Use the chain rule to compute the second derivative:
[tex]f(x)=\ln(\sin(2x))[/tex]
The first derivative is
[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]
[tex]f'(x)=2\cot(2x)[/tex]
Then the second derivative is
[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]
[tex]f''(x)=-4\csc^2(2x)[/tex]
Then plug in π/4 for x :
[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]
The escape time (sec) for oil workers in a simulated exercise, gave the sample mean 370.69, sample standard deviation 24.36, and number of observations as n =26. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypothesis using a significance level of .05.
Answer:
Null hypothesis:[tex]\mu \leq 6[/tex]
Alternative hypothesis:[tex]\mu > 6[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]
[tex]p_v =P(t_{25}>1.335)=0.097[/tex]
And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes
Step-by-step explanation:
Information given
[tex]\bar X=370.69/60 =6.178[/tex] represent the sample mean
[tex]s=24.36/36=0.68[/tex] represent the standard deviation for the sample
[tex]n=26[/tex] sample size
[tex]\mu_o =6[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 6[/tex]
Alternative hypothesis:[tex]\mu > 6[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]
The degrees of freedom are:
[tex]df=n-1=26-1=25[/tex]
The p value would be given by:
[tex]p_v =P(t_{25}>1.335)=0.097[/tex]
And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.
Which rule describes the translation?
5
B
С
(x, y) - (x - 8, y-3)
O (x, y) — (x - 3, y + 8)
O (x, y) = (x + 8, Y-3)
O(x, y) = (x + 3, y + 8)
B'
A
5
D
A
D
5
Answer:
look to rule number five
Step-by-step explanation:
Rule Number 5 best explains the answer
HELP!!! PLEASE!!!
The U.S. Federal Income Tax is a progressive tax, which means that higher incomes are taxed at higher percent rates.
The table shows the 2018 Federal Income Tax rates that are applied to the incomes of unmarried individuals.
Tuan is an unmarried man who earned a taxable income of $48$48,000000 during 2018.
Use the table to complete the statements below.
Answer:
10%$29,175$2,046$6,499.50Step-by-step explanation:
a) The %tax comes from the "Rate" column on the line "up to $9525". It is 10%.
__
b) Simply compute the difference shown:
$38,700 -$9,525 = $29,175
__
c) 22% of $9,300 is ...
0.22 × $9,300 = $2,046
__
d) The total from the three previous calculations is ...
$952.50 +3,501.00 +2,046.00 = $6,499.50
Answer:
10%
$29,175
$2,046
$6,499.50
got it right on ttm.
Step-by-step explanation:
just believe me it works
Which of the following are true? If false, explain briefly.a) A P-value of 0.01 means that the null hypothesis is false.b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.c) A P-value of 0.01 is evidence against the null hypothesis.d) A P-value of 0.01 means we should definitely reject the null hypothesis
Answer:
a) false
b) true
c) false
d) false
Step-by-step explanation:
a) p-value is compared with test statistic to either accept or ereject the null hypothesis. There is no fixed p-value to reject the null hypothesis
b) p-value tells us the probabiltiy of finding null hypothesis to be true
c) There is no fixed p-value for nullyfying the the null hypothesis
d) There is no fixed p-value to reject the null hypothesis
find x.
8
2radius3
8
8radius3
(hurry plz, will give brainliest) -15pts-
Answer:
Answere is X= 8
Step-by-step explanation:
Use sine law
Sin(angle) = Opposite/ Hypotenuse
Sin (30) = 4 /X
X = 4 / sin (30)
X = 8
An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny
Answer:
The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Step-by-step explanation:
Let us denote the events as follows:
Event 1: a sunny day
Event 2: a rainy day
From the provided data we know that the transition probability matrix is:
[tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]
[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex] [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]
In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.
This implies that we need to compute the value of P₁₁².
Compute the value of P² as follows:
[tex]P^{2}=P\cdot P[/tex]
[tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]
The value of P₁₁² is 0.86.
Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Which line is perpendicular to the line Y= -1/3x -2 and passes through the point (1,4)
Answer:
work is shown and pictured
brenna goes on a cave tour with her family.she spots a mysterious crystal that is shaped like a cube the crystal has edge lengths of 5 centimeters what is the volume of the crystal
Answer:
The volume of the crystal is [tex]V=125 \:cm^3[/tex].
Step-by-step explanation:
The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.
To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula
[tex]V=s^3[/tex]
where:
s is the length of any edge of the cube.
From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is
[tex]V=5^3=125 \:cm^3[/tex].
Please answer this correctly
Answer: 207^2 + 9km^2 = 216km^2
Step-by-step explanation:
(my explanation is wrong)
All you want to do is break this figure up into rectangles and triangles.
I see 3 rectangles and 1 triangle.
Three Rectangles:
The bottom one has the dimension of 5 and 20. 5 x 20 = 100 km^2
The middle one has the dimensions of 5+4 and 7. 9 x 7 = 63 km^2
The top one has the dimensions of 4 and 11. 4 x 11 = 44 km^2
Add them all up to get 207km^2
One Triangle:
We can see at the bottom rectangle that the left side is 5 and the right side is 3 + x. X being our missing height of the triangle. The height equals 2.
The triangle now has the dimensions of 2 and 6. 2 x 6 = 12. Then divide by 2 to get 6 km^2
Answer:
216 km²
Step-by-step explanation:
To solve this, you have to divide the figure into different parts. I divided the parts up into four sections. I will work on the parts in numerical order.
1. At the top of the rectangle, it is marked 4 km. On the left side, it is marked 11 km. This is the length and width.
A = lw
A = 11 × 4
A = 44 km²
2. On the left side of this rectangle, it is marked 7 km. At the top it is marked 5 km, but there is a portion that does not have a measurement (the part with a different color than the rest. Because this line is also part of rectangle 1, we know that the line is 4 km. Adding up the two numbers gives you 9 km.
4 + 5 = 9
A = lw
A = 7 × 9
A = 63 km²
3. On the left side, it is marked 5 km. On the bottom, it is marked 20 km.
A = lw
A = 20 × 5
A = 100 km²
4. This is one is a bit more tricky. This is a triangle, so we have to find the base and the height. The base is 6 km. You have to figure the height. Look at the picture with the red lines.
The red line on the right side has a length of 17 + 3 + x = 20 + x. The length is 20 + x because there is a portion of the line that is missing.
The red lines on the left side have a length of 5 + 7 + 11 = 23. The two side should be equal so
23 = 20 + x
x = 3
Now, you have the height. Use the equation for area of a triangle to solve.
A = 1/2bh
A = 1/2(3)(6)
A = 1/2(18)
A = 9 km²
Now you have to add up all the areas to find the total area.
44 km² + 63 km² + 100 km² + 9 km² = 216 km²
simplify (6^7)^3
will give brainlist
Answer:
The answer is D.
Step-by-step explanation:
You have to apply Indices Law,
[tex] { ({a}^{m}) }^{n} \: ⇒ \: {a}^{mn} [/tex]
So for this question :
[tex] { ({6}^{7}) }^{3} [/tex]
[tex] = {6}^{7 \times 3} [/tex]
[tex] = {6}^{21} [/tex]
Solve the inequality -1/2x -3 ≤ -2.5
Answer:
x ≥-1
Step-by-step explanation:
-1/2x -3 ≤ -2.5
Add 3 to each side
-1/2x -3+3 ≤ -2.5+3
-1/2x ≤ .5
Multiply each side by -2, remembering to flip the inequality
-2 * -1/2x ≥ 1/2 * -2
x ≥-1
The expression 12g12g12, g gives the number of kilometers a car can travel using ggg liters of gasoline.
How far can this car travel on 5 \dfrac125
2
1
5, start fraction, 1, divided by, 2, end fraction liters of gasoline?
Answer:
Which of these factors will affect the friction on a road
Step-by-step explanation:
Answer:
66
Step-by-step explanation:
01
The list below shows the prices of T-shirts at a clothing store.
{8, 10, 10, 12, 15, 15, 18)
Which statement best describes the mean of this ser?
the difference between the least and greatest prices
the sum of the prices
the quotient of the difference between the least and greatest prices divided by 7
the sum of the prices divided by 7
dem
Answer:
the sum of the prices divided by 7
Step-by-step explanation:
The mean is the sum of the elements of a set, divided by the number of elements in the set. This set has 7 members, so its mean is ...
the sum of the prices divided by 7
Which set of three angles could represent the interior angles of a triangle? A 26 degrees, 51 degrees, 103 degrees B 29 degrees, 54 degrees, 107 degrees C 35 degrees, 35 degrees, 20 degrees D 10 degrees, 90 degrees, 90 degrees
Answer:
it is option A
Step-by-step explanation:
Which table represents a linear function?
Answer:
Top right option
Step-by-step explanation:
Do the points shown represent additive inverses? Explain why or why not
Answer:
Yes additive inverse is two complete opposite numbers if added = 0
Answer:
additive
Step-by-step explanation:
Because the point is not past the postive live or below the negative.
Amit found and labeled the areas of each of the faces of the triangle prism as shown which area calculation did Amit calculate incorrectly
Complete Question:
Amit found and labeled the areas of each of the faces of the triangular prism as shown.
Which area calculation did Amit calculate incorrectly?
Rectangular face with area 30 cm2
Rectangular face with area 40 cm2
Rectangular face with area 50 cm2
Triangular faces with areas 48 cm2
Answer:
Triangular faces with areas 48 cm2
Step-by-step Explanation:
To find out which area calculation Amit got wrong, let's calculate each faces of the given triangular prism attached below:
There area of theb5 faces should be as follows:
Area of rectangular face with L = 10 and B = 5 would be ==> 10*5= 50cm²
Area of rectangular face with L = 8 and B = 5 would be 8*5 = 40cm²
Area of rectangular face with L = 6 and B = 5 would 6*5 = 30cm²
Area of each of the triangular faces will be ½*8*6 = 48/2 = 24cm²
From our calculations, we'd observe that Amit didn't calculate the area of the triangular faces correctly. Amit got 48cm² instead of 24cm²
Answer:
Triangular faces with areas 48 cm2
Step-by-step explanation:
Identify the word form of this number: 139,204,539,912
One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.
Hope this helped!
What’s the Midpoint of (2,-1) and (1,-2)
Answer:
(3/2,-3/2)
Step-by-step explanation:
The midpoint of (2,-1)(1,-2) is (3/2,-3/2)
Answer:
(1.5,-1.5)
You have to remember the formula to find mid-point and that is:
[tex]midpoint = ( \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} )[/tex]
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Assume that military aircraft use ejection seats designed for men weighing between 133.8 lb and 208.0 lb. If women’s weights are normally distributed with a mean of 172.6 lb and a standard deviation of 42.4 lb, what percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)? Enter your answer as a percent rounded to one decimal place (do not add a "%"); add a trailing zeros as needed. The percentage of women with weights between 133.8 and 208.0 lb is [EjectPct] percent.
Answer:
61.8
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 172.6, \sigma = 42.4[/tex]
What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?
We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.
X = 208
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{208 - 172.6}{42.4}[/tex]
[tex]Z = 0.835[/tex]
[tex]Z = 0.835[/tex] has a pvalue of 0.798
X = 133.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{133.8 - 172.6}{42.4}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a pvalue of 0.180
0.798 - 0.18 = 0.618
0.618*100 = 61.8%
Without the %, the answer is 61.8.
Question: A box contains 160 Iphone XR's.
60% of the IPhones are Forest Green.
How many IPhones are Forest Green?
Answer:
96
Step-by-step explanation:
60% * 160 = 0.6 * 160 = 96.
Answer:
None
Step-by-step explanation:
There is no Forest Green iPhone XR's only the 11 Pros have that color.
Solve sin2x=-1/2 on the interval 0≤ angle≤360°
Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
6(4x - 3) - 30
24x - 18 = 30
24% -18 + 18 = 30 + 18
24x = 48
24x 48
24 24
X = 2
Original Equation
Step 1
Step 2
Step 3
Step 4
Step 5
Which of these is not part of the solution process?
A. Using the associative property
B. Adding 18 to both sides to isolate the variable term
C. Dividing both sides by 24 to isolate the variable
D. Using the distributive property
Answer:
A-using the associative property
Step-by-step explanation:
Joshua ate 2/6 of his sandwich in the afternoon and 2/6 more for a snack later that day. How much of Joshua’s sandwich is left?
Answer:
1/3 left
Step-by-step explanation:
The total sandwich is 1 or in fraction form 6/6
He ate 2/6
6/6 -2/6 = 4/6
Then he ate 2/6 more
4/6 -2/6 = 2/6
He has 2/6 left
Simplifying
2/6 =1/3
Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
They are increasing by 1 vertically. Hope this helps!! :)
Express the following ratio in its simplest form.
4:12
Answer:
1:3
Step-by-step explanation:
divide 4 ...............
.............
ps: idk the explanation
What is the next number in the sequence: 3, 8, 12, 48, 29, __
Answer:
144
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
3x4=12
12x4=48
8x4=32
32-3=29
29x4=116
Hope it's clear
The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 15 days. A distribution of values is normal with a mean of 267 and a standard deviation of 15. What percentage of pregnancies last beyond 246 days? P(X > 246 days) =
Answer:
91.92% of pregnancies last beyond 246 days
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 267, \sigma = 15[/tex]
What percentage of pregnancies last beyond 246 days?
We have to find 1 subtracted by the pvalue of Z when X = 246. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{246 - 267}{15}[/tex]
[tex]Z = -1.4[/tex]
[tex]Z = -1.4[/tex] has a pvalue of 0.0808
1 - 0.0808 = 0.9192
91.92% of pregnancies last beyond 246 days
Please answer this correctly
Answer:
Set the height up to 4
Step-by-step explanation:
Since there are 4 numbers between 1-5, set the height up to 4
Answer:
4 temperature recordings.
Step-by-step explanation:
2, 2, 4, 5
There are 4 recordings in the range of 1-5°C.
Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workforce. Only of the companies were planning to increase their workforce. Use the small-sample method to construct a confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places. A confidence interval for the proportion of companies that are planning to increase their workforce is .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The confidence level interval is [tex]0.016 \le C \le 0.404[/tex]
Step-by-step explanation:
The sample size is [tex]n = 20[/tex]
The number planning to increase workforce is [tex]x = 3[/tex]
The confidence level is [tex]c = 98[/tex]%
The value of proportion for a plus 4 method is
[tex]p = \frac{x+2}{n+4}[/tex]
substituting values
[tex]p = \frac{3+2}{20+4}[/tex]
[tex]p =0.21[/tex]
The z-critical value at confidence level of 98% is
[tex]z_{c}=z_{0.98} = 2.33[/tex]
This values is obtained from the standard normal table
The confidence level interval can be mathematically represented as
[tex]C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }[/tex]
substituting values
[tex]C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }[/tex]
[tex]C = 0.21 \pm 0.194[/tex]
=> [tex]0.016 \le C \le 0.404[/tex]
