Suppose that a company’s sales were $5,000,000 three years ago. Since that time sales have grown at annual rates of 10
percent,–10 percent, and 25 percent.
a Find the geometric mean growth rate of sales over this three-year period.
b Find the ending value of sales after this three-year period.

Answers

Answer 1

Answer:

≈ 0.07

Step-by-step explanation:

To find the geometric mean over this three-year period, we plug in the values  for the yearly return rates into the equation for the geometric mean.

Answer 2

The geometric mean growth rate of sales over this three-year period is 7.36%. Also, the ending value of sales after this three-year period is $6,187,500.

Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.

[tex](1+G)^3 = (1+0.1)(1-0.1)(1+0.25)\\\\(1+G)^3 = 1.2375\\\\(1+G) = \sqrt[3]{1.2375} = 1.0736\\\\G = 0.0736[/tex]

G  = 7.36 %

Also,

sales in year 0 = $5,000,000

annual Growth rate of year 1 = 10%

Sales in year 1 : $5,000,000 + 10% of $5,000,000 = [tex]5,000,000 + \frac{10}{100} *$5,000,000 = $5,500,000[/tex]

annual Growth rate of year 2 = -10%

Sales in year 2 : $5,500,000 - 10% of $5,500,000 = [tex]5,500,000 - \frac{10}{100} *$5,500,000 = $4,950,000[/tex]

annual Growth rate of year 3 = 25%

Sales in year 3 : $4,950,000 + 25% of $4,950,000 = [tex]4,950,000 + \frac{25}{100} *4,950,000 = $6,187,500[/tex]

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Related Questions

The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,425 with a standard deviation ofs = $160.(a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.H0: μ ≥ 1,503Ha: μ < 1,503H0: μ ≤ 1,503Ha: μ > 1,503 H0: μ > 1,503Ha: μ ≤ 1,503H0: μ < 1,503Ha: μ ≥ 1,503H0: μ = 1,503Ha: μ ≠ 1,503(b) What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)

Answers

Final answer:

The hypothesis test to determine the mean annual premium in Pennsylvania compared to the national mean annual premium is H0: μ ≥ 1,503 and Ha: μ < 1,503. The point estimate of the difference between the mean annual premiums is -$78.

Explanation:

(a) To determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium, we need to develop a hypothesis test. The null hypothesis (H0) states that the mean annual premium in Pennsylvania is greater than or equal to the national mean annual premium. The alternative hypothesis (Ha) states that the mean annual premium in Pennsylvania is less than the national mean annual premium. Therefore, the correct answer is:

H0: μ ≥ 1,503
Ha: μ < 1,503

(b) The point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean is calculated by subtracting the national mean annual premium ($1,503) from the mean annual premium in Pennsylvania ($1,425). Therefore, the point estimate is $1,425 - $1,503 = -$78.

Trying to find volume of a right circular cone.

Answers

Volume of the cone is 117.5 π ft³

Step-by-step explanation:

Lateral area of the cone = πrs

s is the slant height = 15 ft

From the above formula, we can find the radius as, 5 ft.

Volume of the cone = π r² h/3

s = √ (5²+ h²)

Squaring on both sides, we will get,

s² = 15² = (5² + h²)

 15² - 5² = h²

225 - 25 = 200 = h²

h = √200 = 14.1 ft

Volume = π × 5² × 14.1  / 3 = 117.5 π ft³

A new streaming service charges 5 dollars per month for students, and 10 dollars per month for everyone else. This month, the service had 55 users, and collected 425 dollars. Set up a system of linear equations, and find the number of students using the service this month.

Answers

Answer:

Number of student = 25

Step-by-step explanation:

Let x be the number of student and y be the others

A new streaming service charges 5 dollars per month for students, and 10 dollars per month for everyone else

[tex]x+y=55\\y=55-x[/tex]

[tex]5x+10y=425[/tex]

replace y with 55-x

[tex]5x+10y=425\\5x+10(55-x)=425\\5x+550-10x=425\\-5x+550= 425[/tex]

Subtract 550 from both sides

[tex]-5x+550= 425\\-5x= -125\\x=25[/tex]

[tex]y=55-x\\y=55-25\\y=30\\[/tex]

Number of student = 25

Answer: 25 students used the service this month.

Step-by-step explanation:

Let x represent the number of students that used the streaming service this month.

Let y represent the number of people apart from students that used the streaming service this month.

This month, the service had 55 users. It means that

x + y = 55

The new streaming service charges 5 dollars per month for students, and 10 dollars per month for everyone else. They collected a total of 425 dollars. It means that

5x + 10y = 425 - - - - - - -1

Substituting x = 55 - y into equation 1, it becomes

5(55 - y) + 10y = 425

275 - 5y + 10y = 425

- 5y + 10y = 425 - 275

5y = 150

y = 150/5 = 30

x = 55 - y = 55 - 30

x = 25

You go to Applebee’s and spend $98.42 on your meal. How much was the bill before 6% sales tax

Answers

answer: 92.51
(98.42•0.06)=5.9052
98.42-5.9052=92.5148

Answer: the bill before 6% sales tax is $92.85

Step-by-step explanation:

Let x represent the bill before the 6% sales tax.

It means that you paid 6% tax on x and the amount of tax paid would be

6/100 × x = 0.06 × x = 0.06x

Total amount that you paid for the meal including the 6% tax would be

x + 0.06x = 1.06x

If you spent $98.42 on the meal after the 6% tax, it means that

1.06x = 98.42

Dividing the left hand side and the right hand side of the equation by 1.06, it becomes

1.06x/1.06 = 98.42/1.06

x = $92.85

Kelly plan to fence in her yard. The fabulous fence company charges $3.25 per foot of fencing and $15.57 an hour for labor. If Kelly needs 350 feet of fencing and the installers work a total of 6 hour installing the fence , how
much will she owe the fabulous fence company.

Answers

Answer:

Kelly will owe $1320.92 to the fabulous fence company.

Step-by-step explanation:

There is a cost related to the number of hours and a cost per feet. So the total cost is:

[tex]T = C_{h} + C_{f}[/tex]

In which [tex]C_{h}[/tex] is the cost related to the number of hours and [tex]C_{f}[/tex] is the cost related to the number of feet.

Cost per hour

Each hour costs $15.57.

They work for 6 hours total. So

[tex]C_{h} = 15.57*6 = 93.42[/tex]

Cost per feet

Each feet costs $3.25.

Kelly needs 350 feet. So

[tex]C_{f} = 350*3.25 = 1137.5[/tex]

The total cost is:

[tex]T = C_{h} + C_{f} = 93.42 + 1137.5 = 1230.92[/tex]

Kelly will owe $1320.92 to the fabulous fence company.

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting: (a) at least one nun? (b) exactly 2 nuns? (c) exactly 1 hei? (d) at most 2 gimels?

Answers

So, the probabilities are: (a) 37/64, (b) 3/64, (c) 27/64, (d) 57/64

In each spin, there are four possible outcomes (nun, gimel, hei, shin), and each outcome is equally likely.

(a) Probability of getting at least one nun:

The probability of getting no nuns in a single spin is 3/4. So, the probability of getting no nuns in three spins is [tex](3/4)^3[/tex]. Therefore, the probability of getting at least one nun is 1 - [tex](3/4)^3[/tex].

Probability of getting at least one nun:

1 - [tex](3/4)^3[/tex] = [tex]1-\frac{27}{64}=\frac{37}{64}[/tex] = 0.58

(b) Probability of getting exactly 2 nuns:

The probability of getting a nun in a single spin is 1/4. So, the probability of getting exactly 1 hei in three spins is [tex]\left(\begin{array}{l}\frac{3}{1} \\\end{array}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)^2[/tex].

= [tex]3 \times \frac{1}{16} \times \frac{3}{4}=\frac{3}{64}[/tex] = 0.05

(c) Probability of getting exactly 1 hei:

The probability of getting a hei in a single spin is 1/4. So, the probability of getting exactly 1 hei in three spins is [tex]\left(\begin{array}{l}\frac{3}{1} \\\end{array}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)^2[/tex]

= [tex]3 \times \frac{1}{4} \times \frac{9}{16}=\frac{27}{64}[/tex] = 0.42

(d) Probability of getting at most 2 gimels:

The probability of getting 0 gimels is [tex](3/4)^3[/tex]. The probability of getting 1 gimel is [tex]\left(\begin{array}{l}\frac{3}{1} \\\end{array}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)^2[/tex]. The probability of getting 2 gimels is [tex]\left(\begin{array}{l}\frac{3}{2} \\\end{array}\right)\left(\frac{1}{4}\right)^2\left(\frac{3}{4}\right)[/tex].

Add these probabilities to get the total probability.

[tex]\left(\frac{3}{4}\right)^3+\left(\begin{array}{l}\frac{3}{1} \\\end{array}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)^2+\left(\begin{array}{l}\frac{3}{2} \\\end{array}\right)\left(\frac{1}{4}\right)^2\left(\frac{3}{4}\right)[/tex]

[tex]=\frac{27}{64}+\frac{27}{64}+\frac{3}{64}=\frac{57}{64}[/tex] = 0.9

Calculating probabilities of specific outcomes when spinning a dreidel multiple times.

Dreidel Probability Calculations:

(a) Probability of getting at least one nun: 1 - Probability of getting no nuns = 1 - [tex](3/4)^3[/tex].(b) Probability of getting exactly 2 nuns: Combination of outcomes with exactly 2 nuns / Total possible outcomes = (3 choose 2) x [tex](1/4)^2[/tex] x (3/4).(c) Probability of getting exactly 1 hei: Combination of outcomes with exactly 1 hei / Total possible outcomes = 3 x (1/4) x [tex](3/4)^2[/tex].(d) Probability of getting at most 2 gimels: Sum of probabilities of getting 0, 1, or 2 gimels.

The circumference of a circle is 5picm.
What is the area of the circle?
A.) 6.25 pi cm2
B.) 2.5 pi cm2
C.) 25 pi cm2
D.) 10 pi cm2

Answers

A=pi(r)squared
d=5
r=2.5
A= 2.5(2.5)(pi)
Area= 6.25

Joe, Megan, and Santana are salespeople. Their sales manager has 21 accounts and must assign seven accounts to each of them. In how many ways can this be done?

Answers

Answer:

116,280 ways

Step-by-step explanation:

The number of ways of assigning the accounts to each of the salesperson is computed by combination

Number of ways = n combination r = n!/(n-r)!r!

n = 21, r = 7

Number of ways = 21 combination 7 = 21!/(21-7)!7! = 21!/14!7! = 116,280 ways

The sum of 5 times a number and
minus −​2, plus 7 times a​ number

Answers

Answer:

12x + 2

Step-by-step explanation:

Let the number be represented by x.

Then five times the number = 5*x

Seven times the number = 7*x

Sum of 5 times the number minus -2 = [tex]\[5*x - (-2)\][/tex] = [tex]\[5x +2\][/tex]

Adding seven times the number to this expression yields, [tex]\[5x+2+7x\][/tex]

[tex]\[= (5+7)x+2\][/tex]

[tex]\[= 12x+2\][/tex]

So the simplified expression corresponds to 12x + 2.

A copyeditor thinks the standard deviation for the number of pages in a romance novel is six. A sample of 25 novels has a standard deviation of nine pages. At , is this higher than the editor hypothesized?

Answers

Answer:

No, the standard deviation for number of pages in a romance novel is six only.

Step-by-step explanation:

First we state our Null Hypothesis, [tex]H_o[/tex] : [tex]\sigma[/tex] = 6

             and Alternate Hypothesis, [tex]H_1[/tex] : [tex]\sigma[/tex] > 6

We have taken these hypothesis because we have to check whether our population standard deviation is higher than what editor hypothesized of 6 pages in a romance novel.

Now given sample standard deviation, s = 9 and sample size, n = 25

To test this we use Test Statistics = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] follows chi-square with (n-1) degree of freedom [[tex]\chi ^{2}_n__-1[/tex]]

       Test Statistics = [tex]\frac{(25-1)9^{2} }{6^{2} }[/tex] follows [tex]\chi ^{2}_2_4[/tex]  = 54

and since the level of significance is not stated in question so we assume it to be 5%.

Now Using chi-square table we observe at 5% level of significance the [tex]\chi ^{2}_2_4[/tex] will give value of 36.42 which means if our test statistics will fall below 36.42 we will reject null hypothesis.

Since our Test statistics is more than the critical value i.e.(54>36.42) so we have sufficient evidence to accept null hypothesis and conclude that our population standard deviation is not more than 6 pages which the editor hypothesized.

Determine if b is a linear combination of a1 a2, and a3. a1 = [ 1 -2 0 ], a2 = [ 0 1 3 ], a3 = [ 6 -6 18 ], b = [ 2 -2 6 ] Choose the correct answer below. Vector b is a linear combination of a1 a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column. Vector b is a linear combination of a1 a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. Vector b is not a linear combination of a1, a2, and a3. Vector b is a linear combination of a1 a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column.

Answers

Answer: Vector b is not a linear combination

Step-by-step explanation:

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

a2(0,1,3)=(0,b,3b);

a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

a+6c=2

-2a+b-6c=-2

3b+18c=6

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

Final answer:

Upon forming a system of linear equations and solving, a solution would imply that vector b is indeed a linear combination of vectors a1, a2, and a3. The observed placement of pivots in the corresponding echelon matrix backs this conclusion.

Explanation:

In this question, you are asked to determine if vector b is a linear combination of vectors a1, a2, and a3. A vector is a linear combination of others if it can be written as a weighed sum of those vectors. To solve this problem, we need to form a system of linear equations based on the vectors and solve this system. If all of the coefficients can be expressed as real numbers, it means that the vector b is a linear combination of a1, a2, and a3.

In this case, our system of equations looks like this:

x∗a1 + y∗a2 + z∗a3 = b

In matrix form it can be written as:

|1 0 6|x| = |2|, |-2 1 -6|y| = |-2|, |0 3 18|z| = |6|.

Solve this system through methods like Gauss-Jordan elimination or row reduction. The pivots in the corresponding echelon matrix should be in the first entry in the first column, the second entry in the second column, and the third entry in the third column.

This suggests that vector b can indeed be a linear combination of vectors a1, a2, and a3.

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Solve 4x2 - x + 5 = 0.

Answers

Answer:

x

=

1

+

i

79

8

,

1

i

79

8

Step-by-step explanation:

Suppose that out of 20% of all packages from Amazon are delivered by UPS, 12% of the packages that are delivered by UPS weighs 2 lbs or more. Also, 8% of the packages that are not delivered by UPS weighs less than 2 lbs.
a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more?
b. What is the probability that a package is not delivered by UPS if it weighs 2 lbs or more?

Answers

Answer:

(a) Probability that a package is delivered by UPS if it weighs 2 lbs or more = 0.0316.

(b) Probability that a package is not delivered by UPS if it weighs 2 lbs or more = 0.9684 .

Step-by-step explanation:

We are given that 20% of all packages from Amazon are delivered by UPS, from which 12% of the packages that are delivered by UPS weighs 2 lbs or more and 8% of the packages that are not delivered by UPS weighs less than 2 lbs.

Firstly Let A = Package from Amazon is delivered by UPS.

                B = Packages that are delivered by UPS weighs 2 lbs or more.

So, P(A) = 0.2  and P(A') = {Probability that package is not delivered by UPS}

                                P(A') = 1 - 0.2 = 0.8

P(B/A) = 0.12 {means Probability that package weight 2 lbs or more given it

                      is delivered by UPS}

P(B'/A') = 0.08 [means Probability that package weight less than 2 lbs given

                         it is not delivered by UPS}

Since, P(B/A) = [tex]\frac{P(A\bigcap B)}{P(A)}[/tex]   ,    [tex]P(A\bigcap B)[/tex] = P(B/A) * P(A) = 0.12 * 0.2 = 0.024 .

Also P(B) { Probability that package weight 2 lbs or more} is given by;

Probability that package weight 2 lbs or more and it delivered by UPS.Probability that package weight 2 lbs or more and is not delivered by UPS.

So, P(B) = [tex]P(B\bigcap A) + P(B\bigcap A')[/tex] = P(B/A) * P(A) + P(B/A') * P(A')

             = 0.12 * 0.2 + 0.92 * 0.8 { Here P(B/A') = 1 - P(B'/A') = 1 - 0.08 = 0.92}

             = 0.76

(a) Probability that a package is delivered by UPS if it weighs 2 lbs or more  is given by P(A/B);

  P(A/B) =   [tex]\frac{P(A\bigcap B)}{P(B)}[/tex] =  [tex]\frac{0.024}{0.76}[/tex] = 0.0316

(b) Probability that a package is not delivered by UPS if it weighs 2 lbs or more = 1 - P(A/B) = 1 - 0.0316 = 0.9684 .            

Find tea. Write your answer in simplest radical form

Answers

Answer:

2√6 ft

Step-by-step explanation:

Tan Ф = opposite/ adjacent

tan 60  = t / 2√2 ft

tan 60 = √3

t = (tan 60 )(2√2 ft)

t = (√3)(2√2 ft)  = 2√6 ft

The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2890 21-24 2190 25-28 1276 29-32 651 33-36 274 37-40 117 Over 40 185 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 32 B = event the student is at least 37 Are the events A and B disjoint? No Yes

Answers

Answer:

Are the events A and B disjoint? Yes

Step-by-step explanation:

Disjoint events are those events that cannot occur at the same time, i.e. for events X and Y to be disjoint, [tex]P(X\cap Y)=0[/tex].

The event A is defined as the number of students whose age is at most 32.

And event B is defined as the number of students whose age is at least 37.

The events A and B are disjoint events.

The sample space for event A consists of all the students of age group (under 21), (21 - 24), (25 - 28) and (29 - 32). Whereas the sample space for event B consists of all the students of age group (33 - 36), (37 - 40) and (Over 40).

The sample space for the intersection of these two events is:

Sample space of (AB) = 0

As there are no common terms in both the sample.

Hence proved, events A and B are disjoint.

Using your knowledge of exponential and logarithmic functions and properties, what is the intensity of a fire alarm that has a sound level of 120 decibels?



A.
1.0x10^-12 watts/m^2
B.
1.0x10^0 watts/m^2
C.
12 watts/m^2
D.
1.10x10^2 watts/m^2

Answers

Option B:

[tex]I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}[/tex]

Solution:

Given sound level = 120 decibel

To find the intensity of a fire alarm:

[tex]$\beta=10\log\left(\frac{I}{I_0} \right)[/tex]

where [tex]I_0=1\times10^{-12}\ \text {watts}/ \text m^2}[/tex]

Step 1: First divide the decibel level by 10.

120 ÷ 10 = 12

Step 2: Use that value in the exponent of the ratio with base 10.

[tex]10^{12}[/tex]

Step 3: Use that power of twelve to find the intensity in Watts per square meter.

[tex]$10^{12}=\left(\frac{I}{I_0} \right)[/tex]

[tex]$10^{12}=\left(\frac{I}{1\times10^{-12}\ \text {watts}/ \text m^2} \right)[/tex]

Now, do the cross multiplication,

[tex]I=10^{12}\times1\times\ 10^{-12} \ \text {watts}/ \text m^2}[/tex]

[tex]I=1\times\ 10^{12-12} \ \text {watts}/ \text m^2}[/tex]

[tex]I=1\times\ 10^{0} \ \text {watts}/ \text m^2}[/tex]

[tex]I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}[/tex]

Option B is the correct answer.

Hence [tex]I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}[/tex].

Final answer:

To find the intensity of a sound at 120 dB, we use the formula SIL = 10 log(I / I0). With I0 as 10⁻¹² W/m², we find that I = 1.0 x 10⁰ W/m², corresponding to choice B.

Explanation:

To determine the intensity of a fire alarm that has a sound level of 120 decibels (dB), we use the relationship between sound intensity level and intensity in watts per meter squared (W/m²). The formula to convert decibel level to intensity is:

SIL = 10 log(I / I0)

Where SIL is the sound intensity level in decibels, I is the intensity of the sound, and I0 is the reference intensity, usually taken as 10⁻¹² W/m², the threshold of human hearing. To find the unknown intensity I, we can rearrange the formula:

I = I0 × 10(SIL/10)

For a sound level of 120 dB, the calculation would be:

I = 10⁻¹² W/m² × 10¹²⁰/¹⁰

I = 10⁻¹² W/m² × 10¹²

I = 1.0 × 10⁰ W/m²

Therefore, the correct answer is B. 1.0 x 10⁰ watts/m².

ln(x+1)3=3
ln
(
x
+
1
)
=
3
Question 7 options:

Answers

Answer:

x=e-1 0r 1.71828

Step-by-step explanation:

Step-by-step explanation:

[tex]In(x + 3)^{3} = 3 \\ \therefore \: 3In(x + 3) = 3 \:\\ \therefore \: In(x + 3) = \frac{3}{3} \: \\ \therefore \: In(x + 3) = 1\\ \therefore \: In(x + 3) = In \: 10\\..( \because \: In \: 10 = 1) \\ \therefore \:x + 3 = 10 \\ \therefore \:x = 10 - 3 \\ \: \: \: \: \: \huge \red{ \boxed{\therefore \:x = 7}}[/tex]

We have N cars on a circular one-way road; they have the same make, same model, same year and the same fuel economy. The total amount of gas in all cars is sufficient to make the full circle.
Prove by induction that it is always possible to find a car that can make the full circle, taking gas from other cars as it passes them.

Answers

Answer: Satisfied for n=1, n=k and n=k+1

Step-by-step explanation:

The induction procedure involves two steps

First is

Basic Step

Here we consider that for the value n=1, there is one car and it will always make the full circle.

Induction Step

Since basic step is satisfied for n=1

Now we do it for n=k+1

Now according to the statement a car makes full circle by taking gas from other cars as it passes them. This means there are cars that are there to provide fuel to the car. So we have a car that can be eliminated i.e. it gives it fuels to other car to make full circle so it is always there.

Now ,go through the statement again that the original car gets past the other car and take the gas from it to eliminate it. So now cars remain k instead of k+1 as it's fuel has been taken. Now the car that has taken the fuel can make the full circle. The gas is enough to make a circle now.

So by induction we can find a car that satisfies k+1 induction so for k number of cars, we can also find a car that makes a full circle.

Two county supervisors are selected from five supervisors, A, B, C, D, and E, to study a recycling plan.
Determine the sample space for the experiment.

Answers

Answer:

The sample space for the experiment is {(A,B), (A,C), (A,D), (A,E), (B,C), (B,D), (B,E), (C,D), (C,E), (D,E)}.

Step-by-step explanation:

Consider the provided information.

Two county supervisors are selected from five supervisors, A, B, C, D, and E, to study a recycling plan.

The sample space for the experiment is:

{(A,B), (A,C), (A,D), (A,E), (B,C), (B,D), (B,E), (C,D), (C,E), (D,E)}

Hence, the possible outcomes are {(A,B), (A,C), (A,D), (A,E), (B,C), (B,D), (B,E), (C,D), (C,E), (D,E)}.

A car rental company charges a one-time application fee of 40 dollars, 55 dollars per day, and 13 cents per mile for its cars. A) Write a formula for the cost, C, of renting a car as a function of the number of days, d, and the number of miles driven, m. B) If C = f(d, m), then f(5, 600) =

Answers

Answer:

A) C(d,m) = 40 + 55d + 0.13m

B) $448

Step-by-step explanation:

Let 'd' be the number of days and 'm' the number of miles driven.

A) The cost function that describes a fixed amount of $40, added to a variable amount of $55 per day (55d) and a variable amount of 13 cents per mile (0.13m) is:

[tex]C(d,m) = 40 +55d +0.13m[/tex]

B) If  d = 5 and m =600, the total cost is:

[tex]C(5,600) = 40 +55*6 +0.13*600\\C(5,600)=\$448[/tex]

The cost is $448.

The formula for the cost, C of renting a car as a function of the number of days, d, and the number of miles driven, m is C f(d, m) = 40 + 55d + 0.13m

Given:

Application fee = $40

cost per day = $55

cost per mile = $0.13

let

Total cost = C

Number of days = d

Number of miles = m

Total cost, C = 40 + 55d + 0.13m

C f(d, m) = 40 + 55d + 0.13m

= 40 + 55(5) + 0.13(600)

= 40 + 275 + 78

= $393

Therefore, the cost of renting the car given the number of days is $393

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Use the square roots property to solve the quadratic equation (y+150)2=50.

Answers

We can take the square root of both sides, adding a plus/minus sign of the right hand side:

[tex]\sqrt{(y+150)^2}=\pm\sqrt{50}\iff y+150 = \pm\sqrt{50}[/tex]

Then, we subtract 150 from both sides:

[tex]y=\pm\sqrt{50}-150[/tex]

So, the two solutions are

[tex]y_1 = \sqrt{50}-150,\quad y_2 = -\sqrt{50}-150[/tex]

There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.2, P(F) = 0.3, and P(E ∩ F) = 0.13.

Answers

Answer:

The question is incomplete, below is the complete question,"There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.2, P(F) = 0.3, and P(E ∩ F) = 0.13.

a) What is the probability that the individual needn't stop at either light?

b) What is the probability that the individual must stop at exactly one of the two lights? c) What is the probability that the individual must stop just at the first light?"

Answer:

A. 0.63

B. 0.24

C. 0.07

Step-by-step explanation:

Data given,

P(E) = 0.2, P(F) = 0.3, and P(E ∩ F) = 0.13.

From the question, we can conclude that the event are dependent, hence

a. P(needn't stop at either light) = 1 - P(Need to stop at either light)

P(EUF)' =1-P(EUF)

P(EUF)' =1- (P(E)+P(F) -P(E ∩ F))

P(EUF)' =1-(0.2+0.3-0.13)

P(EUF)' =1-0.37

P(EUF)' =0.63

b. P(must stop at exactly one of the two lights) = P(must stop at either light) - P(must stop at both lights)

P(must stop at exactly one of the two lights)  = P(E u F) - P(En F)

but P(E u F)=0.37,

P(En F)=0.13,

P(must stop at exactly one of the two lights) = 0.37 - 0.13 = 0.24

c. P(must stop at just the first light) = P(must stop at either light) - P(must stop at the second light)

P(must stop at just the first light) = P(E u F)-P(F)

P(must stop at just the first light) = 0.37 - 0.3 = 0.07

Final answer:

The question deals with the topic of Probability in Mathematics. It presents the probabilities of two events, denoted as E and F, which are stopping at the first and second traffic lights, respectively. The question also provides the concurrent occurrence of both events.

Explanation:

The mathematics topic this question deals with is Probability. In the scenario given, E represents the event that Darlene must stop at the first traffic light and F represents the event that she needs to stop at the second traffic light. The probabilities of these events are given as P(E)=0.2 and P(F)=0.3, respectively. Additionally, we're given that the probability of both events happening (denoted P(E ∩ F)) is 0.13.

In order to analyze the situation, we can leverage the rule of joint probability, which states that the probability of two independent events both happening is the product of their individual probabilities. However, in this case the events E and F are not independent (since the probability of the intersection P(E ∩ F) is not equal to the product of probabilities P(E)*P(F)) so we know that the occurrence of E does influence the occurrence of F, and vice versa.

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Courtney is picking out material for her new quilt. At the fabric store, there are 9 solids, 7 striped prints, and 5 floral prints that she can choose from. If she needs 2 solids, 4 floral prints, and 4 striped fabrics for her quilt, how many different ways can she choose the materials?

Answers

Answer:

N = 6300 ways

She can choose the materials 6300 ways

Step-by-step explanation:

In this case order of selection is not important, so we use combination.

For solids,

She needs 2 out of 9 available solids = 9C2

For striped prints

She needs 4 out of 7 available = 7C4

For floral prints

She needs 4 out of 5 available = 5C4

The total number of ways she can choose the materials is;

N = 9C2 × 7C4 × 5C4

N = 9/(7!2!) × 7/(4!3!) × 5/(4!1!)

N = 6300 ways

Final answer:

To find the number of different ways Courtney can choose the materials for her quilt, we can use the concept of combinations. The total number of ways she can choose the materials is the product of the number of choices for each type of fabric.

Explanation:

To find the number of different ways Courtney can choose the materials for her quilt, we can use the concept of combinations. The total number of ways she can choose the materials is given by the product of the number of choices for each type of fabric. So, the answer is:

Total number of ways = number of ways to choose solids * number of ways to choose floral prints * number of ways to choose striped fabrics

Given that she needs 2 solids, 4 floral prints, and 4 striped fabrics, we can calculate:

Number of ways to choose solids = combinations(9, 2) = 36Number of ways to choose floral prints = combinations(5, 4) = 5Number of ways to choose striped fabrics = combinations(7, 4) = 35

Substituting these values into the formula:

Total number of ways = 36 * 5 * 35 = 6300

So, there are 6300 different ways Courtney can choose the materials for her quilt.

A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 14. Use this information to find the proportion of measurements in the given interval. between 46 and 74

Answers

Approximately 68.26% of the measurements fall between 46 and 74 in this distribution.

To find the proportion of measurements between 46 and 74 in a normal distribution with a mean (μ) of 60 and a standard deviation (σ) of 14, we can use the standard normal distribution (z-score) and the cumulative distribution function (CDF).

First, we need to convert the interval endpoints to z-scores using the formula:

z = (x - μ) / σ

Where x is the value in the interval, μ is the mean, and σ is the standard deviation.

For x = 46:

z₁ = (46 - 60) / 14

z₁ = -1

For x = 74:

z₂ = (74 - 60) / 14

z₂ = 1

Using the Excel functions:

=NORM.S.DIST(-1) and =NORM.S.DIST(1)

The probabilities are 0.1587 and 0.8413 respectively.

Now, we want the proportion of measurements between z₁ and z₂, which is:

Proportion = 0.8413 - 0.1587

                  ≈ 0.6826

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Final answer:

Using the Empirical Rule for a normal distribution, approximately 68% of the measurements would fall between 46 and 74, as this range lies within one standard deviation above and below the mean of 60 in a distribution with a standard deviation of 14.

Explanation:

To find the proportion of measurements between 46 and 74 in a distribution with a mean of 60 and a standard deviation of 14, we can use the Empirical Rule, assuming the distribution is normal (bell-shaped). This rule states that approximately 68% of the data lies within one standard deviation of the mean, 95% within two, and more than 99% within three.

In this case, 46 is one standard deviation below the mean (60 - 14), and 74 is one standard deviation above the mean (60 + 14). So, we would expect approximately 68% of the measurements to lie between 46 and 74.

This is because the data is likely to be distributed symmetrically around the mean in a normal distribution, and the range given includes measurements falling within one standard deviation from the mean.

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king for the second card drawn, if the first card, drawn without replacement, was a king? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

Answer:

the probability of choosing a king for the second card drawn is 3/51 , if the first card, drawn without replacement, was a king

Step-by-step explanation:

defining the variable F= choosing a king in the first drawn , then the probability is

P(F)= 4/52

then using the theorem of Bayes for conditional probability and denoting the event S= choosing a king in the second drawn , then

P(S/F)= P(S∩F)/P(F)

where

P(S∩F) = probability of choosing a king in the first drawn and second drawn = 4/52* 3/51

P(S∩F) =probability of choosing a king in the second drawn given that a king was chosen in the first drawn

then

P(S/F)= P(S∩F)/P(F) =  4/52* 3/51 / 4/52 = 3/51

Final answer:

The probability of choosing a king for the second card drawn is 1/17 or approximately 0.0588.

Explanation:

To find the probability of choosing a king for the second card drawn, given that the first card was a king, we need to consider the total number of cards and the number of kings remaining after the first card was drawn.

After the first king is drawn, there are 51 cards left in the deck, with 3 remaining kings. Therefore, the probability of choosing a king for the second card drawn is 3/51, which can be simplified to 1/17 or approximately 0.0588.

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An urn contains 7 black and 9 green balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are green? Round your answer to three decimal places.

Answers

Step-by-step explanation:

There are 16 balls total.  Since the balls are replaced after selection, the probability that the ball is green is 9/16 each time.  The probability that a green ball is selected 6 times is:

P = (9/16)^6

P = 0.032

A water tank has 1,500 liters of water. It has a leak, losing 4 liters per minute. At the same time, a second tank has 300 liters and is being filled at a rate of 6 liters per second. Make a system of equations. After how many minutes will they have a same amount of water in the tank?

Answers

Let [tex]t[/tex] be the number of minutes.

The first tank starts with 1500 liters, and loses 4 liters per minute, so after [tex]t[/tex] minutes there will be

[tex]1500-4t[/tex]

liters of water.

The second tank is filled at 6 liters per second, i.e.

[tex]6\times 60=360[/tex] liters per minute.

So, there will be

[tex]300+360t[/tex]

liters of water in the second tank after [tex]t[/tex] minutes.

The two quantities will be equal when

[tex]1500-4t=300+360t \iff 1200=364t \iff t=\dfrac{1200}{364}\approx 3.3[/tex]

so, approximately, after 3.3 minutes.

Answer: it will take about 3.3 minutes for both tanks to have the same amount of water.

Step-by-step explanation:

Let x represent the number of minutes it will take both tanks to have same amount of water.

A water tank has 1,500 liters of water. It has a leak, losing 4 liters per minute. This means that in x minutes, the volume of water in the tank would be

1500 - 4x

At the same time, a second tank has 300 liters and is being filled at a rate of 6 liters per second. Converting 6 liters per second to minutes, it becomes 60 × 6 = 360 liters per minute. This means that in x minutes, the volume of water in the tank would be

300 + 360x

For both tanks to have same amount of water, then

1500 - 4x = 300 + 360x

360x + 4x = 1500 - 300

364x = 1200

x = 1200/364 = 3.3 minutes

Five players agree to divide a cake fairly using the last diminisher method. The players play in the following order: Anne first, Betty second, Cindy third, Doris fourth, and Ellen last. In round 1, there are no diminishers In round 2, Doris is the only diminisher In round 3, Cindy and Ellen are the only diminishers Which player gets her fair share at the end of:

Answers

Final answer:

Using the Last Diminisher method, in the first round, Anne gets her fair share because no one diminishes. In the second round, Doris is the only one who diminishes, thus gets her fair share. In the third round, despite Cindy and Ellen both diminishing, Ellen gets her fair share because she is later in turn order.

Explanation:

The Last Diminisher method is a fair division protocol used when a divisible good, like a cake in this example, needs to be divided amongst several players. This method removes discrepancies by having each player in turn reduce the piece until they don't want to diminish it further, and then giving that piece to the last to diminish.

In this case, Anne, Betty, Cindy, Doris, and Ellen are dividing the cake and playing in that order. In the first round, no one diminishes, so Anne gets her fair share of the cake. In the second round, Doris is the only one who diminishes, so she gets her fair share at the end of this round. In the third round, the last to diminish are Cindy and Ellen, but since Ellen is later in order, Ellen is the one who gets her fair share at the end of the round.

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In a Caesar Cipher system, if encryption is done by the rule c = E(p+k) = p + 9, then the letter ‘q’ is encrypted as what other letter?

Answers

Answer:

i

Step-by-step explanation:

There has to be a mod 26 operation for c, since the alphabet only has 26 letters.

But otherwise

[tex]c = E(p+k) = p + 9 \mod{26}[/tex]

p is the initial position of the letter. So for example, a = 0, b = 1, c = 2, q = 16, z = 25...

9 is by how much the encrypted character will change relative to the original.

We want to cipher the letter q.

So p = 25.

[tex]c = E(p+k) = p + 9 \mod{26}[/tex]

[tex]c = 25 + 9 \mod{26}[/tex]

[tex]c = 34 \mod{26}[/tex]

The remainder of 34 divided by 26 is 8.

So

[tex]c = 8[/tex]

Which means that q is encrypted as 'i'.

Final answer:

In a Caesar Cipher system, when the encryption rule is shifting by 9 places, the letter 'q' is encrypted as 'c'.

Explanation:

In a Caesar Cipher system, the letter 'q' is encrypted using the formula:

c = E(p + k)

Where:

c is the ciphertext (the encrypted letter).

p is the plaintext (the original letter).

k is the encryption key.

You mentioned that the encryption is done with the rule c = p + 9. In this case, k is 9.

To encrypt the letter 'q', you would substitute p with 'q' in the formula:

c = 'q' + 9

Adding 9 to 'q' in the alphabet results in:

'q' + 9 = 'z'

So, the letter 'q' is encrypted as the letter 'z' using this Caesar Cipher system.

Therefore, the encrypted letter for 'q' in a Caesar Cipher system with a shift of 9 is 'c'.

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1. A class of 16 students contains five Math majors, eight Engineering majors and three Physics majors. A group of four students from the class is to be selected to form a team for an academic competition.How many teams can be formed that have a representative from each major?

Answers

Answer:

495

Step-by-step explanation:

Using combination without repetition, the formular is given by n!/(r!(n-1)!

= (12 x11 ×10 ×9) /4 !

=11880/24

=495

From the group of 16 students with 5 math majors, 3 physics major and 8 engineering majors a team of 4 students where there has been a student from each majors total no. of teams that can be formed is 111.

What is combination ?

Combination is selecting some things in which order does not matter.

According to the given question

A class of 16 students contains 5 Math majors, 8 Engineering majors and 3 Physics majors. A group of four students from the class is to be selected to form a team for an academic competition.

Here three cases will be formed as group is formed by 4 students and the no. of majors is 3.

First case when 2 math majors, 1 physics major and 1 engineering major is chosen from 16 students.

= ⁵C₂ + ³C₁ + ⁸C₁

= 8 + 5 + 3

= 16.

Second case when 1 math major, 2 physics major and 1 engineering major is chosen from 16 students.

= ⁵C₁ + ³C₂ + ⁸C₁

= 8 + 20 + 3

= 31.

In the third case when 1 math major, 1 physics major and 2 engineering major is chosen from 16 students.

= ⁵C₁ + ³C₁ + ⁸C₂

= 56 + 5 + 3

= 64.

total no of teams that can be formed is

= 16 + 31 + 64

= 111.

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