Solve the equation. Give an exact solution.
log(7x+4)=log5 Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. The solution set is □ 3.
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
B. The solution set is ∅.
Example 6.10. In a triangulation survey, the station C could not be occupied in a triangle ABC, and a satellite station S was established north of C. The angles as given in Table 6.1 were measured at S using a theodolite. Table 6.1
\begin{tabular}{c|c}
\hline Pointing on & Horizontal circle reading \\
\hlineA & 14∘43′27′′ \\
\hlineB & 74∘30′35′′ \\
\hlineC & 227∘18′12′′ \\
\hline
\end{tabular} Approximate lengths of AC and BC were found by estimation as 17495 m and 13672 m , respectively, and the angle ACB was deduced to be 59∘44′53′′. Calculate the distance of S from C.
A proton (rest mass 1.67×10−27kg ) has total energy that is 3.4 times its rest energy. What is
a) the kinetic energy of the proton? b) the magnitude of the momentum of the proton?
□×10−18kg⋅m/s.
c) the speed of the proton?
□ c.
Cobra Limited, a manufacturing company commenced business on 1st November 2020 and prepares
accounts to 31st December each year. He purchased the following assets in the year 2020:Generator
GHC180,000, Refrigerator GHC9,000, Laptops GHC12,000, Office Building GHC1,500,000, Toyota Corolla
GHC55,000, Fittings & fixtures GHC60,000. It was also found out that the trademark of his company was
valued to be GHC50,000 with an estimated useful life of 10 years. What is the written down value for
trademark in the 2020 year of assessment?
OA GHC49,164
OB. GHC52,242
OC.GHC5,000
OD. GHC49,589
REQUIRED 14. Regina charges c dollars per hour to babysit. If she increases her rate by 15%, which expression represents her new rate, in dollars per hour?
c+0.15
c+15
c+0.15cc+15c Show Your Work
The histogram shows the number of miles that each adult, from a survey of 67 adults, drives per week. How many adults drive fewer than 200 miles per week? There are □ adults who drive fewer than 200 miles per week.
(arercise (11)
The number of elements of three sets A, B and E are distributed as shown in the adjoining figure. Calculate the value of x, in each of the following cases:
1) Card (A)=53.
2) Card (B)=37.
3) Card (E)=60.
4) Card(A∩B)=15.
5) Card(A∪B)=51. Brercise(12)
A survey was made on 500 customers in a store which sells only shirts and jackets. The result is presented below:
- 300 customers bought jackets; 240 customers bought shirts; 110 bought nothing.
1) How many customers bought jackets and shirts at the same time?
2) How many customers did not buy jackets?
3) How many customers bought at least one item?
Holden Corporation produces three products, with costs and selling prices as follows:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & \multicolumn{2}{|l|}{Product A} & \multicolumn{2}{|l|}{Product B} & \multicolumn{2}{|l|}{Product C} \\
\hline Selling price per unit & \$ 30 & 100\% & \$ 20 & 100\% & \$ 15 & 100\% \\
\hline Variable costs per unit & 18 & 60\% & 15 & 75\% & 6 & 40\% \\
\hline Contribution margin per unit & \$ 12 & 40\% & \$ 5 & 25\% & \$ 9 & 60\% \\
\hline
\end{tabular} A particular machine is the bottleneck. On that machine, 3 machine hours are required to produce each unit of Product A,1 hour is required to produce each unit of Product B, and 2 hours are required to produce each unit of Product C. Rank the products from the most profitable to the least profitable use of the constrained resource (bottleneck).
Note: Round your intermediate calculations to 2 decimal places.
13. Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?
What ta the GPA for a student who carned the grades shown below? The grades are based on a 4.0 point maximum
\begin{tabular}{|c|c|c|}
\hline Class & Credits & Grade \\
\hline Phys ISOC & 4 & B \\
\hline Phys Lab 160C & 1 & C \\
\hline Math 210A & 4 & B \\
\hline Hist 220A & 3 & D \\
\hline
\end{tabular}
2.41
3.63
2.50
2.42
Below is a graph of a normal distribution with mean μ=4 and standard deviation σ=2. The shaded region represents the probability of obtaining a value from this distribution that is between 2 and 5. Shade the corresponding region under the standard normal curve below.
Topic III Anticipating Patterns: Probability and Simulation 41. Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has 2 out of 10 chances of passing on any one attempt by pure luck. What is Elaine's likelihood of passing, provided that she willhave three attempts to pass the exam? (Assume the attempts are independent because she takes a different exam at each attempt.)
a. Explain how you would use a random digit table to simulate Elaine's attempts at the exam. Elaine will of course stop taking the exam as soon as she passes. 0−1=p25sing,2−cl=failing,100K at e
b. Simulate 10 repetitions using the random digits below. What is your estimate of Elaine's likelihood of passing the course?
59636625688880470206046344032571197036991935271080730892255384898114864578511776
Consider the following demographic data for a hypothetical state. Assume everyone votes along party lines.
The state has 16 representatives and a population of 8.4 million; party affiliations are 90% Democrat and 10% Republican. Complete parts (a) and (b) below.
a. If districts were drawn randomly, what would be the most likely distribution of House seats?
□ Republicans, □ Democrats
Answer the following.
(a) Find an angle between 0 and 2π that is coterminal with 511π.
(b) Find an angle between 0∘ and 360∘ that is coterminal with 815∘. Give exact values for your answers.
(a) Ifradians
π
(b) □∘
Solve for k.
36k2−13k+1=0 Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
k=□
11. Miguel's paycheck is $871.25. The paycheck includes 36.5 hours of work and a $50 bonus. How much does Miguel earn for each hour of work, not including the bonus?
2) ( 0,5 ponto) Um aluno do BCET precisa encontrar a temperatura de um arame quando o tempo t=0,01s. Ele sabe que a função T(t)=(1+2t)41 representa a temperatura do arame no instante 1. Como ele não tem uma calculadora, ele precisará estimar esse valor da temperatura. Use aproximaçāo linear para ajudá-lo a estimar o valor de T(0,01).
3) ( 0,5 ponto) Um pedregulho é jogado em um lago, gerando ondas cinculares concêntgricas. O raio r da ondulação externa aumenta a uma taxa constante de 1 pé por segundo. Quando o raio atingir 4 pés, a que taxa varia à área da onda?
4) ( 0,5 ponto) Quando uma pessoa tosse, o raio da traquéia diminui, afetando a velocidade do ar na traquéia. Se r0 é o raio normal da traquéia, a relação entre a velocidade v do ar e o raio r da traquéia é dada por uma funçāo da forma v(r)=ar2(r0−r), onde a é uma constante positiva. Determine o raio para o qual a velocidade do ar é máxima.
Jenny has a cone (diameter 20cm, slant height 60cm) and a pyramid (edges 4cm). Find the pyramid's surface area and how many pyramids can be made from the cone's volume.
Find point C where lines AC:y=−3x+6 and BC:y=3x−18 intersect. Calculate angle α with x-axis, prove △ABC is scalene, find midpoint P of AC, and determine the perpendicular bisector of AC.