On effectue une augmentation de 8% puis une augmentation de 13%. Détermine l'évolution globale. Ta réponse:
L'évolution globale est une diminution de .... \%
Complète ta
réponse:
diminution -
Arrondi à
l'unité près.
4. Given the line whose equation is 2y−6x=10, for every one unit of increase in x, which of the following is true about y ? (Hint, rearrange into y=mx+b form first.)
(1) y decreases by 6
(2) y increases by 3
(3) y increases by 2
(4) y decreases by 10
Written Lab Task \#3
Due Date: Friday, December 6 at 11:59 PM Mountain Time Upload your solution to Gradescope [Video on how to submit] Question:
The following is a transcription of a real conversation with ChatGPT (the artificial intelligence language model that has been in the news lately) that Jerrod had on January 25, 2023. User input: "How do you integrate f(x)g(x) ?"
ChatGPT: "To integrate f(x)g(x), use the product rule of integration. The product rule states that:
∫f(x)g(x)dx=(∫f(x)dx)⋅(∫g(x)dx)+C
where C is the constant of integration.
It's important to note that this formula only holds if both f(x) and g(x) can be integrated individually. If that's not the case, you may have to use other integration techniques."
(a) Two real-valued functions F(x) and G(x) are not equal if either they have different domains, or if they have the same domain and there is a number x=a so that F(a)=G(a).
Show that F(x)=x1 is not equal to G(x)=ln∣x∣. Note that F and G have the same domain.
(b) Choose non-constant functions f(x) and g(x) and use them to demonstrate that ChatGPT is incorrect.
Do this by computing the righthand side of the above equation to obtain a function h(x) and then showing that h(x) is not an antiderivative of the product function f(x)g(x). That is, show that h′(x) is not equal to f(x)g(x).
(c) For the functions f(x) and g(x) that you chose in part (b). Compute ∫f(x)g(x)dx correctly.
(Optional Challenge) Claudia chose g(x)=cos(x). You get to choose any non-constant function f(x).
Now compute ∫f(x)g(x)dx correctly.
Reminder: Explain your answers using good notation, organized calculations, and a few full sentences.
(C)University of Calgary
5.2
112
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Question 26, 5.2.53
>
Find the measure of the side of the right triangle whose length is designated by the lower case letter c.
HW Score: 67.65%, 23 of 34 points
O Points: 0 of 1
B
T
向
Save
C
23 m
C
ப
33°
A
13. A submarine descends to a depth of 660 feet below the surface in 11 minutes. At this rate, what integer represents the change, in feet, of the submarine's position after one minute? (Example 2)
Andrew walked 24 laps during a walkathon to raise money for his school's art department. Each lap was 41 of a mile, and Andrew's dad donated $5.25 for every mile that Andrew walked. How much money did Andrew's dad donate?
\\square$
The formula for the surface area of a rectangular prism with a square base is SA=2s2+4sh. What is the surface area of this rectangular prism if s=3 a h=5 ?
CLEAR
Un minerai fournit 20 \% de sa masse en fonte. Quelle quantité de minerai faut-il pour obtenir 1560 kg de fonte?
On donnera la réponse sous la forme d'un entier positif ou d'un nombre décimal arrondi au centième suivi de l'unitéqui convient.
Valider
Suivant
A container is in the shape of a hollow inverted right circular cone of height 60 cm and radius 12 cm . The container, which is initially empty, is placed, with its axis vertical, under a tap where water is flowing in at the constant rate of kcm3/s. The rate at which the height of the water in the container is rising 12 minutes after it was placed under the tap is 601cm3/s. Calculate the value of k.
k=□ Expected answer:
(108/125)pi
125108π
Reason Abstractly During a test flight, Jeri's rocket reached a height of 18 yards above the ground. This was 7 yards less than the height that Devon's rocket reached. Did Devon's rocket reach a height greater than 23 yards? Explain.
Choose the best answer and explanation.
A) no; If I solve the equation x−7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18−7, or 11 yards. Because 11<23, Devon's rocket did not reach a height greater than 23 yards.
B) no; If I solve the equation x+7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18−7, or 11 yards. Because 11<23, Devon's rocket did reach a height greater than 23 yards.
C) yes; If I solve the equation x−7=18 to find the height that Devon's rocket reached, I find that Devon's rocket reached a height of 18+7, or 25 yards. Since 25>23, Devon's rocket did reach a height greater than 23 yards.
D) yes; If I solve the equation x+7=18 to find the height that Devon's rocket reached, Ifind that Devon's rocket reached a height of 18+7, or 25 yards. Because 25>23, Devon's rocket did reach a height greater than 23 yards.
A tank of water is connected to a tank of compressed air that produces a gauge pressure Pgauge =2.5×104Pa above the water. A small hole is opened in the side of the tank at a depth d=2.0m below the surface of the water and H=3.0m above the ground. Water leaves the hole moving parallel to the ground. What is the distance R that the water travels from the tank? You may assume atmospheric pressure outside the tank and that the diameter of the hole is very small compared to the diameter of the tank.
Last month, Ed spent $50 in all. He spent 40% of the money at the movies. How much money did Ed spend at the movies? Pick the model that represents the problem. How much money did Ed spend at the movies?
\$
Mara Stratton
12/03/24 6:28 PM
Question 6, 10.3.21-T
HW Score: 47.62%,20 of 42 points
lomework
Part 4 of 5
Points: 0 of 2
Save The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 86.8 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below.
\begin{tabular}{|c|c|}
\hline 105.8 & 82.9 \\
66.1 & 96.3 \\
59.6 & 85.3 \\
76.2 & 72.3 \\
65.2 & 80.3 \\
\hline
\end{tabular} Click the icon to view the table of correlation coefficient critical values.
(b) Is the new system effective? Conduct a hypothesis test using the P -value approach and a level of significance of α=0.01. First determine the appropriate hypotheses.
H0:μ=86.8H1:μ=86.8 Find the test statistic.
t0=−1.73
(Round to two decimal places as needed.)
Find the P -value.
The P-value is □ .
(Round to three decimal places as needed.) Time (sec)
3
xample
Get more help -
Clear all
Final check
Find the sum of the pair of complex numbers.
21+65i,65+21i The sum is □ .
(Simplify your answer. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expressic
Question 4 (1 point)
The function y=−3sinx+1 has an amplitude of -3 .
True
False Question 5 (1 point)
The graph of the function y=sinπx has a period of 2 .
True
False Question 6 (1 point)
The trigonometric equation cos2x−sin2x=0 has the same solutions as the trigonometric equation cos2x=0.
True
False
Part 5 of 6
Points: 0 of 1 A simple random sample of size n is drawn. The sample mean, xˉ, is found to be 17.9 , and the sample standard deviation, s, is found to be 4.2 .
(a) Construct a 95% confidence interval about μ if the sample size, n , is 34 . Lower bound: 16.43 ; Upper bound: 19.37
(Use ascending order. Round to two decimal places as needed.)
(b) Construct a 95% confidence interval about μ if the sample size, n , is 61. Lower bound: 16.83 ; Upper bound: 18.98
(Use ascending order. Round to two decimal places as needed.)
How does increasing the sample size affect the margin of error, E?
A. The margin of error increases.
B. The margin of error decreases.
C. The margin of error does not change.
(c) Construct a 99\% confidence interval about μ if the sample size, n , is 34 . Lower bound: 15.93; Upper bound: 19.87
(Use ascending order. Round to two decimal places as needed.)
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?
A. The margin of error decreases.
B. The margin of error does not change.
C. The marnin of error increases
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
REASONING
a. Rewrite 2x+46x4+2x2−16x2+24x+32 as q(x)+d(x)π(x) using long division.
2x+46x4+2x3−16x2+24x+32=□∫x3−□x2+□∫x+□ , remainder
□ Part B
b. What does the remainder indicate in this problem? Because the remainder is Select Choice v,2x+4 is a Select Choice v of 6x4+2x3−16x2+24x+32.
□
Algebra II 3. Write an equation for the line perpendicular to y=4x−3 through the point (2,0) using point-slope form, then simplify into standard form.
y=4x−3
8. The tape diagram shows the ratio of the hours of work done by you and a friend. Ypeand your frie worked a total of 24 hours. How many hours did you work? You:
\begin{tabular}{|c|c|c|c|}
\hline 4 & 5 & e & ln \\
\hline
\end{tabular} Your friend: □
Question 1 of 12, Step 1 of 2
Correct The price of a meal plus a 12% delivery charge comes to a total cost of $16.80. What was the price of the meal? Step 1 of 2: Describe the above situation as a linear equation using " x " or " y " as variable names to describe the unknowns.
A Exploring Rati...
BOOKMARK
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ANSWER
AY HOL...
LAY
STOP A notebook costs $4.50 plus sales tax. After sales tax, the notebook is $4.86. What is the sales tax rate?
Question 49 (1 point)
Matthew is trying to figure out which value for x is NOT a solution for tanx=0. Do you have an answer? Choose one.
a) −3π
b) 0
c) 2π
d) 2π
Find the best predicted value of y given that x=5 for 6 pairs of data that yield r=0.444,yˉ=18.3 and the regression equation y=2+5x. State the critical level.
Figure it
thomure 6 In Figure 1, a person uses a pulley to lift a bell. The person pulls down on the rope at a constant speed. Power P1 is delvered to the bell and it moves upward at a constant speed. In Figure 2, the person uses a double pulley. The person pulls down on the rope at the same constant speed. The bell again moves upward at a constant speed, but the speed of the bell is half the speed of the bell in Figure 1 . The power delivered to the bell in Figure 2 is P2. Which of the following correctly compares P2 to P1 and provides a valid justification?
(A) P2<P1, because in Figure 2 the force exerted on the bell is the same but it is moving with less speed than in Figure 1.
(B) P2<P1, because in Figure 2 the force exerted on the bell is less than in Figure 1.
(C) P2=P1, because in Figure 2 the speed is half that in Figure 1 , but the force on the bell is twice that in Figure 1.
(D) P2=P1, because in Figure 2 the person is doing the same amount of work on the bell as in Figure 1.
Word problem involving the volume of a sphere BeeBright is a company that makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 15 cm . If the company uses, on average, 34,325cm3 of wax each hour making candles, how many candles does the company make, on average, each hour? If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the π button on the ALEKS calculator. Round your answer to the nearest hundredth.
candles
Think About the Process Karen purchased a DVD player on sale. The original selling price was $179.30. The sale price was $154.15. What is the first step in finding the percent markdown? Find the percent markdown. What is the first step in finding the percent markdown?
A. Find the markdown.
B. Find the cost.
C. Find the greatest markdown possible. The percent markdown was □ \%. (Round to the nearest whole number as needed.)
Kaitlin's company makes solid spherical metal balls for various industrial uses. A customer wants copper balls that have a diameter of 3 in. If Kaitlin must make 90 of these balls, how much copper will she need? If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the π button on the ALEKS calculator. Round your answer to the nearest hundredth.
□3
Kevin's company makes solid spherical balls out of scrap metal for various industrial uses. A large order just came in to make copper balls with a radius of 3 in. If Kevin uses, on average, 33,912 in 3 of copper each day making these balls, how many balls does he make, on average, each day?
If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the π button on the ALEKS calculator. Round your answer to the nearest hundredth.
□ balls
Next question
Get a similar question You can retry this question oetow The population of a country was 119 million in 1982 and the continuous exponential growth rate was estimated at 3.5% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1997. Round your answer to 1 decimal place.
The approximate population in 1997 is □ million people
Enter an integer or decimal number [more..]
Problem Solving
Write the correct answer. 1. In 2002, U.S. consumers bought about 8.1 million new cars. In 2003, that number decreased by about 6%. To the nearest hundred thousand, or tenth of a million, how many new cars did U.S. consumers buy in 2003? 7500000
Mayumi rides her bike around a park. Each lap around the park is 32 mi. Mayumi rides a total of 3 mi . How many laps around the park does Mayumi ride? Write your answer as a whole number of laps, plus a fraction of a lap. You can use the model to help. Mayumi rides whole laps, plus ? of a lap.
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{3}{|c|}{⋅⋯} & x \\
\hline 7 & 8 & 9 & x \\
\hline 4 & 5 & 6 & - \\
\hline 1 & 2 & 3 & - \\
\hline 0 & & -1 & □ \\
\hline
\end{tabular}
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Dec 3
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4.5 Exponential and Logarithmic Equations and Applications
Question 8 of 26 (2 points) I Question Attempt: 2 of Unilimited
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13 Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
2t=19
There is no solution, }.
The exact solution set is □ \}
t≈□
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|l|}{} \\
\hline □ln□ & □log□ & log D \\
\hline ㅁ & □□ & □ \\
\hline × & & 5 \\
\hline
\end{tabular}
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6:56
Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
2700=16,200e−0.2x
There is no solution, \{\}.
The exact solution set is □}.
x≈□
Solve for x.
−2+x32=x−x3 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
x=□
No
solution
1□ □,□,…
Measurement
Word problem involving a conversion between U.S. Customary units of ... Rachel is ordering 3 bags of cat food from Canada. Each bag has a mass of 5 kg . To determine the shipping costs, Rachel needs to know the total weight in pounds. What is the weight of the cat food in pounds? Use 1kg=2.2lb and do not round any computations.
□ 16
PRACTICE 4 Make Sense of Problems Mauricio hits a baseball 4 times as often as Tony each game. He also hits 20 baseballs every Monday at practice. How many baseballs will Mauricio hit this week if Tony hits 4 balls at the game Saturday?
A leader of two support groups tests depression levels. Group 1 mean: μ1=15, Group 2 mean: μ2=11. Find the weighted mean. Then, for alcohol use, Group 1 mean: μ1=16, Group 2 mean: μ2=18. Find the weighted mean.
Weiland Company has sales =$154,500, costs =$81,600, other expenses =$4,900, depreciation =$10,600, interest =$8,100, taxes =$17,255, dividends =$7,350. They issued \$ 2,900 in equity and redeemed \$ 4,500 in debt. Find:
a. operating cash flow
b. cash flow to creditors
c. cash flow to stockholders
d. addition to NWC if fixed assets increased by \$ 20,400. Round to the nearest whole number.
What was Rottweiler Obedience School's net capital spending for 2022 given net fixed assets of \$1,795,000 and \$2,180,000 with \$335,000 depreciation? Round to the nearest whole number.
Bing, Inc. has assets of \$2,270 (current) + \$10,300 (fixed) and liabilities of \$1,400 (current) + \$4,080 (long-term). Find:
a. Shareholders' equity
b. Net working capital