f(x)=2x+7

g(x)=−x+1
What is the solution to the equation f(x)=g(x)
?

Answer:

1- Y=-7/2x+2.

2. Y=-6/4+7

Step-by-step explanation:

Subtract 7x from both sides

Divide both sides by two

Add 4y to both sides

Subtract 6x from both sides

Divide by 4 on both sides

Both the pairs of the points are linear.

Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.

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Answer: Let x be the speed of the eastbound train.

Then the speed of the westbound train is x+3 mph.

We can set up the following equation using the distance formula (rate x time = distance)

x*4 = 648/2 + (x+3)*4

Solving for x,

x= 42

So the speed of the eastbound train is 42 mph and the speed of the westbound train is 45 mph.

Step-by-step explanation:

Answer:

The answer is d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The mean and standard deviation of the sample proportion when random samples of size 100 are taken from an infinite population whose population proportion is 0.2 is:

Mean:0.2 Standard deviation:0.04

A random sample is considered when we pick items in a random manner from a set. When we take samples of size n from a population where proportion p of success, we can find the sample proportion, which is the proportion of successes in the sample.

The sample proportion is usually denoted by p-hat.

The population mean and the population standard deviation for a binary variable are the following:

μ=pσ=√p(1-p)For the sample proportion p-hat, the following apply:

μ=pσ=p(1−p)n

As per the given question, population proportion p = 0.2, sample size n = 100, and using the above formula, we can find the sample proportion as follows:

μ=p=0.2σ=p(1−p)n=0.2(1−0.2)100=0.04

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In an MDP (Markov Decision Process), the following statements are true:

The optimal policy for a given state s is unique.

The problem of determining the value of a state is solved recursively by the value iteration algorithm.

The optimal policy for a given state in an MDP refers to the best course of action to take from that state in order to maximize expected rewards or outcomes. This policy is unique because, given a specific state, there is a single action or set of actions that yields the highest expected value.

The value iteration algorithm is a dynamic programming method used to determine the value of each state in an MDP. It starts with an initial estimate of the state values and then iteratively updates them until convergence. This recursive process involves considering the immediate rewards and expected future rewards obtained by transitioning from one state to another, following the optimal policy. Through this algorithm, the values of states are refined and converge to their optimal values.

The third statement, "V* (s) = 25, T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the value function V*(s) of each state in an MDP. It states that the value of a state is determined based on the transition probabilities T(s, a, s'), immediate rewards R(s, a, s'), discount factor y, and the value of the next state V*(s'). This equation allows us to compute the value of a state by considering the expected rewards and future values.

The fourth statement, "Q* (s, a) = ∑T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the action-value function Q*(s, a) in an MDP. It calculates the expected value of taking action a in state s, considering the transition probabilities, immediate rewards, discount factor, and the value of the next state. However, the specific notation given in the statement, with "2,," is incomplete or incorrect, making it an invalid equation.

In summary, the optimal policy for a given state in an MDP is unique, and the value of each state is determined recursively using the value iteration algorithm. The value function V*(s) and the action-value function Q*(s, a) play key roles in evaluating the expected rewards and future values in an MDP.

Answer:

38.2

Step-by-step explanation:

Answer:

7.75

Explanation:

Order of Operations (P.E.M.D.A.S.)\(please\) \(excuse\) \(my\) \(dear\) \(aunt\) \(sally\)

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

So let's start with the parentheses:

35 ÷ 4 - [3(3) ÷ (4 + 5)] ⇒ 35 ÷ 4 - [3(3) ÷ (9)]

Next let's multiply:

35 ÷ 4 - [3(3) ÷ (9)] ⇒ 35 ÷ 4 - [(9) ÷ (9)]

Next start with the division inside the brackets:

35 ÷ 4 - [(9) ÷ (9)] ⇒ 35 ÷ 4 - 1

Next we'll divide again:

35 ÷ 4 - 1 ⇒ 8.75 -1

Last we'll subtract

8.75 -1 ⇒ 7.75

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The Root cause analysis uses one of the following techniques is (D) Ishikawa diagram.

The Root cause analysis is a problem-solving technique that aims to identify the underlying reasons or causes of a particular problem or issue.

It helps in identifying the root cause of a problem by breaking it down into its smaller components and analyzing them using a systematic approach.

The Ishikawa diagram, also known as a fishbone diagram or cause-and-effect diagram, is one of the most widely used techniques for conducting root cause analysis.

It is a visual tool that helps in identifying the possible causes of a problem by categorizing them into different branches or categories.

The Ishikawa diagram can be used in various industries, including manufacturing, healthcare, and service industries, and can help in improving processes, reducing costs, and increasing efficiency.

In summary, the root cause analysis technique uses the Ishikawa diagram to identify the underlying reasons for a particular problem.

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Step-by-step explanation:

Well, if 1 gallon of gas = 1 hour then

2 hours would be 2 gallons so only 11 gallons of gas would be left in the tank and

13 hours would be 13 gallons, so 0 gallons of gas would be left in the tank

a) To find the marginal cost, we need to find the derivative of the total cost function with respect to the rate of output (Q).

TC = 100Q - Q² + 0.3Q³

Marginal cost (MC) = dTC/dQ

= d/dQ(100Q - Q² + 0.3Q³)

= 100 - 2Q + 0.9Q²

To find the average cost, we need to divide the total cost by the rate of output (Q).

Average cost (AC) = TC/Q

= (100Q - Q² + 0.3Q³)/Q

= 100 - Q + 0.3Q²

b) To find the rate of output that results in minimum average cost, we need to find the derivative of the average cost function with respect to Q. Then, we set it equal to zero and solve for Q.

AC = 100 - Q + 0.3Q²

dAC/dQ = -1 + 0.6Q

= 0-1 + 0.6Q

= 00.6Q

= 1Q

= 1/0.6Q

≈ 1.67

Therefore, the rate of output that results in minimum average cost is approximately 1.67.

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Answer:

D

Step-by-step explanation:

cause Mary needs to know how much fencing to get.

The scale of measurement of the distance between any two locations is typically considered to be interval or ratio scale.

The interval scale represents measurements where the intervals or differences between values are meaningful and consistent. In the case of distance, the intervals between different distances are consistent and can be measured in a standardized unit (e.g., meters, kilometers, miles).

If the measurements of distance also have a meaningful and non-arbitrary zero point, such as absolute zero representing no distance, then the scale would be considered a ratio scale. However, it is important to note that the choice of scale may vary depending on the specific context and purpose of the measurement.

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Answer:

Step-by-step explanation:

ima a braintlest

Using trigonometry, the angle of elevation of the top of the building from A is 36.87 degrees

The angle of elevation of the building from A, we can apply the concept of trigonometry;

tan(θ) = opposite/adjacent

tan(θ) = height/180m

Since we're given that the angle of the top of the building is 45 degrees when the man is 180m away from point A, we can set up the equation:

tan(45°) = height/180m

The tangent of 45 degrees is 1, so the equation becomes:

1 = height/180m

Solving for the height:

height = 180m

Using the tangent of the angle;

tan(θ) = height/distance

tan(θ) = 180m/240m

Simplifying:

tan(θ) = 0.75

θ = tan⁻¹(0.75)

θ = 36.87 degrees

Therefore, the angle of elevation of the top of the building from point A is approximately 36.87 degrees.

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Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7

Answer:  

Step-by-step explanation:

3x   +  6  −  6  =  248

3x  +  6  +  −  6  =  248

(  3x  )   +  (   6   +  −  6  )  =  248      (ℂ  )

3x  =  248

3x  /  3  = 248  /  3

x   =   248  /  3

x  =  82.6

Answer:

-4g^4 -3g^3 + 4g^2 +5g +3

Step-by-step explanation:

g^2 + -4g^4 +5g +9 -3g^3 + 3g^2 -6

-4g^4 -3g^3 + 4g^2 +5g +3

Answer:

B

Step-by-step explanation:

Answer:11/57

Step-by-step explanation:

Jamie's has 3(x+5) toys.

From the question, we have

gem = x toys

max = (x+5) toys

jamie’s = 3(x+5) toys.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

Complete question: Gem has x toys. max has 5 more toys than gem. jamie’s has three times as many toys as max. how many toys does jamie’s have?

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separateAnswer:

A) x = 4/3

Step-by-step explanation:

Multiply each term by 7 so you get

-7x + 3 = 14x - 25

Take the x's and the integers to seperate sides

3 + 25 = 14x + 7x

28 = 21x

Divide the 21 to get the x alone

28/21 = x

Simplify; x = 4/3

The variable x in the equation \(-x+\frac{3}{7} =2x-\frac{25}{7}\) is 4 / 3.

Variables are numbers represented by letters in an equation. Therefore, let's find the variable x in the equation.

\(-x+\frac{3}{7} =2x-\frac{25}{7}\)

add x to both sides of the equation

-x + x + \(\frac{3}{7} = 2x+x-\frac{25}{7}\)

Therefore,

\(\frac{3}{7} =3x-\frac{25}{7}\)

add 25 / 7 to both sides of the equation

\(\frac{3}{7} +\frac{25}{7}=3x\)

\(\frac{3 + 25}{7} = 3x\)

\(\frac{28}{7}=3x\)

cross multiply

28 = 7 × 3x

21x = 28

x = 28 / 21

x = 4 / 3

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The rise and run that would give us a similar right triangle on the same given line is: B. a rise of 8 and a run of 6.

The rise/run of any two points on the same line are have the same slope value.

Given the coordinates:

The rise of triangle ABC = change in y = 4 units

The run of triangle ABC = change in x = 3 units

Rise/run = 4/3

Therefore, a rise of 8 and a run of  6 would give us: 8/6 = 4/3.

This will give us a triangle similar to triangle ABC.

Therefore, the answer is: B. a rise of 8 and a run of 6.

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The given equation of the line is:

It is required to find the x-intercept and the y-intercept.

To find the x-intercept, substitute y=0 into the equation and find x:

Hence, the x-intercept is -4.

To find the y-intercept, substitute x=0 into the equation and find y:

The y-intercept is -7.

Answers:

x-intercept: -4

y-intercepe: -7

Answer:

No.

Step-by-step explanation:

Y=2x goes up twice and to the right once, it passes through the origin, therefore it won't touch or go pass by point (2,1)

Answer:

None

Step-by-step explanation:

Required

Select which is in ascending order

It should be noted that absolute values only return positives.

i.e.

∣a∣ or ∣∣a∣∣ or ∣-a∣ or ∣∣-a∣∣ = a

Having said that:

a.∣∣−514∣∣ , ∣∣−47∣∣ , ∣∣67∣∣

This gives: 514, 47, 67

This is not in ascending order

b.∣∣−23∣∣ , ∣∣−59∣∣ , ∣∣29∣∣

This gives: 23, 59, 29

This is not in ascending order

c.∣∣−38∣∣ , ∣∣34∣∣ , ∣∣−78∣∣

This gives: 38, 34, 78

This is not in ascending order

d.∣∣−110∣∣ , ∣∣−45∣∣ , ∣∣710∣∣

This gives: 110, 45, 710

This is not in ascending order

Hence, none of the list is in ascending order

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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Answer:

y=13

Step-by-step explanation:

2(6)+1

=12+1

=13

Answer:

y=13

Step-by-step explanation:

by replacing x in the equation with 6 the equation becomes y=2(6)+1 this is just a simple equation that you use to get the answer. 2×6 is 12 and 12+1=13 so y=13.

4.1 The tariff for electricity consumption is R2.55 per kilowatt-hour (kWh).

4.2 The cost of electricity for 80 kWh is R204

4.3 One way of saving electricity is by ensuring energy-efficient practices such as putting off lights, electronics, and appliances when not in use and using LED or other energy-efficient light bulbs.

4.4.1 The oven uses 1.5 kilowatts of electricity per hour.

4.4.2 The amount of money left on the meter after baking for 4 hours is  R39.70.

4.2 To calculate the cost of electricity for 80 kWh, we shall use the formula:

Cost = R2,55 x number of kWh of electricity used:

Cost = R2,55 x 80

= R204

Therefore, the cost of electricity for 80 kWh is R204.

4.4.1 We calculate the kilowatts (kW) of electricity the oven uses per hour, by converting the watts to kilowatts.

1 kilowatt (kW) = 1000 watts

Oven uses 1500 watts each hour, so we convert:

1500 watts = 1500/1000 = 1.5 kilowatts (kW)

So, the oven uses 1.5 kilowatts of electricity per hour.

4.4.2 If Mary has R55,00 worth of electricity and bakes for 4 hours, we compute the cost of electricity used during baking.

Cost of electricity used for baking = Cost per kWh x number of kWh used

= R2,55 x (1.5 kW x 4 hours)

= R2,55 x 6 kWh

= R15.30

Next, we estimate the amount of money left on the meter after baking:

Amount left on meter = Initial amount - Cost of electricity used

= R55.00 - R15.30

= R39.70

Hence, Mary will have R39.70 left on the meter after baking for 4 hours.

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Answer:

Sharsta got 12 chips, Nasreen got 18 chips, and Maseeha got 30 chips.

Step-by-step explanation:

To divide 60 chips among Sharsta, Nasreen, and Maseeha in the ratio 2:3:5, we need to first find the total number of parts in the ratio:

2 + 3 + 5 = 10

Then, we can find the share of each person by multiplying their ratio by the total number of parts and dividing by 10:

Sharsta: (2/10) x 60 = 12 chips

Nasreen: (3/10) x 60 = 18 chips

Maseeha: (5/10) x 60 = 30 chips

12,18,30

Step-by-step explanation:

Let chips got by sharsta , nasreen and maseeha be 2x ,3x,5x respectively

then,

2x+3x+5x=60

10x=60

x=6

so,

2x=12

3x=18

5x=30