A simple random sample from a population with a normal distribution of 102 body temperatures has xˉ=98.70∘F and s=0.69∘F. Construct an 80% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Click the icon to view the table of Chi-Square critical values.
105 Campo elettrico di due piani paralleli
Due piani infiniti di carica disposti parallelamente uno all'altro hanno densità superficiale di carica rispettivamente pari a 2,0μC/m2e4,0μC/m2. Determina il campo elettrico all'interno e all'esterno delle piastre.
[3,4⋅105N/C;1,1⋅105N/C]
Thursday, November 28, 2024
Midterm Exam
Calculus I d (0203101 \& 0213105 ) اكتب رمز الإجابة الصحيحة في الجدول بالحروف الكبيزة A, B, C, D
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline Question & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
\hline Answer & & & & & & & & & & & & & & & \\
\hline
\end{tabular} If f(x)=x−14,g(x)=4x, then the value of x at which f∘g(x)=g∘f(x) is:
A) 41
B) 51
C) −31
D) 31 The graph of the function f(x)=x2−25(x2−7x+10) has at x=−5
A) jump
B) Hole
C) Vertical asymptote
D) continuity point
\begin{tabular}{|c|c|c|c|}
\hline Q1 & \begin{tabular}{l}
The curve of y+xy2=1 is symmetric about: \\
A) Origin \\
B) x-axis
\end{tabular} & C) y-axis & D) Not symmetric \\
\hline Q2 & \begin{tabular}{l}
x→+∞limx+21+2x2= \\
A) −2 \\
B) 2
\end{tabular} & C) 2 & D) -2 \\
\hline Q3 & \begin{tabular}{l}
The function f(x)=x2sin(x) is: \\
A) even \\
B) odd
\end{tabular} & C) even and odd & D) neither \\
\hline Q4 & \begin{tabular}{l}
If f(x)=4+x−1x, then f−1(x)= \\
A) 3−x2−x \\
B) 4−x3−x
\end{tabular} & C) 5−x4−x & D) 6−x5−x \\
\hline Q5 & \begin{tabular}{l}
For all real numbers x, a function f(x) satis \\
A) 5 \\
B) -5
\end{tabular} & \begin{tabular}{l}
∣f(x)+1∣≤∣x \\
C) -1
\end{tabular} & \begin{tabular}{l}
5, then limx→−5f(x) \\
D) 1
\end{tabular} \\
\hline
\end{tabular}
7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7. g(x)=∫1xt3+11dt 8. g(x)=∫3xet2−tdt 9. g(s)=∫5s(t−t2)8dt 10. g(r)=∫0rx2+4dx 11. F(x)=∫xπ1+sectdt[ Hint: ∫xπ1+sectdt=−∫πx1+sectdt]
I'm sorry, but I cannot accurately rewrite the math problem in LaTeX format without more information about the shapes and dimensions involved in the problem. Please provide more details or a description of the image.
16) If f(x)=2−(x−1)3, then the graph that represents the function f is
(a)
(b)
(c)
(d)
17) The rule of the function represented in the opposite figure is f(x)=
(a) (x−2)2+1
(b) −(x−2)2+1
(c) −(x−1)2+2
(d) (−x+1)2+2
18) The symmetric point of the function f:f(x)=x3−2 is
(a) (0,2)
(b) (0,−2)
(c) (2,0)
(d) (−2,0)
19) The vertex of the curve of the function f where f(x)=(1+x)2−3 is
(a) (1,3)
(b) (1,−3)
(c) (−1,3)
(d) (−1,−3)
20) If y=f(x) is a real function, then its image by translation 3 units vertically upwards is g(x)=
(a) f(x−3)
(b) f(x+3)
(c) f(x)+3
(d) (x)−3
2. The mean June midday temperature in Desertville is 36∘C and the standard deviation is 3∘C Assuming this data is normally distributed, how many days in June would you expect the midday temperature to be between 39∘C and 42∘C ? What temperature can you expect in 10\% warmest days in June?
13. Ein U-Boot beginnt eine Tauchfahrt in P(100∣200∣0) mit 11,1 Knoten in Richtung des Peilziels Z(500∣400∣−80), bis es eine Tiefe von 80 m erreicht hat.
(1 Knoten =1 Stunde Seemeile ≈1,852hkm) Anschließend geht es ohne Kurswechsel in eine horizontale Schleichfahrt von 11 Knoten ein.
Könnte es zu einer Kollision mit der Tauchkugel T kommen, die zeitgleich vom Forschungsschiff S(700∣800∣0) mit einer Geschwindigkeit von 0,5sm senkrecht sinkt?
```latex
\textbf{Flüssigkeiten bei einem Produktionsprozess} 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≥0 durch eine der in R definierten Funktionen fk mit fk(t)=23+20⋅t⋅e−101⋅k⋅t, wobei k eine positive, reelle Zahl sein soll, beschreiben lässt. Dabei ist t die seit Beginn des Vorgangs vergangene Zeit in Minuten und fk(t) die Temperatur in ∘C. \begin{enumerate}
\item[a)] Die in Abbildung 1 dargestellten Graphen A,B und C gehören jeweils zu einem der Werte k=0,5;k=2 und k=5. Ordnen Sie jedem dieser Werte den zugehörigen Graphen zu.
\item[b)] Begründen Sie, dass der in Abbildung 1 dargestellte Graph D nicht zu einer der Funktionen fk gehören kann.
\item[c)] Zeigen Sie, dass gilt
fk′(t)=20⋅e−101⋅k⋅t⋅(1−101⋅k⋅t)
\item[d)] Ermitteln Sie denjenigen Wert von k, für den die Flüssigkeit im Modell eine Höchsttemperatur von 123∘C erreicht.
\item[e)] Ermitteln Sie die Koordinaten des Wendepunktes des Graphen von f10. Interpretieren Sie anschließend die Bedeutung der x-Koordinate dieses Wendepunkts des Graphen von f10 im Sachzusammenhang.
\item[f)] Der in der Abbildung 2 dargestellte Graph gibt für einen gesteuerten Temperaturverlauf die Änderungsrate der Temperatur in Abhängigkeit von der Zeit an, die seit Beginn des Vorgangs vergangen ist. Bestimmen Sie einen Näherungswert für die Änderung der Temperatur in den ersten vier Minuten nach Beginn des Vorganges und geben Sie an, ob die Temperatur zu- oder abnimmt.
\item[g)] Skizzieren Sie für die ersten zwölf Minuten des in Abbildung 2 dargestellten Vorgangs den Graphen eines möglichen Temperaturverlaufs.
\end{enumerate} \textit{Abbildung 1} \textit{Abbildung 2}
```
13. Ein U-Boot beginnt eine Tauchfahrt in P(100∣200∣0) mit 11,1 Knoten in Richtung des Peilziels Z(500∣400∣−80), bis es eine Tiefe von 80 m erreicht hat.
(1 Knoten =1 Stunde Seemeile ≈1,852hkm) Anschließend geht es ohne Kurswechsel in eine horizontale Schleichfahrt von 11 Knoten ein.
Könnte es zu einer Kollision mit der Tauchkugel T kommen, die zeitgleich vom Forschungsschiff S(700∣800∣0) mit einer Geschwindigkeit von 0,5sm senkrecht sinkt?
TASK 2
(a) Explain the meaning of each of the following statistical terms:
(i) Level of measurement
(02)
(ii) Level of significance
(102)
(b) The following data relate to the number of vehicles owned and road deaths for the populations of 12 countries.
(i) Compute Spearman's rank correlation coefficient.
(17) 100000 population
[D4]
(ii) Interpret the result from question b(i) above.
In which of the scenarios below would it be appropriate to use a One-way Analysis of Variance (ANOVA) method to determine whether or not there is a statistical difference among the groups? Select all that apply. Select all that apply:
You want to conduct a hypothesis test to determine if the average time a person sleeps is different from 8 hours.
You want to conduct a hypothesis test to determine if the average exam scores of a professor's morning, afternoon, and evening classes for one course are different.
You want to conduct a hypothesis test to determine if the average commute time to work is different in Boston, versus New York City, versus Los Angeles, versus Miami.
You want to conduct a hypothesis test to determine if people spend less than $150 a week on food.
The number of square feet per house have an unknown distribution with mean 1670 and standard deviation 140 square feet. A sample, with size n=48, is randomly drawn from the population and the values are added together. Using the Central Limit Theorem for Sums, what is the mean for the sample sum distribution? Provide your answer below:
□ square feet
QUESTION 5 - 1 POINT
A lottery scratch-off ticket offers the following payout amounts and respective probabilities. What is the expected payout of the game? Round your answer to the nearest cent.
\begin{tabular}{|c|c|}
\hline Probability & \begin{tabular}{c}
Payout \\
Amount
\end{tabular} \\
\hline 0.724 & $0 \\
\hline 0.225 & $10 \\
\hline 0.05 & $5,000 \\
\hline 0.001 & $20,000 \\
\hline
\end{tabular} Provide your answer below:
\\square$
FEEDBACK
7. Harold wants to build five identical pigpens, side by side, on his farm A using 30 m of fencing. Determine the dimensions of the enclosure that would give his pigs the largest possible area. Calculate this area.
QUESTION 11 - 1 POINT
Will, an art student, randomly sampled oil paintings in a museum. He wanted to find out how many oil paintings in the museum contained the color ultramarine blue. The proportion of paintings that were created using the color ultramarine blue was 0.17 , with a margin of error of 0.02 . Construct a confidence interval for the proportion of oil paintings that contained ultramarine blue. Provide your answer below:
□ , □)
QUESTION 12 - 1 POINT
The questions on a test consist of 1 multiple choice, 2 essays, and 10 free responses. If the questions are ordered randomly, what is the probability that the first question is a free response? Give your answer as a simplified fraction. Provide your answer below:
□
FEEDBACK
Fill in the blanks below. Find the slope of the line passing through the points (−7,−3) and (5,−3).
slope: □ Find the slope of the line passing through the points (3,9) and (3,−6).
slope: □
7) Joy's monthly statement includes the following items:
- previous balance: $1638.92
- payment: $650.00
- purchases: \879.54−minimummonthlypaymentcorrespondstoatleast5 \%ofherendingbalanceor\10.00 whichever is greater.
a) Calculate Joy's new balance.
b) Calculate Joy's minimum monthly payment.
To find the distance AB across a river, a surveyor laid off a distance BC=351m on one side of the river. It is found that B=115∘30′ and C=13∘15′. Find AB. The distance AB across the river is □ m
(Simplify your answer. Do not round until the final answer. Then round to the nearest whole number as needed.)
7xx=4=4(7)
: MULTIPLE CHOICE QUESTION El número 7 en esta ecuación, que tipo de operacion matematica está ocurriendo.
División
Suma
Resta
Multiplicación
A triangular building is bounded by three streets. The building measures approximately 92 feet on the first street, 193 feet on the second street, and 179 feet on the third street Approximate the ground area A covered by the building
A≈□ square feet
(Round to the nearest hundredth as needed )
A triangular building is bounded by three streets The building measures approximately 92 feet on the first street, 193 feet on the second street, and 179 feet on the third street Approximate the ground area A covered by the building A』 □ square feet
(Round to the nearest hundredth as needed)
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 6 g of gas at 271 K . Flask A contains H2, flask B contains CH4, and flask C contains He. Rank the flask contents in terms of the following: Part 1 of 6
pressure: A>C>B□ . Part 2 of 6
average molecular kinetic energy: □C>A>B J □ Part 3 of 6
diffusion rate after valve is opened: A=B=C□
1. Qual è quella giusta? In un triangolo ABC qual è l'altezza relativa al lato AB ?
(A) Il segmento passante per C parallelo al lato opposto AB.
(B) La retta perpendicolare al lato AB passante per il vertice C.
(c) Il segmento di perpendicolare condotto dal vertice C al lato opposto AB.
Application
Trig Assignment 2
November 28, 2024 1. An airplane flies 210 km due south from airport A and then is diverted on a bearing of 31∘ towards airport B. Airport B is 120 km away from airport A.
[ 4, 4 marks]
a) On what bearing is airport B from airport A , to the nearest degree?
b) How far is the airplane from airport B , to the nearest kilometre?
12) Sketch the function y=−[(x−2)]4+12. Use the mapping formula applied to 5 key points to sketch
[A-5]
13) Write the equation of the transformed parent function y=x3.
[A-5] Simplify your answer. Show your work.
Try Again
Your answer is incorrect. A company has both male and female employees. The company has shirts and jackets with the company logo to give away to employees. For each of the company's 196 employees, a manager asked which piece of clothing the employee prefers. The preferences, based on gender, are summarized in the tab below.
\begin{tabular}{|c|c|c|}
\cline { 2 - 3 } \multicolumn{1}{c|}{} & Shirt & Jacket \\
\hline Male & 34 & 88 \\
\hline Female & 8 & 66 \\
\hline
\end{tabular} Suppose an employee of the company is chosen at random.
Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.
(If necessary, consult a list of formulas.)
(a) What is the probability that the employee prefers a jacket?
□
(b) What is the probability that the employee is female or prefers a jacket?
□
Requirements discovery is the process of gathering information about the required and existing systems and distilling the user and system requirements from this information. Select one:
True
False
Question 3 (1 point)
Which one of the following is true?
Every linear system of 4 equations in 5 unknowns has infinitely many solutions.
Every homogeneous linear system of 4 equations in 5 unknowns has infinitely many solutions.
Every linear system of 5 equations in 4 unknowns has infinitely many solutions.
Every linear system of 5 equations in 5 unknowns has infinitely many solutions.
Every homogeneous linear system of 5 equations in 4 unknowns has infinitely many solutions.
4. Write each of the following as a simplified rational expression.
a) 2c−6c+2
b) 3a+2+5a−3
c) 4t−2−5t−3
d) 42y−3−7y+4
e) 32x−3−95−2x
f) 4x+6x+3+23x 5. Simplify the following.
a) 2−5y−5
b) 123a+4−1
c) 7t−t−3t−3
Solve the triangle.
a=7.232 in c=6.525 in B=73.27∘ What is the length of side b ?
□ in
(Round to the nearest thousandth as needed.)
What is the measure of angle A?
□
(Round to the nearest hundredth as needed.)
What is the measure of angle C?
□
(Round to the nearest hundredth as needed.)
Given the following break-even analysis, Break-Even Analysis
what is the fixed cost of outsourcing production?
Between \$0 and \$100,000.
Between \$100,000 and \$300,000.
Between \$300,000 and \$800,000.
It is not possible to determine from the graph shown in the question.
Aufgabe 2
Untersuchen Sie rechnerisch, ob der Graph der Funktion f achsensymmetrisch zur y-Achse oder punktsymmetrisch zum Ursprung ist.
a) f(x)=x4−x2
b) f(x)=sin(2x)
c) f(x)=cos(x)+1
d) f(x)=x4
e) f(x)=x32+x3
f) f(x)=x3⋅x5 Aufgabe 3
Untersuchen Sie, ob der Graph der Funktion f eine Symmetrie zum Koordinatensystem aufweist. Überprü̈ Sie Ihr Ergebnis mit einem Funktionenplotter.
a) f(x)=sin(x1)
b) f(x)=(x−2)2+1
c) f(x)=sin(x)cos(x)
d) f(x)=(sin(x))2
e) f(x)=x2x−1
f) f(x)=x2x2−1
9. La mesure d'un des angles égaux d'un triangle isocèle correspond à deux fois la mesure du troisième angle. Détermine la mesure exacte (en radians) des trois angles du triangle. Fonctions avancées 12 - Chapitre 4