Step-by-step explanation:
Prove the following?
cos7x+cos5x+cos3x+cosx=4cosxcos2xcos4x
2
SEE ANSWERS
Answer
3.4/5
36
LHS=cos7x + cos5x + cos3x + cosx
=2cos[(7x+5x)/2].cos[(7x-5x)/2] + 2cos[(3x+x)/2].cos[(3x-x)/2]
[∵ cosA + cosB = 2.cos[(A+B)/2].cos[(A-B)/2]]
=2cos[(12x)/2].cos[(2x)/2] + 2cos[(4x)/2].cos[(2x)/2]
=2cos 6x.cosx+2cos2x.cosx
=2cosx(cos 6x+ cos 2x)
=2.cosx(2cos[(6x+2x)/2].cos[(6x-2x)/2]
=2.cosx(2cos4x.cos2x)
=4.cosx.cos2x.cos4x
=RHS.
hope this helps you!!!!! :))))))))
Condense to a single logarithm: 4 log9 11 - 4 log9 7.
O log9, (44/28)
O log9, (11/7)^4
O log9, (11/28)
log9 (44/7)
Answer: Log9,(11/7)^4
Step-by-step explanation:
according to the rules of logarithm
1)Subtraction sign(-) becomes division(÷),while addition(+)becomes multiplication (x)
2) the number in front of the log figure becomes an indices
Answer:
log9 (11/7)4
Step-by-step explanation:
got it right on the test
Lucy, charlie, and Michael have a total of $95 in their wallet. Charlie has $10 more than lucy. Michael has 3 times what Lucy has. How much does each have?
This problem illustrates the limit derivation of a Poisson distribution from Binomial distributions. Suppose an average of 66 arrivals occur during a 30 minute interval. To count arrivals, divide the 30 minute interval into nn sub-intervals. On the previous problem, you found the probability pp of one arrival during a single sub-interval for each n given. Now, compute the (estimated) probability that there will be, in fact, exactly 6 arrivals during a 30 minute interval, with each probability model:
a. Using Binomial with n=30, the chance of 6 arrivals is estimated as:__________
b. Using Binomial with n=60, the chance of 6 arrivals is estimated as:__________
c. Using Binomial with n=100n=100, the chance of 6 arrivals is estimated as:________
d. Using Poisson, the chance of 6 arrivals is estimated as:________
Required:
Use a probability calculator, and enter answers in decimal form, rounded to at least four places after the decimal.
Answer:
1. 0.1795
2. 0.1693
3. 0.1657
4. 0.1606
Step-by-step explanation:
This problem was solved using the binomial distribution
1.
N = 30
P = 6/30 = 0.2
Using binomial distribution
30C6 x 0.2⁶ x 0.8²⁴
= 593775 x 0.000064 x 0.004722
= 0.1795
2.
N = 60
P = 6/60 = 0.1
60C6 x 0.1⁶ x 0.9⁵⁴
= 50063860 x 0.000001 x 0.00338139
= 0.1693
3.
N = 100
100C6 x 0.06⁶ x 0.94⁹⁴
= 1192052400 x 0.000000046656 x 0.00297864
= 0.1657
4.
Poisson distribution was used here
e^-6(6)⁶/6!
= 0.1606
Which statement describes the inverse of m(x) = x^2 – 17x?
a. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
b. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
c. The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
d.The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .
Given:
The function is
[tex]m(x)=x^2-17x[/tex]
To find:
The inverse of the given function.
Solution:
We have,
[tex]m(x)=x^2-17x[/tex]
Substitute m(x)=y.
[tex]y=x^2-17x[/tex]
Interchange x and y.
[tex]x=y^2-17y[/tex]
Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,
[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]
[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]
Add [tex]\dfrac{17}{2}[/tex] on both sides.
[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]
Substitute [tex]y=m^{-1}(x)[/tex].
[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]
We know that, negative term inside the root is not real number. So,
[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]
[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]
Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].
Hence, option D is correct.
Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.
Answer:
C on edu
Step-by-step explanation:
Christopher wanted to save some money. After 4 weeks, Christopher $50, and after 9 weeks, he saved $100. What was the average amount Christopher saved per week? * A.5 B.50 C.12.5 D.10
Step-by-step explanation:
I think 12.5 is the answer
The product of 3 consecutive integers is 4,896. What is the largest of the three consecutive numbers?
Answer:
18
Step-by-step explanation:
1. Try to create an equation. We can say that the first number is x and the following numbers are x+1 and x+2. That means that x*(x+1)*(x+2)=4896.
2. Solve and Simplify. x^3+3x^2+2x=4896.
3. Solve and Simplify (2) I'm assuming that you're not looking for the complex solutions, so x=16.
4. Find the 3rd number. 16+2=18
Answer: 18 is the largest number of the three
Find f(5). f(x) = x2 + 2x
Help please
Answer:
Your answer is: 15
Your equation would have f(5) = x^2 + 2x
Substitute the given value into the function and evaluate.
Step-by-step explanation:
Hope this helped ; )
Kyle invested $ 500 and received $ 650 after three years. What had been the interest rate?
Since Kyle invested $500 and received $650 after three years, the value of Kyles's interest rate is 43.3%.
Given the following data:
Principal = $500Simple interest = $650Time = 3 yearsTo calculate the value of Kyles's interest rate:
Mathematically, simple interest is given by the formula:
[tex]S.I = \frac{PRT}{100}[/tex]
Where:
S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.Making R the subject of formula, we have:
[tex]R = \frac{100S.I}{PT}[/tex]
Substituting the given parameters into the formula, we have;
[tex]R = \frac{100 \times 650}{500 \times 3}\\\\R = \frac{65000}{1500}[/tex]
Interest rate, R = 43.3%
Read more: https://brainly.com/question/22621039?referrer=searchResults
Check the statements that are true.
A. An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers.
B. A geometric sequence is a linear function whose domain is restricted to the set of non-negative integers.
C. An arithmetic sequence is an exponential function whose domain is restricted to the set of non-negative integers.
D. A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers.
Answer:
A and D.
Step-by-step explanation:
A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}
(A)
"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."
The general form an arithmetic sequence is:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.
So, the statement provided is True.
(D)
"A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers."
The general form an geometric sequence is:
[tex]a_{n}=a_{1}\cdot r^{n-1}[/tex]
The function is exponential. The sequence consists of either numbers that are exponentially increasing or decreasing by the factor r, the common ratio.
So, the statement provided is True.
Help me please!!..,,
Answer:
A.
Step-by-step explanation:
1.5 x 0.1 = 0.15
0.15 inches
Dont know if this is for sure right. Hope it is.
¿Cuál es la desigualdad de 3 x - 4> 4-4-3 x
Numbers with zeros
A cleaning service orders 7 large bottles and 5 small bottles of a cleaning product.
Each large bottle has 122 ounces. Each small bottle has 68 ounces.
Which is the best estimate of the total amount of cleaning product the cleaning service orders?
A 800 ounces
w
B. 1.200 ounces
C. 1,600 ounces
o
D. 2.000 ounces
whats 2 plus 2? do u know?
Find the value of 45\75=5
Answer:
.6
Step-by-step explanation:
IMPLAYER
Every day after ser daily walk, Dena drinks 1.06 liters of water. Which decimal is equivalent to 1.06?
A 1.6
O
B. 1.600
C. 1.060
D. 1.006
Answer:
C. 1.060
Explanation:
r Which decimal is equivalent to 1.06? Well, if you look at it, c. 1.060 is just 1.06 with a zero added at the end... And we all know zeros have no value. So you can technically just take off the zero at the end and have 1.06. But this is a multiple-choice so you don't get to choose whether or not to take the zero off. So yeah, the answer is c.
Please mark brainliest!
Solve each of the following equations for the missing variable.
-2.5x – 10 = 40
O x = 20
O x= -20
O 50
-50
Answer:
-20
Step-by-step explanation:
-2.5x = 40 + 10
- 2.5x = 50
x = 50/-2.5 = -20
Please help 60 Points!!!!!!!! my school is glitched :C
Answer:
its the two that are glitched because its not any of the other ones
Step-by-step explanation:
Answer:
reload
Step-by-step explanation:
what is the answer to the first one? pls help
Answer:
Step-by-step explanation:
14.75 - 8.85 = 5.9
5.9/2
**PLEASE HELP THIS IS DUE TODAY** when the sun's declination is at the highest point, what direction does the sun rise and set?
If f(x) = 2x2 + x-1, then f(-5)
= ?
Answer:
-54
Step-by-step explanation:
(-5)^2 = -25
2(-25)+ -5 +1 =-54
Answer:
f(-5) = -2
Step-by-step explanation:
f(-5) = 2x2 + -5 -1
f(-5) = 4 - 6
f(-5) = -2
HELP ME PLSSS SOMEONE HELPP ILL GIVE BRAINLIEST
tom sold 3 cars ( a total value of $112,500) in the month of january. it is paid only by commission for its seller. he receives a commission of 7%. what is tom’s salary for the month of january?
Answer:
First multiply 112,500 times 3 (because of the 3 cars) answer should be $337,500
Then do the percentage (7%) $23,625
I believe that 23625 is the answerrr
can someone tell me what my GPA is.
Answer:
probably 5.00
Step-by-step explanation:
The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?
Answer:
20.8333333
Step-by-step explanation:
6 x 20.8333333 = 125
4.321 × 12.34 AND IF YOU ANSWER YOU GET 10 POINTS JUST PLS HELP
Answer:
53.32114
Step-by-step explanation:
Henry buys a bag of 15 tangerines for $2.85.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Please help with this
Answer:
.19 cents per tangerine
Step-by-step explanation:
.19 x 15 = 2.85
Is 4.95 a terminating decimal
Answer:
Definitely
since the definition of a terminating decimal is one that has an ending, and a Repeating decimal is one that never ends.
Step-by-step explanation:
If the width of a rectangle is 3x+2 and the length is 2(x+4) what is the value of x
Answer:
Step-by-step explanation:
Three high school participated in a study to evaluate the effectiveness of a new computer-based mathematics curriculum. Four 24-student sections of freshman algebra were available for the study. The two types of instruction (standard curriculum, computer-based curriculum) were randomly assigned to the four sections in each of the three schools. At the end of the term, a standard mathematics achievement test was given to each of the 24 students in each section.
a. Is this study experimental, observational, or mixed experimental and observational? Why?
b. Identify important factors, factor levels, and/or factor-level combinations.
c. Classify these factors as within- or between-subjects
d. what’s the dependent measures?
e. What is the basic experiment unit of study?
Answer:
Given that;
There are three high schools, each having four sections of every 24 students
the 2 types of instructions are Standard curriculum & computer based curriculum
a)
this study is experimental
this is because the study did not just observe the student's performance but randomly assign the performance to different techniques that have some certain control over the technique of teaching and then observe their performance afterwards
b)
-important factors are; high schools, instruction type and scores
- Highschool has 2 levels: level one there are three high schools, level 2 each having four sections of every 24 students
-instruction type: has one level which is divided into two namely; standard base and computer based
Scores: doesn't have levels
c)
there are 3 schools and 4 sections so the factor high school has between subjects components
factor instruction type also has between subjects because there are two different types available
there are 24 students in each section which are within subjects
d)
the score on the test is the dependent measures
e)
“STUDENT” in each section is he basic experiment unit of study
A bowl of fruit contains seven pieces of fruit, including two bananas and five apples. Three pieces of fruit are chosen. What is the probability that one banana and two apples are chosen?
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
A combination refers to the selection of objects such that order does not matter. A permutation refers to the arrangement of objects such that order do matter.
Number of bananas = 2
Number of apples = 5
One banana and two apples are chosen.
So,
probability that one banana and two apples are chosen = [tex]\frac{C(2,1)\,C(5,2)}{C(7,3)}[/tex]
[tex]C(2,1)=\frac{2!}{1!(2-1)!}=2[/tex]
[tex]C(5,2)=\frac{5!}{2!(5-2)!}=\frac{5!}{2!31} =10[/tex]
[tex]C(7,3)=\frac{7!}{3!(7-3)!} =\frac{7!}{3!4!}=35[/tex]
So,
Probability that one banana and two apples are chosen = [tex]\frac{2(10)}{35}=\frac{4}{7}[/tex]
Answer:
Or 57.14%
Step-by-step explanation:
Find the slope and y-intercept of the line
f(x) = 4x - 6
Answer:
y=mx+b m= rise/run b= y-intercept (0,b)
hope this helps
Step-by-step explanation: