Answer:
[tex]\frac{10\pi}{3}[/tex]
Step-by-step explanation:
According to the information of the problem we have to compute the following integral.
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]
Where the region of integration is
[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]
If you plot, that is just a circle between [tex]\pi/2[/tex] and [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.
When you switch coordinates
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]
Clarissa has just completed her second semester in college. She earned a grade of Upper D in her 4-hour linear algebra course, a grade of Upper D in her 5-hour sociology course, a grade of Upper D in her 2-hour engineering course, and a grade of Upper D in her 3-hour philosophy course. Assuming that A equals 4 points, B equals 3 points, C equals 2 points, D equals 1 point, and F is worth no points, determine Clarissa's grade-point average for the semester.
Clarissa's grade-point average for the semester is 1.
We have,
To calculate Clarissa's grade point average (GPA) for the semester, we need to assign points to each grade and calculate the weighted average.
Given the grade scale: A = 4 points, B = 3 points, C = 2 points, D = 1 point, and F = 0 points.
Clarissa earned the following grades:
Linear Algebra (4 hours): Upper D (D) = 1 point
Sociology (5 hours): Upper D (D) = 1 point
Engineering (2 hours): Upper D (D) = 1 point
Philosophy (3 hours): Upper D (D) = 1 point
To calculate the weighted average, we need to multiply each grade by the number of credit hours for the course and sum them up.
Then, we divide the total by the sum of the credit hours.
Total points = (1 * 4) + (1 * 5) + (1 * 2) + (1 * 3) = 4 + 5 + 2 + 3 = 14
Total credit hours = 4 + 5 + 2 + 3 = 14
GPA = Total points / Total credit hours = 14 / 14 = 1
Therefore,
Clarissa's grade-point average for the semester is 1.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
If f(x) = 3x+5 and g(x) = -2x^2-5x+3 fins (f+g)(x)
Answer:
f(x) + g(x) = -2x^2 - 2x + 8
Step-by-step explanation:
Given: f(x) = 3x+5 and g(x) = -2x^2-5x+3
Find f(x) + g(x)
f(x) + g(x) = 3x + 5 + (-2x^2 - 5x + 3)
f(x) + g(x) = 5 + -2x^2 - 2x + 3
f(x) + g(x) = -2x^2 - 2x + 8
Answer:
(f+g)(x) = -2x^2 -2x +8
Step-by-step explanation:
(f+g)(x) = f(x) +g(x)
= (3x +5) +(-2x^2 -5x +3)
(f+g)(x) = -2x^2 -2x +8
The two-way table shows the math and language arts course choices of eighth-grade students at Lana's school
Eighth-Grade Student Course Selections
Honors Mathematics Class
Non-Honors
Mathematics Class
18
72
Honors
English Class
Non-Honors English Class
24
111
What percentage of students who take honors English are taking a non-honors math class?
896
1896
20%
28%
Answer:
its c 20% on e2020
Step-by-step explanation:
Dan had 175 dollars to spend on 6 books. After
buying them he had 13 dollars. How much did each book cost ?
Answer:
27 dollars
Step-by-step explanation:
On one side he had 175
One the other side he has 6 books and 13 dollars
175 = 6b+13
Subtract 13 from each side
175 -13 = 6b+13-13
162 = 6b
Divide each side by 6
162/6 = 6b/6
27 = b
Each book is 27 dollars
A coral reef grows 0.16 meters ever week. How much does it grow in 7 weeks
Answer:
1.12 meters
Step-by-step explanation:
Answer:
1.12
Step-by-step explanation:
each week it grows 0.16 m
so,in 7 weeks it will grow 0.16*7m
The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter µ.
Use the accompanying data on absences for 50 days to obtain a 95% large sample CI for µ.
Absences: 0 1 2 3 4 5 6 7 8 9 10
Frequency: 2 3 8 11 8 7 6 2 1 1 1
[Hint: The mean and variance of a Poisson variable both equal m, so
Z = (X - µ)/√(µ/n),
has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1- a) and solving the resulting inequalities for µ.
You first calculate the sample mean, or μ_bar, of the data. Given it's a Poisson distribution, the mean is equal to the variance, giving your standard deviation. Finally, for a 95% CI, you apply the Z score to the formula μ_bar ± Z*(sqrt(μ_bar/n)) to obtain your confidence interval.
Explanation:The subject is related to Poisson distribution and the calculation of a confidence interval (CI) for the population mean (µ).
Firstly, we calculate the sample mean that is the total number of instances divided by the number of days:
(0*2 + 1*3 + 2*8 + 3*11 + 4*8 + 5*7 + 6*6 + 7*2 + 8*1 + 9*1 + 10*1)/50
This gives us the sample mean, µ_bar.
Given the data follows a Poisson distribution, the mean and the variance are equal (µ = variance). For a Poisson distribution, the variance is equal to µ divided by n, hence we get the standard deviation as sqrt(µ/n).
For a 95% CI, Z = 1.96 (from the standard normal table). Our CI will therefore be µ_bar ± Z*(sqrt(µ_bar/n)).
Since n is large, the distribution can be assumed to be approximately normal and the CI can be treated as reliable.
Learn more about Poisson distribution here:https://brainly.com/question/33722848
#SPJ12
To calculate a 95% confidence interval for a Poisson distributed data set, first calculate the sample mean. Consider the variance of Poisson equals to its mean, the standard error would be square-root of (mean divided by sample size). Using z-score of ±1.96 for 95% confidence level, solve for mean in both inequalities will give the interval.
The question pertains to deriving a 95% confidence interval for the mean (µ) of a Poisson distributed data set. In this case, the data set provided represents the number of teacher absences in a school district over 50 days.
Firstly, you will need to calculate the sample mean by multiplying each absence by its frequency, sum those up, then divide the sum by the total number of observations. This serves as an estimator for the Poisson mean µ.
Considering that the variance of a Poisson variable equals to its mean µ. The standard error would then be √(µ/n), where n is the number of observations. For a 95% interval, Z should be approximately ±1.96.
The confidence interval can be calculated using the standard formula for a large sample size:
Z = ±1.96 = (X - µ)/√(µ/n)
Solving for µ in both inequalities will give you the confidence interval.
For more such questions on confidence interval, click on:
https://brainly.com/question/2141785
#SPJ6
[tex] \sqrt{4 - {x}^{2}dx } [/tex]
Answer:
do you know what x or dx =
Step-by-step explanation:
how many feet of outdoor carpet is needed for a hole measuring 6ft,2ft,5ft,2ft,3ft,3ft,and 12ft?
Every day, you take the elevator from the basement parking lot that is at level -2 . The elevator takes two seconds per level and you find that it takes 46 seconds to reach your floor.
Answer:
you live on the 21st floor
Step-by-step explanation:
46-4=42 (level -2 to ground level)
42÷2=21
Rewrite the function by completing the square f(x)=x^2+2x+26
[tex] {x}^{2} + 2x + 26 = ( {x}^{2} + 2x + 26- 25) + 25 = \\ = (x + 1) ^{2} + 25[/tex]
The function f(x) = x² + 2x = 26 can be written as f(x) = (x + 1)² = 27.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as it's degree is two.
Given, f(x) = x² + 2x = 26.
f(x) = (x)² + 2(x)(1) + 1² = 26 + 1.
f(x) = (x + 1)² = 27.
learn more about completing the square method here :
https://brainly.com/question/4822356
#SPJ5
What is the value of tan157.5°
Precalc/Trig is easy. SO please mark me as BRAINLIEST
find the gcf of
24, 14, 21
Answer:
1
Step-by-step explanation:
All the numbers provided can have a factor of 1.
eg.)
1*24=24
1*14=14
1*21=21
This is because there is only one factor they all commonly share, 1.
Answer:
The answer is 1.
Step-by-step explanation:
Nothing else divides into the numbers other than 1.
Hope this helped!!
43. A beam rests against a wall, forming a 65º with the floor. Use the function y = 9 sec 8 to find the
length of the beam to the nearest tenth of a foot.
Answer:
[tex]Length\hspace{3}of\hspace{3}the\hspace{3}beam=y=21.3ft[/tex]
Step-by-step explanation:
Look the picture I attached you. As you can see the beam against the wall form a right triangle. The trigonometry functions on a right triangle are:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\hspace{10}csc(\theta)=\frac{hypotenuse}{opposite}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\hspace{10}sec(\theta)=\frac{hypotenuse}{adjacent} \\\\tan(\theta)=\frac{opposite}{adjacent} \hspace{20}cot(\theta)=\frac{adjacent}{opposite}[/tex]
The problem give us the following data:
[tex]y=9sec(\theta)[/tex]
Using the previous information about the trigonometry functions on a right triangle and the data provided by the problem you can conclude:
[tex]y=Hypotenuse\\Adjacent=9\\\theta=65^{\circ}[/tex]
Therefore:
[tex]y=9sec(65^{\circ})=9*(2.366201583)=21.29581425\approx21.3ft[/tex]
The length of the beam for the given situation is 21.3 ft.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.
Here, given function
y = 9. sec θ
put, θ = 65⁰
then, y = 9 X sec 65⁰
y = 9 X 2.366
y = 21.294 ft. ≈ 21.3 ft.
Thus, the length of the beam for the given situation is 21.3 ft.
Learn more about Trigonometry from:
https://brainly.com/question/13971311
#SPJ5
MATHEMATICAL CONNECTIONS What value of x makes the quadrilateral a parallelogram?
3x + 10
***
Answer:
x = 5 (check the diagram included)
Step-by-step explanation:
The question is incomplete, I have included a diagram to aid the understanding of the question
Parallelograms are quadrilaterals which have their opposite sides parallel and equal. This also means that the opposite angles in a parallelogram are equal
From the attached figure, we have:
|FG| = 3x + 10, |HE| = 7x - 30
To calculate for the value of x that makes the quadrilateral a parallelogram, we have:
Remember the opposite sides of a parallelogram are equal
3x + 10 = 7x - 30
3x - 7x = 10 - 30
-4x = -20
x = 20 ÷ 4
x = 5
x = 5 makes the quadrilateral a parallelogram
The area of a triangle is 1/2*(base)*(height) or base times height divided by two.
Answer:
both
Step-by-step explanation:
Enter 8/10 as hundredths.
Answer:
0.8 or .8
Step-by-step explanation:
multiply the top and bottom by 10
so 8/10=80/100
to get the decimal form, just divide 8 by 10 and it should give you 0.8
The double number line shows that a water park allows 18 people to go down a giant water slide in three minutes. Select the double number line that correctly label the number of people that can go down the slide in one, two, and four minutes.
Answer: B
Step-by-step explanation:
Firstly, we identify the number of people that can use the slide per minute, which is 6. Using this, we find that for 1 minute it's 6 people, for 2 minutes it's 12 people and for 4 minutes it's 24 people.
Explanation:The question provides us that 18 people can go down the water slide in 3 minutes. This suggests that every minute, 18 ÷ 3 = 6 people can go down the slide. So, for the double number line, we would show:
1 minute: 6 people 2 minutes: 6 x 2 = 12 people 4 minutes: 6 x 4 = 24 people
This 'per minute' basis helps in understanding and calculating the number of people going down the slide at different time intervals.
Learn more about Double Number Line here:https://brainly.com/question/13553589
#SPJ3
Five friends are sharing 82 dollars they keep a record of what they do first they split up the ten bills
Answer:
82 divided by 5 = 16.4
Step-by-step explanation:
you divide 82 by 5 and get 16.4 or 82 divided by 10= 8.2
They do first they split up the ten bills and it is 8.0.
We have given that,
Five friends are sharing 82 dollars they keep a record
82 divided by 5
[tex]\frac{82}{5} = 16.4[/tex]
You divide 82 by 5 and get 16.4,
After the split up to ten bills is given by,
What is the split?A split is a situation in a particular frame of a ten-pin bowling game where the player throws the ball and knocks the headpin
82 divided by 10
[tex]\frac{80}{10} =8.0[/tex]
They do first they split up the ten bills.
To learn more about the split visit:
https://brainly.com/question/1325044
#SPJ2
For a Christmas and New Year's week, the National Safety Council estimated that 500 people would be killed and 25,000 injured on the nation's roads. The NSC claimed that 50% of the accidents would be caused by drunk driving. A sample of 120 accidents showed that 67 were caused by drunk driving. Use these data to test the NSC's claim with LaTeX: \alphaα=0.05. What is the value of the test statistic used for this?
Answer:
We conclude that 50% of the accidents would be caused by drunk driving.
Step-by-step explanation:
We are given that the NSC claimed that 50% of the accidents would be caused by drunk driving.
A sample of 120 accidents showed that 67 were caused by drunk driving.
Let p = percentage of the accidents caused by drunk driving.
So, Null Hypothesis, [tex]H_0[/tex] : p = 50% {means that 50% of the accidents would be caused by drunk driving}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 50% {means that % of the accidents that would be caused by drunk driving is different from 50%}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of accidents caused by drunk driving = [tex]\frac{67}{120}[/tex] = 0.56
n = sample of accidents = 120
So, test statistics = [tex]\frac{0.56-0.50}{\sqrt{\frac{0.56(1-0.56)}{120} } }[/tex]
= 1.324
The value of z test statistics is 1.324.
Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to our null hypothesis.
Therefore, we conclude that 50% of the accidents would be caused by drunk driving.
There are 264 students going on a field trip to the city. If the school is only taking 8 buses, what is the total number of students that will be on each bus?
272
256
33
34
Answer:
Step-by-step explanation:
Answer:
272
Step-by-step explanation:
Jamie’s car is 9 yards long. Joey’s car is 27 feet long. When you line them up one in front of the other, how long are they together? (Answer in yards)
Answer:
First, our answer is 18 yards long.
Step-by-step explanation:
It is 18 yards long because first, we have 9, the length of Jamie's car. Joey's car length is 27 feet. Then, since 1 foot converted is 0.333333...., it is very hard to convert so i turn it in to 9 foot converted into 3 yards. Then, both sides multiply by 3 so 27 foot equals to 9 yards. 9 yards+9 yards equals 18 yards.
Hope it helps Hailey!
Pls mark it brainliest.
Thx!
Which of the following is not a way to determine if a relation is a function
At a local community college, 62% of all freshmen take both Statistics and English. What percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics?
(1) 18% (3) 82%
(2) 62% (4) 94%
Answer:
(3) 82%
Step-by-step explanation:
.62/.76=.8157894737 which when rounded is 82%.
If 76 percent of freshmen take Statistics, the percentage of freshmen who take English is 82 percent. Option B is correct.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics is found as;
The percent of freshmen taking Statistics are taking English if 76% of freshmen are taking Statistics is found as;
[tex]\rm \% S=\frac{.62}{.76} \times 100 \\\\ \% S=82\%[/tex][tex]% STATICS = \frac{.62}{.76} \times 100 \\\\ % STATICS = 81.5 \%[/tex]
Sixty-two percent of all freshmen at a nearby community college take both Statistics and English. If 76 percent of freshmen take Statistics,
Hence, the percentage of freshmen who take English is 82 percent.
To learn more about percentages, refer to:
brainly.com/question/13450942
#SPJ2
Two-thirds of a number is equal to 20. What is the number?
Answer:
The number is 30
Step-by-step explanation:
Let x be the number
2/3 x = 20
Multiply each side by 3/2 to isolate x
3/2 *2/3x = 20*3/2
x = 30
Easy 6th grade math ! Help please :)
Answer:
b 2.50 per 2 bottles of sprite
Step-by-step explanation:
Answer:
The answer is B.
2.50 per 2 bottles of sprite
Step-by-step explanation:
1. Find the area of the shaded sector.
- 12m
74
Answer:
888
Step-by-step explanation:
Im pretty sure this is the answer, if helpful please mark me as brainiest :>
What is the shortest possible perimeter for an arrangement with an area of 15 square feet
Answer:
The answer is 16 ft
Step-by-step explanation:
The shape with the smallest possible perimeter for a given area is a circle but among quadrilaterals, it's a square. Given an area of 15 square feet, the length of each side of the square would be approximately 3.87 feet, and the perimeter would be approximately 15.49 feet.
Explanation:The disciplines specified here is Mathematics, and the question is related to the correlation between an area and perimeter of a shape. In this case, the shape with the smallest possible perimeter for a given area would be a circle. However, if we only examine quadilateral shapes, then the shape with the minimum possible perimeter would be a square because a square is the quadrilateral that has the maximum area for a given perimeter.
If the area of the square is 15 square feet, then you can determine each side of the square by taking the square root of the area. The square root of 15 is approximately 3.87 feet. Now, to determine the perimeter of the square, you multiply this value by 4 because a square has four sides of equal length, hence perimeter is ~15.49 feet.
Learn more about Perimeter of a Square here:
https://brainly.com/question/2582010
Carl used some fabric to make a seat cover. Then he used 8 times as much fabric to make a tent. He used 24 yards to make the tent. Write an equation
Answer:
8x = 24
Step-by-step explanation:
[tex]x = \text{The fabric he used to make the seat cover}[/tex]
Then, since he used 8 times as much fabric to make the tent then
[tex]\text{Fabric needed for the tent} = 8x = 24[/tex]
Therefore your equation would be [tex]8x = 24[/tex]
To find the amount of fabric Carl used for the seat cover, the equation is 8x = 24. The variable x represents the amount of fabric for the seat cover, and 24 is the total yards of fabric used for the tent.
Explanation:Carl used some fabric to make a seat cover. Then he used 8 times as much fabric to make a tent. He used 24 yards for the tent. To write an equation to represent this situation, let's designate the amount of fabric used for the seat cover as x.
According to the problem statement, the tent required 8 times more fabric than the seat cover. Therefore, we can write the equation as:
8x = 24
Where:
x = the amount of fabric used for the seat cover8x = the amount of fabric used for the tent24 = the total amount of fabric used for the tent (given)This equation can now be solved to find out the amount of fabric Carl used to make the seat cover.
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 15 in. long and 7 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.) smallest value in in largest value in
Answer:
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
Step-by-step explanation:
The volume of a box can be written as;
V = l×b×h
Where;
Length = l
Breadth = b
Height = h
Let x represent the length of the cube cut out of the four edges.
Using the attached image;
Length l = 15 - 2x
Breadth b = 7 - 2x
Height h = x
Substituting the values to the volume equation;
V = (15-2x)(7-2x)(x)
V = 105x - 30x^2 - 14x^2 + 4x^3
V = 105x - 44x^2 + 4x^3
At Maximum volume, V' = dV/dx = 0
V' = 105 - 88x + 12x^2 = 0
Solving the quadratic equation, we have;
x = 5.83 or x = 1.50
x cannot be 5.83 since 2x > 7 (greater than the breadth of cardboard)
Therefore ;
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
Determine the intercepts of the line. y = − 7 x + 3 y=−7x+3
Answer:
x intercept (3/7, 0) or (0.429, 0)
y intercept (0, -3)
Step-by-step explanation: