A data set of the ages of a sample of 350 Galapagos tortoises has a minimum value of 1 years and a maximum value of 170 years. Suppose we want to group these data into five classes of equal width Assuming we take the lower limit of the first class as 1 year, determine the class limits, boundaries, and midpoints for a grouped quantitative data table. Hint: To determine the class width, subtract the minimum age (1) from the maximum age (170), divide by the number of classes (5), and round the solution to the next highest whole number. Class width Class Limits Lower Boundary Upper Boundary Class Midpoint to 0.5 to to to 170.5 to

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

Answer:

330

Step-by-step explanation:

Answer:

335.5

Step-by-step explanation:

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

(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.

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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.

Answer:

$57.289

Step-by-step explanation:

18% of 48.55

48.55 × 18 ÷ 100

= 8.739

48.55 + 8.739

=$57.289

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.

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.

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Answer:

0.8

Step-by-step explanation:

got it right on edg

Answer:

5/7

Step-by-step explanation:

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

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:

Answer: w=5

Step-by-step explanation: Hope this help

Answer: False

Step-by-step explanation:

Answer:

I think it is positive.

Step-by-step explanation:

Iam soory if Iam wrong.

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

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%.

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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.

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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

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

Answer:2,6

Step-by-step explanation:Edge2021

Answer

2,6

Step-by-step explanation:

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.

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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.

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.

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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 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.

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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! °∪°