Answers
Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]5\sin(2x)=3\cos(x)[/tex]
To do so, we can rewrite the equation.
Recall the double-angle identity for sine:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
By substitution:
[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]
Distribute:
[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]
We can subtract 3cos(x) from both sides:
[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]
And factor:
[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.
Answer:
A. cosx(10sinx-3)=0
Step-by-step explanation:
5(2sinxcosx)=3cosx
10sinxcosx-3cosx=0
cosx(10sinx-3)=0
Related Questions
Samir has collected 35% of the skins on Fortnite. If there are 300 total skins, how many more does he need to collect to be at 50%? Explain or show your work.
Answers
I believe its 45.
Its hard to explain but what I can say is if you subtract the percentage with the total of the skins you would subtract what you had from there and then you would have 45.
Answer:
I think 45
Step-by-step explanation:
Plz, help. In the picture below.
Answers
Answer:
I don't know sorry
Step-by-step explanation:
Perform the indicated operation (x-3y)(3x-11y)
Answers
Answer:
[tex]3x^{2} - 20xy + 33y^{2}[/tex]
Step-by-step explanation:
[tex](x-3y)(3x-11y)\\3x^{2} - 9xy - 11xy + 33y^{2} \\3x^{2} - 20xy + 33y^{2}[/tex]
By next year , 2,125 students are expected to be enrolled in a county's middle schools . This is 25 % of the total student population . What is the total student population ?
Answers
Ms. Bohan drinks 3/5 of her drink from starbucks. What percent of her drink did she have?
Answers
Answer:
30%
Step-by-step explanation:
3/50 = 60/100
Answer:
u
Step-by-step explanation:
Do mice show a preference for using one paw over the other? Attempting to answer this question, a researcher tested a random sample of 48 mice and observed which forepaw (right or left) the mice used to retrieve food from a narrow tube. Eighteen of the mice used their right paw, while the rest used their left paw.
Does this data suggest that mice show a preference towards one paw over the other? Carry out the appropriate test and include all steps for full credit.
During the course of the experiment, the researcher noticed that individual mice sometimes switched which forepaw they used to retrieve the food. So she repeated this study on the same 48 mice, but measured each one 10 times and she recorded which forepaw was used each time. With her new dataset of 480 observations, would you be able to run the same analysis as in part (a)? If so, carry out the analysis and compare the results. If not, why not?
Answers
Answer:
It all depends on the food they are going for, just like humans, mice have instincts. For example, if you were falling forward, which foot would you put out? Most likely the opposite one. I hope this helps you!
Step-by-step explanation:
Using hypotheses testing,
In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.
We have,
(a)
To test whether the data suggest that mice show a preference towards one paw over the other, we can use a one-sample proportion test.
The null hypothesis (H0) is that the proportion of mice that use their right paw is 0.5 (indicating no preference towards one paw over the other).
The alternative hypothesis (Ha) is that the proportion of mice that use their right paw is different from 0.5 (indicating a preference towards one paw over the other).
We can use a significance level (alpha) of 0.05.
To conduct the test, we can calculate the test statistic using the formula:
z = (p - 0.5) / √(0.5 x 0.5 / n)
where p is the proportion of mice that use their right paw, and n is the sample size.
Using the given data, we have:
p = 18/48 = 0.375
n = 48
Plugging in the values, we get:
z = (0.375 - 0.5) / √(0.5 x 0.5 / 48) = -1.714
Using a standard normal distribution table or calculator,
We can find the p-value associated with this test statistic.
The p-value is the probability of observing a test statistic as extreme as -1.714 or more extreme, assuming the null hypothesis is true.
The p-value for this test is 0.0869.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
This means that we do not have sufficient evidence to conclude that mice show a preference towards one paw over the other, based on the given sample.
(b)
With the new dataset of 480 observations, we can still conduct a similar analysis using a one-sample proportion test.
However, since each mouse was measured 10 times, the observations are no longer independent.
Therefore, we need to use a different test that accounts for the dependency between observations, such as McNemar's test.
McNemar's test is a test of the marginal homogeneity of a two-way table, where the same subjects are measured twice on a binary outcome.
In this case, we can create a 2x2 contingency table of the number of times each mouse used their right or left paw, and conduct a McNemar's test on this table.
The null hypothesis for McNemar's test is that there is no difference in the proportions of mice that use their right or left paws.
The alternative hypothesis is that there is a difference.
To conduct the test, we can calculate the test statistic using the formula:
chi-squared = (|b-c|-1)² / (b+c)
where b is the number of mice that used their right paw more often, and c is the number of mice that used their left paw more often.
Using the given data, we have:
b = 214
c = 244
Plugging in the values, we get:
chi-squared = (|214-244|-1)² / (214 + 244) = 2.417
Using a chi-squared distribution table or calculator with 1 degree of freedom (since we have a 2x2 table), we can find the p-value associated with this test statistic.
The p-value is the probability of observing a test statistic as extreme as 2.417 or more extreme, assuming the null hypothesis is true.
The p-value for this test is 0.119.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
This means that we do not have sufficient evidence to conclude that there is a difference in the proportions of mice that use their right or left paws, based on the new dataset.
Thus,
In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.
Learn more about the hypotheses test here:
https://brainly.com/question/28331914
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An initial investment of $2,000 earns 7% interest compounded continuously. What will the investment be worth in 17 years? (Round your answer to the nearest cent.)
Answers
Answer:
Future value, A = $6,317.6
Step-by-step explanation:
Given the following data;
Principal = $2,000
Interest rate = 7%
Time = 17 years
To find the future value, we would use the compound interest formula;
[tex] A = P(1 + \frac{r}{100})^{t}[/tex]
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
t is the number of years for the compound interest.
Substituting into the equation, we have;
[tex] A = 2000*(1 + \frac{7}{100})^{17}[/tex]
[tex] A = 2000*(1 + 0.07)^{17}[/tex]
[tex] A = 2000*(1.07)^{17}[/tex]
[tex] A = 2000 * 3.1588 [/tex]
Future value, A = $6,317.6
I need help with this plz
Answers
Answer:
-5.3, -5/2, 72%, sqrt52, then 49
Step-by-step explanation:
edge 2020
p.s. pls mark brainliest, and have a good day! :)
Draw a histogram for the intervals 16-18, 19-21, 22-24, and 25-27 using the following data: 26, 16, 22, 27, 20, 24, 21, 27, 22, 21, 26, 27, 23, 20, 16, 17, 27, 19, 17, 17
Answers
Answer:
Step-by-step explanation:
Class Interval Variate Frequency
16-18 16 1
19-21 0 0
22-24 0 0
25-27 26,27 2
Answer:
A
Step-by-step explanation:
right on edge 2021
if -2x + 3 = 7 and 3x + 1 = 5 + y, the value of y is
Answers
Answer:
value of y is -10
Step-by-step explanation:
-2x+3=7 equation 1
3x+1=5+y equation 2
by eq 1
-2x=7-3
-2x=4
x=-2
put value of x in equation 2 to get value of y
3(-2)+1=5+y
-6+1=5+y
-5=5+y
-5-5=y
y=-10
PLS Help quick!!
Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle
between the sloping sides is 77º. What is the shortest distance between the tip of the cone and its rim?
A. 177.8 cm
B. 64.3 cm
C. 50.3 cm
D. 51.1 cm
E. 41.1 cm
Answers
Answer:
Option D. 51.1 cm
Step-by-step explanation:
Please see attached photo for explanation.
In the attached photo, c is the distance between the tip of the cone and its rim.
The value of c can be obtained as follow:
Angle θ = 38.5°
Adjacent = WY = 40 cm
Hypothenus = WZ = c =?
Cos θ = Adjacent / Hypothenus
Cos 38.5 = 40 / c
0.7826 = 40 / c
Cross multiply
0.7826 × c = 40
Divide both side by 0.7826
c = 40 / 0.7826
c = 51.1 cm
Thus, the distance between the tip of the cone and its rim is 51.1 cm.
Answer:
Option D. 51.1 centimeters
Step-by-step explanation:
Correct answer for plato users
2) A 0.4 kg ball moves in horizontal circle of radius 3 mat speed of 100m/s. What
is the centripetal force?
file the
Answers
9514 1404 393
Answer:
1333.3 N
Step-by-step explanation:
The centripetal acceleration is given by ...
a = v^2/r
a = (100m/s)^2/(3 m) = (10^4)/3 m/s^2
Then the force on the ball is ...
F = Ma = (0.4 kg)(10^4)/3 kg·m/s^2 ≈ 1333.3 N
Consider this absolute value function.
f(3) = (+31
If function fis written as a piecewise function, which plece will it include?
A. -x- 3, x<3
B. -x + 3, x <-3
C. x+3, x >3
D. x+3, x>-3
Answers
Answer:
D
Step-by-step explanation:
f(x) = |x+3|=x+3 when x+3≥0 ⇒x≥-3
PLEASE HELP ME ON THIS
Answers
9514 1404 393
Answer:
(d) $775.50
Step-by-step explanation:
The parallelogram on the left has an area of ...
A = bh = (4 yd)(2 yd) = 8 yd²
The rectangle in the middle has an area of ...
A = lw = (6 yd)(4 yd) = 24 yd²
The triangle on the right has an area of ...
A = 1/2bh = 1/2(1 yd)(2 yd) = 1 yd²
The total area of the carpet is ...
(8 + 24 + 1) yd² = 33 yd²
__
At $23.50 per square yard, the cost is ...
($23.50/yd²)(33 yd²) = $775.50 . . . . . matches the last choice
Eric spends 4/5 of his pocket money to buy lunches. The rest of the money he will save. If the amount he saves is $2, how much does he spend buying lunch?
Answers
Answer:
Wait u want me to answer your question or the Jono question? Or both?
Step-by-step explanation:
1. $6/5
Subtract 2/3 and 1/4.
Answers
Answer:
5/12
Step-by-step explanation:
Find common denominators. Note that what you multiply to the denominator, you must multiply to the numerator as well. The common denominator is 12:
(2/3) * (4/4) = (8/12)
(1/4) * (3/3) = (3/12)
Subtract:
(8/12) - (3/12) = (8 - 3)/12 = 5/12
5/12 is your answer.
~
(F)x= -4x^2 - 8x - 8 find -3 • f(-1)
Answers
Answer:
12
Step-by-step explanation:
-3[-4 + 8 - 8] = -3(-4) = 12
Use the distributive property to write an expression that is equivalent to 9(c+5
Answers
Answer:
9c+45
Step-by-step explanation:
Please help me
Grade is 6th or 7th
Answers
Answer:
1 a)8 miles per hour 1 b) 1 hour and 90 minutes 2 a) 24 hours and 6minutes 2 b) 3hours 3 a) 260 hours and 45 minutes 3 b) 40 minutes
Step-by-step explanation:
I don't know for sure if this is all correct but at least you'll have something to write down
Answer:
1a. 8 miles per hour
1b. 32 km per hour
2a. 28 miles
2b. 3 hours
3a. 2925
3b. 1/4 hour or 15 minutes
Step-by-step explanation:
For number 1a, think of 2 1/2 hours equals 20 miles as 2 1/2x=20. The x being hours, and the 20 being 20 miles. You want the equation to become x=?. So you divide 2 1/2x=20 by 2 1/2 to make the equation start with x=. You end up with x=8. Or you could just think of it as divide 20 miles by 2 1/2 hours. Either way, you end up with 8 miles per hour. For number 1b, you do the same thing as before, but you have to make 4 hours and 45 minutes a fraction. So, the are 60 minutes in an hour, so the fraction would be 45/60. Then you simplify that down to 3/4. So, 152 km divided by 4 3/4 is 32 km per hour.
For number 2a, set aside 30 minutes for now. She can go 24 miles in 3 hours. Because 8 miles times 3 hours equals 24 miles. It’s like instrad of 8 miles per hour, it’s 24 miles per 3 hours. Then, because 30 minutes is half of an hour, 8 divided by 2 would make it 4 miles per half an hour. So 24 plus 4 is 28 miles. For number 2b, you want to know how many hours it took to travel 1980 miles. Since you already knowmthat is takes one hour to go 660 miles, pretend that each 660 miles is one hour. So you divide 1980 by 660 so see how many one hours fit. You get 3. So, an airplane can fly 1980 miles in 3 hours.
For number 3a, like 2a, you basically multiply the constant speed by the full hours then the fraction, and add them together. You could also just multiply the constant speed by the number 3 3/4. That way you get the miles per 3 3/4 hours. 3 3/4 times 780 is 2925. So the plane can fly 2925. For number 3b, to get the 2 miles per ? hours, you have to divde 8 by 4 to get to 2. So you divide 1 hour by 4 to get the answer. So it’s 1/4, (one fourth of an hour) or 15 minutes 1/4 of 60 (the amount of minutes in an hour) for Mary to go 2 miles.
subtract the fractions
7/39 1/42
Answers
Answer:
7/39-1/42= 85/546
Step-by-step explanation:
so its 85/546
Answer:
7/39 1/42
so it's 85/546
2. WHICH EXPRESSIONS ARE EQUIVALENT TO 6X?
SELECT ALL THAT APPLY
5X+X
3X+3
5+X
9X-3
X+X+4X
Answers
Answer:
5x+x and x+x+4x
Step-by-step explanation:
5x+x is basically 5x+1x which is 6x since x has an "invisible one" in front of it.
x+x+4x is 2x+4x which is 6x
hope this helps. :)
Answer:
4 and 5
Step-by-step explanation:
9x - 3 is 6x
5x + x can be 6x because there's is a x next to it that means it can be any number so if the number is suppose to become 6x we need to add 1 to both sides, and the a swer will be 6x.
sorry of wrong.
144 in the ratio 3:4
Answers
Answer: 132
Step-by-step explanation:
Mrs. Miller and 8 of her closest friends are taking a
Yoga class. The total cost for the class is $78.75.
Write and solve a multiplication equation to show
the cost per person for the Yoga class.
Answers
Answer:
f f f f f ff f f ff f f ff f f f f f f
Step-by-step explanation:
interest earned on both the principal and any previously earned interest?
a. compound interest
b. simple interest
c. interest rate
d. principal
Answers
Answer:
A. Compound Interest
Step-by-step explanation:
Compound interest is interest paid on both the principal and previously earned interest.
Compound interest earned on both the principal and any previously earned interest. Therefore, the correct answer is option A.
What is the rate of interest?An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Therefore, option A is the correct answer.
To learn more about the rate of interest visit:
brainly.com/question/28236069.
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find the surface area of puzzlecube 5.7
Answers
Answer:
9units squared
Step-by-step explanation:
A standard rubix cube is 3 by 3 and therefor 3 x 3 is 9
Pleas help
Today is payday at your job at Toys R Us! You go to the bank to deposit your $150 check into your account. You receive a deposit slip. You decide to go to American Eagle. There you see a pair of jeans you like on sale for $39.99 from the usual $69.99. Wow! This is a steal! You pay the store attendant using your debit card, and you are the proud owner of a brand new pair of American Eagle jeans! With this scene in mind, Name the three uses of money and describe how each use is displayed in this scenario. Be specific.
Answers
Answer:
earning the money,depositing the money, and spending the money.
you worked all week to earn the money.
You deposit your money in your account.
You spent some money at American eagle.
Step-by-step explanation:
Jonathan went shopping for a new pair of pants. Sales tax where he lives is 4.75%. The price of the pair of pants is $20. Find the total price including tax. Round to the nearest cent.
Answers
Answer:
20.95$
Step-by-step explanation:
To find the total price we need to find 4.75% of the 20 and to do that we need to multply 20 with 4.75 and divide it by 100
20 × 4.75 ÷ 100 = 0.95
20$ + 0.95$ = 20.95$
the volume of a rectangle prism is 8cm height 4 width.
Answers
Answer:
Step-by-step explanation:
According to exit polling from the 2014 U.S. midterm elections, 36% of voters had a household income less than $50,000, while 64% had a household income of at least $50,000. Forty-three percent of voters from house-holds making less than $50,000 voted for the Republican party in the election, while 55% percent of voters from households making at least $50,000 voted Republican. What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000
Answers
Answer:
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Republican
Event B: From a household that makes at least $50,000.
Probability of Republican:
43% of 36%(makes less than $50,000).
55% of 64%(makes more than $50,000).
So
[tex]P(A) = 0.43*0.36 + 0.55*0.64 = 0.5068[/tex]
Republican and from a household that makes at least $50,000.
55% of 64%. So
[tex]P(A \cap B) = 0.55*0.64 = 0.352[/tex]
What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.352}{0.5068} = 0.6946[/tex]
0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.
HELP PLEASE PLEASE ASAP
Answers
9514 1404 393
Answer:
150 square units
Step-by-step explanation:
Each of the six squares has an area of 5×5 = 25 square units. (You can count them, if you wish.)
Then the total area is ...
6×(25 square units) = 150 square units