A cell phone company charges a flat rate of $5.25 per month, with an additional charge of $0.29 per minute. How many minutes did Taylor talk on her cell phone if her monthly bill was $27.00?

The relation that is an inverse variation is the one in the first table:

x 2 4 6 8

f(x) 12 6 4 3

An inverse variation between two variables x and y can be written as follows:

y = k/x

Where k is a constant.

Notice that x is on the denominator, so, as x increases, the value of y decreases.

Now, for example if we use the values of the first table:

x 2 4 6 8

f(x) 12 6 4 3

The first pair is (2, 12)

Replacing that in the inverse variation formula we get:

12 = k/2

12*2 = k

24 = k

For the second pair (4, 6) we will get:

6 = k/4

6*4 = k

24 = k

And so on for all the pairs. If the variation is inverse, you should always get the same value of k (like in this case).

So this is the correct answer.

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in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:

If both players choose Split, they both receive a payoff of 50.

If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.

If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.

If both players choose Steal, they both receive a payoff of 0.

To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.

Pure Strategy Nash Equilibria:

(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.

Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.

Mixed Strategy Nash Equilibrium:

To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.

In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.

Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

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For the given function f(a) = a^2 + 1, the values of f(a), f(a+h), and the difference quotient can be calculated as follows: f(a) = a^2 + 1, f(a+h) = (a+h)^2 + 1, and the difference quotient = (f(a+h) - f(a))/h.

The function f(a) is defined as f(a) = a^2 + 1. To find f(a), we substitute the value of a into the function:

f(a) = a^2 + 1

To find f(a+h), we substitute the value of (a+h) into the function:

f(a+h) = (a+h)^2 + 1

The difference quotient is a way to measure the rate of change of a function. It is defined as the quotient of the change in the function values divided by the change in the input variable. In this case, the difference quotient is given by:

(f(a+h) - f(a))/h

Substituting the expressions for f(a+h) and f(a) into the difference quotient, we get:

[(a+h)^2 + 1 - (a^2 + 1)]/h

Simplifying the numerator, we have:

[(a^2 + 2ah + h^2 + 1) - (a^2 + 1)]/h

= (2ah + h^2)/h

= 2a + h

Therefore, the difference quotient for the given function is 2a + h.

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The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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The area of the surface over the given region is -2720 square units.

To find the area of the surface over the given region, we can use the formula for the surface area of a cone, which is:

A = 1/3 πr²h + 2πr¹√h

where r is the radius of the base of the cone, h is the height of the cone, and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given values, we get:

A = 1/3 π(20√65)²(20cos(√65)) + 2π(20√65)√(20cos(√65))

A = 20√65(1/3 π)² + 20√65(20)π(cos(√65))

A = 128√65 π² + 2000πcos(√65)

A = 128√65 π² + 2000π(cos(π/2) - sin(π/2))

A = 128√65 π² - 2000π

A = 128√65 π² - 4000

A = -2720

Since the surface area of a cone is negative, we need to multiply it by -1 to get the correct answer. Therefore, the area of the surface over the given region is -2720 square units.

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The graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

The equation y = 3ex ex − 5 can be rewritten as y = 3x2ex − 5. In order to find the horizontal and vertical asymptotes of this function, we must first find its degree of the numerator and denominator. The numerator is a second degree polynomial while the denominator is a first degree polynomial.

The horizontal asymptote will be the line y = b/a, where b and a are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, b = 3 and a = 1, so the horizontal asymptote is y = 3.

The vertical asymptote of a function is the line x = a/b, where a and b are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, a = 3 and b = -5, so the vertical asymptote is x = -3/5.

Therefore, the graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

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Answer:

-2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The minimum value is the y- coordinate of the vertex

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

y = 3x² - 12x + 10 ← is in standard form

with a = 3 and b = - 12 , then

x = - \(\frac{-12}{6}\) = 2

Substitute x = 2 into the function for corresponding y- coordinate

y = 3(2)² - 12(2) + 10 = 3(4) - 24 + 10 = 12 - 24 + 10 = - 2

Then minimum value of the function is - 2

The simplification of csc²x-cscx+2/CSCX-1 = 1/sin²(x) - sin(x) / (sin²(x)-1)

First, let's recall the definition of cosecant (csc): it's the reciprocal of sine, so csc(x) = 1/sin(x).

Next, we can simplify the equation by substituting the definition of cosecant into the equation:

csc²x-cscx / CSCX-1 = (1/sin(x))² - (1/sin(x)) / (1/(sin(x))-1)

Next, we can simplify the numerator and denominator using algebraic identities:

(1/sin(x))² = 1/sin²(x)

(1/sin(x)) / (1/(sin(x))-1) = sin(x) / (sin²(x)-1)

So, the equation becomes:

1/sin²(x) - sin(x) / (sin²(x)-1)

And this is the simplified form of the equation.

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The geometric probability of landing in the shaded area is 0.17. This is calculated by finding the ratio of the area of the smaller circle to the area of the larger circle.

Given, the diameter of the small circle is 20 in and the diameter of the larger circle is 48 in. In order to find the geometric probability of landing in the shaded area of the picture, we need to calculate the ratio of the area of the smaller circle to the area of the larger circle.

The area of a circle is given by the formula: \($A = \pir^2$\), where r is the radius of the circle. We know that the diameter of the small circle is 20 in, so the radius is 10 in. Similarly, the diameter of the large circle is 48 in, so the radius is 24 in.

Area of the smaller circle = \(\pi(10)^2 = 100\pi in^2\)

Area of the larger circle = \(\pi(24)^2 = 576\pi in^2\)

Area of shaded region = Area of the larger circle - Area of the smaller circle = \(576\pi-100\pi = 476\pi in^2\)

The probability of landing in the shaded region is the ratio of the area of the smaller circle to the area of the larger circle. Hence, geometric probability = \(\frac{100\pi}{576\pi} = 0.17\)(rounded to the nearest hundredth place).

Thus, the geometric probability of landing in the shaded area of the picture is 0.17. In summary, the geometric probability of landing in the shaded area of the picture is obtained by calculating the ratio of the area of the smaller circle to the area of the larger circle.

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Peter will be needing 6 gallons of paint to paint the wall of area 2070 sq ft.

Given that Peter uses 3 gallons of paint to paint an area of 1005 ft², we need to find how many gallons of paint would he need to paint a wall having area between 1,950 and 2,070 square feet of walls.

So,

Since he uses 3 gallons for 1005,

So, for 1 sq ft of area he will need = 1/335 gallons

So, for an area of 2070 sq ft he will need = 2070 x 1/335 ≈ 6 gallons.

Hence he will be needing 6 gallons of paint to paint the wall of area 2070 sq ft.

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The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.

The rate of change of volume is-

dV/dt = 11 ft3/min.

Volume of cylindrical cone = (1/3)πr²h

As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.

Diameter =  22 ft

Thus, radius is 11 ft

By using height and radius of a water in the tank, we may calculate h using similar ratios.

11/44 = r/h

1/4 = r/h

r= h/4

Put into volume;

V = (1/3)π(h/4)h²

V = (1/3)(π)h³ / (16)

dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)

V = [(π)(h)² / 16](dh/dt)

Solve for (dh/dt) ;

dh/dt = (dV/dt)(16) / [((π)(h)²]

Now, the change in volume is dV/dt = 11 ft³/min

dh/dt = (11 ft³/min)(16) / [((π)(h)²]

For h = 1 ft,

dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]

dh/dt ≈ 56.05 ft/min

Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.

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This question is incomplete

Complete Question

Consider greenhouse A with floor dimensions w = 16 feet , l = 18 feet.

A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concrete are needed for the floor?

Answer:

96 cubic feet

Step-by-step explanation:

The volume of the floor of the green house = Length × Width × Height

We convert the dimensions in feet to inches

1 foot = 12 inches

For width

1 foot = 12 inches

16 feet = x

Cross Multiply

x = 16 × 12 inches

x = 192 inches

For length

1 foot = 12 inches

18 feet = x

Cross Multiply

x = 18 × 12 inches

x = 216 inches

The height or depth = 4 inches deep

Hence,

Volume = 192 inches × 216 inches × 4 inches

= 165888 cubic inches

From cubic inches to cubic feet

1 cubic inches = 0.000578704 cubic foot

165888 cubic inches = x

Cross Multiply

x = 16588 × 0.000578704 cubic foot

x = 96 cubic feet

Therefore, 96 cubic feet of concrete is needed for the floor

50% of the students in Ms. Rodriguez's art history class chose Rock as their favorite type of music. We can calculate it in hte following manner.

To find the relative frequency of students who chose Rock as their favorite type of music, we need to divide the number of students who chose Rock by the total number of students in the class.

Let's assume that there are 30 students in Ms. Rodriguez's art history class and the table looks like this:

| Type of Music | Number of Students |
|--------------|--------------------|
| Rock         | 15                 |
| Classical    | 8                  |
| Hip Hop      | 4                  |
| Jazz         | 3                  |

The relative frequency of students who chose Rock as their favorite type of music is:

15 (number of students who chose Rock) / 30 (total number of students) = 0.5 or 50%

Therefore, 50% of the students in Ms. Rodriguez's art history class chose Rock as their favorite type of music.

To calculate the relative frequency of students who chose Rock as their favorite type of music, please provide the data from the table you mentioned. The relative frequency can be determined by dividing the number of students who chose Rock by the total number of students in the class.

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Answer:

I am not sure what you would like me to answer but you can either message me or just make another question with either the rest of the question or a picture of your question. I am happy to help under any circumstance.

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 \(\frac{(X_{1-X} )^2}{n-1}\)

        0 = Summation n to i = 1\(\frac{(X_{1-X} )^2}{n-1}\)

                Summation n to i \({(X_{1-X} )^2\) = 0

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The results of dividing 1 into pieces that are each 1/9 of a whole is 9

1 ÷ 1/9

1 ÷ 1/9

= 1 × 9/1

= (1 × 9) / (1 × 1)

= 9/1

= 9

Complete question:

If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there

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Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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By using the concept of equation, it can be calculated that-

The equation can be solved by using this system of equations

\(3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11\)

What is equation?

At first it is important to know about algebraic expressions.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

Here the system of equation are-

\(3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0\)

So the equation can be solved by using this system of equations

\(3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11\)

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Complete Question

Which equation can be solved by using this system of equations?

\(3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0\)

Answer:

x = -24

Step-by-step explanation:

y = 1/4x+12 (Substitute 6 for y)

6 = 1/4x+12 (Subtract 12 from both sides)

6-12= -6 so its now -6 = 1/4x and since its a fraction you want to multiply both sides by the reciprocal

4*-6 = 1/4x*4 (1/4*4=1 which is 1x or x)

-24 = x

Answer:

y=1/4x+12

6=1/4x+12

1/4x=6-12

1/4x=-6

0.25x=-6

x=-6÷0.25

x=-24

Step-by-step explanation:

first put the given value into the equation

inverse rule:

+ve changes to -ve(vice versa)

÷changes to ÷(vice versa)

Answer:

140:160----simplify by 10

14:16--------simplify by 2

7:8 is the lowest

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=10

Answer:

This function doesn't have zeros because it doesn't touch the x-axis.

EDIT: I didn't see the negative sign before the 3. The function crosses the x-axis at (-5,0) and (5,0). Sorry!

Answer:

1.5:1

Step-by-step explanation:

the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1

Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:

$$PF + PF' = 2a,$$

where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:

$$9 + 12 = 2a,$$

$$21 = 2a.$$

Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$

The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:

$$c = \sqrt{a^2 - b^2}.$$

We can solve for $b$ using the distance to one focus:

$$c = \sqrt{a^2 - b^2},$$

$$c^2 = a^2 - b^2,$$

$$b^2 = a^2 - c^2,$$

$$b = \sqrt{a^2 - c^2}.$$

Substituting the known values:

$$b = \sqrt{10.5^2 - 9^2},$$

$$b = \sqrt{110.25 - 81},$$

$$b = \sqrt{29.25},$$

$$b \approx 5.408.$$

Therefore, the semi-minor axis $b$ is approximately $5.408.$

Finally, we can determine the lengths of the major and minor axes:

The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$

The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$

Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.

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Answer:

2.3333333333333333333333333333333 sec

 x = 5 is the value of x in exterior angle.

Why is this term "exterior angle" used?

∠QRS is exterior angle .

apply exterior angle theorem in ΔPQR

So, ∠QRS = ∠PQR + ∠RPQ

     8x - 9° = 3x + 12° + 3x - 11°

     8x - 9 = 6x + 1

       8x - 6x = 1 + 9

         2x = 10

            x = 10/2

            x = 5

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