent Good Average Poor Marginal Total

16–25                          52                 42       12       7           113

26–35                          33                50         5       9          97

36–45                          58                 12       28      34         132

46–55                          25                17       22       12            76

56 +                               12                 5          3         8             28

Marginal Total             180               126      70      70           446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 [tex]*[/tex] 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

To learn more about data refer to:

https://brainly.com/question/4219149

#SPJ4

In the given diagram, the measure of arc QS is 168°

From the question, we are to determine the measure of arc QS

The measure of the arc is the angle subtended by the arc at the center of the circle.

From one of the circle theorems, we have that

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference

In the given diagram,

The angle subtended by arc at the circumference of the circle = 84°

∴ The angle subtended by the arc QS at the center = 2 × 84°

The angle subtended by the arc QS at the center = 168°

Hence, in the given diagram, the measure of arc QS is 168°

Learn more on Calculating measure of an arc here: https://brainly.com/question/19529058

#SPJ1

Answer:  168°

Step-by-step explanation:  TRUST ME!!!  Answer is correct in Edge!  :)

Answer:

The answer is 1. This table is an example of the principle of independence.

Step-by-step explanation:

This means any Trade activity is performed without reliance on another party.

He got the perfect answer to his question and he can get his answer without any other information.

Answer:

x = 18

y = 18

Step-by-step explanation:

We are given a right triangle (notice the 90 degree angle), with one of the angles being 45°.

We also know that the hypotenuse (the side opposite of the 90° angle) is 18√2.

We want to find the value of x and y.

First, let's figure out what the value of the other angle is.

The angles in a triangle all add up to 180 degrees.

Let's call the value of the angle we don't know s.
s + 45 + 90 = 180

Add 45 and 90 together.

s + 135 = 180

Subtract 135 from both sides.

s = 45

So the value of the other angle is 45 degrees.

When a right triangle is a 45-45-90 triangle (the numbers referring to the measures of the degrees), there is actually something special about it; if the legs (the sides that make up the 90 degree angle) have the value a (they would both be congruent because a 45-45-90 triangle is isosceles), then the hypotenuse will be a√2.

Keeping this in mind, let's solve for a.

Set 18√2 equal to a√2.

18√2=a√2

Divide both sides by √2.

18 = a

The value of a, aka the legs is a.

Both x and y would be equal to a in this case.

Therefore, x = 18, and y = 18.

The answer is J.

The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.

The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.

The probability is equal to :

Answer:

J   [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

• First, let's find the probability of landing a letter B in Spinner 1.

We have a total of eight possibilities, and two of them are the letter B.

∴ [tex]P(B) = \frac{2}{8}[/tex]

            = [tex]\bf \frac{1}{4}[/tex]

• Next, let's find the the probability of landing the number 1 on Spinner 2.

There are a total of six possibilities, and two of them are the number 1.

∴ [tex]P(1) = \frac{2}{6}[/tex]

           = [tex]\bf \frac{1}{3}[/tex]

• Now we have to calculate the probability of spinning a letter B and the number 1:

[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]

                   = [tex]\bf \frac{1}{12}[/tex]

The desired measures for the data-set is given by:

The five number summary is composed by the measures explained below, except the IQR.

In this problem, we have that:

More can be learned about five number summaries at brainly.com/question/17110151

#SPJ1

The expression 25p+18(p+4) represents the total amount spent on shirts and pants

The given parameters are:

Shirts = 4 more than pants (p)

Cost of shirt = $18

Cost of pant = $25

The above means that:

p + 4 represents the number of shirts Chris buys, while p represents the number of pants

The terms of the expression 25p + 18(p+4) are

25p and 18(p+4)

This means that:

25p = The total cost of pants

18(p+4) = The total cost of shirts

Hence, the expression 25p+18(p+4) represents the total amount spent on shirts and pants

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

Step-by-step explanation:

6 > x² - 5x.

The answer for the inequality is -1 the greater than sign x greater than 6

The interval notation is ( -1,6)

Answer:

[tex]-1 < x < 6[/tex]

Step-by-step explanation:

Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.

The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

Read more about exponential decay function at

https://brainly.com/question/27822382

#SPJ1

Answer:

i think this may help you

The diagram to show that the square root of 121 is 11 attached below

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]

Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).

Herewe are given the number as 121

It is perfect root then ;

√121 = 11

The solution that show that the square root of 121 is 11 attached below

Learn more about square root here:

brainly.com/question/7200235

#SPJ2

Answer:

B.) f⁻¹(x) = (1/9)x - 7/9

Step-by-step explanation:

Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.

f(x) = 9x + 7                            <----- Original function

y = 9x + 7                               <----- Substitute f(x) for "y"

x = 9y + 7                               <----- Swap variable positions

x - 7 = 9y                                <----- Subtract 7 from both sides

(x - 7) / 9 = y                           <----- Divide both sides by 9

(1/9)x - 7/9 = y                      <----- Divide each term individually by 9

The inverse function is represented by the symbol f⁻¹(x).

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2

Last term an = [tex]2\frac{1}{2}[/tex] = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

learn more about the arithmetic sequence here:

https://brainly.com/question/503167

#SPJ1

Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?

The value of x for the given equation is 0.632 and -0.632.

According to the statement

We have given that the equation and we have to a find the value of the x.

So, The given quadratic equation are:

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation

The given terms are

[tex]6x^2 + 4(x^2 - 1) = 0[/tex]

Solving the equation the the outcome equation is

[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]

The value of x is 0.632 and -0.632.

So, The value of x for the given equation is 0.632 and -0.632.

Learn more about Quadratic equation here

https://brainly.com/question/1214333

#SPJ1

we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use just the first two points on the given line:

(-8, -2) and (-4, 0)

Then the slope will be:

[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]

Then the linear equation is something like:

y = (1/2)*x + b

To find the value of b, we can use one of the two given points, I will use (-4, 0), then:

0 = (1/2)*(-4) + b

0 = -2 + b

2 = b

Then we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

Then the correct option is the first one.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

In this question,

The curves are y = 2/x, y = 2/x^2, x = 4

The diagram below shows the region enclosed by the given curves.

From the diagram, the limit of x is from 1 to 4.

The given curves are integrated with respect to x and the area is calculated as

[tex]A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx[/tex]

⇒ [tex]A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx][/tex]

⇒ [tex]A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx][/tex]

⇒ [tex]A=2[lnx-\frac{1}{x} ] \limits^4_1[/tex]

⇒ [tex]A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )][/tex]

⇒ A = 2[(1.3862-0.25) - (0-1)]

⇒ A = 2[1.1362 + 1]

⇒ A = 2[2.1362]

⇒ A = 4.2724 square units.

Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

Learn more about region enclosed by the curves here

https://brainly.com/question/28166201

#SPJ4

It looks like you have

[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]

and the integral you want to compute is

[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]

Split the integral up at [tex]x=0[/tex]. Then

[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]

After evaluating the integral we get 15

Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.

Given,

f(x) = 3         if   - 4 ≤ x ≤ 0

f(x) = 4 - [tex]x^{2}[/tex]  if   0 < x ≤ 3

Then,

[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]

We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

Elaborate the integral with x = 0

                                             -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]

                                          = 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])

                                          = 15

Learn more about integrals here :- brainly.com/question/14510286

#SPJ4

the parallel linear equation is:

y = (2/5)*x - 3

Two lines are parallel if the lines have the same slope but different y-intercept.

Here we know the line equation:

y = (2/5)*x + 4

Then a parallel line is of the form:

y = (2/5)*x + c

Where c is different than 4.

We want this line to pass through (5, -1), then:

-1 = (2/5)*5 + c

-1 = 2 + c

-1 - 2 = -3 = c

Then the parallel linear equation is:

y = (2/5)*x - 3

If you want to learn about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)  (the last choice).

Step-by-step explanation:

Im ignoring the 2^2 in the equation

The equation transforms to

2x^2 - 3x - 5 = 0    (standard form)

So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)

Answer:

Step-by-step explanation:

The vertical distance between the given points is:

Answer:

19,497m

Step-by-step explanation:

8,856-(-10,911)

=8856+10,911

=19,497m

Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)

Product of numbers refers to the multiplication of two or more values to arrive at a single result.

4n / (4n - 1) × (n - 1) / (n + 1) 2/x

= 4n / (4n - 1) × 2(n - 1) / x(n + 1)

= 4n / (4n - 1) × (2n - 2) / (nx + x)

= 4n(2n - 2) / (4n - 1) (nx + x)

= 4n² - 8n / (4n²x - 4nx - nx - x)

= (4n² - 8n) / (4n²x - 5nx - x)

Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)

Learn more about product:

https://brainly.com/question/10873737

#SPJ1

The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

A cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

larger-sized candle = 2(smaller-sized candle)

= 2(240 cubic centimeters)

= 480 cubic centimeters

Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

Learn more about cylinder:

https://brainly.com/question/9554871

#SPJ1

Answer:

A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Hope this helps!

Step-by-step explanation:

The the biggest 5 digit number based on the computation will be 87,978.

The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.

An example is that 34871903 is divisible by 11

3+8+1+0=12

4+7+9+3=23

23-12=11

Here, we want (b + b) - (a + c + a) to be divisible by 11.

2b - (2a + c) to be divisible by 11

ab,cba (using 7 and 8 and 9 since they biggest)

78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Therefore, the biggest 5 digit number is 87,978.

Learn more about computations on:

https://brainly.com/question/4658834

#SPJ1

The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

According to the statement

we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.

So, The given expression are:

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]

And we have to prove the answer.

So, For this

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]

[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]

Then the equation become

[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]

Now solve it then

[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]

Now take 2 common from answer then equation become

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]

Hence proved.

So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

Learn more about equations here

https://brainly.com/question/2972832

#SPJ1

[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

We can find the A as shown below:

Given A^2=I

We know that A^2=A×A

And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

Hence, option C is correct

Learn more about matrix here:

https://brainly.com/question/94574

#SPJ1

Disclaimer: Given question is incomplete. Complete question is attached.

Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

the correct inequality is"any rational number less than 9"

x < 9

Remember that when we have a number line, an open circle means that we can use the symbols > or <.

While a closed circle uses the symbols ≤ or ≥.

Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.

To the left of 9 there are the numbers smaller than 9, then the inequality would be:

x < 9

Then the correct option is "any rational number less than 9"

If you want to learn more about inequalities:

https://brainly.com/question/18881247

#SPJ1

Answer: x<9

any rational number less than 9"

Step-by-step explanation:

Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

Learn more about common ratio:

https://brainly.com/question/1509142

#SPJ1