A pizzeria owner wants to know which pizza topping is least liked by her customers so she can take it off the menu. She used four different methods to find this information.
Method 1: The owner asked every third customer to rate all the pizza toppings in order of preference.
Method 2: The owner gave all customers a toll-free telephone number and asked them to phone in their topping preferences.
Method 3: The owner asked the preferences of every other teenager who entered the pizzeria.
Method 4: The owner reviewed the pizzeria’s complaint cards and assessed all complaints related to pizza toppings.
Which method is most likely to give a valid generalization

1 degree = 0.0174533 radians

85* 0.0174533 = 1.4835305 radians

Round answer as needed

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.

To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.

The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.

By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.

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The solution of expression is, 7/2.

A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

We have to give that,

An expression is,

⇒ x¹ + x⁻¹ + x⁰

Now, Substitute x = 2 in the above expression and find the value,

⇒ x¹ + x⁻¹ + x⁰

⇒ 2¹ + 2⁻¹ + 2⁰

⇒ 2 + 1/2 + 1

⇒ 3 + 1/2

⇒ (6 + 1)/2

⇒ 7/2

Therefore, The solution is, 7/2

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward

Find the inverse function

Exchange variables x for y and y for x

[tex]x=3y^{2}-5[/tex]

Isolate the variable y

[tex]3y^{2}=x+5[/tex]  -----> inverse function (horizontal parabola open to the right)

or

[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]

using a graphing tool

see the attached figure

The graph of function and it's inverse of the graph is shown in image.

We have to given that,

To graph the function y = 3x² - 5 and it's inverse.

Here, The equation is,

y = 3x² - 5

So, We can find it's inverse as,

y = 3x² - 5

y + 5 = 3x²

(y + 5) / 3 = x²

x² = (y + 5)/3

x = √(y + 5)/3

Hence, the inverse of function is,

f ⁻¹ (x) = √ (x + 5)/3

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The probability that at least one of the four randomly chosen items will be defective is 34.39%. This is calculated by subtracting the probability that all items are not defective from 1.

The subject of the question relates to the field of Probability. This problem pertains to the concept known as 'probability of at least one' event. In this case, we are considering the probability that at least one item will have a defect.

To calculate this, it's easier to find the probability that none of the items have a defect and then subtract that from 1. Since the machine has a 10% defect rate, it means there's a 90% chance that any item chosen will NOT be defective. If we choose 4 items, the probability that all are good is 0.9 * 0.9 * 0.9 * 0.9 = 0.6561.

So, the probability that at least one defective item will be chosen is 1 - 0.6561 = 0.3439 or 34.39%.

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The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.

The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.

Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.

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To calculate the total fraction of tickets sold for the movie Fist Bump by Thursday, we find the least common denominator for the fractions (21), convert each fraction, and then sum them up to get 16/21 of the tickets sold.

The question is asking how much of the tickets were sold by Thursday for the movie Fist Bump. To find the total fraction of tickets sold from Monday to Wednesday, we need to add up the fractions:

First, let's find a common denominator for the fractions. The least common multiple of 7 and 3 is 21, so we'll convert all fractions to have a denominator of 21:

Now we can add the fractions:

3/21 + 7/21 + 6/21 = 16/21

Therefore, by Thursday, a total of 16/21 of the tickets have been sold.

Starting at vertex V going until vertex S, we make our calculations.

VR = 14

Rx = x

therefore, xS = VR – Rx

xS = 14 – x                           ---> 1

Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R

VR  = 14 - x

at UV = 15 – (14 – x)

at UV = 1 + x

at TU = 7 – (1 + x)

at TU = 6 – x

at ST = 9 – (6 – x)

at ST = 3 + x                        ---> 2

Equate 1 and 2:

14 – x = 3 + x

2 x = 11

x = 5.5

To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.

Pentagon RSTUV and the Value of x

Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,

where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.

For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:

RS + TU + x = ST + UV + VR

Substituting the given values:

6 + 7 + x = 9 + 15 + 14

Simplifying the right-hand side:

Thus, the value of x is 25.

Answer:

Sequence will be $6.50, $6.75, $7.0, $7.25.......

Step-by-step explanation:

Ahmed is working at the burger joint and he was paid by his boss $6.50 per hour.

His boss promised him to raise $0.25 per hour every six months.

So we have to find the sequence which describes Ahmed's expected hourly wages starting with his current wage.

As at every 6 months increase in wages is $0.25 so the sequence formed will be an arithmetic sequence with common difference of 0.25 and first term 6.50

Sequence will be $6.50, $6.75, $7.0, $7.25,.........

Answer:

8 1/4

Step-by-step explanation:

Final answer:

The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.

Explanation:

The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.

To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.

Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:

(11/12) * (10/11) * (9/10) * (1/9) = 1/12.

A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:

s = −16 t^2 + v0 t + s0

Where,

s = distance of the plane from the ground = - 6000 ft       (negative since the package moves from top to bottom)

t = time for it to strike the ground = unknown

v0 = 0 since the package starts from rest

s0 = 0 since we take the plane as the reference point

Substituting the given values:

- 6000 = -16 t^2 + 0 * t + 0

16 t^2 = 6000

t^2 = 375

t = 19.36 s

B. s = v * t

where v = 600 miles / hr = 0.17 miles / s

s = (0.17 miles / s) * 19.36 s

s = 3.23 miles = 17,054 ft

Final answer:

The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.

Explanation:

The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.

First, we calculate the new balance:

Total Amount = $950(1 + 0.07)^8

Total Amount = $950(1.07)^8

Total Amount = $950 * 1.718186

Total Amount = $1632.77 (rounded to two decimal places)

Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:

Interest Amount = Total Amount - Original Principal

Interest Amount = $1632.77 - $950

Interest Amount = $682.77

Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.

Answer:

2004

Step-by-step explanation:

Answer: [tex]x^2+y^2=16[/tex]

Step-by-step explanation:

The general equation of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given: Radius of the circle : r= 4 units

The center of the circle :  (h,k)=(0,0)

Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-

[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]

Answer:

X²+Y²=16

Step-by-step explanation:

A p e x

To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.

The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.

The distance formula given two points is:

d^2 = (x2 – x1)^2 + (y^2 – y^1)^2

Now we calculate the distance between 2 points:

d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2

d^2 = 169

d = 13

Therefore the length of each side of the park is 13 units.

Answer:

13 units

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:

By following these steps, you should be able to determine the length of each side of the hexagon.

The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.

The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.

To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:

μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4

The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:

σ2 = Σ [(x - μ)2 * P(x)] = 2.0

And the standard deviation (σ) is simply the square root of the variance:

σ = √σ2 = 1.4