If f(x) = x + 1 and g(x) = 2x - 7, which expression is equivalent to [fo g|(3)?

A fair coin is tossed three times and is tails each time. What is the probability that the next toss will be

Sergio [31]

The probability that the next toss will be heads is 1/8.

<h3>What is probability?</h3>

The likelihood of an event occurring is described by probability. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.

Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the probability of an event happening can range from 0 to 1.

Probability of getting two tails and next heads in three tosses is,

=1/2*1/2*1/2

=1/8

Learn more about probability here:

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4 0

2 years ago

If f(x)=3x+2,find f(f^-1(14)).

lisov135 [29]

Answer: 14

<u>Step-by-step explanation:</u>

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

$\dfrac{x-2}{3}=y$

$\implies f^{-1}(x)=\dfrac{x-2}{3}$

$\implies f^{-1}(14)=\dfrac{14-2}{3}$

$\implies f^{-1}(14)=\dfrac{12}{3}$

$\implies f^{-1}(14)=4$

f(f⁻¹(14)) = f(4)

f(4) = 3(4) + 2

= 12 + 2

= 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14

4 0

3 years ago

HELP ASAP You are preparing to move into a new house. The walls of your room will measure 10 feet by 12 feet.

faltersainse [42]

The Scale used on blueprint is 1 inches represents 4/3 feet

Scaling is the increase or decrease in size of a figure or object so as to create an image of that object.

Since on the blueprint, the walls measure 10 feet by 12 feet but on the blue print it measures 7.5 inches by 9 inches. Hence:

Scale used on blueprint is 7.5 inches = 10 feet or 9 inches = 12 feet

1 inches = 4/3 feet

The Scale used on blueprint is 1 inches represents 4/3 feet

Find out more at: brainly.com/question/20095188

7 0

2 years ago

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must p

rusak2 [61]

The answer is incomplete. Here is the complete question:

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each. Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella does because Stella only has enough supplies to make 40 pies. let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes.

Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.

Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.

Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.

Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.

Answer:

Part 1: $25x\geq 600$

Part 2: $15y\geq 600$

Part 3: $y\leq 40$

Part 4: Yes, she makes exactly 600 dollars by making 40 pies.

Step-by-step explanation:

Given:

Total money needed for the trip is 600 dollars.

Money earnt by Jamie for washing one car is $25.

Money earnt by Stella for making one pie is $15.

Let $x$ represent the number of cars Jamie washes. Let $y$ represent the number of pies Stella makes.

Part 1:

Since the cost for washing one car is $25

Therefore, the cost of washing $x$ cars is $25x$ .

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600.

Therefore, $25x\geq 600$

Part 2:

Since the cost for making one pie is $15

Therefore, the cost of making $y$ pies is $15y$ .

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600.

Therefore, $15y\geq 600$

Part 3:

As per the question, the maximum number of pies that Stella can make is 40. So, the value of $y$ can't exceed 40 and must be less than or equal to 40. Therefore,

$y\leq 40$

Part 4:

Now, in order to sign up for the trip, Stella's total earning must be at least $600. So, $15y=600$ is the minimum condition for signing up for the trip. Now, let us solve the above equation for $y$ . This gives,

$15y=600\\y=\frac{600}{15}=40$

Therefore, minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

8 0

3 years ago

Use The Divergence Theorem To Calculate The Surface Integral and Sis a sphere centered at the origin with a radius of 2. Confirm

marin [14]

Answer: hi your question is incomplete below is the complete question

Use the Divergence Theorem to calculate the surface integral S F dS   with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral

answer : surface integral = 384/5 π

Step-by-step explanation:

Representing the vector field as

F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k

assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.

Hence the divergence will be represented as :

Attached below is the detailed solution

6 0

3 years ago