What is the inverse of the logarithmic function

f(x) = log gX

The $2 and $3 profits from the sale of sandwiches and wraps respectively, and the equation that is used to calculate the profit gives;

1. The equation is; \( \displaystyle{y = 490 - \frac{2}{3} \cdot x}\)

The slope, m = \( \displaystyle{ - \frac{2}{3}}\)

The y–intercept, c = 490

2. The graph can be drawn by joining the y–intercept to a point found by moving along the slope from the y–intercept

3. \( \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}\)

4. Please find attached the graph of the number of wraps to the number of sandwiches

5. Please find attached the combined graph of the two functions

The similarity is the common slope

The difference is the y–intercept

The slope is the ratio of the rise to the run of the graph.

The given function is; 2•x + 3•y = 1470

Where;

x = The number of sandwich sold

y = The number of wraps sold

The profit per sandwich sale = $2

Profit per each wrap sale = $3

1. The slope and intercept form is; y = m•x + c

Where;

m = The slope

c = The y–intercept

Therefore, 2•x + 3•y = 1470 gives;

3•y = 1470 - 2•x

y = (1470 - 2•x)÷3 = 490 - (2/3)•x

\( \displaystyle{y = \frac{1470-2\cdot x}{3} = 490 - \frac{2}{3} \cdot x}\)

Therefore;

By comparison, we have;

2. Using the slope and intercept method to graph the line involves the following steps.

3. The equation in function notation is; \( \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}\)

The meaning of the function is that the number of wraps sold is given by the difference between 490 and two thirds of the number of sandwiches sold, or that as the number of sandwiches sold increases by by 1, the number of wraps sold decreases by 2/3

4. The graph can be created using a spreadsheet application

Please find attached the graphs of the function

5. With a profit next month of $1,593, we have;

2•x + 3•y = 1593

Which gives;

\( \displaystyle{y = 531 - \frac{2}{3} \cdot x}\)

Given that the equation of the graph of the previous month is y = 490 - (2/3)•x, we have;

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Answer:

Direction of the boat is 43.05° and the speed is 21.66 knot

Step-by-step explanation:

yacht speed = 20 knots

yacht bearing = 185° = 85°  below the negative horizontal x-axis

wind speed = 15 knots

wind bearing = 290° = 20° above the negative horizontal x-axis

we find the x and y components of the boat velocities

for yacht,

x component = -20 cos 85° = -1.74 knots

y component = -20 sin 85° = -19.92 knots

for the wind,

x component = -15 cos 20° = -14.09 knots

y component = 15 sin 20° = 5.13 knots

total x component  Vx = -1.74 + (-14.09) = -15.83 knots

total y component Vy =  -19.92 + 5.13 = -14.79 knots

Resultant speed of the boat = \(\sqrt{Vx^{2} + Vy^{2} }\)

==> \(\sqrt{15.83^{2} + 14.79^{2} }\) = 21.66 knot

direction of boat = \(tan^{-1} \frac{Vy}{Vx}\)

==> \(tan^{-1} \frac{14.79}{15.83}\) = 43.05°

Answer:

Step-by-step explanation:

50%

Answer:

50/50

Step-by-step explanation:

Answer:

Its A. The initial out-of-pocket cost is less for the lease.

Step-by-step explanation:

I just got it right:)

Tim needs a new car when he is in college for 3 years. The car is like a $15,000 a local dealer got him a deal of 7% of interest worth a 3 year loan. If Tim can give him $1500 as a down payment.

He needs initially make out of the pocket costs less when taking the lease.

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We have to apply the rule of three to solve this.

We will use the equivalencies of the first row to complete the others.

The cups of flour needed are 3 cups/loaf.

The water needed is 12 tablespoons/loaf.

The salt needed 1 teaspoon/loaf.

With these equivalencies we can calculate the ingredients needed for any number of loaves:

Answer:

T(x,y)=(x,y) is false

Step-by-step explanation:

The general solution to the given differential equation is:

r = ±Ce^θ

To find the general solution of the given differential equation:

dr/dθ - rsec(θ) = cos(θ)

We can solve this differential equation by separating the variables and integrating:

1/(rsec(θ)) dr = cos(θ) dθ

Multiplying both sides by sec(θ) gives:

1/r dr = cos(θ)sec(θ) dθ

Integrating both sides:

∫ (1/r) dr = ∫ (cos(θ)sec(θ)) dθ

ln|r| = ∫ (cos(θ)/cos(θ)) dθ

ln|r| = ∫ dθ

ln|r| = θ + C

where C is the constant of integration.

Exponentiating both sides:

|r| = e^(θ + C)

|r| = e^θ * e^C

|r| = Ce^θ

where C = ±e^C (a constant of integration).

Therefore, the general solution to the given differential equation is:

r = ±Ce^θ

where C is an arbitrary constant.

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The average value of  the function f on the interval \(∫1(3f(x) + 2x)dx\) is 56.

The average value of the function f on the interval 1 ≤ x ≤ 4 is 8 To Find: The value of\(∫1(3f(x) + 2x)dx\)  Approach: We know that if the average value of the function f on the interval [a,b] is given by Avg.

value of \(f = (1/(b-a)) ∫baf(x)dx\)  Then, \(∫baf(x)dx = Avg. value of f * (b-a)\)Formula Used: \(∫baf(x)dx = Avg. value of f * (b-a)\)

The average value of the function f on the interval 1 ≤ x ≤ 4 is 8Therefore, Avg. value of \(f = (1/(4-1)) ∫41f(x)dx⇒ Avg.alue of f = (1/3) ∫41f(x)dx\)Multiplying both sides by (3),

we ge\(t∫41f(x)dx = 3 * 8 = 24\)  Using the formula, we get\(∫1(3f(x) + 2x)dx= 3∫1f(x)dx + 2∫1xdx⇒ 3 * 24 + 2[(1/2) * (1)^2] - 2[(1/2) * (4)^2]⇒ 72 - 16⇒ 56\)

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Answer: Width = 6 ft, length = 18 ft

Step-by-step explanation:

If the width is w, then the length would be 3w.

3 * 3w * w = 324

9w^2 = 324

w^2 = 36, since w is positive it has to be 6.

So, the width = 6 and the length = 18.

Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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Answer:

14112

Step-by-step explanation:

USE A CALCULATOR

Answer: 14112

Step-by-step explanation:

42 x 336 = 14112

The probability of A or B would be 0.3269. Probability can be used to make predictions and make decisions based on uncertain information in fields such as finance, engineering, and science.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event will not occur and 1 indicating that an event will definitely occur. Events with probabilities closer to 1 are considered more likely to happen, while events with probabilities closer to 0 are considered less likely.

Since A and B are mutually exclusive events, they cannot occur at the same time. Therefore, the probability of A or B is the sum of their individual probabilities.

p(A or B) = p(A) + p(B) = 0.07692 + 0.25 = 0.32692

To four decimal places, the probability of A or B is 0.3269.

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Answer:If the jetliner uses 3,600 gallons per hour, then after x x x hours it has used 3 , 600 x 3,600x 3,600x gallons of fuel. The tank initially had 15,000 gallons

Step-by-step explanation:

Answer:

the value of p is 7

Step-by-step explanation:

Given function;

f(x) = 2x³ - 7px + (p - 12)

factor of the given function = x - 5

Apply remainder theorem to solve for p

f(x - 5) = 0

x - 5 = 0

x = 5

f(5) = 2(5)³ - 7p(5) + (p - 12) = 0

        2(125) - 35p  + p - 12 = 0

         250 - 34p  - 12 = 0

        238  - 34p = 0  

           34p  = 238

                p = 238/34

                 p = 7

Therefore, the value of p is 7

Rounding to the nearest dollar, the value of the car after 12 years is $11,215. The initial value of the car can be found by evaluating the exponential function at t=0

v(0) = 27,500(0.84)^0 = 27,500

So the initial value of the car is $27,500.

The value of the car after 12 years can be found by evaluating the exponential function at t=12:

v(12) = 27,500(0.84)^12 = 11,215.47

Rounding to the nearest dollar, the value of the car after 12 years is $11,215.

The dollar value of a car is modeled by an exponential function: v(t) = 27,500(0.84)^t, where t is the number of years since the car was new. The initial value of the car, v(0), can be found by evaluating the function at t=0, which gives us v(0) = 27,500. This means that the car had an initial value of $27,500 when it was new. To find the value of the car after 12 years, we evaluate the function at t=12, which gives us v(12) = 27,500(0.84)^12 = 11,215.47. Rounding to the nearest dollar, the value of the car after 12 years is $11,215. The exponential function used to model the car's value takes into account the decrease in value over time, represented by the factor 0.84^t.

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The maximum possible cost in dollars is $226.76 (approx).

Standard deviation = $88

Let X be the cost of the automobile repair, then X ~ N(367, 88^2) (normal distribution)

Now, we need to find the following probabilities:

(a) P(X > 480)(b) P(X < 240)(c) P(240 < X < 480)(d)

Find X such that P(X < X1) = 0.05, where X1 is the lower 5% point of X(a) P(X > 480)

We need to find P(X > 480)P(X > 480) = P(Z > (480 - 367)/88) [Standardizing the random variable X]P(X > 480) = P(Z > 1.2955)

Using the standard normal table, the value of P(Z > 1.2955) = 0.0983 (approx)

Hence, the required probability is 0.0983 (approx)(b) P(X < 240)

We need to find P(X < 240)P(X < 240) = P(Z < (240 - 367)/88) [Standardizing the random variable X]P(X < 240) = P(Z < -1.4432)

Using the standard normal table, the value of P(Z < -1.4432) = 0.0749 (approx)

Hence, the required probability is 0.0749 (approx)(c) P(240 < X < 480)

We need to find P(240 < X < 480)P(240 < X < 480) = P(Z < (480 - 367)/88) - P(Z < (240 - 367)/88) [Standardizing the random variable X]P(240 < X < 480) = P(Z < 1.2955) - P(Z < -1.4432)

Using the standard normal table, the value of P(Z < 1.2955) = 0.9017 (approx)and the value of P(Z < -1.4432) = 0.0749 (approx)

Hence, the required probability is 0.9017 - 0.0749 = 0.8268 (approx)(d)

Find the maximum possible cost in dollars, if the cost for your car repair is in the lower 5% of automobile repair charges.

This is nothing but finding the lower 5% point of X.We need to find X1 such that P(X < X1) = 0.05.P(X < X1) = P(Z < (X1 - 367)/88) [Standardizing the random variable X]0.05 = P(Z < (X1 - 367)/88)

Using the standard normal table, the value of Z such that P(Z < Z0) = 0.05 is -1.645 (approx)

Hence, we get,-1.645 = (X1 - 367)/88

Solving for X1, we get: X1 = 88*(-1.645) + 367 = $226.76 (approx)

Therefore, the maximum possible cost in dollars is $226.76 (approx).

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Answer:

434.9

Step-by-step explanation:

\(\frac{4}{3}\) × π (4.7)²

434.893

Answer:

434.893

Step-by-step explanation:

hope this helps

Answer:

yeah (:

Step-by-step explanation:

19+11= 30+8 = 38 so 102-38= 64

Answer:

with a mean of zero and standard deviation of 1

Answer:

Step-by-step explanation:

For the pairs of sides to be proportional to each other, they must have the same scale factor. In other words, similar figures have congruent angles and sides with the same scale factor. A scale factor of 2 means that each side of the larger figure is twice as long as its corresponding side is in the smaller figure.

An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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Consequently, 119,143 votes were cast in all. Bill received 53,130 votes and Corrine received 66,013 votes.

Consequently, 119,143 votes were cast in all.

The result is: 119,143 - 12,883 = 106,260

if we deduct the sum from what Corrine received. The result is 106,260 divided by 2

106,260 / 2 = 53,130

which equals 53,130.

53,130 plus the additional 12,883 votes

Corrine received equals 66,013.

Bill received 53,130 votes and Corrine received 66,013 votes.

For instance, if a property is damaged, three insurers who each provide $60,000 in coverage are each given 50% of the claim. Real estate, workers' compensation, and the distribution of financial advantages are further examples of allocation. Establish the appropriate representational threshold for each representative. Calculate this by dividing the total number of representatives by the combined population of all the states.

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The people have a pet dog or a pet cat would be 30.

What is Union and Intersection of a numbers?

The set of elements that are contained in either set X, set Y, or both sets X and Y is referred to as the union of two sets X and Y. The set of items that are a part of both sets X and Y is known as the intersection of two sets X and Y.

Given that:

In survey of students,

20 have dogs, 15 have cats, and 5 have both. 1 has a pet squirrel.

n(A)=Student who has dogs.

n(B)=Student who has cats.

and n(AUB)= Student who having both dogs and cats.

So,

n(A)=20

n(B)=15

n(AUB)=5

According to formula,

n(AUB)=n(A)+n(B)-n(A∩B)

i.e. n(A∩B)=n(A)+n(B)-n(AUB)

     n(A∩B)=20+15-5

     n(A∩B)=30

Hence, The people have a pet dog or a pet cat would be 30.

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The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end\)

Now, we will substitute the given function, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end\)

Further, we will simplify this, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end\)

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

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Answer:

Same back to you

Step-by-step explanation:

I hope you smile today and don't let corona stop you from anything

Answer: thank you

Step-by-step explanation:

We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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Answer:

$13,082.60 more

Step-by-step explanation:

Melanie:

\(A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36\)

Amelia:

\(A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95\)

Amelia-Melanie= $13,082.60

The equation of the line that contains (-4, 6) and (7, -5) in point slope form is y + 5 = - 1(x - 7).

The point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, the equation of the line that contains (-4, 6) and (7, -5) can be found in point slope form as follows:

Hence,

m = -5 - 6 / 7 + 4

m = - 11 / 11

m = -1

Therefore, using (7, -5)

y + 5 = - 1(x - 7)

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The solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

To find all solutions to the equation 2sin(θ) = 1 on the interval [0, 2π), we can solve for θ by isolating the sin(θ) term and then using inverse trigonometric functions.

Given: 2sin(θ) = 1

Dividing both sides by 2:

sin(θ) = 1/2

Now, we can use the inverse sine function to find the solutions:

θ = sin^(-1)(1/2)

The inverse sine of 1/2 is π/6. However, we need to consider all solutions on the interval [0, 2π).

Since the sine function has a period of 2π, we can find the other solutions by adding integer multiples of 2π to the principal solution.

The principal solution is θ = π/6. Adding 2π to it, we get:

θ = π/6 + 2π = π/6, 13π/6

So, the solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

These are the two solutions that satisfy the given equation on the specified interval.

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Answer:

50

Step-by-step explanation:

10 to every 6

x to every 30

30/6 = 5

10* 5 = 50

50 for every 30

Hope this helps! :D

Have a wonderful Day!

Answer:

50

Step-by-step explanation:

there are 6 cups alr and it used 10 cups of water

30 divded by 6 equals 5

5 times 10 equals 50