Points: 0 of 1
Save Jinney wants to deduct the sales tax that she paid this year on her state income tax return. She spent $4970.40 during the year, including 9% sales tax. How much sales tax did she pay? She paid \\square$ sales tax. (Type an integer or a decimal.)
12.3 Performing Linear Regressions with Technology 1. An economist is trying to understand whether there is a strong link between CEO pay ration and corporate revenue. The economist gathers data, including the CEO pay ratio and the corporate revenue for 10 companies for a particular year. The pay ratio data is reported by the companies themselves and represents the ratio of CEO compensation to the median employee salary. The data has been reproduced in the table below. Corporate Revenue (million \$)
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline CEO & 286 & 944 & 321 & 268 & 183 & 309 & 132 & 264 & 236 & 259 \\
\hline Revenue & 21,973 & 29,846 & 38,507 & 18,912 & 25,947 & 97,023 & 35,888 & 59,131 & 60,579 & 27,242 \\
\hline
\end{tabular}
a) What is the equation of the line of best fit?
b) What is "r "and determine if it is a strong, moderate, or weak correlation.
www. helpyourmath.com is an OER website to help students to save money on textbooks and homework systems. A survey of 24 randomly selected students finds that they save a mean of $86 per semester by using www.helpyourmath.com. Assume the date comes from a normal distribution and the sample standard deviation is $19 per month. Confidence Interval: What is the 95% confidence interval to estimate the population mean? Round your answers to two decimal places.
□
Solve a Consumers' or Producers' Surplus Problem. The price-supply equation for some commodity is given by
p=S(x)=14+1.8x
and the equilibrium point is (23,55.4) Find the producers' surplus. The surplus is □ (Your answer must begin with \$.)
Solve a Consumers' or Producers' Surplus Problem. A popular three-story dollhouse has a price-demand equation given by
p=D(x)=340−0.9x
dollars, which gives the price per dollhouse when x dollhouses are demanded. The price-supply equation for the dollhouse is given by
p=S(x)=29.5+1.4x
dollars, which gives the price per dollhouse when x dollhouses are supplied. Find (a) the consumers' surplus and (b) the producers' surplus.
The consumers' surplus is □ (Your answer must begin with $. The producers' surplus is □ (Your answer must begin with \$.)
Solve a Consumers' or Producers' Surplus Problem. A cordless leaf blower has a price-demand equation given by
p=D(x)=5749.8−2.1x2
dollars, which gives the price per leaf blower when x leaf blowers are demanded. The price-supply equation for the leaf blower is given by
p=S(x)=2.1x2
dollars, which gives the price per leaf blower when x leaf blowers are supplied. Find the consumers' surplus and the producers' surplus. The consumers' surplus is □ ( Your answer must begin with \$.) The producers' surplus is □ (Your answer must begin with \$.)
4. Given the following sequence, which statement below is true? (1 Point) −18,−9,0,9,18,………648
The ratio of the sequence is 9
The common difference of the sequence is 9
The sequence above has 70 terms
The sum of the sequence is 23620
How to round Decimals? Click this video! If μ=3.4,σ=0.8,n=36, what is a μxˉ and σxˉ (HINT: μxˉ and σxˉ are just names of variables)? (Round to the nearest hundredth)
μxˉ=μ=σxˉ=nσ=□□
Question Help:
□ Video
The lawyer for a credit union member has sent a cheque for $2525.09 in full settlement of the member's loan balance including simple interest at 443% for 8 months. How much of the payment is interest? The amount of the payment that is interest is $□□
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
4.
[-/4 Points]
DETAILS
MY NOTES
MARSVECTORCALC6 3.4.015. Find the extrema of f(x,y)=4x+2y, subject to the constraint 2x2+3y2=189.
maximum □ at (x,y)=(□ )
minimum □ at (x,y)=(□ ) Additional Materials
□ eBook
The ends of a bar have to be machined down until the bar is 3 m long. After 5% of the length had been removed, it was found that 0.5% of the new length still had to come off. What length was removed at each machining and what was the original length of the bar?
The half-life of the radioactive element unobtanium-41 is 20 seconds. If 176 grams of unobtanium-41 are initially present, how many grams are present after 20 seconds? 40 seconds?
60 seconds? 80 seconds? 100 seconds?
The amount left after 20 seconds is grams.
Pada lingkaran yang berpusat di O , titik P berada di luar lingkaran. PA dan PB garis singgung dengan panjang PA=20cm dan PO=25cm. panjang tali busur AB adalah...
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
A system of two equations in two variables whose graphs are a circle and a line can have four real ordered-pair solutions. Choose the correct answer below.
A. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have two or one real ordered-pair solutions."
B. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have only three real ordered-pair solutions."
C. The statement is false. The correct statement is "A system of two equations in two variables whose graphs are a circle and a line can have only one real ordered-pair solution."
D. The statement is true.
The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6 -inch claw on one toe of each hind foot. The age of the dinosaur was estimated using a radioactive substance dating of rocks surrounding the bones.
A2A021ln(21)−0.55452=A0ekt=A0e1.25k=e1.25k=1.25k=k Substitute. Divide both sides of the equation by A0. Take the natural logarithm on both sides and simplify.
Solve for k.
(Round to five decimal places as needed.)
b. Analysis of the rocks surrounding the dinosaur bones indicated that 94.4% of the original amount of radioactive substance was still present. Let A=0.944A0 in the model in part ( a ) and estimate the age of the bones of the dinosaur. The estimated age of these dinosaur bones is about □ billion years.
(Round to four decimal places as needed.)
Setting up the math for a one-step quantitative problem
0/5
Yatziri The average adult heart pumps about 84.mL/s of blood at 72 beats per minute. Suppose you need to calculate how long it would take the average heart to circulate 3500.mL of blood. Set the math up. But don't do any of it. Just leave your answer as a math expression.
Also, be sure your answer includes all the correct unit symbols.
time =□ μ□
A bird species in danger of extinction has a population that is decreasing exponentially ( A=A0ckt ). Six years ago the population was at 1800 and today only 1000 of the birds are alive. Once the population drops below 200, the situation will be irreversible. How many years from now will this happen? The population will drop below 200 birds approximately □ years from now.
(Round the final answer to the nearest whole number as raeded. Round all intermediate values to 3 decimal places as needed.)
A bottle of ginger ale initially has a temperature of 72∘F. It is left to cool in a refrigerator that has a temperature of 34∘F. After 10 minutes the temperature of the ginger ale is 62∘F. Complete parts a through c.
a. Use Newton's Law of Cooling, T=C+(T0−C)ekt, to find a model for the temperature of the ginger ale, T , after t minutes.
T=□+□e□
(Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.)
A bottle of ginger ale initially has a temperature of 72∘F. It is left to cool in a refrigerator that has a temperature of 34∘F. After 10 minutes the temperature of the ginger ale is 62∘F. Complete parts a through c.
a. Use Newton's Law of Cooling, T=C+(T0−C)ekt, to find a model for the temperature of the ginger ale, T , after t minutes.
T=34+(38)e−0.0305t
(Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed)
b. What is the temperature of the ginger ale after 15 minutes?
□∘F
(Round to nearest degree as needed.)
A bottle of ginger ale initially has a temperature of 72∘F. It is left to cool in a refrigerator that has a temperature of 34∘F. After 10 minutes the temperature of the ginger ale is 62∘F. Complete parts a through c.
a. Use Newton's Law of Cooling, T=C+(T0−C)ekt, to find a model for the temperature of the ginger ale, T , after t minutes.
T=34+(38)e−0.0305t
(Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.)
b. What is the temperature of the ginger ale after 15 minutes?
58∘F
(Round to nearest degree as needed.)
c. When will the temperature of the ginger ale be 52∘F ?
□ minute(s)
(Round to nearest minute as needed.)
3. Mackenzie Insurance Company collected a premium of $15,000 for a 1-year insurance policy on May 1. What amount should Mackenzie report as a current liability for Unearned Insurance Revenue at December 31?
a. $0.
(b.) $5,000.
c. $10,000.
d. $15,000.
3. Rajah 3 menunjukkan graf jarak-masa bagi Johann semasa membuat latihan larian. Diagram 3 shows the distance-time graph of Johann doing a running exercise. Rajah 3 / Diagram 3
Diberi bahawa laju purata Johann bagi keseluruhan latihan lariannya ialah 381ms−1.
Given that the average speed of Johann for the whole running exercise is 381ms−1.
(a) Cari nilai t. Find the value of t.
[2 markah/marks]
(b) Seterusnya, cari kadar perubahan jarak, dalam ms−1, yang dilalui oleh Johann dari minit ke-4 hingga minit ke-t.
Hence, find the rate of change of distance, in ms−1, travelled by Johann from the 4th minute to tth minute.
[2 markah/marks]
A bottle of seltzer water initially has a temperature of 79∘F. It is left to cool in a refrigerator that has a temperature of 40∘F. After 10 minutes the temperature of the seltzer water is 66∘F. Complete parts a through C .
a. Use Newton's Law of Cooling, T=C+(T0−C)ekt, to find a model for the temperature of the seltzer water, T , after t minutes.
T=40+(39)e−0.0405t
(Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.)
b. What is the temperature of the seltzer water after 15 minutes?
□∘F
(Round to nearest degree as needed.)
A bottle of seltzer water initially has a temperature of 79∘F. It is left to cool in a refrigerator that has a temperature of 40∘F. After 10 minutes the temperature of the seltzer water is 66∘F. Complete parts a through c .
a. Use Newton's Law of Cooling, T=C+(T0−C)ekt, to find a model for the temperature of the seltzer water, T, after t minutes.
T=40+(39)e−0.0405t
(Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed)
b. What is the temperature of the seltzer water after 15 minutes?
61∘F
(Round to nearest degree as needed.)
c. When will the temperature of the seltzer water be 49∘F ?
□ minute(s)
(Round to nearest minute as needed.)
Using the Avogadro Number A virus has a mass of 9.0×10−12mg and an oil tanker has a mass of 3.0×107kg.
Use this information to answer the questions below. Be sure your answers have the correct number of significant digits.
\begin{tabular}{|l|l|}
\hline What is the mass of 1 mole of viruses? & \\
Round your answer to 2 significant digits. & \\
\hline \begin{tabular}{l}
How many moles of viruses have a mass equal to the mass \\
of an oil tanker?
\end{tabular} & \\
Round your answer to 2 significant digits. & \\
\hline
\end{tabular}
The least-squares regression equation is y^=762.7x+13,048 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7285 . Complete parts (a) through (d).
(a) Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.
\35929(Roundtothenearestdollarasneeded.)(b)Inaparticularregion,29.6percentofadults25yearsandolderhaveatleastabachelor′sdegree.Themedianincomeinthisregionis\38,860. Is this income higher than what you would expect? Why? This is higher than expected because the expected income is $35,624
(Round to the nearest dollar as needed.)
(c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal. Do not round.)
A. For 0% of adults having a bachelor's degree, the median income is predicted to be $□ .
B. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is □%, on average.
C. For a median income of $0, the percent of adults with a bachelor's degree is □ \%.
D. For every percent increase in adults having at least a bachelor's degree, the median income increases by $□ , on average.
Use Newton's Law of Cooling, T=C+(T0−C)ekt, to solve.
A frozen steak initially has a temperature of 26∘F. It is left to thaw in a room that has a temperature of 75∘F. After 9 minutes, the temperature of the steak has risen to 36∘F. After how many minutes will the temperature of the steak be 50∘F ? The temperature will be 50∘F after □ minutes.
(Round to nearest minute as needed.)
As you walk through Gate 4 , you realize that Gate 5 is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is an alert for this area. The warning states that this desert is almost entirely quicksand, with only one path safely through the desert. That path is defined by a piecewise function but requires that some parameters be determined before your computer can generate the plot. Thinking back on what you learned in calculus, you realize that your path will need to be continuous. You just need to tell your computer what the parameters below should be in order to create this continuous path. What parameters do you give your computer?
f(x)=⎩⎨⎧4,−4x+A,Bx+7,−x+C,Dx+4,8,x≤−2−2<x≤−1−1<x≤00<x≤11<x≤2hx>2
\begin{tabular}{|c|c|c|c|}
\hline A & B & C & D \\
\hline Number & Number & Number & Number \\
\hline
\end{tabular} Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.
35. Do this problem on a worksheet. Both car A and car B leave school when a clock reads zero. Car A travels at a constant 75km/h, and car B travels at a constant 85km/h.
a. Draw a position-time graph showing the motion of both cars.
b. How far are the two cars from school when the clock reads 2.0 h ? Calculate the distances using the equation for motion and show them on your graph.
c. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph.
Part A
A hot air balloon is at an altitude of 10051 yards. The balloon's altitude decreases by 1054 yards every minute. Which equation can be used to determine the number of minutes, m, it will take the balloon to reach an altitude of 57 yards?
A) 1054+10051m=57
B) 1054−10051m=57
C) 10051+1054m=57
D) 10051−1054m=57
Part A
The current temperature is 48∘F. It is expected to drop 1.5∘F each hour. Which equation can be used to find ir how many hours, h, the temperature will be 36∘ F?
A) 36+48h=1.5
B) 48−1.5h=36
C) 48+1.5h=36
D) 36−1.5h=48
Stella is a high school basketball player. In a particular game, she made some free throws (worth one point each) and some two point shots. Stella scored a total of 12 points and made twice as many free throws as two point shots. Graphically solve a system of equations in order to determine the number of free throws made, x, and the number of two point shots made, y.
Elizabeth is at the racetrack and bets on her favorite horse. The odds in favor o her horse winning are 6:7. What is the probability that Elizabeth's horse will win?
677613616
horizontal
1.10 A stunt rider is propelled upward from his motorbike by a spring loaded ejector seat. The rider was travelling horizontally at 60kmh−1 when the ejector seat was triggered, and as they leave the seat they are travelling with a vertical velocity of 15ms−1. The seat is 1.0 m off the ground.
(a) What is the initial velocity of the stunt rider (in kmh−1 )?
(b) How high does the stunt rider reach?
(c) How far along the track does the stunt rider land on the ground?
(d) What is the velocity of the stunt rider when they hit the ground (in kmh−1 )? Answer: (a) 81kmh−1,42∘ above the horizontal (b) 12 m (c) 51 m (d) 82kmh−1,43∘ below the horizontal
1.11 A bullet is fired horizontally from a gun that is 1.5 m from the ground. The bullet travels at 1000ms−1 and strikes a tree 150 m
Calculate the requested percentage. Show the caloulation that leads to your answer.
(a) What is 60% of 80 ?
(b) What is 45% of 90 ?
(c) What is 80% of 360 ?
Problem 6
An apple weighs 31 pound. Diego cuts the apple into 5 equal pieces. How many pounds does each piec of the apple weigh? Explain your reasoning.
5. Determine the final number after increasing or decreasing by the given percentage. Show ho you arrived at your final answer.
(a) increase 48 by 25%
(b) decrease 150 by 20%
(c) increase 55 by 2%
Which intercepts will help you find the roots of the equation if 3x+4=−2 ? Select one:
a. x-intercepts of the graph of the function y=3x+4−2
b. x-intercepts of the graph of the function y=3x+4+2
c. y-intercepts of the graph of the function y=3x+4−2
d. y-intercepts of the graph of the function y=3x+4+2
8 Adaeze, Rachael, and Sam run a relay race.
- Adaeze runs the first 94 of the race.
- Rachael runs 43 of the distance that Adaeze ran.
- Sam runs 32 of the distance that Rachael ran. What fraction of the race did Sam run? A 91 B 92
C 31
D 21
Point S is the midpoint of line RT. RS is 3x+20 and RT is 12x−10. What is the length of RS? Round your answer to the nearest hundredth if necessary.
Your Answer: Answer Question 3 (2 points)
(c) At the school across the street, 127 of the students like neither superhero nor s This represents 189 members of the student body. Set up and solve an calculate the total number of students, T, that go to this school.
in Louisiana have a 10% sales tax. Talal buys a coat for $45
The Fifth Gate
After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's directions to you. "The passcode for this gate is the number found by first entering m′(−1) and then entering n′(7) using the definitions below." What values do you provide to your computer?
f(x)=(x8−2x)g(x)=(x2+6x−90)h(x)=2x−13m(x)=f(x)⋅g(x)n(x)=h(x)g(x)m′(−1)=
\begin{tabular}{l|c|c|c|c|c}
\hlinea & ba & a & ∣a∣ & π & sin(a) \\
\hline
\end{tabular}
n′(7)=
A cone has a volume of 1899.7 cubic meters and a height of 15 meters. What is its radius?
Use π≈3.14 and round your answer to the nearest hundredth.
r≈□ meters
Submit
11 Marina purchases a square bookshelf that measures 21 of a meter by 2−0 of a meter. Ine bookshelf is divided into equal compartments, as shown below. Marina wants to use 65 of the compartments to display only books, and the rest to display decor.
\begin{tabular}{|l|l|l|}
\hline & & \\
\hline & & \\
\hline & & \\
\hline & & \\
\hline
\end{tabular} What is the total area, in square meters, of the compartments that will display only books? A 245 square meters
B 41 square meters
c 125 square meters
D 65 square meters
3. Two horizontal forces act on a 5.0−kg mass. One force has a magnitude of 8.0 N and is directed due north. The second force toward the east has a magnitude of 6.0 N . What is the acceleration of the mass?
A) 1.6m/s2 due north
B) 1.2m/s2 due east
C) 2.0m/s2 at 53 e N of E ㅇ) 2.0m/s2 at 53mE of N
63. Pollution Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time l is given by
P′(t)=140t5/2
where t is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a total level of pollution of 4850 units before all the fish life in the lake ends. Can the factory operate for 4 years without killing all the fish in the lake?
The volume of this cone is 1,519.76 cubic meters. What is the height of this cone? Use π≈3.14 and round your answer to the nearest hundredth.
h≈□ meters
8 Abiturprüfung 2011 (Bayern), Analysis, Aufgabengruppe I, Teil 1, Aufgabe 3
Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form N(x)=N0⋅ek⋅(x−2000) beschreiben, wobei N(x) die Anzahl der Menschen zu Beginn des Jahres x ist. Bestimmen Sie N0 und k.
Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form N(x)=N0⋅ek⋅(x−2000) beschreiben, wobei N(x) die Anzahl der Menschen zu Beginn des Jahres x ist. Bestimmen Sie N0 und k.
2. (4 punti) Una gru, il cui motore ha una potenza di 3,00kW, solleva di 10,4m, a velocità costante, un carico che ha massa di 359 kg . Calcola il tempo impiegato dalla gru per sollevare il carico.
11 Bei dem Reaktorunfall in Tschernobyl am 26. April 1986 wurde u.a. radioaktives Cäsium-137 freigesetzt. Cäsium-137 zerfällt exponentiell mit einer Halbwertszeit von ca. 30 Jahren. Über der damaligen Bundesrepublik Deutschland hatten sich nach Angaben der Gesellschaft für Strahlenund Umweltforschung etwa 230 Gramm radioaktives Cäsium-137 abgelagert, ein Großteil davon in Bayern.
a) Beschreiben Sie den Zerfall dieser Menge Cäsium-137 durch eine Funktion f:t↦b⋅ekt ( t in Jahren und f(t) in Gramm).
b) Geben Sie die Bedeutung des Faktors b im Sachzusammenhang an und berechnen Sie den prozentualen Anteil, um den die Masse des Cäsium-137 jedes Jahr abnimmt.
c) Berechnen Sie, nach welcher Zeit weniger als ein Gramm des Cäsium-137 übrig ist.
d) Bestimmen Sie die Funktion der Wachstumsgeschwindigkeit für die gegebene Menge Cäsi-um-137. Berechnen Sie die Wachstumsgeschwindigkeit zu Beginn und zum heutigen Zeitpunkt. Beschreiben Sie die Werte im Sachzusammenhang.
ANSWERS 12. sin51.9∘= .997
cos51.9∘≈tan51.9∘=csc51.9∘=sec51.9∘=cot51.9∘= 13. B=a≈c= 14. 15. 16. sinθ=tanθ=cscθ=secθ=cotθ= 17. 18. 19. Find the length of an are of a circle, given a central angle of 35π and a radius of 6 m . 18. Convert 95π to degree measure. 12. Given that sin38.1∘≈0.6170,cos38.1∘≈0.7869, and tan38.1∘=0.7841, find the six trigonometric function values for 51.9∘. Round to four decimal places. 13. Solve the right triangle with A=14.2∘ and b=9.5. Standard lettering has been used. 14. Find a positive angle and a negative angle coterminal with a 103∘ angle. 15. Find the complement of 103π. 16. Given that cosθ=−5189 and that the terminal side is in quadrant I, find the other five trigonometric function values. 17. Convert 150∘ to radian measure in terms of π.
6. Baher Company acquired 100 percent of the voting common shares o: Sami Videu Corporation by issuing bonds with a par value and fair value of $150,000. Immediately prior to the acquisition, Baher reported total assets of $500,000, liabilities of $280,000, and stockholders' equity of $220,000. At that date, Sami Video reported total assets of $400,000, liabilities of $250,000, and stockholders' equity of $150,000. Based on the preceding information, what anount of total liabilities was reported in the consolidated balance sheet immediately after acquisition?
\begin{problem}
Which of the following is NOT an advantage of the sole proprietorship?
\begin{enumerate}
\item Limited liability
\item No legal requirements for starting a business
\item Easy and inexpensive to set up
\item No time limit is imposed on its existence
\end{enumerate}
\end{problem}
Carlos had 194 seeds and 11 flower pots. He put the same number of seeds in each flower pot. Which is the best estimate for the number of seeds in each flower pot?
(1 point)
10
20
30
40
```latex
\text{Flüssigkeiten bei einem Produktionsprozess} \\
\text{In einem Produktionsprozess werden Flüssigkeiten erhitzt und anschließend abgekühlt. Der Temperaturverlauf kann gezielt gesteuert werden, sodass er sich für den gesamten Erhitzungs- bzw. Abkühlungsvorgang für } t \geq 0 \text{ durch eine der in } \mathbb{R} \text{ definierten Funktionen } f_{k} \text{ mit } f_{k}(t)=23+20 \cdot t \cdot e^{-\frac{1}{10} \cdot k \cdot t}, \text{ wobei } k \text{ eine positive, reelle Zahl sein soll, beschreiben lässt. Dabei ist } t \text{ die seit Beginn des Vorgangs vergangene Zeit in Minuten und } f_{k}(t) \text{ die Temperatur in } { }^{\circ} C. \\
\text{a) Die in Abbildung 1 dargestellten Graphen } A, B \text{ und } C \text{ gehören jeweils zu einem der Werte } k=0,5 ; k=2 \text{ und } k=5. \text{ Ordnen Sie jedem dieser Werte den zugehörigen Graphen zu.} \\
\text{b) Begründen Sie, dass der in Abbildung 1 dargestellte Graph } D \text{ nicht zu einer der Funktionen } f_{k} \text{ gehören kann.} \\
\text{c) Zeigen Sie, dass gilt} \\
f_{k}^{\prime}(t)=20 \cdot e^{-\frac{1}{10} \cdot k \cdot t} \cdot\left(1-\frac{1}{10} \cdot k \cdot t\right) \\
\text{d) Ermitteln Sie denjenigen Wert von } k, \text{ für den die Flüssigkeit im Modell eine Höchsttemperatur von } 123^{\circ} \mathrm{C} \text{ erreicht.} \\
\text{e) Ermitteln Sie die Koordinaten des Wendepunktes des Graphen von } f_{10}. \text{ Interpretieren Sie anschließend die Bedeutung der x-Koordinate dieses Wendepunkts des Graphen von } f_{10} \text{ im Sachzusammenhang.}
```
How many years are required for an investment to double in value if it is appreciating at the rate of 11% compounded continuously? At 11\% compounded continuously, the investment doubles in □ years.
(Round to one decimal place as needed.)
Aufgabe 26
Aus einem großen Reservoir wird das Wasser über eine gerade Rohrleitung mit freier Ausmündung einem Bewässerungsgraben zugeführt. Die Leitung besteht aus Polyethylenrohren. Der Einlauf der Leitung ist gut ausgerundet, ein Einlaufverlust soll nicht berücksichtigt werden. Gegeben: T=10∘
a) Bestimmen Sie den Durchfluss in der Leitung für den Fall, dass die Reibungsverluste vernachlässigt werden
b) Bestimmen Sie den Durchfluss in der Leitung für den Fall, dass die Rohrreibung berücksichtigt wird
c) Zeichnen Sie den Verlauf der Druck- und Energielinie.
Hydromechanik
The Seventh Gate
As you approach the seventh gate, you notice that it is only a short distance to the area where your computer indicated the communication device was stored. You look past the gate hopefully, as your computer translates: The passcode for this gate is found by determining the domain of the derivative of f(x) and then evaluating the derivative at x=−3812. Enter the domain in interval notation.
f(x)=4−38x Domain of f′(x) : □固朝
a^bsin(a)∞αf′(−3812)□ Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.
How much money must you invest now at 4.1% interest compounded continuously in order to have $10,000 at the end of 4 years? You must invest \\square$
(Round to the nearest cent as needed.)
To test H0:μ=100 versus H1:μ=100, a simple random sample size of n=20 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). Click here to view the t-Distribution Area in Right Tail.
(a) If xˉ=105.3 and s=8.3, compute the test statistic.
t=□ (Round to three decimal places as needed.)
13. A function f(x) is one-to-one. If the graph of f−1(x) lies in the fourth quadrant. In which quadrant does the graph of f(x) lie?
A. First Quadrant
B. Second Quadrant
b) Given the graph of the function h(x). graph h−1(x)
C. Third Quadrant
D. Fourth Quadrant
Jerome wants to rent a rowboat to go fishing at the lake. The cost of the rental can be represented by the equation y=18x, where x is the number of hours the boat is rented for, and y is the total cost. What is the cost per hour for renting the boat?
There is no cost per hour, because the value for b in the slope-intercept form of the equation y=mx+b equals 0 . It costs $18 to rent the boat all day.
Renting the boat costs $0.18 per hour.
The cost per hour can't be determined without determining the number of hours it is used.
Renting the boat costs $18 per hour.
Four thousand dollars is deposited into a savings account at 4.5% interest compounded continuously.
(a) What is the formula for A(t), the balance after t years?
(b) What differential equation is satisfied by A(t), the balance after t years?
(c) How much money will be in the account after 9 years?
(d) When will the balance reach $8000 ?
(e) How fast is the balance growing when it reaches $8000 ?
(c) $5997.21 (Round to the nearest cent as needed.)
(d) After □ years the balance will reach $8000.
(Round to one decimal place as needed.)
The Eighth Gate
Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this gate for me." Your computer replies with the follow:
The function f(t)=a(sin(t6))10 models the position of an oscillating particle that has recently been discovered. Assume that a is a constant. What is the function that represents the velocity of this particle? Note: If you want to write a power of a trigonometric function, remember that writing sin(x) to the fourth power as sin4(x) is just a shorthand method. To be mathematically correct, you should write that as (sin(x))4. which is what your computer expects and can translate. Velocity Function:
□absin(a)∞α□
Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.
Question 50
The temperature of a nuclear reactor rises at a steady rate of 100 degrees per minute, while the temperature of a thermal reactor doubles every minute. Given that the starting temperatures of the nuclear reactor and the thermal reactor are 400 degrees and 15 degrees, respectively, after how many whole minutes will the temperature of the thermal reactor exceed that of the nuclear reactor? Marks:1.0 Negative Marks: 0.25
```latex
\text{Given:} \triangle OFG \text{ is a right triangle at } O, \text{ where } OF = 4 \text{ cm and } OG = 3 \text{ cm. Let } M \text{ be the midpoint of } GO, \text{ and let } H \text{ be the reflection of } F \text{ with respect to } AM. \text{ Draw the figure accurately.} \text{1. What type of quadrilateral is } OFGH? \text{ Justify your answer.} \text{2. Prove that line } AL \text{ is perpendicular to } GO \text{ at } M \text{ and intersects } GF \text{ at point } L. \text{ Show that } L \text{ is the midpoint of } GF. \text{3. Calculate the length of } ML. \text{4. Draw accurately the circumcircle of } \triangle OFG.
```
2 Ein Betrieb stellt ein Produkt mit den Inputfaktoren x (in ME) und y ( Output soll 1000 ME betragen. Die Faktormengenkombinationen, die zu diesem Output führen, lassen sich mit der Isoquantengleichung y(x)=x−240+3 beschreiben. Bei einem Kostenbudget in Höhe von 730 GE lautet die Gleichung der Isokostengeraden y(x)=−10x+73, bei einem Kostenbudget von 550 GE lautet sie y(x)=−10x+55.
a) Untersuchen Sie, ob sich mit diesen Kostenbudgets der angestrebte Output erzielen lässt. Geben Sie ggf. die Kombinationsmengen der Inputfaktoren an.
b) Berechnen Sie die Minimalkostenkombination.
c) Bestimmen Sie die Gleichung der kostenminimalen Isokostengeraden.
d) Berechnen Sie, wie hoch das Kostenbudget mindestens sein muss, wenn ein Output von 1000 ME produziert werden soll.
e) Erstellen Sie eine Grafik, die Ihre Ergebnisse veranschaulicht. Geben Sie für die Isoquante die Gleichung der Polgeraden und der Asymptote an.
GENERAL MATHEMATICS
Long Quiz S.Y. 2024 - 2025 1. What do we call the monetary charge for the amount we borrow?
d. Time
a. Interest
b. Final amount
c. Principal
11 2. What do we call the accumulated amount after an interest rate is being applied in a specified year?
a. Interest
b. Final amount
c. Principal
d. Time 3. How many compounding periods does a bimonthly have? c. 12
a. 2
b. 6 4. What is periodic interest rate does a 9% compounded quarterly?
d. 24
a. 9
b. 18 5. What is the final value if principal is 4,500 , time is 2 years, and interest rate is 6% ?
d. 45
a. 5,040
b. 5,400
c. 9,000
d. 50,400
d. 46,332.55
a. 46,232.55
b. 46,233.55
a. 219,291.76
b. 219,291.67
c. 219219.67
d. 219,291.76 8. What is the interest for the item \#5?
c. 540
d. 5400
a. 900
b. 4500
d. 832.55 9. What is the interest for the item \#6?
c. 823.55
a. 732.55
b. 733.55
d. 29,291.76 10. What is the interest for the item \#7?
c. 29219.67
a. 29,291.76
b. 29,291.67
d. 76%
c. 67%
d. 5.3 years
0
Write the letter of the correct match next to each problem.
equiangular tri.
Created on TheTeachersCorner.net Match-up Maker
a. original geometric figure
equilateral tri.
b. extra line drawn to help analyze geometric relationships
isosceles triangle
c. turn around a fixed point through a specific angle
scalene triangle
d. at least 2 congruent sides
auxiliary line
e. polygon(s) with all congruent corresponding parts
congruent
congruent polygons
f. operation that maps an original geometric figure onto a new figure
corresponding
g. 3 congruent sides
included angle
h. 3 congruent acute angles
included side
base angle
transformation
preimage
m. no congruent sides
image
n. new geometric figure
reflection
o. slide that moves all points the same distance
translation
p. side located between 2 consecutive angles
rotation
q. angle formed by two adjacent sides of a polygon
GENERAL MATHEMATICS
Long Quiz S.Y. 2024 - 2025 1. What do we call the monetary charge for the amount we borrow?
a. Interest
b. Final amount
c. Principal
d. Time 2. What do we call the accumulated amount after an interest rate is being applied in a specified year?
a. Interest
b. Final amount
c. Principal
d. Time
!!!11\% 3. How many compounding periods does a bimonthly have?
a. 2
b. 6
c. 12
d. 24 4. What is periodic interest rate does a 9% compounded quarterly?
d. 45
a. 9
b. 18
c. 36 5. What is the final value if principal is 4,500 , time is 2 years, and interest rate is 6% ?
c. 9,000
a. 5,040
b. 5,400
b. 46,233.55
d. 50,400
a. 219,291.76
b. 219,291.67
c. 219219.67
ompor
valiy 8. What is the interest for the item \#5?
c. 540
d. 5400
a. 900
b. 4500
d. 832.55 9. What is the interest for the item #6 ?
c. 823.55
a. 732.55
b. 733.55
d. 29,291.76 10. What is the interest for the item #7 ?
c. 29219.67
a. 29,291.76
b. 29,291.67
d. 76%
c. 67%
The Sugar Sweet Company is going to transport its sugar to market. It will cost $4500 to rent trucks plus $225 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function.
C(n)=4500+225n Answer the following questions.
(a) If the total cost is $9900, how many tons is the company transporting?
□
ns
(b) What is the total cost of transporting 12 tons?
\\square$
The Sugar Sweet Company is going to transport its sugar to market. It will cost $4500 to rent trucks plus $225 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function.
C(n)=4500+225n Answer the following questions.
(a) If the total cost is $9900, how many tons is the company transporting?
□ tons
(b) What is the total cost of transporting 12 tons?
\$7200
Which equation shows a valid step in solving 32x−6+32x+6=0 ?
(32x−6)2=(32x+6)2(32x−6)2=(−32x+6)2(32x−6)3=(32x+6)3(32x−6)3=(−32x+6)3
Mark this and return
sessmentViewer/Activit...
13 Finde den Fehler!
a) Zeige durch Einsetzen eines Werts für x oder mithilfe einer Probe, dass die Rechnungen falsch sein müssen.
b) Erkläre, was falsch gemacht wurde, und korrigiere im Heft.
(1) ==4x−(x+2)4x−x+23x+2
(2) 5x+3=0∣−27x=01:7
(3)
4x+2=2x−22x=−4∣−2x=−6 (4) 52x+512x+512xx=0,3∣⋅5=0,15∣∣−51=−0,05∣:2=−0,25
3. A certain mass hangs from a spring above a table. It is released from a height of 0.9 metres above the table and falls to a height of 0.1 m above the table before reversing direction and bouncing back to 0.9 m . The mass continues to move in a periodic up and down motion. It takes 1.2 seconds for the mass to return to the same position each time.
b) Write an equation which expresses the height h as a function of sinθ.
2. Assume the following transactions occured during 2023: Jan I, Purple purchases 30% of Yellow's common stock for $150,000.
June 30, Yellow reported net income of $50,000.
June 30, Yellow declared \20,000Dividends.July1,Purplepurchasesadditional10 \%ofYellow′scommonstockfor\50,000.
Dec 31, Yellow reported net income of $65,000.
Dec 31, Yellow declared $20,000 dividends.
The Investment in Yellow account balance reported by Purple at December 31, 2023 would be
A. $250,000
B. $275,000
C. $227,000
D. $222,500
8.. Two years ago, Print Co, acquired 30% of Stamp Co, common stock for $750,000. Today, Print acquired the remaining 70% shares of Stamp for $2,100,000 cash. Print's total investment would a mount to
A. $3,200,000,
B. $2,500,000,
C. $3,000,000,
D. $2,850,000.
Green plants need light in order to survive. Structures in the leaves absorb light, which in turn, helps plants make their own food. Under which color of light will plants be least likely to make food?
red
blue
orange
green
1 Forces 19. Two ropes are attached to a tree, and forces of F1=2.0i^+4.0j^N and F2=3.0i^+6.0j^N are applied. The forces are coplanar (in the same plane).
(a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.
20. A telephone pole has three cables pulling as shown from above, with F1=(300.0i^+500.0j^),F2=−200.0i^, and F3=−800.0j^. (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force.