A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population prefers the color green. If 12 12 buyers are randomly selected, what is the probability that between 5 5 and 9 9 (both inclusive) buyers would prefer green? Round your answer to four decimal places.

The function f(x) = (x + 7)^2 is one-to-one and non-decreasing for any domain on the real numbers. The inverse of f(x) restricted to this domain is y = √x - 7.

To find a domain on which the function f(x) = (x + 7)^2 is one-to-one and non-decreasing, we need to determine where the function is strictly increasing or non-decreasing and has a one-to-one correspondence.

First, let's examine the graph of f(x) = (x + 7)^2 to understand its behavior. The function is a parabola that opens upward, centered at x = -7, and the vertex is the lowest point on the graph.

Since the vertex is the lowest point and the parabola opens upward, the function is non-decreasing for all x-values. Therefore, the function is non-decreasing over its entire domain.

To find a domain on which the function is one-to-one, we observe that the function is not symmetric about the y-axis. Hence, the domain can be any subset of the real numbers.

Now, let's find the inverse of f(x) restricted to this domain. Since f(x) is non-decreasing, the inverse will also be non-decreasing. The inverse function can be found by interchanging the roles of x and y in the original equation and solving for y.

Let's proceed with finding the inverse:

Start with the equation f(x) = (x + 7)^2.

Interchange x and y: x = (y + 7)^2.

Solve for y:

Take the square root of both sides: √x = y + 7.

Subtract 7 from both sides: y = √x - 7.

The inverse function of f(x) restricted to any domain on which it is one-to-one and non-decreasing is given by y = √x - 7.

Note that the domain can be any subset of the non-negative real numbers, since the square root function is defined only for non-negative values.

In summary, the function f(x) = (x + 7)^2 is one-to-one and non-decreasing for any domain on the real numbers. The inverse of f(x) restricted to this domain is y = √x - 7.

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(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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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:

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

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

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:

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! °∪°

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:

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:

$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 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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y=0.5x+2

y=4

4=0.5x+2

-2        -2

2=0.5x

/0.5 /0.5

4=x

---

hope it helps

Answer:

[tex]x[/tex] = 4

Step-by-step explanation:

If [tex]y[/tex] = 4 then it would look like:

[tex]y[/tex] = .5[tex]x[/tex] + 2

Since .5 is 0.5, Half of 4 equal 2, PLUS the other 2 making it 4!!

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:

I think it is positive.

Step-by-step explanation:

Iam soory if Iam wrong.

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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Answer:

m=7/36

Step-by-step explanation:

we need two points in order to find the ratio of the change in y and change in x, which is the slope

m=(y-y1)/(x-x1) (you can choose any point as y1 but be careful that you use the corresponding x1 value in the denominator)

m=(11-4)/(17-(-19))

m=7/36

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

Answer:

0.8

Step-by-step explanation:

got it right on edg

Answer:

5/7

Step-by-step explanation:

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: False

Step-by-step explanation:

Answer:

330

Step-by-step explanation:

Answer:

335.5

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:2,6

Step-by-step explanation:Edge2021

Answer

2,6

Step-by-step explanation:

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