Water leaks from a vertical cylindrical tank through a small hole in its base at a volumetric rate proportional to the square root of the volume of water remaining. The tank initially contains 300 liters and 22 liters leak out during the first day A. When will the tank be half empty?t16 day (include units.) B. How much water will remain in the tank after 5 days? volume 198 L (include units)

Answer: P(3) is True

Step-by-step explanation:

The given statement is an inequality denoted as P(x). To find out which of the options is true you have to evaluate each given value of X in the inequality and perform the arithmetic operations, then you have to see if the expression makes sense.

For P(0): Replace X=0 in 2x+5>10

2(0)+5>10

0+5>10

5>10 is false because 5 is not greater than 10

For P(3): Replace X=3 in 2x+5>10

2(3)+5>10

6+5>10

11>10 is true because 11 is greater than 10

For P(2): Replace X=2 in 2x+5>10

2(2)+5>10

4+5>10

9>10 is false

For P(1): Replace X=1 in 2x+5>10

2(1)+5>10

2+5>10

7>10 is false

Answer:

20%

Step-by-step explanation:

To find what percentage is $10 out of $50, we divide 10 by 50:

[tex] \frac{10}{50}=0.2[/tex]

If we want to get the result in percentage form, we simply multiply it by 100%:

[tex]0.2\cdot 100\%=20\%[/tex]

So a tip of $10 on a $50 bill is a tip of 20%.

Answer:

[tex]2e^{y'}y=0[/tex]

Step-by-step explanation:

The solution for this differential equation [tex]2e^{y'}y=0[/tex] have to be the trivial solution y=0. Because the function [tex]e^{x}[/tex] always have values different of zero, then the only option is the trivial solution y=0.

Answer:

The 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Step-by-step explanation:

The given sequence is

[tex]40,10, \frac{5}{2}, \frac{5}{8}, ....[/tex]

The given sequence is a geometric​ sequence because it have common ratio.

[tex]r=\frac{10}{40}=\frac{\frac{5}{2}}{10}=\frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}[/tex]

In the given sequence the first term of the sequence is 40.

[tex]a_1=40[/tex]

The nth term of a GP is

[tex]a_n=a_1r^{n-1}[/tex]

where, [tex]a_1[/tex] is first term and r is common ratio.

Substitute [tex]a_1=40[/tex] and [tex]r=\frac{1}{4}[/tex] in the above formula.

[tex]a_n=40(\frac{1}{4})^{n-1}[/tex]

Substitute n=10 , to find the 10th term.

[tex]a_{10}=40(\frac{1}{4})^{10-1}[/tex]

[tex]a_{10}=\frac{5}{32768}[/tex]

Therefore the 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Answer:

p-value = 0.1277

Step-by-step explanation:

p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.

Firstly we find the mean and standard deviation of the given data set.

⇒ Mean = [tex]\frac{4.41 +4.37+ 4.33+ 4.35 +4.30 +4.39 +4.36+ 4.38+ 4.40+ 4.39}{10}[/tex]

⇒ Mean = 4.368

[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }[/tex]

where, [tex]\bar{x}[/tex] is mean of the distribution.

⇒ Standard Deviation = 0.034

Applying t- test:

Let out hypothesis is:

H₀: μ = 4.35

H₁: μ ≠ 4.35

Now,

Here, μ = Population Mean = 4.35

[tex]\bar{x}[/tex]= Sample Mean = 4.368

σ = Standard Deviation = 0.034

n = 10

[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.

Then the p-value at 99% level of significance.

⇒ p-value = 0.1277

To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We will calculate the t-value and the p-value and compare the p-value with the significance level of 0.01.

To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We can set up the null hypothesis as follows:

H0: μ = 4.35

And the alternative hypothesis as:

H1: μ > 4.35

We will calculate the t-value and the p-value.

t-value = (mean of the sample - mean of the population) / (standard deviation of the sample / sqrt(sample size))

p-value = P(T > t)

In this case, we have to compare the p-value with the significance level of 0.01.

If the p-value is less than 0.01, we reject the null hypothesis and conclude that the special additive has increased the mean weight of the chickens.

Answer:

Look to the attached figure

Step-by-step explanation:

* Lets revise the steps of constructing with the same length of a given

 segment

- Use a ruler to draw a segment PQ of length 2 inches long

- Mark a point M that will be one endpoint of the new line segment

- Set the compasses pin on the point P of the line segment PQ

- Open the compass to the point Q

- The compasses width is now equal to the length of the segment PQ

- Without changing the compasses width place the pin of the compass

 at point M and draw an arc where the other endpoint will be on it

- Pick a point N on the arc that will be the other endpoint of the new

 line segment

- Draw a line from M to N

- The length of MN = The length of PQ

- The attached figure for more understand

Answer:

[tex]x=-\frac{7}{2}[/tex] Extrema point.

The function does not have inflection points.

Step-by-step explanation:

To find the extrema points we have:

[tex]f'(x)=0[/tex]

Then:

[tex]f(x)=(2x+7)^4[/tex]

[tex]f'(x)=4(2x+7)^3(2)[/tex]

[tex]f'(x)=8(2x+7)^3[/tex]

Now:

[tex]f'(x)=8(2x+7)^3=0[/tex]

[tex]8(2x+7)^3=0[/tex]

[tex](2x+7)^3=0[/tex]

[tex]2x+7=0[/tex]

[tex]2x=-7[/tex]

[tex]x=-\frac{7}{2}[/tex]

To find the inflection points we need to calculate [tex]f''(x)=0[/tex] but due to that que have just one extrema point, the function does not have inflection points.

Answer: 120000 W and 0.12 MW

Step-by-step explanation:

The expression 120 kW uses a metric prefix "k" (kilo) which is the same as multiply by 1000. So you can replace k by 1000 to convert the expression to the unit W.

120 kW= 120(1000) W= 120000 W.

To convert 120kW to MW, where the prefix M (mega) is equivalent to 1000000, you can use a conversion factor like (1 MW / 1000 kW) and multiply the expression by it.

Notice that (1 MW / 1000 kW) = 1, so the expression remains unaltered.

Then,

120 kW (1 MW / 1000 kW) = 0.12 MW

Answer: [tex]20.38\ cm^2[/tex]

Step-by-step explanation:

We know that the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle .

Given : Circumference of circle = 16 cm

Then, [tex]16=2\pi r[/tex]

i.e [tex]r=\dfrac{16}{2\pi}=\dfrac{8}{\pi}[/tex]          (1)

We know that the area of circle is given by :-

[tex]A=\pi r^2[/tex]

i.e. [tex]A=\pi (\dfrac{8}{\pi})^2[/tex]                    [From (1)]

i.e. [tex]A=\pi (\dfrac{64}{\pi^2})[/tex]

i.e. [tex]A=\dfrac{64}{\pi}[/tex]

Put [tex]\pi=3.14[/tex]

[tex]A=\dfrac{64}{3.14}=20.3821656051approx20.38\ cm^2[/tex]

Hence, area of circle = [tex]20.38\ cm^2[/tex]

In order to get the answer to this question you will have to use KCC (Keep, Change, Change) and then solve.

[tex]-1.8 - 3.9=[/tex]

Using KCC:

[tex]-1.8-3.9=-1.8+-3.9[/tex]

[tex]-1.8 + -3.9 = -5.7[/tex]

[tex]= -5.7[/tex]

Therefore your answer is option D "-5.7."

Hope this helps.

Answer:

D "-5.7."

Step-by-step explanation:

Answer:

x = 22

Step-by-step explanation:

9x = 99y

y = 2

9x = 99 * 2

99 * 2 = 198

9x = 198

---     ----

9        9

x = 22

Hey!

------------------------------------------------

Solution:

9x = 99y

~Substitute

9x = 99(2)

~Simplify

9x = 198

~Divide 9 to both sides

9x/9 = 198/9

~Simplify

x = 22

------------------------------------------------

Answer:

x = 22

------------------------------------------------

Hope This Helped! Good Luck!

Step-by-step explanation:

Let's consider C is a matrix given by

[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]

them determinant of matrix C can be written as

[tex]\begin{vmatrix}a & b & c\\ d & e & f\\  g & h & i \end{vmatrix}\ =\ 4.....(1)[/tex]

Now,

[tex]det (C+C)\ =\ \begin{vmatrix}a & b & c\\ d & e & f\\  g & h & i \end{vmatrix}\ +\ \begin{vmatrix}a & b & c\\ d & e & f\\  g & h & i \end{vmatrix}[/tex]

                  [tex]=\ \begin{vmatrix}2a & 2b & 2c\\ 2d & 2e & 2f\\  2g & 2h & 2i \end{vmatrix}[/tex]

                   [tex]=\ 2\times 2\times 2\times \begin{vmatrix}a & b & c\\ d & e & f\\  g & h & i \end{vmatrix}[/tex]

                   [tex]=\ 8\times 4\ \ \ \ \ \ \ \         from\ eq.(1)[/tex]

                    = 32      

Hence, det (C+C) = 32

Answer:

Company A is a better deal than Company B for the number of miles greater than 295 miles

Step-by-step explanation:

Let

y ----> the charge per week in dollars

x ----> the number of miles

we have

Company A

[tex]y=331.35[/tex] -----> equation A

Company B

[tex]y=0.53x+175[/tex] -----> equation B

Solve the system by substitution

Equate equation A and equation B and solve for x

[tex]331.35=0.53x+175[/tex]

[tex]0.53x=331.35-175\\0.53x=156.35\\x=295\ mi[/tex]

For x=295 miles the charge in Company A and Company B is the same

therefore

Company A is a better deal than Company B for the number of miles greater than 295 miles

Answer:

(4.5, 4.7)

Step-by-step explanation:

Hi!

Lets call X to the consumption of milk per week among males over age 32. X has a normal distribution with mean μ and standard deviation σ.

[tex]X \sim N(\mu, \sigma)[/tex]

When you know the population standard deviation σ of X  ,  and the sample mean is [tex]\hat X[/tex], the  variable q has distribution N(0,1):

[tex]q = \frac{\hat X - \mu}{\sigma} \sim N(0,1)[/tex]

Then you have:

[tex]P(-k < q <k ) = P(\hat X -\frac{\sigma}{\sqrt{N} }<\mu<\hat X +\frac{\sigma}{\sqrt{N} })=C[/tex]

This defines a C - level confidence interval. For each C the value of k is well known. In this case C = 0.98, then k = 2.326

Then the confidence interval is:

[tex](4.6 - 2.326*\frac{0.8}{\sqrt{710}}, 4.6 + 2.326*\frac{0.8}{\sqrt{710}})\\ (4.5, 4.7)[/tex]

Answer:

It isn't possible.

Step-by-step explanation:

Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.

Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.

Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.

Answer:

The angle between the lines [tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex] is [tex]\sqrt{\frac{6}{7}}[/tex]

Step-by-step explanation:

The equation of a line with direction vector [tex]\vec{d}=(l,m.n)[/tex] that passes through the point [tex](x_{1},y_{1},z_{1})[/tex] is given by the formula

[tex]\frac{x-x_{1}}{l}= \frac{y-x_{1}}{m}=\frac{z-z_{1}}{n},[/tex] where l,m, and n are non-zero real numbers.

This is called the symmetric equations of the line.

The angle between two lines [tex]\frac{x-x_{1}}{l_{1} }= \frac{y-y_{1}}{m_{1} }=\frac{z-z_{1}}{n_{1}}[/tex] and [tex]\frac{x-x_{2}}{l_{2} }= \frac{y-y_{2}}{m_{2} }=\frac{z-z_{2}}{n_{2}}[/tex] equal the angle subtended by direction vectors, [tex]d_{1}[/tex] and [tex]d_{2}[/tex] of the lines

[tex]cos (\theta)=\frac{\vec{d_{1}}\cdot\vec{d_{2}}}{|\vec{d_{1}}|\cdot|\vec{d_{2}}|}=\frac{l_{1} \cdot\l_{2}+m_{1} \cdot\ m_{2}+n_{1} \cdot\ n_{2}}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}} \cdot \sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}}[/tex]

Given that

[tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex]

[tex]l_{1}=3, m_{1}=2,n_{1}=1\\ l_{2}=1, m_{2}=1,n_{2}=1[/tex]

We can use the formula above to find the cosine of the angle between the lines

[tex]cos(\theta)=\frac{3 \cdot 1+2 \cdot 1 +1 \cdot 1}{\sqrt{3^{2}+2^{2}+1^{2}} \cdot \sqrt{1^{2}+1^{2}+1^{2}}} = \sqrt{\frac{6}{7}}[/tex]

Answer:

10.50x ≤ 205

The maximum number of tickets, x, would be 19.

Step-by-step explanation:

Given,

The cost of one ticket = $ 10.50,

The cost of x tickets = 10.50x dollars,

Since,  the total cost can not exceed  $ 205,

⇒ 10.50x ≤ 205

∵ 10.50 > 0 thus, when we multiply both sides by 1/10.50 the inequality sign will not change,

⇒ x ≤  [tex]\frac{205}{10.50}[/tex] ≈ 19.52

Hence, the maximum number of tickets would be 19.

Answer:

2x - y - 7 = 0

Step-by-step explanation:

Since the slope of parallel line are same.

So, we can easily use formula,

y - y₁ = m ( x ₋ x₁)

where, (x₁, y₁) = (8, 9)

and m is a slope of line passing through (x₁, y₁).

and since the slope of parallel lines are same, so here we use slope of parallel line for calculation.

and, Slope = m = [tex]\dfrac{y_{b}-y_{a}}{x_{b}-x_{a}}[/tex]

here, (xₐ, yₐ) = (2, 7)

and, [tex](y_{a},y_{b}) = (1, 5 )[/tex]

⇒ m = [tex]\dfrac{5-7}{1-2}[/tex]

⇒ m = 2

Putting all values above formula. We get,

y - 9 = 2 ( x ₋ 8)

⇒ y - 9 = 2x - 16

⇒ 2x - y - 7 = 0

which is required equation.

Answer:

y=2x-8

Step-by-step explanation:

In order to solve this you first have to calculate the slope of the parallel line, since that would be equal to the slope of our line:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

Now we insert the values into the formula:

[tex]Slope=\frac{y2-y1}{x2-x1}\\Slope=\frac{5-7}{1-2}\\Slope= \frac{-2}{-1}\\ Slope:2[/tex]

And remember that the formula for general line is:

[tex]Y-y1= M(x-x1)\\y-9=2(x-8=\\y=2x-16+9\\y=2x-7[/tex]

So the equation for the line passing through point 8,9 and parallel to the line joining 2,7 and 1,5 would be y=2x-7

Answer:

0.2s is the time from the initial launch of the warhead to impact.

Step-by-step explanation:

This is a rule of three problem

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, our measures have a direct relationship.

The problem states that in a second, the warhead travels 489 meters. How long it takes to travel 100 meters? So

1s - 489m

xs - 100m

489x = 100

[tex]x = \frac{100}{489}[/tex]

x = 0.2s.

0.2s is the time from the initial launch of the warhead to impact.

Answer:

x=-3

|-x| = 3

|x| = 3

Step-by-step explanation:

we know that

If a number is a solution of a equation, then the number must satisfy the equation

Verify each case

case 1) we have

x=3

substitute the value of x=-3

-3=3 -----> is not true

therefore

x=-3 is not a solution of the given equation

case 2) we have

x=-3

substitute the value of x=-3

-3=-3 -----> is true

therefore

x=-3 is  a solution of the given equation

case 3) we have

|-x| = 3

substitute the value of x=-3

|-(-3)| = 3

|3| = 3

3=3-----> is true

therefore

x=-3 is a solution of the given equation

case 4) we have

|x| = 3

substitute the value of x=-3

|(-3)| = 3

3=3-----> is true

therefore

x=-3 is a solution of the given equation

case 5) we have

-|x| = 3

substitute the value of x=-3

-|(-3)| = 3

-3=3-----> is not true

therefore

x=-3 is not a solution of the given equation

Answer:

The probability that a student is proficient in mathematics, but not in reading is, 0.10.

The probability that a student is proficient in reading, but not in mathematics is, 0.17

Step-by-step explanation:

Let's define the events:

L: The student is proficient in reading

M: The student is proficient in math

The probabilities are given by:

[tex]P (L) = 0.81\\P (M) = 0.74\\P (L\bigcap M) = 0.64[/tex]

[tex]P (M\bigcap L^c) = P (M) - P (M\bigcap L) = 0.74 - 0.64 = 0.1\\P (M^c\bigcap L) = P (L) - P (M\bigcap L) = 0.81 - 0.64 = 0.17[/tex]

The probability that a student is proficient in mathematics, but not in reading is, 0.10.

The probability that a student is proficient in reading, but not in mathematics is, 0.17

Step-by-step explanation:

On a field every element different from 0 should have a multiplicative inverse. Let's check that in Z2[i] not ALL nonzero elements have multiplicative inverses.

Z2 is made of two elements: 0 and 1, and so Z2[i] is made of four elements: 0+0i,0+1i, 1+0i, 1+1i (which we can simplify from now on as 0, i, 1, 1+i respectively). Now, let's check that the element 1+i doesn't have a multiplicative inverse (we can do this by showing that no matter what we multiply it by, we're not getting 1, which is the multiplicative identity)

[tex](1+i)\cdot 0 = 0[/tex] (which is NOT 1)

[tex](1+i)\cdot i = i+i^2=i-1=1+i[/tex] (which is NOT 1) (remember -1 and 1 are the same in Z2)

[tex](1+i)\cdot 1 = 1+i[/tex] (which is NOT 1)

[tex](1+i)\cdot (1+i) = 1+i+i+i^2=1+2i-1=0+0i=0[/tex] (which is NOT 1) (remember 2 is the same as 0 in Z2)

Therefore the element 1+i doesn't have a multiplicative inverse, and so Z2[i] cannot be a field.

Answer:

Width = 15.

Length = 22.

Step-by-step explanation:

If the length is L then the width W =  1/2L + 4.

The perimeter = 2L + 2W, so

2L + 2(1/2L + 4) = 74

2L + L + 8 = 74

3L = 66

L = 22.

So W = 1/2 *22 + 4 = 11 + 4

= 15.

Answer:

This was an observational study.

Step-by-step explanation:

Given is that parents of children completed a questionnaire on the child’s light exposure both at present and before the age of 2 years.

This was an observational study since there is no treatment or control group.

We know that treatment, control groups or treatment groups are not specific to randomized control experiments.

The study where parents of pediatric ophthalmology patients completed questionnaires about light exposure is an observational study because data were collected without manipulating any variables.

The study described in which parents filled out questionnaires about their children's light exposure is an example of an observational study, not a controlled experiment. In an observational study, researchers collect data without manipulating any variables. In this case, the researchers gathered information on light exposure by asking parents to complete a questionnaire, but they did not control or alter the children's light exposure themselves.

Unlike in an observational study, a controlled experiment involves actively manipulating one variable (the independent variable) to determine if it causes a change in another variable (the dependent variable), often comparing against a control group in a systematic way. An example of a controlled experiment includes the trial of Jonas Salk's polio vaccine, in which one group received the vaccine and another group received a placebo.

Answer:

The present value (or initial investment) is $4000.00

Step-by-step explanation:

I'm going to assume that the correct formula here is

[tex]A(t)=P(1+r)^t[/tex]

and we are looking to solve for P, the principle investment.  We know that A(t) is 4370.91; r is .03 and t is 3:

[tex]4370.91=P(1+.03)^3[/tex] and

[tex]4370.91=P(1.03)^3[/tex] and

4370.91 = 1.092727P so

P = 4000.00

Answer: 3253

Step-by-step explanation:

Given : A test requires that you answer either part A or part B.

Part A consists of 7 true-false questions.

i.e.  there are 2 choices to answer each question.

Now, the number of ways to answer Part A : [tex]2^7=128[/tex]    (1)

Part B consists of 5 multiple-choice questions with one correct answer out of five.

i.e.  there are 5 choices to answer each question.

Now, the number of ways to answer Part B : [tex]5^5=3125[/tex]                           (2)

Now, the number of  different ways to completed answer sheets are possible=  [tex]128+3125=3253[/tex]          [Add (1) and (2) ]

The number of different completed answer sheets possible is 400,000.

To find the number of different completed answer sheets, we need to determine the number of ways to choose either part A or part B, and then calculate the number of possible combinations for each part.

For part A, since there are 7 true-false questions, each with 2 choices (true or false), there are 2^7 = 128 possible answer combinations.

For part B, since there are 5 multiple-choice questions, each with 5 choices, there are 5^5 = 3125 possible answer combinations.

To calculate the total number of different completed answer sheets, we multiply the number of choices for part A (128) by the number of choices for part B (3125), giving us a total of 128 * 3125 = 400,000 possible answer sheets.

Answer:

8%

Step-by-step explanation:

Motivation to learn represents a 40% of the learning acquired and its rated from 1 to 10. An increase from 7 to 9 represents an increase (of motivation to learn of 20%) But since this quality represent 40% of the total, the real increase in learning is 0.2*0.4=0.08 or 8%.

Answer:

Step-by-step explanation:

Given that

[tex]r(t) = (6cost, 6sint, t), 0\leq t\leq 2\pi\\r'(t) = (-6sint, 6cost, 1),\\||r'(t)||=\sqrt{(-6sint)^2 +(6cost)^2+1} =\sqrt{37}[/tex]

Hence arc length = [tex]\int\limits^a_b {||r'(t)||} \, dt[/tex]

Here a = 0 b = 2pi and r'(t) = sqrt 37

Hence integrate to get

[tex]\int\limits^{2\pi}  _0  {\sqrt{37} } \, dt\\ =\sqrt{37} (t)\\=2\pi\sqrt{37}[/tex]

Answer:

$482

Step-by-step explanation:

Data provided:

Total earning per week = $518

Medicare, federal withholding, state disability insurance, state withholding, union dues = $15

charitable contributions = $21

Now,

The total deductions = $15 + $21 = $36

also,

Net pay = Total income - Total deductions

thus,

Net pay = $518 - $36

or

Net Pat = $482

Answer:

[tex]0\le x\le 400[/tex]

x can take infinitely many values

Step-by-step explanation:

Vanessa walks from her house to a bus stop that is 400 yards away.

Let the variable x represent Vanessa's varying distance from her house (in yards). Then 400 - x yards is how far Vanessa is from the bus stop.

The variable x can take any value from 0 to 400 (0 when Vanessa is at home and 400 when Vanessa is at bus station), so

[tex]0\le x\le 400[/tex]

x can take infinitely many values, because there are infinitely many real numbers between 0 and 400.

Vanessa is 378 yards from the bus stop when she is 22 yards from her house and 236.6 yards away when she is 163.4 yards from her house. The variable x denoting Vanessa's distance from home assumes infinitely many values as she walks to the bus stop.

When Vanessa is 22 yards from her house, the distance remaining to reach the bus stop is simply the total distance to the bus stop minus her current position from the house. So, it's 400 yards - 22 yards = 378 yards. Similarly, if Vanessa is 163.4 yards from her house, the remaining distance to the bus stop is 400 yards - 163.4 yards = 236.6 yards.

As Vanessa walks from her house to the bus stop, variable x represents her varying distance from her house. The value of x starts at 0 when she is at her house and increases up to 400 yards as she reaches the bus stop. The variable x can assume infinitely many values, as it can represent any real number between 0 and 400, indicating her position at any given moment along her path.