To group the ages of the Galapagos tortoises into five classes of equal width, with a minimum age of 1 year and a maximum age of 170 years, the class limits, boundaries, and midpoints for the grouped quantitative data table are as follows:
Class Width:
The class width is determined by subtracting the minimum age (1) from the maximum age (170) and dividing by the number of classes (5). Rounding the solution to the next highest whole number gives a class width of 34.
Class Limits:
The class limits define the range of values that belong to each class. Starting with the lower limit of the first class as 1 year, the class limits for the five classes are:
Class 1: 1 - 35
Class 2: 36 - 70
Class 3: 71 - 105
Class 4: 106 - 140
Class 5: 141 - 175 (175 is the next whole number greater than the maximum age of 170)
Class Boundaries:
The class boundaries are the values that separate adjacent classes. They are obtained by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class. The class boundaries for the five classes are:
Class 1: 0.5 - 35.5
Class 2: 35.5 - 70.5
Class 3: 70.5 - 105.5
Class 4: 105.5 - 140.5
Class 5: 140.5 - 175.5
Class Midpoints:
The class midpoints represent the central values within each class. They are obtained by calculating the average of the lower and upper class boundaries. The class midpoints for the five classes are:
Class 1: 18
Class 2: 53
Class 3: 88
Class 4: 123
Class 5: 158
To know more about grouped quantitative data refer here:
https://brainly.com/question/17293083#
#SPJ11
From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 2.1., # 40) Using polar coordinates, describe the level curves of the function defined by f (x, y) = - 2xy (22+y2) if (x, y) + (0,0) and f(0,0) = 0.
The level curves of the function f(x, y) = -2xy / (2^2 + y^2) in polar coordinates consist of lines θ = π/2 + kπ and θ = kπ, as well as the upper half and lower half of the unit circle depending on the sign of the function. These level curves represent the points (r, θ) where the function f(r, θ) is constant.
To describe the level curves of the function f(x, y) = -2xy / (2^2 + y^2), we can first express the function in terms of polar coordinates. Let's substitute x = r cos(θ) and y = r sin(θ) into the function:
f(r, θ) = -2(r cos(θ))(r sin(θ)) / (r^2 + (r sin(θ))^2)
Simplifying this expression, we get:
f(r, θ) = -2r^2 cos(θ) sin(θ) / (r^2 + r^2 sin^2(θ))
Now, we can further simplify this expression:
f(r, θ) = -2r^2 cos(θ) sin(θ) / (r^2(1 + sin^2(θ)))
f(r, θ) = -2 cos(θ) sin(θ) / (1 + sin^2(θ))
The level curves of this function represent the points (r, θ) in polar coordinates where f(r, θ) is constant. Let's consider a few cases:
1. When f(r, θ) = 0:
This occurs when -2 cos(θ) sin(θ) / (1 + sin^2(θ)) = 0. Since the numerator is zero, we have either cos(θ) = 0 or sin(θ) = 0. These correspond to the lines θ = π/2 + kπ and θ = kπ, where k is an integer.
2. When f(r, θ) > 0:
In this case, the numerator -2 cos(θ) sin(θ) is positive. For the denominator 1 + sin^2(θ) to be positive, sin^2(θ) must be positive. Therefore, the level curves lie in the regions where sin(θ) > 0, which corresponds to the upper half of the unit circle.
3. When f(r, θ) < 0:
Similar to the previous case, the level curves lie in the regions where sin(θ) < 0, which corresponds to the lower half of the unit circle.
In summary, the level curves of the function f(x, y) = -2xy / (2^2 + y^2) in polar coordinates consist of lines θ = π/2 + kπ and θ = kπ, as well as the upper half and lower half of the unit circle depending on the sign of the function.
To know more about level curves refer here:
https://brainly.com/question/32198067#
#SPJ11
A survey was conducted that asked 1014 people how many books they had read in the past year. Results indicated that x = 12.7 books and s= 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval Click the icon to view the table of critical t-values. Construct a 90% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice (Use ascending order. Round to two decimal places as needed) OA. There is 90% confidence that the population mean number of books read is between __ and __. if repeated samples are taken, 90% of them will have a sample mean between __ and __. There is a 90% probability that the true mean number of books read is between __ and __ .
There is 90% confidence that the population mean number of books read is between 9.85 and 15.55. If repeated samples are taken, 90% of them will have a sample mean between 9.85 and 15.55. There is a 90% probability that the true mean number of books read is between 9.85 and 15.55.
What is the 90% confidence interval for the mean number of books read?The survey results indicate that the mean number of books read in the past year is estimated to be 12.7, with a standard deviation of 16.6. To construct a 90% confidence interval, we can use the t-distribution and the sample size of 1014. Using the critical t-values from the table, we calculate the margin of error by multiplying the standard error (s / √n) with the t-value. Adding and subtracting the margin of error from the sample mean gives us the lower and upper bounds of the confidence interval.
The confidence interval for the mean number of books read is calculated as 12.7 ± (t-value * 16.6 / [tex]\sqrt{1014}[/tex]), which simplifies to 12.7 ± 2.58. Therefore, the confidence interval is (9.85, 15.55).
In interpretation, this means that we can be 90% confident that the true mean number of books read in the population falls between 9.85 and 15.55. If we were to repeat the survey and take different samples, 90% of those samples would produce a mean number of books read within the range of 9.85 to 15.55. The confidence interval provides a range of values within which we can reasonably estimate the true population mean.
Learn more about Probability
brainly.com/question/31828911
#SPJ11
increase 50$ by 15%
Can you say how to do it and answer?
A rectangular swimming pool is 6 it deep. One side of the pool is 3.5 times longer than the other. The amount of water needed to fill the swimming pool is
1344 cubic feet. Find the dimensions of the pool.
Answer:
8 feet by 28 feet by 6 feet
Step-by-step explanation:
So volume is length times width times height
It tells us that the volume is 1344 cubic feet (the water used to fill it)
And it also tells us that the height/depth (which are the same thing in this case) is 6ft
All we need now are length and width
We know that one of the sides is 3.5 times the other one. So we can just say length is x and width is 3.5x
So plugging that in, the equation becomes
[tex]3.5x*x*6=1344[/tex]
3.5 x times x is just 3.5x squared so
[tex]3.5x^2*6=1344[/tex]
divide both sides by 6
[tex]3.5x^2=244[/tex]
divide by 3.5
[tex]x^2 =64[/tex]
[tex]x=\sqrt{64}[/tex]
x = 8
So that means the one side is 8 feet long and the other side is 3.5 times that, which is 28 feet long.
So the dimensions of the pool are 8 feet by 28 feet by 6 feet
The units for square centimeters are written as
Check all that apply.
O A. cm2
B. sq. cm
C. km2
D. sq.m
E cm
solve for x. round your answer to the nearest tenth
Answer:
11.9
Step-by-step explanation:
Use sin
Sin ratio is opposite over hypotenuse
Sin [tex]57^{o}[/tex] = [tex]\frac{10.8}{x}[/tex]
x = [tex]\frac{10.8}{sin57^{o} }[/tex]
x = 11.9
Solve the system of equations using the substitution method. Show your work and be sure to include the solution to the system.
which of the following expressions is equivalent to -10?
a.-7 3
b.-3 - 7
c.3 - 7
d.7 - 3
The expression which is equivalent to -10 is the option b, -3 - 7.
Explanation:
We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;
-3 - 7 = -10 (-3 - 7)
The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.
If we add -3 and -7 we will get -10. This makes the option b the correct answer.
Learn more about expression here:
https://brainly.com/question/28170201
#SPJ11
find the shaded region of the figure below
Answer:
-x³ + 3x² - 14x + 12
Step-by-step explanation:
Area of outer rectangle = (x² + 3x - 4) * (2x - 3)
= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)
=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)
=2x³ + 6x² - 8x - 3x² - 9x + 12
= 2x³ + 6x² - 3x² - 8x - 9x + 12 {Combine like terms}
= 2x³ + 3x² - 17x + 12
Area of inner rectangle = (x² - 1)* 3x
= x² *3x - 1*3x
= 3x³ - 3x
Area of shaded region = area of outer rectangle - area of inner rectangle
= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)
= 2x³ + 3x² - 17x + 12 -3x³ + 3x
= 2x³ - 3x³ + 3x² - 17x + 3x + 12
= -x³ + 3x² - 14x + 12
Simple word problem. 40 POINTS!!!!Thank you.
Answer:
$50
Step-by-step explanation:
Hello There!
We are given that for 1 hour of work 250 dollars is charged and for 3 hours of work 350 dollars is charged
This could also be represented in two points (1,250) and (3,350)
The question wants us to find the hourly charge rate (slope)
we can easily find the slope ( hourly charge rate ) by using the slope formula
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
we have our two points so all we need to do is plug in the values (remember y values go on top and x values go on the bottom.)
[tex]slope=\frac{350-250}{3-1} \\350-250=100\\3-1=2\\slope=\frac{100}{2} or50[/tex]
So we can conclude that the hourly charge rate is $50
Tell which value of the variable is the solution of the equation 30 = 6w W = 3, 5, 6, 8??
Answer: w=5
Step-by-step explanation: Hope this help
PLEASE HELP! all u have to do is determine if it is positive or negative!
Answer:
I think it is positive.
Step-by-step explanation:
Iam soory if Iam wrong.
For 25 pts
Pls Help this is hard as hell
Answer: For the first one Independent variable would be Cars age and the dependent would be cars price. For the second one, independent variable would be number of training miles and dependent would be Time to finish the race in minutes.
Step-by-step explanation:
Answer:
First one:
The independent variable is the car’s age
The dependent variable is the car’s price according tot he age
Second one:
The independent variable is the number of training miles
The dependent variable is the time it takes to finish
Step-by-step explanation:
Just think of the independent variable as the cause and the dependent variable as the effect.
The term to term rule for a sequence is Multiply by 2 the sequence starts a 2a ___ ___ the total value of the first three terms is 63 work out the total value of the first four terms
Answer:
135
Step-by-step explanation:
The sequence are:
a, 2a, 4a, 8a, 16a.....
the total value of the first three terms is 63
That is,
a + 2a + 4a = 63
7a = 63
a = 63/7
a = 9
work out the total value of the first four terms
First four terms are: a, 2a, 4a, 8a
Where,
First term, a = 9
Second term, 2a = 2*9 = 18
Third term, 4a = 4*9 = 36
Fourth term, 8a = 8*9 = 72
The total value of the first four terms = 9 + 18 + 36 + 72
= 135
The total value of the first four terms = 135
helppppppppppp meeeeeeeeeee
Answer:
330
Step-by-step explanation:
Answer:
335.5
Step-by-step explanation:
Can someone please help me with math.
Please help me with my math( if you help i will give you brainliest)
Answer:
4. 50
5. 35
6. 45
7. 30
8. No mode
9. 42
10. 22, 25, 45, 73, 80
11. 15, 25, 30, 48, 50
12. 58
13. 35
14. 51
15. 24
16. 22.13
17. 10.22
18. Iffy's team had a lower performance than Kaiya's team. Iffy's team collected an average of 35 cans, whereas, Kaiya's team collected an average of 50 cans!! Kaiya's team also had very versatile and active players who were able to collect more, individually, unlike Iffy's team.
Step-by-step explanation:
the radius of a circle is 8 miles. what is the area of a sector bounded by a 144° arc
Answer:
Step-by-step explanation:
The area of a sector and the properties of circles bounded by a 144° arc in a circle with a radius of 8 miles can be calculated using the formula: Area of sector = (θ/360°) * π * r² where θ is the central angle of the sector and r is the radius of the circle.
In this case, the central angle is 144° and the radius is 8 miles. Plugging these values into the formula, we get: Area of sector = (144°/360°) * π * (8 miles)². Simplifying the equation, we have: Area of sector = (0.4) * π * (8 miles)².
To know more about area of a sector here: brainly.com/question/29055300
#SPJ11
7.) Jessica took her parents out to dinner. The total
bill was $48.55. She left an 18% tip. What was
Jessica's total cost for dinner?
Answer:
$57.289
Step-by-step explanation:
18% of 48.55
48.55 × 18 ÷ 100
= 8.739
48.55 + 8.739
=$57.289
Let S = {3,4,5,6,7,8,9) be a sample space such that the following are true. Use the information to answer the questions. E = (8,9) F = {7,8) G = {4,6,9) a) Are E and F mutually exclusive? Ο Nο Yes O Cannot be determined b) Are F and G mutually exclusive? Ο Nο Yes Cannot be determined.
(a) E and F are not mutually exclusive due to the overlapping value of 8. So the answer is No or option A.
(b) F and G are mutually exclusive since they have no common outcomes. So the answer is No or option A.
a) E and F are not mutually exclusive. To be mutually exclusive, two events cannot occur simultaneously. In this case, both E and F have an overlapping value of 8. The interval (8,9) is included in both E and F, indicating that there is a common outcome (8) between the two events.
Therefore, E and F are not mutually exclusive.
b) F and G are mutually exclusive. In order for two events to be mutually exclusive, they must have no common outcomes. Looking at the intervals (7,8) and (4,6,9), there is no overlapping value between F and G. F includes the value 7, which is not present in G, and G includes the values 4, 6, and 9, which are not present in F.
Therefore, there are no common outcomes between F and G, making them mutually exclusive.
In summary, E and F are not mutually exclusive due to the overlapping value of 8, while F and G are mutually exclusive since they have no common outcomes.
Learn more about Mutually Exclusive:
https://brainly.com/question/12961938
#SPJ4
Find the Wronskian for the set of functions (3x^2, e^x, xe^x}, then determine if they are linearly dependent or independent.
The Wronskian for the set of functions (3[tex]x^2[/tex], [tex]e^x[/tex], x[tex]e^x[/tex]) is W(0) = 1 and the set of functions (3[tex]x^2[/tex], [tex]e^x[/tex], x[tex]e^x[/tex]) are linearly independent.
To find the Wronskian for the set of functions (3[tex]x^2[/tex], [tex]e^x[/tex], x[tex]e^x[/tex]) and determine if they are linearly dependent or independent, we calculate the determinant of the matrix formed by taking the derivatives of these functions and evaluating them at a specific point.
The Wronskian is a determinant that helps determine if a set of functions is linearly dependent or independent.
For the given set of functions (3[tex]x^2[/tex], [tex]e^x[/tex], x[tex]e^x[/tex]), we need to calculate the Wronskian.
First, we take the derivatives of the functions:
f₁(x) = 3[tex]x^2[/tex]
f₂(x) = [tex]e^x[/tex]
f₃(x) = x[tex]e^x[/tex]
Taking the first derivatives, we get:
f₁'(x) = 6x
f₂'(x) = [tex]e^x[/tex]
f₃'(x) = [tex]e^x[/tex] + x[tex]e^x[/tex]
Next, we form a matrix with these derivatives:
| 6x [tex]e^x[/tex] [tex]e^x[/tex] + x[tex]e^x[/tex] |
To calculate the Wronskian, we evaluate this matrix at a specific point, let's say x = 0, and take the determinant:
W(0) = | 6(0) [tex]e^0[/tex] [tex]e^0[/tex] + 0[tex]e^0[/tex] |
| 0 1 1 |
| 1 1 1 |
Simplifying, we find:
W(0) = | 0 1 1 |
| 1 1 1 |
| 1 1 1 |
Calculating the determinant, we have:
W(0) = (0)(1)(1) + (1)(1)(1) + (1)(1)(1) - (1)(1)(1) - (1)(1)(0) - (1)(1)(1) = 1
Since the Wronskian is non-zero (W(0) ≠ 0), the set of functions (3[tex]x^2[/tex], [tex]e^x[/tex], x[tex]e^x[/tex]) are linearly independent.
Learn more about Derivatives here:
https://brainly.com/question/30401596
#SPJ11
(q17) A geologist finds out that a radioactive substance A that he found in the caves of Africa decays at a rate of 0.03 percent every year. What is the probability that an atom of this substance chosen at random will decay in the next 70 years?
None of the given options is the answer.
To calculate the probability of decay for substance A over the next 70 years, we need to consider the decay rate of 0.03 percent per year.
The decay rate of 0.03 percent per year can be converted to a decimal by dividing it by 100: 0.03 / 100 = 0.0003.
The probability of an atom decaying in a given year is equal to the decay rate, which is 0.0003.
To calculate the probability of an atom not decaying in a given year, we subtract the decay rate from 1: 1 - 0.0003 = 0.9997.
The probability of an atom not decaying over the next 70 years can be calculated by multiplying the probability of not decaying in each year together: (0.9997)^70 ≈ 0.9704.
Therefore, the probability of an atom decaying in the next 70 years is equal to 1 minus the probability of not decaying: 1 - 0.9704 ≈ 0.0296.
So, the probability that an atom of substance A chosen at random will decay in the next 70 years is approximately 0.0296 or 2.96%.
For more questions on probability
https://brainly.com/question/25839839
#SPJ8
In the process of completing the square, 3x^2+7x-12 becomes x^2+7/4x=4. True or False
Answer: False
Step-by-step explanation:
Someone please help!!! will give brainliest!!!
Round your answer to the nearest hundredths, if necessary.
Find the surface area of the figure
Answer:161.56
Step-by-step explanation:
8 x5=40
8 x 7.07=56.56
1/2 x 5 x 5 x 2= 25
8 x 5=40
Add that all together
Calculate the perimeter of the composite figure. Round your answer to the nearest hundredth. Use 3.14 for $\pi$ .
th sides are 8 and 10
1. Perimeter is 3 + 3 +3 +4 +5 = 18 feet
Area = 3*3 = 9, 1/2*3*4 = 6, 9 + 6 =15 square feet
2. perimeter = 2.5 +2.5+ 2.5+2.5+0.5+0.5 = 11 meters
Area = 3*.5 = 1.5, 3*2=6, 6+1.5 = 7.5 square meters
3. perimeter = 3.14*2*3 = 18.84 +8 = 26.8 inches
Area = 6*4 = 24 + 3.14*3^2 = 28.26 = 28.26 +24 = 52.3 inches
4. surface area = 2*π*6*20+2*π*6^2= 980.2 yards
Volume = π*6^2*20 = 2261.9 cubic yards
5.surface area = 2*(9*7+2*2+2*9) = 190 cm
Volume = 2*7*9 = 126 cubic cm
6. surface area = 2*(11*11+11*11+11*11) = 726 mm
Volume = 11 *11*11 = 1331 cubic cm
Worth 50 points
The table shows the inputs and corresponding outputs for the function f(x) = StartFraction 1 Over 8 EndFraction(2)x. A 2-column table with 5 rows. Column 1 is labeled x with entries 0, 2, 4, 6, 8. Column 2 is labeled f (x) with entries StartFraction 1 Over 8 EndFraction, one-half, 2, 8, 32. Find the following values of the function. f -1 (one-half) = f -1 (8) =
Answer:2,6
Step-by-step explanation:Edge2021
Answer
2,6
Step-by-step explanation:
Write a simplified polynomial expression that can be used to represent the perimeter of the rectangle. 3x-7 and x-7
Answer:
P = 8x-28
Step-by-step explanation:
Given that,
Length = (3x-7)
Width = (x-7)
We need to find the perimeter of the rectangle. The formula for the perimeter of a rectangle is given by :
[tex]P=2 (l+b)\\\\P=2(3x-7+x-7)\\\\P=2(4x-14)\\\\P=8x-28[/tex]
So, the perimeter of the rectangle is equal to 8x-28.
Which of the following sets of angle measures can be used to draw an acute isosceles triangle? Select all that apply. 75°, 30°, 75° 80°, 55°, 45° 80°, 80°, 40° 60°, 60°, 60° 50°, 50°, 80° 20°, 140°, 20°
Answer:
1. 80°, 80°, 40°
2. 60°, 60°, 60°
3. 20°, 140°, 20°
4. 50°, 50°, 80°
5. 75°, 30°, 75°
6. 80°, 55°, 45°
6, 2, and 4
Answer:
I think its 6,2, and 4
Step-by-step explanation: hope that helps! °∪°
Which equation best represents the relationship between x and y in the graph?
A. y = -2x + 1.5
B. y = -2x + 3
C. y = -1/2x + 3
D. y = -1/2x + 1.5
A number,
n
n, is multiplied by
−
0.7
−0.7. The product is
−
1
2
−
2
1
. What is the value of
n
n?
Answer:
0.8
Step-by-step explanation:
got it right on edg
Answer:
5/7
Step-by-step explanation: