By Green's theorem,
[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]
The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.
We'll verify this by actually computing the integral. Convert to polar coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]
The interior of the circle is the set
[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]
So we have
[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]
as expected.
Simplify the following expression:
7y + 2x − 10y + 3x2 − 10x
convert from degrees to radians
250°
Answer: the radians should be 125
Step-by-step explanation:
What is the most precise name for quadrilateral ABCD with vertices A(–5,2), B(–3, 5),C(4, 5),and D(2, 2)?
Answer: ABCD is a parallelogram.
Step-by-step explanation:
First we plot these point on a graph as given in attachment.
From the attachment we can observe that AD || BC || x-axis .
also, AB ||CD, that will make ABCD a parallelogram , but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".
Mid point of AC= [tex](\dfrac{-5+4}{2},\dfrac{2+5}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]
Mid point of BD= [tex](\dfrac{-3+2}{2},\dfrac{5+2}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]
Thus, Mid point of AC=Mid point of BD
i.e. diagonals bisect each other.
That means ABCD is a parallelogram.
Answer: ABCD is a parallelogram.
Step-by-step explanation:
First, we plot these points on a graph as given in the attachment. From the attachment, we can observe that AD || BC || x-axis. Also, AB ||CD, which will make ABCD a parallelogram, but to confirm, we check the parallelogram property "diagonals bisect each other," i.e., "Midpoint of both diagonals is equal."
The midpoint of AC=. The midpoint of BD=. Thus, the Midpoint of AC=Mid point of BD diagonals bisects each other. That means ABCD is a parallelogram.
Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?
Answer:
10
Step-by-step explanation:
Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.
Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:
5! / 2! * 3!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1
= 5 * 4 / 2 * 1
= 10
A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.) from a large batch of cups. They take a random sample of 200 cups from the batch of a few thousand cups and found 18 to be defective. The goal is to perform a hypothesis test to determine if the proportion of defective cups made by this machine is more than 8%.
Required:
a. Calculate a 95% confidence interval for the true proportion of defective cups made by this machine.
b. What is the sample proportion?
c. What is the critical value for this problem?
d. What is the standard error for this problem?
Answer:
a
The 95% confidence interval is [tex]0.0503 < p < 0.1297[/tex]
b
The sample proportion is [tex]\r p = 0.09[/tex]
c
The critical value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
d
The standard error is [tex]SE =0.020[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is [tex]H_o : p = 0.08[/tex]
The alternative hypothesis is [tex]H_a : p > 0.08[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{18}{200}[/tex]
[tex]\r p = 0.09[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the standard of error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]
substituting values
[tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]
[tex]SE =0.020[/tex]
The margin of error is
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 * 0.020[/tex]
=> [tex]E = 0.0397[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < \mu < p < \r p + E[/tex]
=> [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]
=> [tex]0.0503 < p < 0.1297[/tex]
5. Two unbiased dice are rolled. Calculate the probability that the sum of the two dice is:
ws
(a) 4
(b) 7
(c) Less than 7
-50 POINTS- (2/5) please no wrong answers for points. A) y = [tex]\frac{9}{2}[/tex] x + [tex]\frac{1}{2}[/tex] B) y = - [tex]\frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x +9[/tex] D) [tex]y=4x+15[/tex]
This problem is about creating a linear regression model.
First, we should take note of the points:
(-4,8)
(-2,4)
(-1,2)
(1,5)
(2,2)
(6,-5)
(7,6)
It's necessary to find a equation y = ax + b that brings us the least MSE (Mean Squared Error). You can calculate at hand, but I bet it is going to be tiresome.
So, basically intuitively you just need to choose a line that fits closer to the given points.
First: remember if y = ax+b, a is the slope which means if a > 0 the line is " / " and a < 0 the line is " \ ".
A) No, this equation is " / "
B) It could be this one.
C) It could be this one too.
D) Nope. " / "
B) a = -1/2
C) a = -4
You can draw those two lines and see that B) gets closer to the points.
Equation:
Y = -0.4957*X + 3.780
Answer: B)Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
surface area of a prism please help its my last day 120 points
Answer:
Area of the base = (8×6)/2 = 24 yd²
Height of the prism = 8 yd
Perimeter of the base = 8+6+10 = 24 yd
Surface area = 2B + Ph = (2×24)+(24×8) = 48+192 = 240 yd²
the area of triangle ABC is 31 1/4 square centimeters. What is the measure of b?
Answer:
102 cm
Step-by-step explanation:
22)
Subtract (4 - 21) - (3 - 51)
A)
1+3i
B)
1-71
7+3i
D)
7-7i
Answer:
1 +3i
Step-by-step explanation:
(4 - 2i) - (3 - 5i)
Subtract the reals
4 - 3 =1
Subtract the imaginary
-2i - -5i
-2i + 5i = 3i
1 +3i
Answer:
A
Step-by-step explanation:
Subtract all real numbers
4 - 3 = 1
Subtract all imaginary numbers
-2i - (-5i) = 3i
Put back together
1 + 3i
Best of Luck!
Suppose a life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $220. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the insurance company.
Answer:
$101.44
Step-by-step explanation:
To calculate expected value, we can multiply each outcome by its probability. The probability that the female will pay is 100%, so to start, the expected value is (100%) * $220 = 1 * $220 = $220
Next, the only way the insurance loses or gains money outside of this value is if the female dies. The probability of this happening is 1 - 0.999544 (the probability that the female survives) = 0.000456 . Therefore, the expected value that the insurance company will pay to the woman is
(260000) * (0.000456) = 118.56
Overall, the insurance company is expected to gain $220 from the woman and lose $118.56. Adding these two up, we get
220-118.56 = $101.44 as the overall expected value of the policy to the insurance company
Look at the pattern below. If the
pattern continues, what will be
the tenth number?
3. 11, 9, 17, 15, 23, 21...
Answer:
35
Step-by-step explanation:
We are adding 8 and then subtracting 2
3, 11, 9, 17, 15, 23, 21
The 8th number is 21+8 = 29
The 9th number
Subtract 2
29-2 = 27
10th number
Add 8
27+8 = 35
First is adding 8 to get the next number then subtract 2 to get the number after.
21 is the 7th number.
8th number = 21 + 8 = 29
9th number = 29-2 = 27
10th number = 27 + 8 = 35
Answer: 35
When ________ angles made by two lines and a transversal are supplementary, the lines are parallel. Question 20 options: A) corresponding B) same side interior C) alternate exterior D) alternate interior
Answer:
B) same side interior
Step-by-step explanation:
Supplementary angles are angles that can add up to the sum of angles on a straight line, [tex]180^{0}[/tex]. While a transversal in a line that passes through two parallel lines at two points.
If two lines are parallel to each other and a transversal through the lines, the sum of either same side interior angles would be supplementary.
The correct option for the given question is B, same side interior.
Answer:
B
Step-by-step explanation:
The quotient of three times a number and 4 is at least -16.
If anyone can help me I need to Define the variable and write an inequality, then solve.
Answer:
3x4≥−16
3x≥−64
x≥−643
x≥−2113
The answer is x≥−2113
musah stands at the center of a rectangular field . He first takes 50 steps north, then 25 step west and finally 50 steps on a bearing of 315°. How far west and how far north is Musah final point from the center?
Answer:
85.36 far north from the center
10.36 far east from the center
Step-by-step explanation:
The extra direction taken in the north side is x
X/sin(360-315)=50/sin 90
Sin 90= 1
X/sin 45= 50
X= sin45 *50
X= 0.7071*50
X= 35.355 steps
X= 35.36
Then the west direction traveled
West =√(50² - 35.355²)
West = √(2500-1249.6225)
West= √1250.3775
West= 35.36 steps
But this was taken in an opposite west direction
From the center
He is 35.36 +50
= 85.36 far north from the center
And
25-35.36=-10.36
10.36 far east from the center
find the measure of a
Answer:
C. 70°
Step-by-step explanation:
but c = 180° - (2×20°) = 140°
b = 180° - c
b = 180° - 140° = 40°
[tex]{ \sf{a = \frac{1}{2}c }} \\ { \sf{a = ( \frac{1}{2} \times 140 \degree)}} \\ { \sf{a = 70 \degree}}[/tex]
What is 1/3 of 675 is left
Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?
Answer:
There has been no significant change in the number of students in each major between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: There has been no change in the number of students.
Hₐ: There has been a significant change in the number of students.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 1.662.
The degrees of freedom is:
df = 4 - 1 = 4 - 1 = 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]
*Use a Chi-square table.
The p-value is 0.645.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.
Help me solve this and get marked branliest:
Answer:
75°
Step-by-step explanation:
Let's find the size of x°
BCFE has four sides so the sum of its angles sizes is 360°.
● CBE + 110 + 110 + CFE = 360
CFE is equal to 65° since they have the same vertex
● CBE + 220 + 65 = 360
● CBE + 285 = 360
● CBE = 360-285
● CBE = 75
CBE and x° have the same size since they share the same vertex.so:
● x° = 75°
Answer:
75°
Step-by-step explanation:
CBE = x (vertically opposite angles are equal)
CFR = 65° (vertically opposite angles are equal)
C+F+E+B= 360 (angles in a quadrilateral sum up to 360°)
110+65+110+x=360
x= 75°
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
The P-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ________.
Answer:
The P-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.
Step-by-step explanation:
The P-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.
The p-value is the probability that, if the null hypothesis were true,sampling variation would yield and estimate that is further away from the hypothesised value than our data estimate. The p-value shows us how possible it is to get a result like this if the null hypothesis is true.
Assuming we have a null hypothesis and an alternative hypothesis computed as follows.
[tex]H_o : \mu = 5 \\ \\ H_1 : \mu \neq 0.5[/tex]
If P-value is less than or equal to [tex]\mu[/tex] , we will reject the null hypothesis.
In some sparsely populated areas of the United States, the speed limit on highways can be as high as 80 miles per hour (mph).
What is this speed in meters per second (m/s)?
Conversion Factors:
1 mile = 1609 meters
1 hour = 3600 seconds
A. 2.98 m/s
B. 35.8 m/s
C. 1206.8 m/s
D. 2145.3 m/s
[tex](B)\:\:35.8\:\text{m/s}[/tex]
Step-by-step explanation:
[tex]80\:\dfrac{\text{mi}}{\text{hr}}×\left(\dfrac{1609\:\text{m}}{1\:\text{mi}}\right)×\left(\dfrac{1\:\text{hr}}{3600\:\text{s}}\right)[/tex]
[tex]= 35.8\:\text{m/s}[/tex]
Answer: b
Step-by-step explanation:
Graph the line.
Y=-1/4x+4
150,75,50 what number comes next
Answer:
35 or 25
Step-by-step explanation:
factor x-a in such a way that square root of x - square root of a is a factor
We want to factor the expression x - a, in such a way that we have one factor written as:
(√x - √a)
We will find that the factorized expression is:
(√x - √a)*(√x + √a)
Here we need to remember two things:
First, (√x)^2 = √(x^2) = x
also:
(x^2 - y^2) = (x + y)*(x - y)
Now, using the first property, we can rewrite our original expression as:
(x - a) = ( (√x)^2 - (√a)^2)
Now, using the second property, we can rewrite it as:
( (√x)^2 - (√a)^2) = (√x - √a)*(√x + √a)
Then we have:
(x - a) = (√x - √a)*(√x + √a)
Thus, we have factorized (x - a) in such a way that one of the factors is equal to (√x - √a)
If you want to learn more, you can read:
https://brainly.com/question/19386208
2(4×+2)=10
[tex]6 \times + 4 = 10 \\ \\ 6 \times = 10 - 4 \\ \\ 6 \times = 6 \\ \\ [/tex]
that is the answer
Answer:
x = 3/4
Step-by-step explanation:
2(4x + 2) = 10 Remove the brackets
8x + 4 = 10 Subtract 4 from both sides
8x = 6 Divide by 8
x = 6/8
x = 3/4
Check
2(4*3/4 + 2) =?10
2( 3 + 2) = 10
2*5 = 10
10 = 10
Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths. 72.3 degrees f
Answer:
72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees
Step-by-step explanation:
The number, 72.3 degrees, can be rewritten by breaking up the place value of each digit in the expression as folliws,:
70 degrees + 2 degrees + 0.3 degrees
The place value of 7 is tens
The place value of 2 is ones
The place value of 3 is tenths
[tex] 72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees [/tex]
Answer:
72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)
Step-by-step explanation:
got the off the assignment
You found the prime factorization of the number 73 explain how you can check your answer
9514 1404 393
Explanation:
You can check your answer by making sure that each of the primes you found is actually a prime. (Compare to a list of known primes, for example.) After you have determined your factors are primes, multiply them together to see if the result is 73. If so, you have found the correct prime factorization.
__
Additional comment
73 is prime, so its prime factor is 73.
73 = 73
Principal=2000,R=12percent,Time=2years and 6 months.
[tex]\boxed{\sf I=\dfrac{PRT}{100}}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{2000(12)(2.5)}{100}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{24000(2.5)}{100}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{60000}{100}[/tex]
[tex]\\ \sf\longmapsto I=600[/tex]
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} [/tex]
Basic TermsSimple Interest - Simple interest is the method of calculating interest charged on the amount invested in a fixed deposit.Principle - The principal is the amount due on any debt before interest, or the amount invested before returns.Rate - An interest rate is the percentage of principal charged by the lender for the use of its money.Time = Time is duration (in months or years) in Simple Interest.SolutionAs we know that , first we need to convert 2 years 6 months into years.
[tex] \sf \ \implies \: 1 \: \: year \: = \: 12 \: \: months[/tex]
[tex] \sf \implies \: 2 \: \: years \: \: and \: \: 6 \: \: months \: = \: 30 \: \:months[/tex]
[tex] \sf \implies \: \:\frac{ \cancel{30} \: \: ^{2.5 \: \: years} }{ \cancel{12 \: }} \\ [/tex]
[tex]\bf{\blue{ Time \: = \: 2.5 \: \: years}}[/tex]
Now , we have to find the Simple interest.[tex]\Large\rm{\orange{ \begin{cases} \large\begin{gathered} {\underline{\boxed{ \rm {\purple{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} \end{cases}}}[/tex]
Substuting the values[tex] \tt \large \longrightarrow \: \: S.I \: = \: \frac{2000 \: × \: 12 × \: 2.5}{100} \\ [/tex]
[tex] \tt \large \longrightarrow \: \: S.I \: = \frac{60000}{100} \\ [/tex]
[tex]\tt \large \longrightarrow \: \: S.I \: = \frac{600 \cancel0 \cancel0}{1 \cancel0 \cancel0} \\ [/tex]
[tex]\tt \large \longrightarrow \: \: S.I \: = \: 600[/tex]
[tex]\large \underbrace{\textrm {{{\color{navy}{Simple Interest \: = \: 600}}}}}[/tex]
In how many years will the compound amount on Ås 1250 beR 1,458 at 8%
Answer:
rate of interest per annum 8% step by step
Step-by-step explanation:
C.i is 1458 - 1250 = 208
there fore C.i = p [ C1 +r / 100 ) ^2_ 1
hope this help u