Answer:
Yes, hypertension drugs lowers blood pressure.
Step-by-step explanation:
Claim: The hypertension medicine lowered blood pressure.
The null and alternative hypothesis is
H0:\mu_{d}\geq 0
H1:\mu_{d}< 0
Level of significance = 0.05
Sample size = n = 13
Sample mean of difference = \bar{d} = 10.1
Sample standard deviation of difference = s_{d} = 11.2
Test statistic is
t=\frac{\bar{d}}{s_{d}/\sqrt{n}}
t = ((10.1) / (11.2 /squre root of 13)) = 3.251
Degrees of freedom = n - 1 = 13 - 1 = 12
Critical value =2.179( Using t table)
Test statistic | t | > critical value we reject null hypothesis.
In Conclusion: The hypertension medicine lowered blood pressure
What is the area of the parallelogram below?
A. 7 in
B. 14 in
C. 15 in
D. 12 in
Answer:
D. 12 in²
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
Substituting the given values for the length of the base (b) and the height (h), we have ...
A = (4 in)(3 in)
A = 12 in²
The area is 12 square inches.
Answer:
D 12
Step-by-step explanation:
I just did the lesson and got it right.
Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. Net growth rate was computed by comparing the initial and final abundance of G. semen in the experiment, with a negative value indicative of a decrease in abundance. Here are the findings:Number of D. magna grazers 1 2 3 4 5 6Net growth rate of G. semen −1.9 −2.5 −2.2 −3.9 −4.1 −4.3Using the above information, software tells us that the least-squares slope is b = −0.5286 with standard error SEb = 0.1059.(a) What is the t statistic for testing H0: β = 0? (Round your answer to two decimal places.)t = (b) How many degrees of freedom does t have?df = Use this table to approximate the P-value of t against the one-sided alternative Ha: β > 0 (as the grazers would be expected to reduce algal growth).0.001 < P < 0.00250.0025 < P < 0.005 0.005 < P < 0.0100.010 < P < 0.0200.020 < P < 0.025(c) What do you conclude? (Use α = 0.05.)There is strong evidence that the population slope β is negative.There is not enough evidence to conclude that the population slope β is negative.
Answer:
Step-by-step explanation:
Hello!
To study if the biomass of Gonyostomum semen can be controlled by grazing zooplankton species the research team examined the relationship between:
Y: Net grow rate of G. semen in a test tube.
X: Number of D. magna grazers introduced in test tubes.
Since they are testing the relationship between two variables, i.e. how one variable affects the other, the researchers made a linear regression analysis and estimated the slope of the regression:
The point estimate of the slope: b= -0.5286
Standard deviation of the slope: Sb= 0.1059
n= 6 test tubes.
a)
For the hypotheses:
H₀: β = 0
H₁: β ≠ 0
The formula for the t-statistic is:
b)
The statistic has n-2 degrees of freedom.
So in this case you are working with a Student's t with 6-2= 4 degrees of freedom.
c)
Considering a one-sided alternative hypothesis H₁: β > 0, the calculated value of the statistic under the null hypothesis doesn't change, what change is the direction and size of the rejection region. In item a, the hypotheses had a two-tailed rejection region, for this item the rejection region is one-tailed to the right. This means that you'll reject at hight values of the statistic. The p-value is also one-tailed and you'll find it in the right tail of the distribution (That's why it's positive):
P(t₄≥4.99)= 1 - P(t₄<4.99)
Looking at the t-table. For this distribution, the value of 4.99 is between the t values that accumulate P(t₄<4.604)= 0.995 and P(t₄<7.173)= 0.999 of probability, so it will be between:
1 - 0.995= 0.005
and
1 - 0.999= 0.001
Using the given table and considering the value is closer to 4.064 than 7.173, the p-value will be approximate:
0.00025 < P < 0.005
The p-value is less than the significance level, α: 0.05, so the decision is to reject the null hypothesis. You can conclude that the population slope is not negative (β > 0)
⇒There is not enough evidence to conclude that the population slope β is negative.
I hope you have a SUPER day!
The answers are: a) The t statistic is approximately -4.99. b) the degrees of freedom are 4. c) There is strong evidence that the population slope β is negative.
(a) The t statistic for testing the null hypothesis H0: β = 0 is calculated using the formula:
t = (b - 0) / SEb
Where:
b = slope coefficient = -0.5286
SEb = standard error of the slope coefficient = 0.1059
Substitute the values into the formula:
t = (-0.5286 - 0) / 0.1059 ≈ -4.99
So, the t statistic is approximately -4.99.
(b) The degrees of freedom for the t statistic can be calculated using the formula:
df = n - 2
Where n is the number of data points, which is the number of observations (in this case, the number of Daphnia grazers), minus 2 for the two estimated coefficients (intercept and slope).
Given that there are 6 data points:
df = 6 - 2 = 4
So, the degrees of freedom are 4.
we see that the P-value falls between 0.001 and 0.0025. Therefore, we can approximate the P-value as:
0.001 < P < 0.0025
(c) Using α = 0.05 as the significance level, we compare the P-value to α. Since the P-value is less than α (0.0025 < 0.05), we reject the null hypothesis.
Therefore, the conclusion is: There is strong evidence that the population slope β is negative. In other words, based on the provided data and statistical analysis, it can be concluded that there is strong evidence that an increase in the number of Daphnia magna grazers is associated with a decrease in the net growth rate of Gonyostomum semen, indicating that the grazers are likely reducing the algal growth.
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Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009. These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by 40% or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed a mean of 1,114 per square meter with a standard deviation of 230. Annual lease rates for a sample of 40 commercial properties in Paris showed a mean lease rate of 989 per square meter with a standard deviation of 195. On the basis of the sample results, can we conclude that the mean annual lease rate is higher in Hong Kong than in Paris? Develop appropriate null and alternative hypotheses. At the 5% level of significance, what is your conclusion?
Answer:
Conclusion
The average rental rate in Hong Kong are higher than in Paris
Step-by-step explanation:
From the question we are told that
The sample size for Hong Kong is [tex]n_1 = 30[/tex]
The mean for Hong Kong is [tex]\mu_h = 1,114 \ m^2[/tex]
The standard deviation for Hong Kong is[tex]s = 230[/tex]
The sample size for Paris is [tex]n_2 = 40[/tex]
The mean for Paris is [tex]\mu_p = 989 \ m^2[/tex]
The standard deviation for Paris is [tex]s_p = 195[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The alternative hypothesis is
[tex]H_a: \mu_1 - \mu_2 >0[/tex]
The test statistics is mathematically represented as
[tex]t = \frac{\mu _1 - \mu_2 - d }{\sqrt{(\frac{s^2}{n1} )+(\frac{(s_p^2}{n_2} )}}[/tex]
Substituting values
[tex]t = \frac{1114 - 989 - 0 }{\sqrt{(\frac{230^2}{30} )+(\frac{(195^2}{40} )}}[/tex]
[tex]t = 2.399[/tex]
Since the value of the test statistics is higher than the significance level then there is enough evidence to conclude that the average rental rate in Hong Kong are higher than in Paris
Using the t-distribution, it is found that since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
At the null hypothesis, it is tested if the average is not higher in Hong Kong, that is, the result of the subtraction if not greater than 0.
[tex]H_0: \mu_H - \mu_P \leq 0[/tex]
At the alternative hypothesis, it is tested if it is higher, that is:
[tex]H_1: \mu_H - \mu_P > 0[/tex]
The standard errors for both samples are:
[tex]s_H = \frac{230}{\sqrt{30}} = 42[/tex]
[tex]s_P = \frac{195}{\sqrt{40}} = 30.83[/tex]
The distribution of the differences has mean and standard deviation given by:
[tex]\overline{X} = \mu_H - \mu_P = 1114 - 989 = 125[/tex]
[tex]s = \sqrt{s_H^2 + s_P^2} = \sqrt{42^2 + 30.83^2} = 52.1[/tex]
The test statistic is:
[tex]t = \frac{\overline{X} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence, the value is:
[tex]t = \frac{125 - 0}{52.1}[/tex]
[tex]t = 2.4[/tex]
The critical value, for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 40 - 2 = 68 df, is [tex]t^{\ast} = 1.67[/tex]
Since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
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A circle has a radius of 5. An arc of 162 degrees. What is the length of the arc?
Answer:
242
Step-by-step explanation:
Answer:
14.14 units
Step-by-step explanation:
Klan Academy- I checked and it was correct.
Help please I really do need help
Answer:
P'(-6, -4)
Step-by-step explanation:
The (x, y) coordinates of the plotted point P are (-2, 2).
Putting those values into the translation formula, you get ...
(x, y) ⇒ (x -4, y -6)
(-2, 2) ⇒ (-2 -4, 2 -6) = (-6, -4)
The coordinates of the translated point P' are ...
P'(-6, -4)
When calculating the successive discounts of 15% and 10% on a $100 item,
а. take 10% of $85
b. take 10% of $90
C. take 15% of $85
d. take 25% of $100
Answer:
A. Take 10% of $85
Step-by-step explanation:
Taking away 15% from $100 leaves you with $85 to take the second discount away from (10%)
Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. On a coordinate plane, triangle O M N has points (1, 3), (2, 1), (negative 1, 2). Triangle O prime M prime N prime has points (4, 1), (5, 3), (2, 2). How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?
Answer: the answer is i think* A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation: it's the only one that makes sense im takin the test
Answer:
A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation:
I took the test hope this helps!!!!!!!!!!!!!!
Which of the following choices is equivalent to 1 + 8(2x + 3)?
16x + 12
10x + 12
16x + 25
10x + 25
Answer:
16x + 25
Step-by-step explanation:
First, distribute the 8 to both numbers within the parenthesis.
1 + 16x + 24
Then, add similar terms together.
16x + 25
Final answer:
To simplify the expression 1 + 8(2x + 3), distribute the 8 across the terms inside the parentheses, leading to the equivalent expression 16x + 25 that is option C is correct.
Explanation:
To simplify 1 + 8(2x + 3), we distribute the 8:
1 + 8(2x) + 8(3)
1 + 16x + 24
16x + 25
"We keep tossing a fair coin n = 10^6 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? I also want the numerical value. 5. We rand
Answer:
Check the explanation
Step-by-step explanation:
Let [tex]X_{i}[/tex] be the indicator random variable that takes the value 1 if the ith coin is the first coin in a sequence of 19 consecutive heads.
For any sequence of length 19, the starting coin can be from toss i ,
such that i is between 1 and n - 19+1
Thus the number of such sequences is
Kindly check the attached image below for the step by step explanation to the question above.
what is equivalent to 601/2
Answer:
as a mixed number: 300 1/2 (reduced or equivalent)
as a decimal: 300.5 (reduced or equivalent)
as a percentage: 30,050% (reduced or equivalent)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
im smart
5x + 7y = 2 and -2x + 7y = 9
Answer:
conclusion one solution (-1 , 1)
Step-by-step explanation:
hello :
5x + 7y = 2 ...(*)
-2x + 7y = 9....(**)
by(*) and (**) calculate 7y
7y = 2-5x
7y = 9+2x
9+2x = 2-5x
2x+5x = 2-9
7x=-7 so : x= - 1
put this value in expression : 7y = 9+2x
7y = 9+2(-1)
7y =7
y =1
conclusion one solution (-1 , 1)
You fill an aquarium with water. The water is 22 inches deep. The water evaporates at a rate of 2 inches per week. a. Write an equation that approximates the depth y of water in the aquarium c weeks after you fill it. b. After two weeks, you have not yet refilled the aquarium. What is the depth of the water?
The equation for water depth in the aquarium after evaporation is y = 22 - 2c.
a. Equation: The equation approximating the depth y of water in the aquarium c weeks after filling it is y = 22 - 2c.
b. Depth after Two Weeks: Substitute c = 2 into the equation, y = 22 - 2(2) = 18 inches.
What is bigger 2 gallons or 16 quarts?
Answer:
16 quarts
Step-by-step explanation:
16 quarts is bigger than 2 gallons because every 4 quarts equals 1 gallon.
Ella drew 40 different pictures for an art show. Twenty of them include a dog in the picture. If she shuffles the pictures and picks one at random to give to her friend, what is the probability that she will pick one that includes a dog?
A.
0.2
B.
0.05
C.
0.1
D.
0.5
Answer:
0.05
Step-by-step explanation:
A group of 4 people share 1/2 pounds of almonds how many pounds of almonds does each person get choose an equation you can use to answer the question
Answer:
1/2 x 1/4=1/8
Step-by-step explanation:
A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. There is no fire There is a fire (b) Define Type I and II errors. A smoke detector sounds an alarm when there is no fire A smoke detector does not sound an alarm when there is a fire (c) In this case, which type of error has the more severe consequences
Answer:
(a) H₀: There is no fire vs. Hₐ: There is a fire.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
(c) In this case, type II error has the more severe consequences.
Step-by-step explanation:
It is provided that a hotel installs smoke detectors with adjustable sensitivity in all public guest rooms.
(a)
The hypothesis can be defined as follows:
H₀: There is no fire.
Hₐ: There is a fire.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case a type I error will be committed if we conclude that there is a fire and the smoke detector sounds an alarm, when in fact there is no fire.
In this case a type II error will be committed if we conclude that there is no fire and the smoke detector does not sounds an alarm, when in fact there is a fire.
(c)
In this case, type II error has the more severe consequences.
Concluding that there is no fire as the smoke detector did not sound an alarm, when in fact there is a fire, will cause casualties and is harmful for the health of the guests.
Guests would not be alert about the fire as there was not any alarm, and many may loose their lives because of this.
The null hypothesis is 'There is no fire', the alternative hypothesis is 'There is a fire'. A Type I error would be sounding an alarm when there is no fire (rejecting the null hypothesis when it is true), a Type II error would be not sounding an alarm when there is a fire (failing to reject the null hypothesis when it is false). The more severe consequence would be due to a Type II error, as it could result in unrecognized danger.
Explanation:In this scenario, the null hypothesis would be 'There is no fire' and the alternative hypothesis would be 'There is a fire'. In terms of type I and II errors, a Type I error would occur if the smoke detector sounded an alarm when there is no fire, or in other words, rejecting the null hypothesis when it is in fact true. A Type II error would occur if the smoke detector does not sound an alarm when there is a fire, meaning failing to reject the null hypothesis when it is in fact false.
Considering the consequences of these errors, a Type II error would be more severe in this scenario, as it could lead to a serious danger not being recognized, potentially resulting in damage or harm.
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Find the sum of the first 10 terms if a(n) = n^2 - n +1
Answer:
The formula to find the sum of the first n terms of our sequence is n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
Determine whether the data described below are qualitative or quantitative and explain why. The postal codes of survey respondents Choose the correct answer below. A. The data are quantitative because they consist of counts or measurements. B. The data are quantitative because they don't measure or count anything. C. The data are qualitative because they don't measure or count anything. D. The data are qualitative because they consist of counts or measurements.
Answer:
C
Step-by-step explanation:
Postal code numbers are qualitative data because on these numbers, we can't perform any calculations.
The data are qualitative because they don't measure or count anything.
The correct option is C.
What is qualitative data?
Information that cannot be quantified, tallied, or simply stated using numbers is referred to as qualitative data.
Given:
The postal codes of survey respondents.
Here, no numbers are given.
Data visualization technologies like word clouds, idea maps, graph databases, timelines, and infographics are used to communicate the information that is gathered from text, audio, and visual sources.
And the data can not be calculated.
Therefore, Postal code numbers are qualitative data.
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each shape is divided into equal parts. select the shapes that show thirds. mark all that apply
Answer:
Triangle,Circle,Square, 3 cubes
Step-by-step explanation:
Lisa rides a bicycle 30 miles every 5 hours at this rate how many hours did Lisa ride is she rode 150 miles
Answer:
25 hours
Step-by-step explanation:
30 times 5 is 150 and 5 times 5=25
In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t).)
Answer: equation = dA/dt = K₁ (M - A) - K₂A
Step-by-step explanation:
Let us follow this carefully to get our equation right.
From the question we are told to (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t) ).
The Rate of memorizing the material is ∝ [Total amount to be memorized] - [Amount memorized]
remember using A for A(t).
where A rep the amount memorized at a time t and M is the Total amount memorized.
so we have that dA/dt ∝ M - A
which is dA/dt = K₁ (M - A) ---------------(*)
remember it was stated that forgetfulness is taken into account
Forgetfulness, F ∝ A
F = K₂A --------------- (**)
which implies the rate of memorization is decreased as a result of forgetting;
this leads to
dA/dt = K₁ (M - A) - K₂A
The rate of differential equation is ⇒ dA/dt = K₁ (M - A) - K₂A
cheers i hope this helped!!!!
The following data gives the monthly sales (in thousands of dollars) for different advertising expenditures (also in thousands of dollars) and sales commission percentages. Sales 245 138 352 322 228 275 560 366 Advertising 16.5 18.0 22.3 18.4 19.0 19.5 30.0 18.6 Commission 10.5 2.0 4.0 3.5 4.5 1.8 9.0 8.5 1. What amount of sales would this model predict for advertising expenditures of 25,000 and sales commission of 8%? [Show your code in "R Code" section. Show the answer in "Answer" section. Leave "Comments" section blank.] 2. Find the correlation coefficients for advertising expenditure and commission compared to sales. Explain the results of these findings. [Show your code in "R Code" section. Show the answer in "Answer" section. Leave "Comments" section blank.] 3. At the 5% level of significance, are advertising expenditure or sales commission percentage significant? Why? [Show your code in "R Code" section. Show the answer in "Answer" section. Include the mathematical notations of two sets of null and alternate hypotheses and the phrase "advertising expenditure" or "sales commission percentage" or "both" along with a justification in a few sentences in "Comments" section.]
Answer:
Check the explanation
Step-by-step explanation:
Use the below R Code
Sales=c(245,138,352,322,228,275,560,366)
Advertising=c(16.5,18,22.3,17.4,19,20,32,18.6)
Commission=c(10.5,2,4,3.5,4.5,1.8,9,8.5)
data=as.data.frame(cbind(Sales,Advertising,Commission))
model1=lm(Sales~Advertising+Commission, data = data)
dat2=data.frame(Advertising=25,Commission=8)
predict(model1,dat2)
The predicted value of Sales for 25000 dollar on Advertising and 8% on Commission is 424685 dollars approximately (rounded to 0 decimal places)
Can someone help me ...
On one day a Plumber Joe earned $80 on a plumbing job. Out of his earnings he spent $6.85 on tea and snacks, $5.50 on food and $21.40 on tools. Before reaching home that evening his boss sent Plumber Joe $22 on "cash app", which his boss said was a tip from his early morning plumbing job. How much did he save on that day?
Answer:
Joe saved 68.25
Step-by-step explanation:
Subtract 6.85 from 80, you get 73.15
Subtract 5.50 from 73.15 and you get 67.65.
Subtract 21.40 from 67.65 and you get 46.25.
Add 22 to that amount, you get 68.25.
P.S
Have an Amazing Day! I Hope this Helps and Good Luck!!
~Faker/Tosrel
if you were to roll a standard 6 sided game die 60 times, approximately how many times would you expect to roll each of the six faces?
Answer:
1/10(1 out of every 10)
Step-by-step explanation:
6/60 = 1/10
Find f(-2) for the function fwd) = 3x - 2x +7
Answer:
23
Step-by-step explanation:
Maybe you want to evaluate ...
f(x) = 3x^2 -2x +7
for x = -2.
Put the value of x where x is, then do the arithmetic.
f(-2) = 3(-2)^2 -2(-2) +7 = 3(4) +4 +7
f(-2) = 23
The sum of 20.7 and a number is 50.5. Which equation could you use to solve the problem? What should you do to each side of the equation to isolate the variable? What is the solution of the equation?
Answer:
Which equation could you use to solve the problem?
✔ g + 20.7 = 50.5
What should you do to each side of the equation to isolate the variable?
✔ Subtract 20.7 from each side.
What is the solution of the equation?
✔ 29.8
Step-by-step explanation:
An equation that could be used to solve this word problem is 20.7 + x = 50.5.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In order to solve this word problem, we would assign a variable (x) to the unknown number and then translate the word problem into algebraic equation as follows:
20.7 + x = 50.5
Subtract 20.7 from each side:
20.7 - 20.7 + x = 50.5 - 20.7
x = 50.5 - 20.7
x = 29.8.
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Which choice could represent the volume of a cake pan
Answer:
3150^3
Step-by-step explanation:
100 POINTS.
PLEASE PROVIDE STEPS
Step-by-step explanation:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Answer:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Step-by-step explanation:
which of the functions below have period pi? check all that apply
The functions that actually have period pi are:
B. y = csc x
C. y = sec x
Let's understand what the period of a function is all about.
What is period of a function?Period of a function is known to be the distance that exists between the repetition of any function. In trigonometry, the length of a complete cycle is known as a period.
So, we can see that the functions that actually have period pi are y = csc x and y = sec x.
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Answer:
Step-by-step explanation: