Rewrite the following fractions as partial fractions using the given formats.
(a) x2+3x−28x−1=F1(x)A1+F2(x)A2
where A1 and A2 represent constants.
F1(x)=F2(x)=
A rectangular bird feeder costs $18.00. A cylindrical bird feeder costs $24.00. The expected cost to keep the rectangular bird feeder filled is $3.00 per week. The expected cost to keep the cylindrical bird feeder filled is $2.00 per week. The equation models the break-even point.
18+3x=24+2x What does x represent?
the total cost to fill the rectangular bird feeder the total cost to fill the cylindrical bird feeder after
the number of weeks the after any number of weeks any number of weeks bird feeders are filled Y
the number of bird feeders purchased each week
Ali sedang merenovasi rumahnya. la membeli 5 buah paralon berdiamater sama di sebuah toko bangunan. Paralon tersebut diangkut menggunakan mobil pick up. Agar menghemat tempat, paralon-paralon tersebut diikat menggunakan sebuah tali pada pangkal dan ujung paralon (seperti tampak pada gambar). Jika Panjang tali minimal yang diperlukan untuk mengikat 5 paralon tersebut 325,6cm, maka panjang diameter tiap paralon adalah....
㸚, Solve for k.
11k2−5k=0
(xi. Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
k=
Submit
2 Chelsea spent the same amount of time writing in a journal every day for 14 days. She wrote in the journal for a total of 3.5 hours, as shown in the diagram below. How much time did Chelsea spend writing in the journal each day?
(F) 2.5 h
(H) 0.37 h
(G) 0.24 h
(3) 0.25 h
11
B
I
U
A
Name: Exponential Growth/ Exponential Decay
Date: Period:
d. In how many days total will the video stop being a fan favorite? The typical student loan has an interest rate of approximately 5%. This means a $20,000 loan paid off over 10 years will end up costing you $28,900 The New Jersey Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated. Create an equation that represents the number of teams, t, that remained in the tournament after r rounds. I
The equation −7(w−3)=70 is solved in several steps below.
For each step, choose the reason that best justifies it.
\begin{tabular}{|c|l|}
\hline Step & Reason \\
\hline−7(w−3)=70 & Given equation \\
\hline−7−7(w−3)=−770 & "Choose one" \\
\hlinew−3=−10 & "Choose one" \\
\hlinew−3+3=−10+3 & \begin{tabular}{l}
Sddition Property of Equality \\
Subtraction Property of Equality \\
Multiplication Property of Equality \\
Division Property of Equality \\
Simplifying
\end{tabular} \\
\hline & \begin{tabular}{l}
Distributive Property
\end{tabular} \\
\hline
\end{tabular}
Express the following equations in logarithmic form:
(a) 52=25 is equivalent to the logarithmic equation:
□
(b) 10−3=0.001 is equivalent to the logarithmic equation:
□
The equation −7(w−3)=70 is solved in several steps below.
For each step, choose the reason that best justifies it.
\begin{tabular}{|c|l|}
\hline Step & Reason \\
\hline−7(w−3)=70 & Given equation \\
\hline−7−7(w−3)=−770 & "Choose one" \\
\hlinew−3=−10 & "Choose one" \\
\hlinew−3+3=−10+3 & "Choose one" \\
\hlinew=−7 & "Choose one" \\
\hline
\end{tabular}
Jack is a great chess player. He wins 76% of the games. He is scheduled to play 120 games this year. What is the expected number of games that he will lose?
"ints A. Assessmentic
1 For a school celebration, Principal Johnson purchased a large sheet cake that was cut into 100 pieces. She kept 8 pieces for the office staff and divided the remaining pieces equally among the 4 fifth-grade classes. The shaded diagram below shows the part of the cake that was given to the classes. Which equation shows the part of the cake each class received?
(A) 100÷4=25
(B) 0.92÷4=0.23
(c) 0.08÷4=0.02
(D) 0.92÷4=23
Solve the equation on the interval 0≤θ<2π.
(cotθ−1)(cscθ−1)=0 Select the correct choice below and fill in any answer boxes in your choice.
A. The solution set is □ \}.
(Simplify your answer. Type an exact answer, using π as needed. Type your answer i any numbers in the expression. Use a comma to separate answers as needed.)
B. There is no solution on this interval.
10. If secθ=2 and 0≤θ≤2π, determine the exact value(s) of cscθ. Include a diagram. 11. If sinθ=−1 and π≤θ≤2π, determine the exact value(s) of cosθ and cotθ. Include a diagram. 12. If cosθ=−53 and sinθ<0, determine the exact value(s) of cscθ. Include a diagram. 13. Solve for θ given tanθ=−3 for −2π≤θ≤2π 14. Solve for θ given cotθ=5 for −π≤θ≤π
Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850 , with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is lower than the cutoff of 720 . She finds that a random sample of 55 people had a mean FICO score of 685 with a standard deviation of 80 . Can the economist conclude that the mean FICO score is less than 720 ? Use the α=0.10 level of significance and the P-value method with the TI-84 Plus calculator. Part: 0/5□ Part 1 of 5
(a) State the appropriate null and alternate hypotheses.
H0:□H1:□ This hypothesis test is a □ (Choose one) test. □
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warch a vides Helen made a scale drawing of an office building. A desk, which is 6 feet long in real life, is 2 inches long in the drawing. What scale did Helen use for the drawing? 1 inch : □ feet Subrit
The population of deer in South Bend, Tennessee is being monitored for research purposes. There were 56 deer tagged initially in January 2023. Researchers found the deer growing at a monthly rate of 3.5%, which can be represented by the model: y=56e.035t. Following this trend, how many months did it take for the deer population to reach 103. Round up.
En la siguiente figura, m∠MKJ=137∘.
(a) Escribir una ecuación para hallar x. Asegurarse de utilizar un signo de "=" en su respuesta. Ecuación: □
(b) Resolver para x.
□x=
Lola drew a scale drawing of a city park. The soccer field is 232 millimeters long in the drawing. The actual field is 116 meters long. What is the scale of the drawing? 2 millimeters : □ meters
Submit
Utilizar la figura para hallar el valor de x.
(a) Escribir una ecuación para hallar x. Asegúrese de utilizar un signo de " = " en la respuesta. Ecuación: □□
(b) Resolver para x.
x=1□
a) What does the differential equation y′(x)=−7∗y(x) tell us about the graph of y against x (the conventional way to plot x and y )?
(Clear my choice)
The slope of y against x is always -7 times the y-coordinate.
The slope of y against x is always -7 times the x-coordinate.
The rate of change of x is always -7 times the x-coordinate.
The slope of y against x is always -7
The slope of y against x is always −1/7 times the y-coordinate.
En la figura, m∠1=(8x)∘ y m∠2=(x−9)∘.
(a) Escribir una ecuación para hallar x. Usar el signo de " = " en la respuesta. Ecuación: □
(b) Calcular la medida en grados de cada ángulo.
m∠1=□∘m∠2=□∘
Moneysaver's Bank offers a savings account that earns 5% interest per year, compounded continuously. If Michael deposits $2600, how much will he have in the account after seven years, assuming he makes no withdrawals? Do not round any intermediate computations, and round your answer to the nearest cent.
\【I\square$
The point (585,241) lies on the graph of a linear function that represents a proportional relationship.
Part A
Write an equation for this function. What is the slope?
Boyle's Law involves the pressure and volume of gas in a container. It can be represented by the formula P1V1=P2V2. When the formula is solved for P2, the result is
1) P1V1V2
2) P1V1V2
3) V2P1V1
4) V1P1V2
When solving for the value of x in the equation 4(x−1)+3=18, Aaron wrote the following lines on the boarc
[line 1]
4(x−1)+3=18
[line 2]
4(x−1)=15
[line 3]
4x−1=15
[line 4]
4x=16
[line 5]
x=4 Which property was used incorrectly when going from line 2 to line 3 ?
1) distributive
3) associative
2) commutative
4) multiplicative inverse
Suppose the amount of a certain radioactive substance in a sample decays from 5.20 mg to 1.90 mg over a period of 6.21 minutes. Calculate the half life of the substance. Round your answer to 2 significant digits.
□□×10
- Student A drives a car and hits other causes a loss of \12,000−Theinsurancefeaturesareasfollwing.−1.Ifdriverhitsothersonpurpose,nopayment.−2.Otherwises,themaximumis\9,000
- 3. The customer should pay $1,200 from their own pocket.
- 4. The copayment rate is 16%.
- How much can A claim from insurance company?
Kala-needs $8346 for a future project. She can invest $6000 now at an annual rate of 3.4%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project? Do not round any intermediate computations, and round your answer to the nearest hundredth.
□
years
Find the solution of the exponential equation 13ex−19=12
The exact solution, in terms of the natural logarithm is: x=□
The approximate solution, accurate to 4 decimal places is: x=□
Indium-116 is radioactive and has a half life of 14.10 seconds. What percentage of a sample would be left after 48.7 seconds?
Round your answer to 2 significant digits. 形 %□×10
1. You can write an equation to solve comparison problems. An equation is a number sentence that uses the equal sign ( = ) to show that two expressions have the same value. Phrases, such as times as many as or more than, can be used to compare quantities. Compare with Multiplication
There are 6toys and 3 times as many books. How many books, b, are there? Compare with Addition
There are 6 toys. There are 12 more books than toys. How many books are there?
b=3×6b=6+12b= books
b= books
7. Power lines 12 m from the ground carry 4.50×103A of current across a farmer's field. What magnetic field strength do the cattle directly underneath experience? ( 3 marks)
Part 2:
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\end{tabular} 1. If the entire grid has a value of $100, what is the value of each small square in the grid? 2. If the entire grid has a value of $100, what is the value of 10 small squares in the grid? 3. If the entire grid has a value of $200, what is the value of each small square in the grid? 4. If the entire grid has a value of $200, what is the value of 10 small squares in the grid? 5. If the entire grid has a value of $80, what is the value of each small square in the grid? 6. If the entire grid has a value of $80, what is the value of 10 small squares in the grid? 7. If the entire grid has a value of $120, what is the value of each small square in the grid? 8. If the entire grid has a value of $120, what is the value of 10 small squares in the grid? 9. If the entire grid has a value of $24, what is the value of each small square in the grid? 10. If the entire grid has a value of $24, what is the value of 10 small squares in the grid?
6WB2 - 10
e2014 University of Utah Middle School Math Project in partnenthip with
Find the equation of the exponential function represented by the table below
\begin{tabular}{|c|c|}
\hlinex & y \\
\hline 0 & 5 \\
\hline 1 & 2.5 \\
\hline 2 & 1.25 \\
\hline 3 & 0.625 \\
\hline
\end{tabular} Answer Attempt 1 out of 2
CL 3-113. Two brothers, Martin and Horace, are in their backyard. Horace is taking down a brick wall on one side of the yard while Martin is building a brick wall on the other side. Martin lays 2 bricks every minute. Meanwhile, Horace takes down 3 bricks each minute from his wall. They both start working at the same time. It takes Horace 55 minutes to finish tearing down his wall.
a. How many bricks were originally in the wall that Horace started tearing down?
b. Represent this situation with equations, tables, and a graph.
c. When did the two walls have the same number of bricks?
Exponential and Logarithmic Functions
Finding the time in a word problem on compound interest Suppose that $2000 is placed in a savings account at an annual rate of 10.8%, compounded monthly. Assuming that no withdrawals are made, how long will it take for the account to grow to $3130 ? Do not round any intermediate computations, and round your answer to the nearest hundredth.
□
years
7. The area of the trapezoid is 40 square millimeters.
a. Find two possible values for each base length.
b. Is it possible for b2 to equal 9 millimeters? Explain.
Solve.
x=7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x=□
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
B. The solution set is the empty set.
The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 16% per hour. Suppose that a sample culture has an initial population of 268 bacteria. Find the population predicted after three hours, according to the model. Do not round any intermediate computations, and round your answer to the nearest tenth.
□ bacteria
Question 6 (1 point)
Solve 3cscx+2=0 on the interval x∈[0,2π], to the nearest hundredth of a radian.
a) x≐1.05,x≐2.09
b) x≐4.19,x≐5.24
C) x=60,x=120
d) x=240,x=300
an wof find What is the
? 16. Stancha diganith Ste has 28 magness Sne amanges the magness impo 4 equal couss wite an equarion using a lener to = equesent the urkioum value to find how thand magness are in each rour.
One can convert temperature from Kelvin into Fahrenheit using the formula F=59(K−273)+32. What is the temperature in Kelvin corresponding to F degrees Fahrenheit?
A. 59(F−273)−32
B. 95(F−32)+273
C. 59(F−32)+273
D. 95(F−32)−273
Question 13 (1 point)
Solve 2sinx+1=0 on the interval x∈[0,2π], to the nearest hundredth of a radian.
a) x=210,x=330
b) x≐0.52,x≐2.62
C) x=30,x=150
d) x≐3.67,x≐5.76
Tell which property of equality was used.
5353×61=w318=(w318)×61 Choose the correct answer below.
Multiplication Property of Equality
Subtraction Property of Equality
Addition Property of Equality
Division Property of Equality
Calculating equilibrium concentrations when the net reaction proceeds in reverse
Consider mixture C, which will cause the net reaction to proceed in reverse.
\begin{tabular}{lllll}
& & ← net & & \\
Concentration (M) & {[XY]} & ⇌ & {[X]} & {[Y]} \\
initial: & 0.200 & & 0.300 & 0.300 \\
change: ≶ & +x & & −x & −x \\
equilibrium: & 0.200+x & & 0.300−x & 0.300−x
\end{tabular} The change in concentration, x, is positive for the reactants because they are produced and negative for the products because they are consumed. Part C Based on a Kc value of 0.130 and the data table given, what are the equilibrium concentrations of XY,X, and Y , respectively?
Express the molar concentrations numerically.
View Available Hint(s)
□□AΣϕ[XY],[X],[Y]= M
?
Submit
Review
Constants
Pe MISSED THIS? Watch KCV 15.8, IWE 15.9; Read Section 15.8. You can click on the Review link to access the section in your eText. For the following reaction, Kc=255 at 1000 K . CO(g)+Cl2(g)⇌COCl2(g)
A reaction mixture initially contains a CO concentration of 0.1530 M and a Cl2 concentration of 0.172M at 1000 K . What is the equilibrium concentration of CO at 1000 K ?
Express your answer in molarity to three significant figures.
View Available Hint(s)
□
Submit Part B What is the equilibrium concentration of Cl2 at 1000 K ?
Express your answer in molarity to three significant figures.
View Available Hint(s)
□
Submit
Review
Constants What is the equilibrium concentration of CO at 1000 K ?
Express your answer in molarity to three significant figures. MISSED THIS? Watch KCV 15.8, IWE 15.9; Read
Section 15.8. You can click on the Review link to access the section in your eText. For the following reaction, Kc=255 at 1000 K . CO(g)+Cl2(g)⇌COCl2(g)
A reaction mixture initially contains a CO concentration of 0.1530 M and a Cl2 concentration of 0.172 M at 1000 K .
Katherin deposits \$75,000 in a 3-year CD account that yields 3.5\% interest, compounded weekly. What is the amount of his interest, to the nearest cent, at the end of 3 years?
Jo has 27 stickers and 6 model cars. She puts the same number of stickers on each car, and she uses as many stickers as she can. How many stickers does Jo put on each car? How many stickers are left? Does Jo have enough stickers to put 2 stickers on each car?
Figure 7. Typical WWTP energy consumers
Source: Malcolm Pirnie, the Water Division of ARCADIS https://www.nrel.gov/docs/fy12osti/53341.pdf
(Note: Other is the 1\%.)
A wastewater treatment plant used 327 KWh of electricity per day. How many KWh do they use for Pumps?
□
5 pts Question 4 Daniah deposits $4,000 in a savings account at New York State Bank that pays 5.4% interest, compounded monthly. What is the amount of interest at the end of the year?
A sinusoidal wave is traveling on a string with speed 107cm/s. The displacement of the particles of the string at x=16cm is found to vary with time according to the equation
y=(1cm)sin[0.84−(5.6s−1)t] The linear density of the string is 1.8g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t)=ymsin(kx−ωt),
what are (c) ym, (d) k, and (e) ω, and (f) the correct choice of sign in front of ω ? (g) What is the tension in the string?
2. Critical Thinking: Rhoda is saving up money for a down payment on a condominium. She currently has $2571 but knows she can get a loan at a lower interest rate if she can put down $3308. If she invests the $2571 in an account that earns 4.9% annually, compounded monthly, how long will it take Rhoda to accumulate the $3308 ?
Round your answer to two decimal places, if necessary.
5 pts Daniah deposits $4,000 in a savings account at New York State Bank that pays 5.4% interest, compounded monthly. What is the APY for this account to the nearest hundredth of a percent?
Guillermo finished 4 math problems. These problems represent 20% of the assigned math problems, as shown in the diagram. What is the total number of math problems Guillermo was assigned?
□ problems
□
In a poll of 510 human resource professionals, 45.9% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (d) below.
a. Among the 510 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags?
□ (Round to the nearest integer as needed.)
b. Construct a 99\% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags.
□<p<□
(Round to three decimal places as needed.)
c. Repeat part (b) using a confidence level of 80%.
□ < <<□
(Round to three decimal places as needed.)
d. Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider. Why is it wider?
proportion.
proportion.
proportion.
proportion.
Problem 33
Let X and Y be two random variables. Suppose that σX2=4, and σY2=9. If we know that the two random variables Z=2X−Y and W=X+Y are independent, find Cov(X,Y) and ρ(X,Y).
Two buildings in a sports complex are shaped and positioned like a portion of the branches of the hyperbola 625x2−225y2=140,625, where x and y are in meters.
(a) How far apart are the buildings at their closest point?
(b) Find the distance d in the figure.
(a) The two buildings are □ meters apart at their closest point.
(Type an integer or a decimal.)
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15 one Dicit DivisoRs
The teacher worked a total of 68 hours one school week (five days). She worked the same amount of time every day except for Thursday when she worked extra (your remainder). How many hours did she work each day? How many hours did she work Thursday?
Find the equation for the parabola that has its focus at the (45,−3) and h directrix at x=435.
equation is
(y+3)2=30(x−9.375)
Video 1
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Question 24 Suppose that $6500 is placed in an account that pays 17% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
\\square(b)Findtheamountintheaccountattheendof2years.$\square$
Manuel deposit \5,300intoabankaccountforsevenandahalfyears.Hecomparestwodifferentoptions.Option1willpay6.4 \%interest,compoundedsemiannually.Option2willpay6.4 \%interest,compoundedcontinuously.Manueldeposita\5.300 dólares en una cuenta bancaria durante siete años y medio. Compara dos opciones diferentes. La opción 1 pagará un interés del 6.4%, compuesto semestralmente. La opción 2 pagará un interés del 6.4%, compuesto continuamente. What is the ending balance of Option 1?
¿Cuál es el saldo final de la Opción 1? □
What is the ending balance of Option 2?
¿Cuál es el saldo final de la Opción 2? □
How much interest does Option 1 pay?
¿Cuánto interés paga la opción 1? □
How much interest does Option 2 pay?