a. Draw the image of ΔDEF after a rotation of 90° clockwise about the point (1,0). Label the image ΔD’E’F’.

b. Draw the image of ΔD’E’F’ after a reflection across the line x = 1. Label the image ΔD”E”F”.

Please help!!

Answer:

Step-by-step explanation:

$3x6=18 the six represents the apples and the 3 is the cost of each apple, 18 is the cost.

$2x9=$18 the nine is the oranges and the two is the money spent on each one. The total would be $36 in total for all the fruit.

So (9x2)+(3x6)=$36

Answer with Step-by-step explanation:

Susan needs to buy apples and oranges to make fruit salad.

She needs 15 fruits in all.

Let m represent the number of apples.

Number of oranges= 15-m

Apples cost $3 per piece, and oranges cost $2 per piece.

Amount spent= $ (3m+2(15-m))

                       = $ (3m + 2×15 - 2m)

                       = $ (m+30)

If she bought 6 apples.

i.e. m=6

Amount spent =$ (6+30)

                        = $ 36

Hence,

Expression that represents the amount Susan spent on the fruits is:

m+30

The amount Susan spent if she bought 6 apples is:

$ 36

Answer:

970m^{2}

Step-by-step explanation:

This polygon can be divided in two figures: one is a triangle, an the other one is a square.

We'll begin calculating the triangle's area, using the following formula:

[tex]At= \frac{b.h}{2}[/tex]

Where:

[tex]H= height = 30 m[/tex]

[tex]B = 9 m + 9 m + 20 m = 38 m[/tex]

As you can see, I added both sides of the triangle that measure 9 m and also the lenght of the square that measures 20 m! This added up is what the base of the triangle measures on total.

[tex]At= \frac{38 m .30 m}{2}[/tex]

[tex]At= \frac{1140 m^{2} }{2}[/tex]

[tex]At= 570 m^{2} [/tex]

Now we are going to calculate the square's area, that is much more simple:

[tex]As= L^{2} [/tex]

Where:

[tex]L=20 m [/tex]

[tex]As= (20 m)^{2} = 400m^{2} [/tex]

To know the whole figure's area, we add up both areas:

[tex]A = At+As = 570m^{2} +400m^{2}=970m^{2} [/tex]

Answer:

The answer to your question is: d) 50°F

Step-by-step explanation:

Data

n = 52 chirps/min

Formula

F = n/4 + 37

Substitution

F = 52/4 + 37

F = 13 + 37         simplifying

F = 50 °F        result

Answer:

eventually the gender ratio of population in this society will be 50% male and 50% female.

Step-by-step explanation:

For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.

As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.

We will denote for P(Bₙ) the probability of a couple to have exactly n boys.

Observe that statement 1 implies that:

[tex]P(B_{n-1})=(0.5)^{n}[/tex].

Then, the average number of boys per couple is given by

[tex]\sum^{\infty}_{n=1}(n-1)P(B_{n-1})=\sum^{\infty}_{n=1}(n-1)(\frac{1}{2} )^n=\sum^{\infty}_{n=2}n(\frac{1}{2} )^n=\\\\=\sum^{\infty}_{m=2}\sum^{\infty}_{n=m}(\frac{1}{2} )^n=\sum^{\infty}_{m=2}(\frac{1}{2} )^{m-1}=\sum^{\infty}_{m=1}(\frac{1}{2} )^{m}=1.\\[/tex]

This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.

Answer:

Complete the square on x by adding​ 49 to both sides.

Complete the square on y by adding​ 81 to both sides.

Step-by-step explanation:

We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.

We know to complete a square, we add the half the square of coefficient of x or y term.

Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.

[tex](\frac{14}{2})^2=7^2=49[/tex]

[tex](\frac{18}{2})^2=9^2=81[/tex]

Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:

[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]

Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:

[tex](x+7)^2+(y+9)^2=135[/tex]

Therefore, We can complete the square on x by adding​ 49 to both sides and the square on y by adding​ 81 to both sides.

Answer: 11

Step-by-step explanation:

We know that the degree of freedom for a t-distribution is given by :-

[tex]df=n-1[/tex], where n is the sample size.

Given : A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.

Then, the number of  individuals participated in each study = [tex]df+1=10+1=11[/tex]

Hence, the number of  individuals participated in each study =11.

Final answer:

The limit of f(x)/g(x) as x approaches 3 is negative infinity, since f(x) approaches 150 and g(x) approaches 0 with g(x) < 0.

Explanation:

We are given that as x approaches 3, f(x) approaches 150, and g(x) approaches 0 while being less than zero. The question is to determine the limit of f(x)/g(x) as x approaches 3.

To find this limit, we should consider the behavior of both f(x) and g(x) as x approaches 3.

Since f(x) approaches a finite number and g(x) approaches 0, the limit of the quotient could potentially be infinity or negative infinity, depending on the sign of g(x).

Since g(x) is less than 0 as x approaches 3, the quotient f(x)/g(x) will approach negative infinity.

Hence, the limit limx→3 f(x)/g(x) = -∞.

Answer:

If the mean of the sample standard deviations is equal to the population standard​ deviation, then the sample standard deviations target the population standard deviation and are called an unbiased estimator.  

If the mean of the sample standard deviations is not equal to the population standard​ deviation, then the sample standard deviations target the population standard deviation and are called a biased estimator.

A biased estimator regularly underestimates or overestimates the parameter.  

Final answer:

Sample standard deviations do not target the population standard deviation but serve as estimators. The accuracy of the estimation depends on the sample size.

Explanation:

The sample standard deviations do not target the exact value of the population standard deviation. Instead, they serve as estimators of the population standard deviation. In general, sample standard deviations can be good estimators of population standard deviations, but the accuracy of the estimation depends on the sample size. When the sample size is large, the sample standard deviation tends to be close to the population standard deviation. However, when the sample size is small, the sample standard deviation may not accurately estimate the population standard deviation.

Answer:

  5 1/2

Step-by-step explanation:

Your calculator can give you the correct answer.

___

[tex]\sqrt[3]{343}+\dfrac{3}{4}\sqrt[3]{-8}=7+\dfrac{3}{4}(-2)=7-\dfrac{3}{2}=5\frac{1}{2}[/tex]

Answer:

  $607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

_____

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

  $500 × 1.21550625 = $607.753125 ≈ $607.75

Answer:

Answer: $607.75

Step-by-step explanation:

Answer:

 $607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

_____

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

 $500 × 1.21550625 = $607.753125 ≈ $607.75

answer is x is less than or equal to -13

hope this helps:-)

Answer:

x  ≤ -13.

Step-by-step explanation:

2(x + 1 ) - 3(x + 5) ≥ 0      Distribute the 2 and -3 over the parentheses:

2x + 2 - 3x - 15   ≥  0

-x  ≥  15 - 2

-x  ≥  13

x  ≤  -13      Note: when dividing by a negative the inequality sign is flipped .

Answer:

V = 9

Step-by-step explanation:

You can see it in the picture.

The side length of the square is found using the diagonal, which is the distance between the two parabolas. The area of each square cross section is then integrated from 0 to 3 to find the solid's volume, which is 9 cubic units.

For these types of volume problems, you'll need to integrate. However, first you have to find the area of the square formed by the diagonals. The distance between the parabolas y=-√x and y=√x forms the square's diagonal. This distance, or length of the diagonal, can be obtained by adding the y-values of the two parabolas which gives 2√x. Given the diagonal, the side length of the square (s) can be obtained from the diagonal using Pythagoras theorem: s=diagonal/√2 => s=2√x/√2 => s=√2* √x => s=√2x. The area of the square is the side length squared, A=s² => A= 2x. Now, integrate the area function from 0 to 3 to get the volume of the solid: Volume= ∫ from 0 to 3 [2x dx] = [x²] from 0 to 3 = 9 - 0 = 9 cubic units.

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Answer:

  your selection is correct

Step-by-step explanation:

You can divide by 9 to get ...

  | x+4 | ≥ 6

This resolves to two inequalities:

These are disjoint intervals, so the solution set is the union of them:

  x ≤ -10 or 2 ≤ x

Answer:

Step-by-step explanation: A is correct

Answer:

x = 2

Step-by-step explanation:

Since the parabola is opening vertically up then the equation of symmetry is vertical and of the form x = c

The axis of symmetry passes through the vertex (2, 0), thus

equation of axis of symmetry is x = 2

Answer: the 3rd one

Step-by-step explanation: you can type it into a graphing calculator and get the answer

Answer:

The answer to your question is: m∠LOM = 44°

Step-by-step explanation:

Data

m< LOM = 3x +38

m< MON= 9x+28

m< LOM = ?

Process

They are complementary angles

                    m∠LOM + m∠MON = 90°

                   3x + 38 + 9x + 28 = 90°

                   12x + 66 = 90°

                   12x = 90 - 66

                   12x = 24

                   x = 24/12

                   x = 2

m∠LOM = 3(2) + 38

             = 6 + 38

            = 44°

m∠ MON = 9(2) + 28

m∠MON = 18 + 28

m∠MON = 46°

The average rate of change of a function is found with the formula (f(b) - f(a)) / (b - a). When applying this formula to the function p(x) = 6x + 7 over the interval [2, 2 + h], we find that the average rate of change is 6.

In Mathematics, the average rate of change of a function on the interval [a, b] is given by the formula (f(b) - f(a)) / (b - a). In this case, our function is p(x) = 6x + 7, and the interval is [2, 2 + h]. So, we can plug these values into the formula to get an expression for the average rate of change.

First, calculate p(2 + h) and p(2). Here they are:

Substitute these expressions into the average rate of change formula:

(P(2 + h) - P(2)) / (2 + h - 2) = (19 + 6h - 19) / (h) = 6h / h = 6.

So, the average rate of change of the function p(x) = 6x + 7 on the interval [2, 2 + h] is 6.

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Answer:

Suppose that you initially have $100 to spend on books or movie tickets.

The books start off costing $25 each and the movie tickets start off costing $10 each.

a. Your budget increases from $100 to $150 while the prices stay the same.

Increase

b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.

Decrease

c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.

Increase

Step-by-step explanation:

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

[tex](0.3)^2(0.7)^{18}[/tex].

Then, we must multiply this quantity by

[tex]{20\choose2}=\frac{20!}{18!2!}=\frac{20\times19}{2}=190,[/tex]

which is the number of ways to choose 2 students from the total of 20. Therefore:

Following an analogous process we can determine that:

Finally, the probability that 2 or fewer students will withdraw is

[tex]190(0.3)^2(0.7)^{18}+20(0.3)(0.7)^{19}+(0.7)^{20}=(0.7)^{18}(190(0.3)^2+20(0.3)(0.7)+(0.7)^2)\approx0.0355[/tex]

b) Compute the probability that exactly 4 will withdraw.

Following the process explained in a), the probability that 4 student withdraw is given by

[tex]{20\choose4}(0.3)^4(0.7)^{16}=\frac{20\times19\times18\times17}{4\times3\times2} (0.3)^4(0.7)^{16}=4845(0.3)^4(0.7)^{16}\approx 0.1304.[/tex]

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

[tex]{20\choose3}(0.3)^3(0.7)^{17}=\frac{20\times19\times18}{3\times2} (0.3)^3(0.7)^{17}=1140(0.3)^3(0.7)^{17}\approx 0.0716.[/tex]

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929

d) Compute the expected number of withdrawals.

As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

This problem involves using the binomial distribution to compute probabilities of student withdrawal and the expected number of withdrawals. Probability values are computed using the binomial probability formula and the expected number of students withdrawing from the course is given by n*p.

To solve the probability and expected value questions, we need to use the binomial distribution since the event (a student withdraws or not) is independent and repeated a fixed number of times.

1. The probability that 2 or fewer will withdraw is [tex]P(X < =2) = P(0)+P(1)+P(2) where P(x) = C(n, x) * (p^x) * (q^(n-x)). For n=20, p=0.3, q=0.7.[/tex]

2. The probability that exactly 4 withdraw is given by the binomial probability formula P(X=4). Again, use the same values of n, p, and q.

3. The probability that more than 3 will withdraw is P(X > 3) which is 1 - P(X<= 3). Compute P(X<=3) similar to the first situation and subtract it from 1.

4. The expected number of withdrawals, or the expectation of a binomial distribution, is given by n*p.

Calculations using these formulas will give you the desired probabilities to the accuracy you require.

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Answer:

2

Step-by-step explanation:

You have to find a number that added with -6 equals -4, and multiplied equals -12.

Just have to do the opperations and that is all!

[tex](x-6)(x+2)=x^2+2x-6x-12=x^2-4x-12[/tex]

Hope you like it!

Answer:

Option C is the answer.

Step-by-step explanation:

Simon is factorizing the polynomial x² - 4x - 12 = (x - 6)( x + ......)

We will factorize the left hand side of the given expression

x² - 4x - 12

= x² - 6x + 2x - 12  

Now we will break 12 into the factors so that sum of the factors should equal to 4

{ 6 × 2 = 12 and 6 - 2 = 4]

= x(x - 6) + 2(x - 6)

= (x + 2)(x - 6)

Therefore, the blank space should be replaced by 2.

Option C is the answer.

To determine the number of different eight-note melodies that alternate between black and white keys within a single octave, you calculate the permutations starting with either type of key and add them together, resulting in 141,120 possible melodies.

The question asks: How many different eight-note melodies within a single octave can be written if the black keys and white keys need to alternate? To solve this, we need to understand the structure of a piano octave, which consists of seven white keys and five black keys. Since melodies must alternate between black and white keys, starting with a white key will always result in a pattern of white-black-white-black, and so on, until eight notes are reached. Conversely, starting with a black key follows a black-white pattern.

If we start with a white key, we have 7 options for the first note. The next note (a black key) gives us 5 options. This alternating pattern continues, decreasing the number of options by 1 for each type of key used, until we have selected all eight notes. Mathematically, this calculates as 7 × 5 × 6 × 4 × 5 × 3 × 4 × 2. Similarly, starting with a black key would result in a calculation of 5 × 7 × 4 × 6 × 3 × 5 × 2 × 4.

However, since an eight-note melody can start with either a white or a black key, we calculate both scenarios and add them together for the total amount of possible melodies. The sum of the series for both starting options gives us 141,120 possible eight-note melodies that alternate between black and white keys within a single octave.

Answer:

Your travel time will be 32.71 secs.

Step-by-step explanation:

Let the total distance be x feet.

Speed while walking = [tex]\frac{x}{54}[/tex] feet per second

Speed on the sidewalk = [tex]\frac{x}{83}[/tex] feet per second

Therefore, total speed while walking on moving sidewalk =

[tex]\frac{x}{54} +\frac{x}{83y}[/tex]

= [tex]\frac{83x+54x}{54\times83}[/tex]

= [tex]\frac{137x}{4482}[/tex]

= [tex]\frac{x}{32.71}[/tex]

Hence, your travel time will be 32.71 secs.

Answer:

Karen has been a member of Girl Scouts for 22 months

Step-by-step explanation:

Let

x -----> the time in months

we know that

The total number of patches must be equal to the number of months multiplied by 3 patches each month plus 4 patches

so

[tex]70=3x+4[/tex]

Solve for x

Subtract 4 both sides

[tex]70-4=3x\\66=3x[/tex]

Divide by 3 both sides

[tex]22=x[/tex]

Rewrite

[tex]x=22\ months[/tex]

therefore

Karen has been a member of Girl Scouts for 22 months

Karen has been a member of the Girl Scouts for 22 months.

To determine the number of months Karen has been a member of the Girl Scouts, we can set up an equation using the information given.

Let's assume that Karen has been a member for x months.

Since she earns 3 patches each month, the total number of patches she has earned is 3x.

Adding the initial 4 patches she received upon joining, we have the equation 3x + 4 = 70.

To solve for x, we can subtract 4 from both sides of the equation: 3x + 4 - 4 = 70 - 4, which simplifies to 3x = 66.

Finally, we can divide both sides of the equation by 3 to solve for x: x = 66 ÷ 3 = 22.

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Answer: 3

Step-by-step explanation:

Given : Pooled variance : [tex]\sigma^2=18[/tex]

Sample sizes of each sample = [tex]n_1=n_2=4[/tex]

We know that the standard error for the sample mean difference is given by :-

[tex]S.E.=\sqrt{\sigma^2(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\\\=\sqrt{(18)(\dfrac{1}{4}+\dfrac{1}{4})}\\\\=\sqrt{(18)(\dfrac{1}{2})}=\sqrt{9}=3[/tex]

Hence, the estimated standard error for the sample mean difference =3

Answer:

x = 24

Step-by-step explanation:

Given that y varies directly with x the the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 10 when x = 8, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{8}[/tex] = 1.25, thus

y = 1.25x ← equation of variation

When y = 30, then

30 = 1.25x ( divide both sides by 1.25 )

x = 24

Answer:

The answer to your question is: Perimeter = 108 in

Step-by-step explanation:

Data

Length (l) = 5 width (w)

A = 405 in²

Perimeter = ?

Formula

Area = l x w

Perimeter = 2w + 2l

Process

                      405 = 5w x w

                       405 = 5w²

                     405/5 = w²

                       w = √81

                       w = 9 in

                       l = 5(9) = 45 in

Perimeter = 2(9) + 2(45)

                 = 18 + 90

                 = 108 in

Answer:

[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]

So a 5% relative increase in R would mean a 20% relative increase in F

Step-by-step explanation:

First we need to remind the definition of relative increase of a variable.

For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].

Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].

Let's then start by deriving F with respect to R:

[tex]\frac{dF}{dR}=4kR^3[/tex]

thus

[tex]dF=4kR^3dR[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]

[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].

If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get

[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]

According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.

Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.

To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.

By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.

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Answer:

The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 3 shelves

- You have  one piece of lumber 14 feet long

- Your plane is:

# The top shelf is 1 foot shorter than the middle shelf

# The Bottom shelf a foot shorter than twice the length of the top shelf

* Assume that the length of the middle shelf is x feet

∵ The length of the middle shelf = x

∵ The top shelf is shorter by 1 foot

∴ The length of the top shelf = x - 1

∵ The length of the bottom shelf is 1 less than twice the length of

   the top shelf

- That means multiply the length of the top shelf by 2 and subtract

 1 from the product

∵ The length of the top shelf is x - 1

∴ The length of the bottom shelf = 2(x - 1) - 1

- Simplify it by multiplying the bracket by 2 and add like terms

∴ The length of the bottom shelf = 2x - 2 - 1

∴ The length of the bottom shelf = 2x - 3

* The sum of the lengths of the 3 shelves equal the length of lumber

∵ The length of the lumber is 14 feet

∵ The length of the 3 shelves are x - 1 , x , 2x - 3

∴ x - 1 + x + 2x - 3 = 14

- Add like terms in the left hand sides

∴ 4x - 4 = 14

- Add 4 for both sides

∴ 4x = 18

- Divide both by 4

∴ x = 4.5

- Lets find the length of each shelf

∵ The length of the top shelf is x - 1

∴ The length of the top shelf = 4.5 - 1 = 3.5 feet

∵ The length of the middle shelf is x

∴ The length of the middle shelf = 4.5 feet

∵ The length of the bottom shelf is 2x - 3

∴ The length of the bottom shelf = 2(4.5) - 3 = 9 - 3 = 6 feet

* The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet

Final answer:

To find the length of each shelf, a system of equations is created based on the conditions given. Solving this system shows the middle shelf to be 4.5 feet, the top shelf to be 3.5 feet, and the bottom shelf to be 6 feet long.

Explanation:

The question involves using a piece of lumber that is 14 feet long to make three shelves with specific relative lengths. We can let the length of the middle shelf be x feet. Therefore, the top shelf will be x - 1 feet long, and the bottom shelf will be 2(x - 1) - 1 feet long, which simplifies to 2x - 3 feet. Adding together the lengths of the three shelves gives us the total length of the lumber:

So: x + (x - 1) + (2x - 3) = 14.

Solving the equation:

Therefore, the middle shelf is 4.5 feet long, the top shelf is 3.5 feet (4.5 - 1), and the bottom shelf is 6 feet (2(3.5) - 1).

Answer:

  p(at most one space between) = (4n-6)/(n(n-1))

Step-by-step explanation:

There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...

  (n -1) +(n -2) = 2n-3

The number of ways that 2 cars can be parked in n spaces is ...

  (n)(n -1)/2

So, the probability is ...

  (2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))

___

If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.

__

Check

For n=2 or 3, p=1 as you expect.

For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.

The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.

We have,

To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:

Mary and Tom park their cars in adjacent spaces.

Mary and Tom park their cars in spaces with one empty space in between them.

Scenario 1: Mary and Tom park their cars in adjacent spaces.

In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.

Scenario 2: Mary and Tom park their cars with one empty space between them.

In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.

Now, we add up the probabilities of both scenarios because they are mutually exclusive:

Total Probability = Probability of Scenario 1 + Probability of Scenario 2

Total Probability = [(n - 1) / n] + [(n - 2) / n]

To make these fractions have a common denominator, we can rewrite them as:

Total Probability = [(n - 1) + (n - 2)] / n

Total Probability = [2n - 3] / n

Thus,

The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.

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Answer:

24

Step-by-step explanation:

The air pressure in tire should be 32.135 pounds per square inch. Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The air pressure in the tire should be  pounds per square inch. This pressure is in the form of a mixed fraction. It is required to convert this pressure into a decimal form. We can convert it as follows;

The air pressure in tire  =32 27/200

It is given in the form of a mixed fraction.

32 27/200 = ( 32 x 200) 27/200

First we, convert this mixed fraction into unlike fraction and then convert it into a decimal number;

32 27/200 = ( 32 x 200) 27/200

= 6427 /200

= 32.135

Therefore, the air pressure in tire should be 32.135 pounds per square inch.

Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.

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