I assume [tex]C[/tex] is oriented counterclockwise. If [tex]C[/tex] is the closed rectangle, then by Green's theorem we have
[tex]\displaystyle \int_C F\cdot dr = \int_0^3 \int_0^9 \frac{\partial (x-y)}{\partial x} - \frac{\partial (x^2+y^2)}{\partial y} \, dy \, dx \\\\ ~~~~~~~~~~~~ = \int_0^3 \int_0^9 (1 - 2y) \, dy \, dx = 3 \int_0^9 (1-2y)\, dy = \boxed{-216}[/tex]
It seems unlikely, but if you actually are omitting the integral along the line segment joining (0, 9) and (0, 0), let [tex]x=0[/tex] and [tex]y=9-t[/tex] with [tex]0\le t\le9[/tex]. Then the integral along this line segment would be
[tex]\displaystyle \int_{(0,9)\to(0,0)} F\cdot dr = \int_0^9 \bigg((0^2 + (9-t)^2) i + (0 - (9-t)) j\bigg) \cdot (0i - j) \, dt \\\\ ~~~~~~~~ = \int_0^9 (9-t) \, dt = \frac{81}2[/tex]
so that the overall integral would instead have -216 - 81/2 = -513/2.
Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle
[tex]5th \: row = 1 \: \: \: 5 \: \: \: 10 \: \: \: 10 \: \: \: 5 \: \: \: 1[/tex]
[tex](x - 4) {}^{5} = x {}^{5} + 5x {}^{4} ( - 4) {}^{1} + 10x {}^{3} ( - 4) {}^{2} + 10x {}^{2} ( - 4) {}^{3} + 5x( - 4) {}^{4} + ( - 4) {}^{5} [/tex]
[tex](x - 4) {}^{5} = x {}^{5} - 20x {}^{4} + 160x {}^{3} - 640x {}^{2} + 1280x - 1024[/tex]
The sum of two consecutive even integers is 26. What is the product of the two integers?
A) 168
B) 160
C) 132
D)120
Listed below are systolic blood pressure measurements (in mmHg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.
The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67
How to determine the regression equation?From the table of values, we make use of the following representations:
Represent the Right Arm on the x axisRepresent the Left Arm on the y axisUsing the above representations, we can now plot our data values on a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 458Sum of Y = 782Mean X = 91.6Mean Y = 156.4Sum of squares (SSX) = 601.2Sum of products (SP) = 618.8The regression equation is
y = bx + a
Where
b = SP/SSX = 618.8/601.2 = 1.02927
a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843
This gives
y = 1.03x + 62.12
Hence, the regression equation between the variables is y = 1.03x + 62.12
To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have
y = 1.03 * 85 + 62.12
Evaluate
y = 149.67
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dilate the line segment by a scale factor of 2 with a center of dilation at the origin. Draw the dilated segment on the provided graph.
Answer:
See attached
Step-by-step explanation:
Each point on the line segment moves to 2 times its previous distance from the origin.
Invariant pointThe center of dilation, the origin, is an invariant point. It doesn't move for any dilation factor. One end of the line segment is there, so it will not move.
Dilated pointsThe coordinates of each point are multiplied by the dilation factor. The other end of the line segment is (5, 5), so it moves to 2×(5, 5) = (10, 10).
The dilated line segment extends from (0, 0) to (10, 10). It is shown in red in the attached graph.
Which equation is represented by the graph below?
The equation of the graph, in slope-intercept form, is: C. y = 2/3x + 6.
How to Write a Linear Equation in Slope-Intercept Form?The linear equation of a graph in slope-intercept form is expressed as y = mx + b. Where the variable in the equation are as follows:
b = y-intercept (this is the point on the y-axis where the line intercepts).m = slope (this is the rise/run along the line = change in y / change in x).Considering the graph given, to write the linear equation it represents, find the slope (m) and the y-intercept (b) of the line.
Slope (m) = rise/run = 2 units/3 units
Slope (m) = 2/3.
The line intercepts the y-axis at y = 6, thus, the y-intercept (b) would be 6. b = 6.
Substitute m = 2/3 and b = 6 into the slope-intercept form equation, y = mx + b:
y = 2/3x + 6
Thus, the equation, in slope-intercept form, that represents the linear graph as shown in the image given is: C. y = 2/3x + 6.
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Research that analyzes a portion of an entire population is carried out on a(n):____.
a. sample.
b. population.
c. census.
d. survey
Option (a) Sample
Sample is the research that analyzes a portion of an entire population.
A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.
By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.
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Determine how the strategies are similar. Picture below
Answer: Look at stwp by step
Step-by-step explanation:
Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2
solve for x: 5^x/5^14=1/5^5
Answer:
[tex] \frac{1 \\ }{3125} [/tex]
Answer:
x = 9
Step-by-step explanation:
Law of exponents:[tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]
[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]
Base are same. Compare the exponents.
x - 14 = -5
x = -5 + 14 {Addition property of equality}
x = 9
A group of 5 students took 15 days to finish a project. After 9 days, 3 students left the group. How many days did it take the students to finish the project in this case?
Using proportions, it is found that it took 15 days for the students to finish the project.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, we have that:
100% of the project is done by 5 students in 15 days.After the 3 students left, 2 students will have a time of x days to do 100 - (9/15) = 40% of the project.The compound rule of three is given as follows:
1 project - 5 students - 15 days
0.4 project - 2 students - x days
Increasing the number of students, the number of days is reduced, hence the measures are inverse proportional and the rule of three is given by:
[tex]\frac{15}{x} = \frac{2}[5} \times \frac{1}{0.4}[/tex]
[tex]\frac{15}{x} = \frac{2}{2}[/tex]
15/x = 1
x = 15 days.
It took 15 days for the students to finish the project.
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What is the slope of the line that passes through the points (6, 2) and
(
-18, 2)? Write your answer in simplest form.
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )
m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0
The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m = ( y₂ - y₁) / (x₂ - x₁)
It is given that the two points are (6, 2) and (-18, 2).
The two-point can be represented as,
(x₁, y₁ ) = (6, 2)
(x₂, y₂ ) =(-18, 2)
The slope of the line can be obtained as,
m = ( y₂ - y₁) / (x₂ - x₁)
m = (2-2) / (-18-6)
m =0 / -24
m =0
Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
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The idea that group work theories are appropriate for all clients all the time is a(n)? empirical truth professional tenet myth lie
The idea that group work theories are appropriate for all clients all the time is a myth (Third option).
About Group Process:
The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.
Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.
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Translate the triangle by
(-2 and -4)
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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Consider the line y equals 2 over 5 x plus 4.
Find the equation of the line that is parallel to this line and passes through the point left parenthesis 5 comma negative 1 right parenthesis.
the parallel linear equation is:
y = (2/5)*x - 3
How to find the parallel line?Two lines are parallel if the lines have the same slope but different y-intercept.
Here we know the line equation:
y = (2/5)*x + 4
Then a parallel line is of the form:
y = (2/5)*x + c
Where c is different than 4.
We want this line to pass through (5, -1), then:
-1 = (2/5)*5 + c
-1 = 2 + c
-1 - 2 = -3 = c
Then the parallel linear equation is:
y = (2/5)*x - 3
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I have been staying up studying all night i and have ming so mich trouble with this will someone help
Answer:
may be like this
its 32cm³
What do you get when you combine the following numbers? -4-4-4-4
Answer:
-16
Step-by-step explanation:
you just add all of them together
PLS HELP ASAP....i need to finish this soon
A GDP per capita of $13,000 would correspond to the following corruption score of: B. 42.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in the table above, we can logically deduce that the situation can be modeled by this linear function:
y = 511x - 8540
Where:
x is the corruption score.
y is GDP per capita in dollars.
How to calculate the corruption score?Based on the model, a GDP per capita of $13,000 would correspond to the following corruption score:
y = 511x - 8540
13,000 = 511x - 8540
511x = 13,000 + 8540
511x = 21,540
x = 21,540/511
x = 42.1 ≈ 42.
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√(2x+1)
Evaluate the integral
2
(2x + 1) In (2x + 1)
dx.
Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that
[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]
Triangle Angle Sum Theorem
Answer:
Step-by-step explanation:
Comment
The sum of the remote interior angles = The exterior angle not connected to them
What that means is that
<C + <D = <KEB
Givens
<C = 60
<KED = <C + <D
Solution and answer
<KED = <C + <D Substitute the givens into this equation
100 = 60 + <D Turn this around
<60 + <D = <100 Answer first equation
Subtract 60 from both sides
<60-<60 + <D = <100 - 60
<D = <40 Answer second Equation
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:
▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]
▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]
[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.
[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°
[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]
[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]
[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]
As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]
[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]
Instructions: Find the missing side. Round your answer to the
nearest tenth.
x=
30
38⁰
X
The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.
Find the value of the missing side:Trigonometric identities,
If in a right triangle ΔABC where A is the right angle
sin A = [tex]\frac{opposite\ side}{hypotenuse}[/tex]cos A =[tex]\frac{adjacent\ side}{hypotenuse}[/tex]tan A = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
In the question,
x is the adjacent side of the angle 38° and 30 units is the opposite side.
The ratio with opposite side and adjacent side is tan A
Therefore,
⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
⇒ tan 38° = 30/x
⇒ x = 30/tan 38°
∵ tan 38° = 0.781285627
⇒ x = 30/0.781285627
⇒ x = 38.398249
⇒ x = 38.40
Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.
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A cylinder has a radius of 1 inch and height of 1 inch.what is the approximate volume of the cylinder? round to the nearest hundredth. use 3.14 for π.1.05 cubic inches1.57 cubic inches3.14 cubic inches6.28 cubic inches
The volume of the cylinder is [tex]3.14 inch^3[/tex]
Given that
radius = 1 inch
height = inch
we know that volume =[tex]V = \pi \times r^2 \times h[/tex]
now put the value in the above equation we get
[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]
What is Volume?Volume is a measurement of three-dimensional space that is occupied.Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes.If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects with dimensions of zero, one, and two have no volume;To know more about volume with the given link
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the sum of three consecutive even integers if the largest is y
Answer: 3y-3
Step-by-step explanation: Largest is y. They are consecutive so the 2nd and 3rd and y-1 and y-2. So, the sum is y+y-1+y-2 which is 3y -3.
Sam has 3/4 ton of stones to divide evenly among for sidewalks. how much stone will it be used in each sidewalk
The amount of stone in each sidewalk is 3/16
How to determine the amount of stone in each sidewalk?The given parameters are
Stones = 3/4 tons
Side walks = 4
The amount of stone in each sidewalk is calculated using
Amount = Stones/Side walks
Substitute the known values in the above equation
Amount = 3/4 / 4
Evaluate the quotient
Amount = 3/16
Hence, the amount of stone in each sidewalk is 3/16
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Find the least positive integer N so that the value of 2020 + N
is both
• a perfect cube, and
• a multiple of 56.
Answer:724
Step-by-step explanation: Let us go through trail and error method.
Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.
2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01
Let us divide, 2744 with 56.
i.e., 2744/56= 49. ___ equation -02
As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.
i.e., 2020+N= 2744
N= 2744-2020
Therefore; N= 724.
Answer:
724,
Step-by-step explanation:
14^3 = 2744 is the next perfect cube > 2020.
2744 / 56 = 49.
So that fits the requirements in the question.
So N = 2744 - 2020
= 724,
What is a population parameter? a population parameter is a numerical descriptive measure of a population. give three examples. (select all that apply. )
Examples of population parameter are mentioned below .
According to the question
Population parameter :
A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.
The examples of population parameter is
1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.
2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.
3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.
Hence, examples of population parameter will depend on the population .
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Combine the like terms to create an equivalent expression.
7+4c+2d+3
Answer:
4c+2d+10
Step-by-step explanation:
7+4c+2d+3
4c+2d+(3+7)
4c+2d+10
Answer: 4c+2d+10
Step-by-step explanation:
plsssss help w math functions
Answer:
The second option:
[tex]2\sqrt{x}[/tex]
Step-by-step explanation:
If you need work please ask!
Have a nice day!
To the nearest foot what is the length of a pendulum that makes one full swing in 1.9s
A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.
What is the length of a pendulum?A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.
Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".
Given the equation:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
where L is the length in feet and T is the time in seconds.
Given that T = 1.9sec,
Hence:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
L = 2.93 feet
A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.
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The lines below are perpendicular.
the slope of the solid line iS 4, what is the slope of the dashed line?
Answer:
[tex]\frac{-1}{4}[/tex]
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.
If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]
At an airport screening, every 4th passenger will be selected to have their hands swabbed to screen for traces of explosives. Which sampling method is being used
The sampling method used is classified as Systematic.
How are sampling strategies classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, every 4th element is taken, which is a systematic sample with k = 4.
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There are 6 dogs and 5 cats. In how many different orders can these animals be placed in line if any animal can be next to any other animal?
120=!3÷!6
!2-!5=!3
to 120 modes
