The length of the parametric curve (call it C ) is given by
[tex]\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t[/tex]
[tex]y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t[/tex]
Now,
[tex]\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t[/tex]
so that the arc length integral reduces to
[tex]\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt[/tex]
which has an approximate value of 53.4596.
What is the center of the circle?
Answer:The point from which circle is drawn is called center of circle.
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...
ide length
Recall that in a 30° -60° - 90° triangle, if the shortest leg
measures x units, then the longer leg measures x/5 units
and the hypotenuse measures 2x units.
(150/3 – 757) ita
(300 - 757) ft
(150/3 - 257) ft
(300 - 257) ft?
Help out
Question Correction
A circle is inscribed in a regular hexagon with side length 10 feet. What is the area of the shaded region? Recall that in a 30–60–90 triangle, if the shortest leg measures x units, then the longer leg measures [tex]x\sqrt{3}[/tex] units and the hypotenuse measures 2x units.
[tex](150\sqrt{3}-75\pi) $ ft^2[/tex] (300 – 75π) [tex]ft^2[/tex][tex](150\sqrt{3}-25\pi) $ ft^2[/tex](300 – 25π) ft2Answer:
(A)[tex](150\sqrt{3}-75\pi) $ Square Units[/tex]
Step-by-step explanation:
Area of the Shaded region =Area of Hexagon-Area of the Circle
Area of Hexagon
Length of the shorter Leg = x ft
Side Length of the Hexagon =10 feet
Perimeter of the Hexagon = 10*6 =60 feet
Apothem of the Hexagon (Length of the longer leg)
= [tex]x\sqrt{3}[/tex] feet
[tex]=5\sqrt{3}$ feet[/tex]
[tex]\text{Area of a Regular hexagon}=\dfrac{1}{2} \times $Perimeter \times $Apothem[/tex]
[tex]=\dfrac{1}{2} \times 60 \times 5\sqrt{3}\\=150\sqrt{3}$ Square feet[/tex]
Area of Circle
The radius of the Circle = Apothem of the Hexagon [tex]=5\sqrt{3}$ feet[/tex]
Area of the Circle
[tex]=(5\sqrt{3})^2 \times \pi\\ =25 \times 3 \times \pi\\=75\pi $ Square feet[/tex]
Therefore:
Area of the Shaded region [tex]= (150\sqrt{3}-75\pi) $ Square feet[/tex]
Answer:
it’s A
Step-by-step explanation:
i took the test
you will get alot of points if you answer this explain your answer
Answer:
The surface area of stand is 46 feet.
First
taking the upper rectangular prism only.
so we get
l=3
w=1
h=3
surface area of rectangular prism = 2lw+2lh+2hw
= 2×3×1+2×3×3+2×3×1
= 30
taking the lower rectangular prism only.
surface area of rectangular prism = 2lw+2lh+2hw
=2×7×2+2×1×7+2×2×1
=46
add both the rectangular prism.
we get,
30+46
76
Yes, $15 is enough
Taking out the square of all the rectangle the total would be 52m²
52/25×6.79 ( as 6.79 dollars for 25 m²)
$14.1232
Answer:
freecoins
Step-by-step explanation:
What are the solutions to the quadratic equation 2x^2 + 10x - 48 = 0?
A. x= -4 and x = 6
B. X= -8 and x = 2
c. x= -6 and x = 8
D. X = -8 and x = 3
pls help, you will get branliest !!
Answer:
4.......................
A company produces product with a mean weight of 10 and a standard deviation of 0.200. A new process supposedly will produce products with the same mean and a smaller standard deviation. A sample of 20 products produced by the new method has a sample standard deviation of 0.126. At a significance level of 10%, is it appropriate to conclude that the new process is less variable than the old?
Answer:
[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:
Now we can calculate the p value with this probability:
[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]
Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.
Step-by-step explanation:
Information given
[tex]n_1 = 10 [/tex] represent the sampe size old
[tex]n_2 =20[/tex] represent the sample size new
[tex]s_1 = 0.2[/tex] represent the sample deviation for old
[tex]s_2 = 0.126[/tex] represent the sample deviation for new
The statistic is given by:
[tex]F=\frac{s^2_1}{s^2_2}[/tex]
Hypothesis to test
We want to test if the new process is less variable than the old, so the system of hypothesis are:
H0: [tex] \sigma^2_1 \leq \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 >\sigma^2_2[/tex]
The statistic is given by:
[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:
Now we can calculate the p value with this probability:
[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]
Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x)) your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]
Therefore you answer choice would be B. [tex](x+6)^4[/tex]
The following data summarizes results from 945 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.
Pedestrian
intoxicated not intoxicated
Driver intoxicated 64 68
not intoxicated 292 521
Answer:
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
945 accidents.
In 64 of them, the pedestian was intoxicated.
In 292 of them, the driver was intoxicated.
Probability that the pedestrian was intoxicated or the driver was intoxicated.
(64+292)/945 = 0.3767
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
a^3b^2 divided by a^-1b^-3
Answer:
[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]
And simplifying we got:
[tex] a^3 b^2 a b^3[/tex]
[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]
Step-by-step explanation:
We want to simplify the following expression:
[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]
And we can rewrite this expression using this property for any number a:
[tex] a^{-1}= \frac{1}{a}[/tex]
And using this property we have:
[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]
And simplifying we got:
[tex] a^3 b^2 a b^3[/tex]
[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]
There are two fields whose total area is 56 square yards. One field produces grain at the rateof34bushel per square yard; the other field produces grain at the rate of23bushel per squareyard. If the total yield is 40 bushels, what is the size of each field
Answer:
the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
Step-by-step explanation:
With the statement we can make a system of 2x2 equations, where:
"x" is the area of the first field
"y" is the area of the second field
However,
x + y = 56 => x = 56 - y
3/4 * x + 2/3 * y = 40
replacing we have:
3/4 * (56 - y) + 2/3 * y = 40
42 - 3/4 * y + 2/3 * y = 40
-0.0833 * y = 40 - 42
y = -2 / -0.0833
y = 24
now for x:
x = 56 - 24
x = 32
This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
please need help asap!
Answer:
2/8 or 1/4
Step-by-step explanation:
There are 4 sections so if you spin it twice, we would double it so we have 2/8 and simplified to 1/4
I hope it helps you!
30 pontos de graça
Quanto é 100X4=?
Answer:
me marca como melhor resposta ☺️❤️
Step-by-step explanation:
.....
Answer:
400
brigadaaaaaaaaaaaaaa
find the perimeter of of the shaded figure. ? units
Answer:
38 Units
Step-by-step explanation:
7 each down each side
10 each across top and bottom
2 more for each indent on bottom
7+7+10+10+2+2
14+20+4
38
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
g(x) = x2 – 5x + 2.
Answer:
Use the quadratic formula:
a = 1 b= -5 c= 2
x = - -5 +-sqr root (25 - 4 * 1 * 2) / 2 * 1
x = 5 +-sqr root (25 - 8) / 2
x = 5 +- sqr root (17) / 2
x1 = 5 +4.1231056256 / 2
x1 = 4.5615528128
x2 = 5 -4.1231056256 / 2
x2 = 4.5615528128
Step-by-step explanation:
This chart shows Dan’s budget:
A 3-column table has 5 rows. The first column is labeled Item with entries Internet, food, rent, discretionary spending, income. The second column is labeled Amount budgeted with entries 35, 100, 500, 100, 750. The third column is labeled Amount spent with entries 35, 95, 500, 140, blank.
Did Dan stay on budget? Why or why not?
Yes, Dan spent as much as he earned.
No, Dan should move to a new apartment.
Yes, Dan uses his savings to cover extra expenses.
No, Dan should reduce his discretionary spending
The correct answer is D No, Dan should reduce his discretionary spending
Explanation:
For Dan to stay on the budget he needs to spend the amount budgeted for each expense or less than the amount budgeted. This occurred in the case of the Internet, food, and rent; for example, the amount budgeted for the internet was $35 and Dan spent this money, also, the amount budgeted for food was $100 and Dan spent $95, which means he stood in the budget. However, this did not occur with discretionary spending, which refers to other non-necessary expenses, because in this case, Dan spent $140 even when the budget limit was $100. Also, this exceeds the total income considering 35 + 95 + 500+ 140 = $770, which is above the income ($750). Thus, Dan did not stay in the budget because he spent more money than expected in discretionary spending and should reduce this.
The correct answer is D. No, Dan should reduce his discretionary spending.
Hope this helps
:)
A
B
C
D
Help me out
Answer:
2x^2 + 3/2x -5
Step-by-step explanation:
f(x) = x/2 -2
g(x) = 2x^2 +x -3
f(x)+ g(x) = x/2 -2+ 2x^2 +x -3
Combine like terms
= 2x^2 + 3/2x -5
Solve 2x - 11 = k for x.
!Please help!
When representing a frequency distribution with a bar chart, which of these bars will be the shortest?
A. A bar representing a frequency of 24
B. A bar representing a frequency of 48
C. A bar representing a frequency of 36
D. A bar representing a frequency of 12
Answer:
D
Step-by-step explanation:
12 is lowest.
A bar chart is one of the most commonly used representations or visually translate groups of data.
We have given that,
When representing a frequency distribution with a bar chart.
What is the frequency distribution?
frequency distribution, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times.
It is drawn in such a way that the x-axis of the graph would represent the items and the y-axis will be for the frequency.
Out of the choices given, the shortest among the bars will be that would frequency is only 36.
Hence, the answer to this item is the letter C.
To learn more about the frequency distribution visit:
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6500 rounded to the nearest thousand is __. Enter your answer without commas
Answer:
7000
Step-by-step explanation:
If the hundreds place is higher than 5, then add 1 to the thousands place.
The figure shows three lines that intersect at point N.
3 lines intersect. Lines G K and J M intersect at point N to form a right angle. Line H L intersects the other lines at point N. Angle H N G is 48 degrees.
Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL?
42°
48°
132°
138°
Answer
The figure shows three lines that intersect at point N.
3 lines intersect. Lines G K and J M intersect at point N to form a right angle. Line H L intersects the other lines at point N. Angle H N G is 48 degrees.
Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL?
42°
48°
132°
138°
Step-by-step explanation:
42
The required measure of angle MNL is 42°. Option A is correct.
3 lines intersect lines G K and J M intersect at point N to form a right angle. Line H L intersects the other lines at point N. Angle H N G is 48 degrees. Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL is to determine
The angle can be defined as the one line inclined over another line.
unit of measure of an angle is degree and radians.
Angle GNH is congruent to angle KNL.
∠KNL = 48°
Angle MNL is complementary to angle KNL
Since angle MNK = 90°
∠MNL + ∠KNL = 90°
∠MNL = 90-48
∠MNL = 42°
Thus, the required measure of angle MNL is 42°. Option A is correct.
Learn more about Angles here:
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please help image attached!
Answer:
The unit circle centered at the origin in the Euclidean plane is defined by the equation:
[tex]x^2+y^2=1\\[/tex]
Given an angle , there is a unique point P on the unit circle at an angle θ from the x-axis, and the x- and y-coordinates of P are:
[tex]x=cos \theta \\y = sin \theta[/tex]
Consequently, from the equation for the unit circle:
[tex]cos^2\theta+sin^2\theta=1[/tex]
the Pythagorean identity.
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3/4
Step-by-step explanation:
Find two points on the line
(0,1) and (-4,4)
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (4 -1)/(-4 -0)
= 3/-4
= -3/4
PLEASE HELPPPPPPPPPP <3
Answer:
y = 1/2x + 4
Step-by-step explanation:
Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.
When we count rise over run, we find that the slope is 1/2
y = 1/2x + b
The line intersects the y-axis at 4, so the y-intercept is 4.
y = 1/2x + 4
I hope this helps :))
Assume that SAT scores are normally distributed with mean mu equals 1518 and standard deviation sigma equals 325. If 1 SAT score is randomly selected, find the probability that it is greater than 1600. If 81 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.
Answer:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
Step-by-step explanation:
Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1518,325)[/tex]
Where [tex]\mu=1518[/tex] and [tex]\sigma=325[/tex]
We want to find this probability:
[tex]P(X>1600)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\frac{sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
The mean of three numbers is 4
Two of the numbers are 1, 9
What is the missing number?
Answer:2
Step-by-step explanation: 9+1+2=12
12\3=4
ANSWER : 2
Assuming the below results were obtained in a study used to test the accuracy of the rapid diagnostic test for influenza, calculate and interpret the sensitivity of the rapid diagnostic influenza test.
Frequency of Flu Cases Frequency of Non-Fu Cases
Frequency of Individuals who 47 10
Screened Positive
Frequency of individuals who 43 100
Screened Negative
A) When the rapid diagnostic influenza test is used, 52.22% of individuals who have the flu test positive for the flu.
B) When the rapid diagnostic influenza test is used, 90.91% of individuals who have the flu test positive for the
C) When the rapid diagnostic influenza test is used, 47.78% of individuals who have the flu test positive for the flu.
D) When the rapid diagnostic influenza test is used, 9.09% of individuals who have the flu test positive for the flu.
Answer:
c
Step-by-step explanation:
Determine whether the study depicts an observational study or an experiment.
A study is conducted to determine if there is a relationship between stomach cancer and alcohol consumption.alcohol consumption. Everyone treated at a hospital for stomach cancer was asked Everyone treated at a hospital for stomach cancer was asked about their alcohol consumption.
a. The study is an experiment because the researchers control one variable to determine the effect on the response variable.
b. The study is an observational study because the researchers control one variable to determine the effect on the response variable.
c. The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.
d. The study is an experiment because the study examines individuals in a sample, but does not try to influence the variable of interest.
Answer:
Option c
Step-by-step explanation:
The study is an observational study. An observational study is made when the researchers collect data based on what they see, hear or observe without any form of manipulation or treatment plan from the researchers. Thus, in this case, the study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable/influence their responses.
What is the value of lifeee, and when do you think corona will stop! Will mark brainliest cuz why not
Answer:
LIFE: Your life purpose consists of the central motivating aims of your life—the reasons you get up in the morning. Purpose can guide life decisions, influence behavior, shape goals, offer a sense of direction, and create meaning. For some people, purpose is connected to vocation—meaningful, satisfying work. Also always be your self (:
Corona: I think corona depending on were you live will stop next year when they find a treatment for it.
Hope this helped!
Answer:
Your life is the most important thing. It shouldn't be worth 1 million dollars, or even 1 billion dollars, because it's worth everything.
Corona can't really stop. It's a matter of the government to try to contain the virus, so it won't spread even further. I think the right time to reopen the economy is when we find a vaccine. But of course, places all over the U.S. are already reopening which will cause a spike in cases, therefore making our "self-isolation" even longer.
A battery with 20% percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% percent of its capacity is charged. How do you graph this
Answer:
The relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
The graph is attached.
Step-by-step explanation:
We will graph the charged capacity of the battery in function of time.
The rate of charge is constant, so we can conclude the relation is linear.
At time t=0, the battery capacity is at 0.2 (or 20%).
Every minute that passes, an additional 5% percent of its capacity is charged. So we can say that at t=1, the battery capacity is 0.2+0.05=0.25 (or 25%).
We can calculate the slope of the linear function as:
[tex]m=\dfrac{\Delta Y}{\Delta t}=\dfrac{0.05}{1}=0.05[/tex]
Then, the relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
