A question includes logarithm and trigonometry. Could anybody help me to solve this,please?
Answers
[tex]\log_2(2\sin x)+\log_2(\cos x)=-1[/tex]
Condense the logarithms on the left side:
[tex]\log_2(2\sin x\cos x)=-1[/tex]
Recall the double angle identity for sine, [tex]\sin(2x)=2\sin x\cos x[/tex]:
[tex]\log_2(\sin(2x))=-1[/tex]
Write both sides as powers of 2:
[tex]2^{\log_2(\sin(2x))}=2^{-1}[/tex]
Simplify this:
[tex]\sin(2x)=\dfrac12[/tex]
Solve for [tex]2x[/tex]:
[tex]2x=\sin^{-1}\left(\dfrac12\right)+2n\pi\text{ OR }2x=\pi-\sin^{-1}\left(\dfrac12\right)+2n\pi[/tex]
(where [tex]n[/tex] is any integer)
Recall that [tex]\sin^{-1}\left(\frac12\right)=\frac\pi6[/tex]:
[tex]2x=\dfrac\pi6+2n\pi\text{ OR }2x=\dfrac{5\pi}6+2n\pi[/tex]
Solve for [tex]x[/tex]:
[tex]x=\dfrac\pi{12}+n\pi\text{ OR }x=\dfrac{5\pi}{12}+n\pi[/tex]
We get solutions in the interval [tex]2\pi <x<\frac{5\pi}2[/tex] when [tex]n=2[/tex], giving
[tex]\boxed{x=\dfrac{25\pi}{12}}\text{ OR }\boxed{x=\dfrac{29\pi}{12}}[/tex]
Related Questions
PLEASE HELP! A) 6,135º C B) 6,681º C C) 502º C D) 47º C
Answers
Answer:
[tex]\huge \boxed{\mathrm{47\° C}}[/tex]
Step-by-step explanation:
The velocity is given as 358 meters per second.
358 = 20√(273 + t)
Solve for t.
Divide both sides by 20.
17.9 = √(273 + t)
Square both sides.
320.41 = 273 + t
Subtract 273 from both sides.
47.41 = t
Round to nearest degree.
t = 47°C
Angles W and X are supplementary. If m∠W is 37°, what is m∠X?
Answers
Supplementary angles = 180
X = 180 - 37
X = 143
write (n^3)^2 without exponents
Answers
Answer:
(n×n×n)(n×n×n)
Step-by-step explanation:
Expand the exponential function.
hope this helps :)
Question 9
11 pts
The legs of a right triangle measure 89 centimeters and 38 centimeters.
How long is the hypotenuse in centimeters? Round to the nearest
hundredth if necessary.
Answers
Answer:
The answer is 96.8 cmStep-by-step explanation:
Since we have the legs of the right angled triangle we can use Pythagoras theorem to find the hypotenuse
That's
[tex] {h}^{2} = {a}^{2} + {b}^{2} [/tex]where
h is the hypotenuse
From the question
The legs of the right angled triangle are 89cm and 38 cm
So the hypotenuse is
[tex] {h}^{2} = {89}^{2} + {38}^{2} \\ {h}^{2} = 7921 + 1444 \\ h = \sqrt{9365} [/tex]h = 96.7729
We have the final answer as
96.8 cm to the nearest tenth
Hope this helps you
Which statements are true about x? Select three options
Answers
Quadrilateral QRST is similar to quadrilateral EDGF. What's the scale factor from EDGF to QRST
A) 5∕4
B) 6∕7
C) 6∕5
D) 5∕6
Answers
Answer:
C. [tex] \frac{6}{5} [/tex]
Step-by-step explanation:
The ratio of the corresponding sides of a polygon is said to be equal. The ratio gives us the scale factor.
Therefore, assuming that quadrilateral QRST was the original polygon that was scaled up to give a similar polygon, EDGF, the scale factor would be expressed as [tex] \frac{42}{35} [/tex]
The scale factor = [tex] \frac{42}{35} = \frac{6*7}{5*7} = \frac{6}{5} [/tex]
(90) points and brainly! Sameen works at an office. During her lunch break, she rides her bicycle to her favorite sandwich shop and eats lunch at a local park. The graph below shows the distance she is from work over time. Select the statement that is true regarding Sameen's lunch break based on the graph. A Between 0 minutes and 6 minutes, Sameen's distance from work is constant. B Between 6 minutes and 9 minutes, Sameen's distance from work is decreasing. C Between 9 minutes and 27 minutes, Sameen's distance from work is 0 miles. D Between 27 minutes and 30 minutes, Sameen's distance from work is increasing.
Answers
Answer:
(B) Between 6 and 9 minutes, Sameen's distance from work is decreasing
Step-by-step explanation:
Looking at the graph, we want to make sure we are looking at the right axis.
The x-axis, the horizontal one, is minutes.
The y-axis, the vertical one, is distance from work.
We can see that while x is between 6 and 9 minutes, the graph slopes downwards. This signifies a decrease in distance from work.
So between 6 and 9 minutes, Sameen's distance from work is decreasing.
Hope this helped!
Answer:
Between 6 and 9 minutes, Sameen's distance from work is decreasing
Step-by-step
The mean age of judges in Dallas is greater than 50.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
Answers
Answer:
There is insufficient evidence to support the claim that the mean age is greater than 50.2 years. i.e ( μ > 50.2)
Step-by-step explanation:
Given that:
The mean age of judges in Dallas is greater than 50.2 years.
If a hypothesis test is performed, then the null and the alternative hypothesis can be computed as follows:
The null hypothesis is that the mean age of the judges in Dallas is equal to 50.2
i.e
[tex]H_o : \mu =50.2[/tex]
The alternative hypothesis is that the mean age of the judges in Dallas is greater than 50.2
i.e
[tex]H_1 : \mu > 50.2[/tex]
Decision Rule: Fail to reject the null hypothesis.
The interpretation of this decision rule implies that:
There is insufficient evidence to support the claim that the mean age is greater than 50.2 years. i.e ( μ > 50.2)
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 523, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
Answers
Answer:
There is no sufficient evidence to support the owner's claim that he average attendance at games is over 523
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 523[/tex]
Generally
The null hypothesis is [tex]H_o : \mu = 523[/tex]
The alternative hypothesis [tex]H_a : \mu > 523[/tex] ( Original claim )
Given in the question that the conclusion is failure to reject the null hypothesis
Then we can conclude that there is no sufficient evidence to support the owner's claim that he average attendance at games is over 523
Note : In every hypothesis test the null hypothesis must contain a equality sign and any other inequality sign
warehouse A has 200 tons of coal and sells 15 tons every day. warehouse B has 80 tons and buys 25 everyday in how many days does a=b
Answers
Hey there! I'm happy to help!
Let's represent the number of days with x.
WAREHOUSE A
200-15x
WAREHOUSE B
80+25x
We want to find how many days it will take for the two warehouses to have the same amount of coal. Let's put these expressions into an equation to show that they are equal and see what x is.
200-15x=80+25x
We subtract 25x from both sides.
200-40x=80
We subtract 200 from both sides.
-40x=-120
We divide both sides by -40
x=3
Therefore, warehouse A and warehouse B will have the same amount of coal after 3 days.
Have a wonderful day! :D
How many pennies could you have if: When you break the pennies into groups of 2, you have 1 penny left over, AND when you break the pennies into groups of 3, you have 1 penny left over, AND when you break the pennies into groups of 5, you have 1 penny left over?
Answers
Answer:
31 pennies
Step-by-step explanation:
Given that:
Breaking the number of pennies into 2 groups, there is 1 penny left over.
Breaking the pennies into 3 groups, there is 1 penny left over.
Breaking the pennies into 5 groups, there is 1 penny left over.
Breaking the pennies into groups implies that the same number of pennies are in each group for each case. Since there is no restriction to the number of pennies in the groups for all cases, then the total number of pennies would be 31.
So that;
31 = 15 + 15 + 1 = 2 groups + 1
31 = 10 + 10 + 10 + 1 = 3 groups + 1
31 = 6 + 6 + 6 + 6 + 6 + 1 = 5 groups + 1
There are 31 pennies.
Based on the information provided in the graph, for wich of the following situations could you expect to have the greatest increase in salary?
A.Having a highschool diploma and getting an associate's degree
B.Having a bachelor's degree and getting a master's degree
C.Having a master's degree and getting a professional degree
D.Having an associate's degree and getting a bachelor's degree
Answers
Answer: your answer is D
Step-by-step explanation:
Consider the function f(x) = log8 x. (a) What is the domain of f? (Enter your answer using interval notation.)
Answers
Answer:
The domain of f is equal to x = log8 x.
Step-by-step explanation:
if 270kg of corn would feed 42 horses for 21 days, for how many days would 36okg of it feed 21 horses?
Answers
Hi!
To find this, multiply 42, 21 and 360 first:
317520
Now, multiply 21 and 270:
5670
Now, divide 317520 by 5670:
56 days
(I've had problems like these before, this is how my teacher taught me to solve them. If you have any more trouble, try to use these steps!)
Hope this helps!
(x-3) (x+9) need help asap
Answers
We will use the F.O.I.L method.
-multiplying the First terms,
-multiplying the Outer terms,
-multiplying the Inner terms,
-and multiplying the Last terms
So we have x² + 9x - 3x - 27 which simplifies to x² + 6x - 27.
Just multiply them out
Jacob charges $10 per hour to babysit and $60 to clean the house. Write the expression which represents Jacob's earning for cleaning one house and babysitting?
Answers
Answer:
60 + 10h
Step-by-step explanation:
Since cleaning the house is a flat fixed cost ($60 no matter how long it takes), you dont use a variable to find it. For baby sitting on the other hand, the cost of it is reliant on how long you do it ($10 for every hours). Therefore you need to use a variable (h).
I hope this helps!
-TheBusinessMan
5. John and Mary are taking a math course. The course has only 3 grades: A, B, and C. The probability that John gets a B is 0.3 .The probability that Mary gets a B is 0.4 . The probability that neither gets an A but at least one gets a B is 0.1 .What is the probability that at least one gets a B but neither gets a C
Answers
Answer:
0.6
Step-by-step explanation:
In the question, we are told that:
The probability that John gets a B is 0.3 .
The probability that Mary gets a B is 0.4 .
The probability that neither gets an A but at least one gets a B is 0.1
The probability that at least one gets a B but neither gets a C
=( The probability that John gets a B ) +( The probability that Mary gets a B )- (The probability that neither gets an A but at least one gets a B is 0.1
= 0.3 + 0.4 - 0.1
= 0.7 - 0.1
= 0.6
Therefore, the probability that at least one gets a B but neither gets a C is 0.6
3 days converted to seconds
Answers
hope this helps :)
Answer:259,200 seconds
Step-by-step explanation:
24 hours in one day
1 hour= 60 minutes
1 minute =60seconds
60x60=3,600
3,600x24=86,400 seconds
86,400x3(days)=259,200 seconds
f(x)= -3x+7 what is f(-20)?
Answers
Answer:
67
Step-by-step explanation:
Evaluate 7 - 3 x where x = -20:
7 - 3 x = -3 (-20) + 7
Hint: | Multiply -3 and -20 together.
-3 (-20) = 60:
60 + 7
Hint: | Evaluate 60 + 7.
60 + 7 = 67:
Answer: 67
a muffin recipe calls for a ratio of 5 cups of flour to 2 cups of sugar. for each cup of sugar that is used how many cups of flour are needed
Answers
Step-by-step explanation:
2 cups of sugar =5 cups of flour
1 cup of sugar =x cups of flour
2x=5
x=5/2
for the data values below construct a 95 confidence interval if the sample mean is known to be 12898 and the standard deviation is 7719
Answers
Answer:
A 95% confidence interval for the population mean is [3315.13, 22480.87] .
Step-by-step explanation:
We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample proportion of defective items = 12,898
s = sample standard deviation = 7,719
n = sample size = 5
[tex]\mu[/tex] = population mean
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.776 < [tex]t_4[/tex] < 2.776) = 0.95 {As the critical value of t at 4 degrees of
freedom are -2.776 & 2.776 with P = 2.5%}
P(-2.776 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.776) = 0.95
P( [tex]-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.776 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.776 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]12,898-2.776 \times {\frac{7,719}{\sqrt{5} } }[/tex] , [tex]12,898+2.776 \times {\frac{7,719}{\sqrt{5} } }[/tex] ]
= [3315.13, 22480.87]
Therefore, a 95% confidence interval for the population mean is [3315.13, 22480.87] .
1 point
Jayden is making a chain from construction paper from red and green paper links. The
pattern of the links is red, red, green, green, green. If there are 30 links all together, how
many are red and green?
Answers
Someone, please help me with this.
Answers
Answer:
[tex]\large\boxed{x=14}[/tex]
Step-by-step explanation:
Because the angles are adjacent to each other and form a straight line, they are supplementary angles. Supplementary angles add up to 180 degrees, therefore, you can add the two angle measures together and set them equal to 180.
(7x - 1) + (6x - 1) = 180 combine like terms
13x - 2 = 180 add 2 to both sides
13x = 182 divide by 13 on both sides
[tex]\boxed{x=14}[/tex]
Answer:
x = 14°Step-by-step explanation:
Since the two angles lie on a straight line the sum of their angles is equal to 180°.
To find x add up the two angles and equate it to 180° and solve for x
That's
7x - 1 + 6x - 1 = 180
13x - 2 = 180°
Move 2 to the right side of the equation
That's
13x = 180 + 2
13x = 182
Divide both sides by 13
That's
[tex] \frac{13x}{13} = \frac{182}{13} [/tex]
We have the final answer as
x = 14°Hope this helps you
sarah set up a lemonade stand and sold each glass for $1.25. write an algebraic expression to represent sarah's profit.
Answers
Answer:
Y=1.25M
Step-by-step explanation:
Y represents the total amount of money being earn
1.25 is how much 1 lemonade drink cost
M represents the number of lemonade that was sold
The amount of lemonade sold time's How much each lemonade drink cost shall give you the total amount of money earn.
Find f(-3) for f(x) = -2x + 5.
A. -1
B. 10
C. -10
D. 11
Answers
Answer:
[tex] \boxed{ \sf{ \bold{ \boxed{11}}}}[/tex]Option D is the correct option.
Step-by-step explanation:
Given,
[tex] \sf{f(x) = - 2x + 5}[/tex]
To find : f ( - 3 )
Let's find:
[tex] \sf{f( - 3) = - 2 \times ( - 3) + 5}[/tex]
Calculate the product
[tex] \sf{ = 6 + 5}[/tex]
Add the numbers
[tex] \sf{ = 11}[/tex]
Hope I helped!
Best regards!!
Answer: f(-3) = 11
Step-by-step explanation: Here we're given the function
f(x) = -2x + 5 and we're asked to find f(-3).
In other words, if we put an x into our function, we get a -2x + 5 out.
So what happens when we put a -3 into the function?
Well if we put a -3 into the function,
that's f(-3), we get a -2(-3) + 5 out.
Now all we have to do is simplify on the right side,
-2(-3) is 6, so we have 6 + 5 which is 11.
So f(-3) is 11.
Hershey’s bar were purchased at $6 per dozen and sold at 1.25 each. find the profit on 14 dozen Hershey’s bar.
Answers
Answer:
$126.00
Step-by-step explanation:
The Hershey bars were purchased for $6 per dozen. There are 12 bars per dozen. First, find the cost per bar.
cost / bar
$6 / 12 bars
$0.50 / bar
Next, find the profit on one bar. The bars costs $0.50 each and are being sold for $1.25. The profit will be the difference between the two numbers.
$1.25 - $0.50
$0.75
Finally, find the profit on 14 dozen bars.
There are 168 bars in 14 dozen. ( 12 per dozen, 14 dozen, 12*14= 168).
Multiply the profit of one bar ($0.75) by 168.
168 *$ 0.75
$126
The profit on 14 dozen Hershey bars is $126.00
Find the standardized test statistic, z to test the hypothesis that p1 = p2. Use α = 0.05. The sample statistics listed below are from independent samples. Sample statistics: n1 = 50, x1 = 35, and n2 = 60, x2 = 40
Answers
|0.4552| < 1.96, we fail to reject the null hypothesis that p₁ = p₂.
Therefore, at the 0.05 significance level, there is not enough evidence to conclude that the proportions of success in the two samples are significantly different.
To find the standardized test statistic (z) to test the hypothesis that p₁ = p₂, where p₁ and p₂ are the proportions of success in two independent samples, we can use the following formula:
z = (p₁ - p₂) / √(p * (1 - p) * ((1/n₁) + (1/n₂)))
where:
p₁ and p₂ are the sample proportions of success in the two samples.
p = (x₁ + x₂) / (n₁ + n₂) is the pooled proportion of success in both samples.
n₁ and n₂ are the sample sizes of the two samples.
x₁ and x₂ are the number of successes in the two samples.
Given the sample statistics:
n₁ = 50, x₁ = 35 (sample 1)
n₂= 60, x₂ = 40 (sample 2)
First, calculate the pooled proportion (p):
p = (x₁ + x₂) / (n₁ + n₂)
p = (35 + 40) / (50 + 60)
p = 75 / 110
p ≈ 0.6818
Now, calculate the standardized test statistic (z):
z = (p₁ - p₂) / √(p * (1 - p) * ((1/n₁) + (1/n₂)))
z = (35/50 - 40/60) / √(0.6818 * (1 - 0.6818) * ((1/50) + (1/60)))
z = (0.7 - 0.6667) / √(0.6818 * 0.3182 * (0.02 + 0.0167))
z = 0.0333 / √(0.1456 * 0.0367)
z = 0.0333 / √(0.00534272)
z = 0.0333 / 0.073068
z ≈ 0.4552
Now, compare the standardized test statistic (z) with the critical value at α = 0.05. Since this is a two-tailed test, the critical value is approximately ±1.96 (at a 5% significance level).
Since |0.4552| < 1.96, we fail to reject the null hypothesis that p₁ = p₂.
Therefore, at the 0.05 significance level, there is not enough evidence to conclude that the proportions of success in the two samples are significantly different.
To know more about standardized test statistic,
brainly.com/question/17241369
#SPJ4
rated Math (Ist quarter)
Which expression uses the distributive property to show equivalent expressions for this situation?
O 54 + 42 = (3)(18) + (6)(7)
54 + 42 = (9)(10) + 6
54 + 42 = 90 + 6
O 54 + 42 = 6(9 + 7)
Answer:
54+42=6(9+7)
Answers
Answer:
yes
Step-by-step explanation:
2 = (3)(18) + (6)(7)
54 + 42 = (9)(10) + 6
54 + 42 = 90 + 6
O 54 + 42 = 6(9 + 7)
1. Brandon has $12. He will
eam $8 for every
hour he works. He would
like to have $52 at
the end of the day. Let h
represent the
number of hours
Brandon works.
Equation:
Solve it to find how many
hours he needs. Solve the problem, and also write the equation
Answers
8h=40
h=5
5 hours
Answer:
h=5
Step-by-step explanation:
h/8+12=52
12 dollars is what he originally starts with so it would be added with h.
Now, subtract 12 dollars from the 52 he wnats to end the day with.
52-12=40
Now take 40 and divide it 8
h=40/8
h=5
Hope that helps :)
Can anyone help me find the value please?
Answers
Answer:
the answer is x=15 cm
Step-by-step explanation:
here the above given figure is a rectangle ABCD with diagonals AC and BD measuring AC= (x+10)cm and BD=(3x-20) cm
Now,
AC=BD
or, 3x-20 = x+10 [ diagonals of a rectangle are equal]
or, 2x = 30
or, x= 15 cm
I HOPE IT WILL HELP YOU!!!