(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.
- 10,946
- 17,711
- 22,897
- 28,656
Given:
[tex]\phi=1.618[/tex]
22nd number in Fibonacci sequence = 17,711
To find:
The 23rd number in the Fibonacci sequence.
Solution:
The nth term of a Fibonacci sequence is:
[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]
Substituting [tex]\phi=1.618, n=21[/tex], we get
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=10941.1724024[/tex]
[tex]f_{21}\approx 10941[/tex]
Now,
[tex]f_{23}=f_{21}+f_{22}[/tex]
[tex]f_{23}=10941+17711[/tex]
[tex]f_{23}=28652[/tex]
It is about 28,656. Therefore, the correct option is D.
The slope of diagonal AB is ___ , and it’s equation is ___.
Answer:
The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].
Step-by-step explanation:
Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.
Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].
SCALCET8 3.11.501.XP. Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(4)) (b) sinh(4)
sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875
sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789. What is the appropriate conclusion
Answer:
The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
Step-by-step explanation:
It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.
At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.
Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.
Which function is shown in the graph below?
Answer:
B is the answer
the graph is shifted up +3
the graph is curving upward, so the power has to be positive
an oil tank, which is a shape of a cylinder, is 3m high and has a diameter of 6m. the oil tank is two-thirds full. find the number of cubic meters of oil in the tank. use 3.14 for pi
Answer:
Step-by-step explanation:
The key is to find out the entire volume the tank can hold when it is full, then take 2/3 of that amount. The volume of a cylinder is
[tex]V=\pi r^2h[/tex] and filling in:
[tex]V=3.14(3)^2(3)[/tex] (if the diameter is 6 m, the radius is 3) so
V = 84.78 m³ when it is full all the way. If we need the amount that makes up 2/3 of that:
[tex]\frac{2}{3}(84.78)=56.52m^3[/tex]
The control department of a light bulb manufacturer randomly picks light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is . When or more of the light bulbs in the sample of are defective, the control unit calls repair technicians for service.
Required:
a. Find the mean of p, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction.
b. Find the standard deviation of p.
Answer:
The answer is a
Step-by-step explanation:
answer please don't skip plz answer
What is the value of x^2
-2xy+y^2
if x-y = 4 ?
please answer
Answer:
16
Step-by-step explanation:
[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]
[tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]
The value of x^2-2xy+y^2
will be 16 .
Explanation is in the attachment .
hope it is helpful to you ☺️
solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.
Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]
Step-by-step explanation:
Given
In equality is [tex]x^3+4x>5x^2[/tex]
Taking terms one side
[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]
Using wavy curve method
[tex]x\in (0,1)\cup (4,\infty)[/tex]
A decorative wall in a garden is to be build using bricks that are 3 3/4 inches thick and mortar joints that are 1/4 inch. Use the diagram to find the height of the wall
Step-by-step explanation:
we cannot see the diagram, so we don't know how many layers of bricks are used. and therefore it is impossible to tell the height of the wall.
What does point b represent on the graph ?
Answer:
Step-by-step B represents the $14 John earned in the 2 hours he worked.
explanation:
HELP ME PLEASE ASAP! So the answer for the question I got is 113.1. Is my answer correct or is it wrong? Please let me know how to solve this problem if the answer is wrong. Thank you for your time.
Answer: 113.01m - You are almost right
Step-by-step explanation:
Simply by using pir^2, you get the number you calculated, but it is asking for at least 2 decimal places. So it would be "113.01"
15. Which of the following is a rational number?
O A.V-
O B. 18
O C. T (3.141592...)
OD.3.59
Answer:
c
Step-by-step explanation:
non terminating recurring. i think option c must be the answer
Find the value for the side marked below.
Round your answer to the nearest tenth.
у
100
49°
y = [?]
Answer:
y = 75.5
Step-by-step explanation:
Reference angle (θ) = 49°
Hypotenuse = 100
Opposite = y
Apply trigonometric function, SOH. Which is:
Sin θ = Opp/Hyp
Plug in the values
Sin 49 = y/100
100*Sin 49 = y
y = 75.5 (nearest tenth)
We have the number of emergency room admissions to SWTRHA hospital on 6 different Friday the 13ths along with the number of admissions to the same hospital on the previous Friday the 6th. Is there any difference between admissions on the 6th and the 13th. Conduct a depedent samples t-test to find out. What is the value of your t Stat
Answer:
Test statistic = - 2.71
Step-by-step explanation:
Table of the sample data is attached below :
Using a dependent sample t test :
H0 : μd = 0
H0 : μd ≠ 0
The difference in the 6th and 13th date data is :
Difference, d = -4, -6, -3, -1, 1, -7
The sample size, n = 6
The mean of d ; μd = Σd/ n = - 3.667
Standard deviation of difference, Sd = 3.011
The test statistic : μd/(Sd/√n)
Test statistic = - 3.33 / (3.011/√6)
Test statistic = - 3.33 / 1.2292356
Test statistic = - 2.709
Test statistic = - 2.71
What is the area of triangle ABC? - OP 03 square units 0 7 square units o 11 square units 0 15 square units see pic
Answer:
7 sq unit
Step-by-step explanation:
Area of triagle ABC = Area of rectangle mnBp - Area of trangle AmC - Are of triangle CnB - Area of triangle ABp
Area of rectangle mnBp = 5x3 = 15 sq unit
Area of trangle AmC = 4x2 /2 = 4 sq unit
Are of triangle CnB = 5x1 /2 = 2.5 sq unit
Area of triangle ABp = 3x1 /2 = 1.5 sq unit
I believe you can work out thd answer from the above
what is equivalent to x-2(3x-1)=3x
Answer:
1/4 = x
Step-by-step explanation:
x - 2( 3x - 1 ) = 3x
Step 1 :- Distribute 2
x - 2 × 3x - 2 × 1 = 3x
x - 6x + 2 = 3x
Step 2:- Combine like terms
-5x + 2 = 3x
Step 3 :- Add 5x to both sides
-5x + 5x + 2 = 3x + 5x
2 = 8x
Step 4 :- Divide both side by 8
2/8 = 8x / 8
1/4 = x
Sidney's retirement party costs $28, plus an additional $1 for each guest she invites. What is the maximum number of guests there can be if Sidney can afford to spend a total of $44 on her retirement party?
Answer:
16 guests
Step-by-step explanation:
Firstly, we know Sidney's retirement party costs a starting amount of $28. We also know that she can only spend $44 on her retirement party. The easiest way to do it in my opinion is subtract 28 from 44, giving you 16. Since we know that each guest is only $1, we know that the maximum number of guests Sidney can afford is 16 guests. I hope this helped and please don't hesitate to ask for clarification!
$44-$28=$16
$16÷$1=16 guests at most
What is the meaning proportion between 3 and 27?
Answer:
you mean the mean not the meaning right?
The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.
Write the equations for a line parallel to the line:
y=-4/3x-4
That goes through the point (-7,-6)
Write your equation in slope intercept form, using reduced fractions for the slope and intercept if necessary.
Answer:
y = -4/3x -46/3
Step-by-step explanation:
The question tells us to write an equation that is:
- parallel to the given line
- goes through the point (-7, -6)
Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.
We are going to use the point-slope form to find the other line.
Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).
(I attached the point-slope form as an image below)
m = slope
x1 = x coordinate of the point
y1 = y coordinate of the point
We are going to substitute our slope into the form first:
y - y1 = (-4/3)(x - x1)
Next let's put in our point (-7, -6):
(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )
y - (-6) = -4/3(x - (-7))
(cancel out the negatives to make them positive)
y + 6 = -4/3 (x +7)
Now solve for x using basic algebra:
y + 6 = -4/3 (x +7)
(distribue the -4/3)
y + 6 = -4/3x - 28/3
(subtract 6 from both sides)
y = -4/3x -46/3
That's your answer!
Hope it helps (●'◡'●)
Answer:
Step-by-step explanation:
y + 6 = -4/3(x + 7)
y + 6 = -4/3x - 28/3
y + 18/3 = -4/3x - 28/3
y = -4/3x - 46/3
please give full solutions
√8281
Answer:
the answer is 91
Step-by-step explanation:
Annual earnings, including bonuses, for Financial Analysts and Personal Financial Advisors, are currently following a skewed to the right distribution with a mean of $66,500 and a standard deviation of $10,500. According to the 68-95-99.7 rule, it is correct to say that (select ALL that apply):______.
a. the middle 95% of all Financial Analysts and Personal Financial Advisors make between $45.500 and $77,000 annually.
b. only 2.5% of all Financial Analysts and Personal Financial Advisors make less than $45,500 annually.
c. both of the above statements are false
Answer:
c. both of the above statements are false
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Distribution skewed to the right
This means that the Empirical Rule is not applicable, and the two statements are false, and thus, the correct answer is given by option c.
The first would be false nonetheless, but the second would be true if the distribution was normal.
In order to test for the significance of a regression model involving 4 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are Select one: a. 3 and 43 b. 4 and 43 c. 4 and 42 d. 3 and 42
Answer:
c. 4 and 42
Step-by-step explanation:
Given
[tex]p = 4[/tex] -- independent variables
[tex]n = 47[/tex] ---- observations
Required
The numerator and denominator degrees of freedom
The denominator degrees of freedom is:
[tex]df =n - p - 1[/tex]
[tex]df =47 - 4 - 1[/tex]
[tex]df =42[/tex]
For the numerator, we have:
[tex]df = p[/tex]
[tex]df = 4[/tex]
helppp!! 21 - 3y = -18
3x+ y = -5
Answer:
(-3,4)
Step-by-step explanation:
A system of equations is given to us. The given equations are ,
[tex]\implies 2x - 3y = -18[/tex]
[tex]\implies 3x + y =-5[/tex]
We need to plot the graph and find the solution of the given system . For that refer to attachment . The point at which both the lines of the graph will intersect each other will be the solution of the given system of equations .
From the graph we can see that it intersect at (-3,4) . Therefore the Solution is ,
[tex]\longrightarrow \underline{\underline{ Solution = (-3,4)}}[/tex]
Answer: If you graphing it’s (-6, 13) or (3, 4)
Step-by-step explanation:
21 - 3y = -18- y = 13
3x + y = -5- x = -6
What is the probability that in a sample of 400 registered voters to at least 290 voted in their most recent local
Answer:
The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:
= 72.5%
Step-by-step explanation:
Sample of registered voters = 400
Sample of voters that actually voted = 290
Probability = 290/400 * 100
= 72.5%
b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted. Probability measures the chance of an event occurring given other events. Therefore, one can conclude that the voting was at least 72.5%. Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.
Simplify 6/x^2−2x/x^2+3.
Answer:
3x2−2x+6/x2
Step-by-step explanation:
have a great day <33333
Find the value of x pls help
9514 1404 393
Answer:
x = 36°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles. A linear pair is supplementary. So, you can find x either of two ways:
2x = x + (180 -4x) ⇒ 5x = 180 ⇒ x = 36
Or ..
4x = x + (180 -2x) ⇒ 5x = 180 ⇒ x = 36
The value of x is 36°.
In July 2014 one Mexican peso was worth 0.075 U.S. dollars. How many Mexican pesos was $133.00 U.S. dollars worth?
Answer:
1,773.33 Mexican pesos
Step-by-step explanation:
Create a proportion where x was how many Mexican pesos it was worth:
[tex]\frac{1}{0.075}[/tex] = [tex]\frac{x}{133}[/tex]
Cross multiply and solve for x:
133 = 0.075x
1773.33 = x
So, it was worth approximately 1,773.33 Mexican pesos
3.6 subtract by 1.487 is egual to ______.Pls write in step by step.
Answer:
2.113
Step-by-step explanation:
[tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]
Which of the following best describes the relationship between angle a and angle bin the image below?
