6 cm + 10 cm + 4 cm + 3 cm + 5 cm = 28 cm

Question

asked 2021-02-25

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. \(\displaystyle{\left({1},{3}\right)},{\left({2},{6}\right)},{\left({3},{12}\right)},{\left({4},{24}\right)}\)

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

asked 2020-10-23

1. Find each of the requested values for a population with a mean of \(? = 40\), and a
standard deviation of \(? = 8\)
A. What is the z-score corresponding to \(X = 52?\)
B. What is the X value corresponding to \(z = - 0.50?\)
C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores?
D. What is the z-score corresponding to a sample mean of \(M=42\) for a sample of \(n = 4\) scores?
E. What is the z-scores corresponding to a sample mean of \(M= 42\) for a sample of \(n = 6\) scores?
2. True or false:
a. All normal distributions are symmetrical
b. All normal distributions have a mean of 1.0
c. All normal distributions have a standard deviation of 1.0
d. The total area under the curve of all normal distributions is equal to 1
3. Interpret the location, direction, and distance (near or far) of the following zscores: \(a. -2.00 b. 1.25 c. 3.50 d. -0.34\)
4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with \(\mu = 78\) and \(\sigma = 12\). Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: \(82, 74, 62, 68, 79, 94, 90, 81, 80\).
5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about \($12 (\mu = 42, \sigma = 12)\). You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the \(\alpha = 0.05\) level of significance.

asked 2021-01-28

A 1300 kg car is constructed on a frame that is is in turn supported by four springs. each spring has aspring constant of \(\displaystyle{2}\cdot{104}\ \frac{{N}}{{m}}\). Two passengers in the car have a combined mass of 160 kg. What is the frequency of free vibration of the car when it is driven ovr arough road?

How long does it take the car to execute three complete oscillations?

How long does it take the car to execute three complete oscillations?

asked 2020-11-12

Finance bonds/dividends/loans exercises, need help or formulas

Some of the exercises, calculating the Ri is clear, but then i got stuck:

A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?

A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?

At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.

What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€

You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.

Some of the exercises, calculating the Ri is clear, but then i got stuck:

A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?

A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?

At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.

What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€

You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.

asked 2021-02-09

Two children, Ferdinand and Isabella, are playing with a waterhose on a sunny summer day. Isabella is holding the hose in herhand 1.0 meters above the ground and is trying to spray Ferdinand,who is standing 10.0 meters away. I know so far that she cannotspray Ferdinand at the current position and with the curreentspeed of spray. I got stuck inthe following question:

To increase the range of the water, Isabellaplaces her thumb on the hose hole and partially covers it. Assumingthat the flow remains steady, what fraction f of the cross-sectional area of the hose hole does shehave to cover to be able to spray her friend?

To increase the range of the water, Isabellaplaces her thumb on the hose hole and partially covers it. Assumingthat the flow remains steady, what fraction f of the cross-sectional area of the hose hole does shehave to cover to be able to spray her friend?

asked 2021-02-22

The spring of a spring gun has force constant k =400 N/m and negligible mass. The spring is compressed 6.00 cm and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring.The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. Calculate the speed with which the ballleaves the barrel if you can ignore friction. Calculate the speed of the ball as it leavesthe barrel if a constant resisting force of 6.00 Nacts on the ball as it moves along the barrel. For the situation in part (b), at what position along the barrel does the ball have the greatest speed?

asked 2021-01-27

Draw a diagram to represent the situation. Start by drawing a segment to represent the distance between Sam and the base of the building. Place a point on the segment and label the portion from Sam to this point as 1.22 m and the other portion as 7.32 m. Then draw two right triangles that have right angles at the endpoints of the first segment. Label the height for Sam's triangle as 1.82 m and the height of the building's triangle as h:

asked 2020-11-29

Part II

29.[Poles] (a) For each of the pole diagrams below:

(i) Describe common features of all functions f(t) whose Laplace transforms have the given pole diagram.

(ii) Write down two examples of such f(t) and F(s).

The diagrams are: \((1) {1,i,-i}. (2) {-1+4i,-1-4i}. (3) {-1}. (4)\) The empty diagram.

(b) A mechanical system is discovered during an archaeological dig in Ethiopia. Rather than break it open, the investigators subjected it to a unit impulse. It was found that the motion of the system in response to the unit impulse is given by \(w(t) = u(t)e^{-\frac{t}{2}} \sin(\frac{3t}{2})\)

(i) What is the characteristic polynomial of the system? What is the transfer function W(s)?

(ii) Sketch the pole diagram of the system.

(ii) The team wants to transport this artifact to a museum. They know that vibrations from the truck that moves it result in vibrations of the system. They hope to avoid circular frequencies to which the system response has the greatest amplitude. What frequency should they avoid?

29.[Poles] (a) For each of the pole diagrams below:

(i) Describe common features of all functions f(t) whose Laplace transforms have the given pole diagram.

(ii) Write down two examples of such f(t) and F(s).

The diagrams are: \((1) {1,i,-i}. (2) {-1+4i,-1-4i}. (3) {-1}. (4)\) The empty diagram.

(b) A mechanical system is discovered during an archaeological dig in Ethiopia. Rather than break it open, the investigators subjected it to a unit impulse. It was found that the motion of the system in response to the unit impulse is given by \(w(t) = u(t)e^{-\frac{t}{2}} \sin(\frac{3t}{2})\)

(i) What is the characteristic polynomial of the system? What is the transfer function W(s)?

(ii) Sketch the pole diagram of the system.

(ii) The team wants to transport this artifact to a museum. They know that vibrations from the truck that moves it result in vibrations of the system. They hope to avoid circular frequencies to which the system response has the greatest amplitude. What frequency should they avoid?

asked 2020-12-30

Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). Toe researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient \(\displaystyle{\left(\text{measured on a 7-point scale where}\ {1}=\ \text{"not at all" and}\ {7}=\ \text{to a great extent"}\right)}.\) Participants for the study were those who used a popular Web site for engaged couples. The Web site's directory was searched for those with "average" American names (e.g., "John Smith," "Sara Jones"). These individuals were then invited to participate in an online survey in exchange for a $10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents.
a) Identify the experimental units for this study.
b) What are the variables of interest? Are they quantitative or qualitative in nature?
c) Describe the population of interest.
d) Do you believe the sample of 33 respondents is representative of the population?
Explain. e. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. Toe participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.

asked 2021-02-06

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl
a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}&{C}{r}{a}{w}{l}\in{g}\ {a}\ge\backslash{h}{l}\in{e}{B}{i}{r}{t}{h}\ {m}{o}{n}{t}{h}&{M}{e}{a}{n}&{S}{t}.{d}{e}{v}.&{n}\backslash{h}{l}\in{e}{J}{a}\nu{a}{r}{y}&{29.84}&{7.08}&{32}\backslash{M}{a}{y}&{28.58}&{8.07}&{27}\backslash{S}{e}{p}{t}{e}{m}{b}{e}{r}&{33.83}&{6.93}&{38}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations
of crawling ages have Normal distributions.
A partial ANOVA table is given below.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{o}{u}{r}{c}{e}&{S}{u}{m}\ {o}{f}\ \boxempty{s}&{D}{F}&{M}{e}{a}{n}\ \boxempty\ {F}\backslash{h}{l}\in{e}{G}{r}{o}{u}{p}{s}&{505.26}\backslash{E}{r}{r}{\quad\text{or}\quad}&&&{53.45}\backslash{T}{o}{t}{a}{l}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
What are the degrees of freedom for the groups term?