A decision problem X is self-solvable if X = L(MX) for some polynomial-time oracle TM M, whose oracle queries are always strictly shorter than its input. In other words, when M is executed on an input of length n, it queries its oracle only on strings of length less than n. This is a strange situation, where M has oracle access to the problem that it is trying to solve. But when M is trying to determine whether x € X, it cannot simply query its oracle on x for the answer. ከ. (a) Show that TQBF is self-solvable. Be explicit about what assumptions are you making about how for- mulas are encoded into bit strings. (b) Prove that if L is self-solvable then L E PSPACE.

Answer:

122 adults

Step-by-step explanation:

1049.20(price of tickets sold)÷8.60(ticket price per adult)=122

Answer:

Step-by-step explanation:

25, i think

Answer:

\(g(x) = -3x\)

Step-by-step explanation:

Given

\(f(x) = 3x\)

Required

Reflect over \(y = 0\)

This means that we reflect over the x-axis

And the rule of reflection is:

\((x,y) \to (x,-y)\)

Hence:

\(f(x) = 3x\)

Will become:

\(g(x) = -f(x)\)

So, we have:

\(g(x) = -3x\)

Answer:

Option B.

Step-by-step explanation:

A function is a relationship that maps elements from a set (the domain, set of the inputs) into elements from another set (the range, set of the outputs), such that each element from the domain can be mapped into only one element from the range.

Remember that in the 2d case, the horizontal axis represents the values from the domain while the vertical axis represents the values from the range.

So, one criterion to check if a graph belongs to a function or not, is to see if there is a vertical line that intersects the graph at two different points, (because that would mean that a single input value has two different output values) if there is no vertical line that does that, then the graph shows a function. (this is called the vertical line test)

Now that we know all this, let's look at the graph for a second and see that yea, the graph passes the vertical line test, so the graph represents a function.

Then the correct option is B

Answer:

4.393 * 10^6

Step-by-step explanation.

Hello. Oh I've done this problem before.

\(\frac{2.1*10^{19} }{4.78*10^{12} } = 4393305\)

4.393 * 10^6

Hope this helps - please mark brainliest if possible :)

The time that Ron needs to calculate for the sound wave to travel from the earth to Venus, at the speed of 4.78 * 10¹² miles per year, with the distance between them being 2.1 * 10¹⁹ miles, is 4.4*10⁶ years.

The speed of a body is directly related to the distance traveled, while it is inversely related to the time taken.

The equation for speed is written as:

Speed = Distance/Time.

This equation can be used to determine distance and time like this:

Distance = Speed*Time.

Time = Distance/Time.

In the question, we are asked to calculate the time taken for a sound wave at the speed of 4.78 * 10¹² miles per year, to cover the distance between the earth and Venus, where distance = 2.1 * 10¹⁹ miles.

As we already know, the time taken is determined using the formula:

Time = Distance/Speed,

or, time = (2.1 * 10¹⁹ miles)/(4.78 * 10¹² miles per year),

or, time = (2.1/4.78)*10⁷ years = 4.4*10⁶ years.

Therefore, the time that Ron needs to calculate for the sound wave to travel from the earth to Venus, at the speed of 4.78 * 10¹² miles per year, with the distance between them being 2.1 * 10¹⁹ miles, is 4.4*10⁶ years.

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The values of a and b to expand the binomial expression (2x^3 + 3y^2)^7 using the binomial theorem are a = 2x^3 and b = 3y^2.

To use the binomial theorem to expand the expression, we can write it as (a + b)^7, where a = 2x^3 and b = 3y^2. The binomial theorem states that (a + b)^n = Σ(n choose k) * a^(n-k) * b^k, where Σ is the summation symbol, k is a non-negative integer less than or equal to n, and (n choose k) is the binomial coefficient.

Applying the binomial theorem to our expression with a = 2x^3 and b = 3y^2, we get (2x^3 + 3y^2)^7 = Σ(7 choose k) * (2x^3)^(7-k) * (3y^2)^k, where k ranges from 0 to 7. Simplifying this expression gives us the expanded form of (2x^3 + 3y^2)^7.

In summary, to expand the binomial expression (2x^3 + 3y^2)^7 using the binomial theorem, we substitute a = 2x^3 and b = 3y^2 into the formula (a + b)^n and simplify the resulting expression using the binomial theorem formula.

The binomial theorem is a powerful tool that allows us to expand binomial expressions quickly and efficiently. It is based on the idea that any power of a binomial expression can be written as a sum of terms involving the binomial coefficients. The binomial coefficient (n choose k) represents the number of ways to choose k objects from a set of n objects, and is given by the formula (n choose k) = n! / (k! * (n-k)!). When we apply the binomial theorem to a given expression, we can use the formula to calculate each term in the expansion, and then add them up to get the final result. This saves us a lot of time and effort compared to expanding the expression by hand.

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Answer:

Histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables

Answer:

its called a Domain

Step-by-step explanation:

All of the x-values or inputs are called Domain.

"x-values" is the word used in mathematics and statistics to describe the input values or independent variables in a function or equation.

These x-values stand for a function's inputs, arguments, or the points at which a mathematical connection is being assessed.

The outputs or dependent variables of a function are represented by the appropriate y-values, which are often paired with the associated x-values. The link between the independent and dependent variables can be seen on a graph by plotting the x-values and y-values together as data points.

For example, in the equation y = 2x + 3, "x" represents the x-values or inputs, while "y" represents the corresponding y-values or outputs. By substituting different values for x, you can calculate the corresponding y-values and observe how changes in the x-values affect the relationship described by the equation.

Hence the answer is Domain.

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Mesh technology has been introduced at two levels: the device level, enabling devices to form local mesh networks, and more recently at the network level, where mesh networking spans larger areas and provides decentralized and robust connectivity options

Mesh technology has revolutionized the way devices communicate and form networks. Initially, mesh technology was introduced at the device level, enabling devices to create a local mesh network where each device acts as a node and can communicate with other devices in the network directly. This device-level mesh networking provides several advantages, such as increased range, improved reliability, and self-healing capabilities. It allows for seamless communication between devices, even if one or more nodes fail or are out of range, by automatically rerouting data through alternate paths in the network.

More recently, mesh technology has been extended to operate at the network level, introducing mesh networks on a larger scale. In this context, mesh networks refer to a decentralized network architecture where multiple interconnected devices create a network that spans a broader area. These networks typically consist of various access points, routers, and other devices that work together to form a mesh topology. By employing mesh networking at the network level, organizations and communities can create expansive wireless networks that cover large areas, such as campuses, cities, or even entire regions. This approach offers increased scalability, flexibility, and robustness compared to traditional centralized network architectures.

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Answer:

11 years old

Step-by-step explanation:

33+11=44 (four times of Jerry's age)

44÷4=11 (Jerry's age)

Hope this helps! Thanks.

Answer:

15 hours

Step-by-step explanation:

The number of hours is 15 hours if Caroline's baby sister sleeps 5/8 of the day.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Caroline's baby sister sleeps 5/8 of the day.

As we know,

In one day there are 24 hours

1 day = 24 hours

5/8 day  = x hours

Here x is the number of hours

1/(5/8) = 24/x

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

8/5 = 24/x

1/5 = 3/x

x = 3×5

x = 15 hours

Thus, the number of hours is 15 hours if Caroline's baby sister sleeps 5/8 of the day.

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Answer:

Percentage decrease = 28%

Step-by-step explanation:

Original distance = 25 miles

New distance = 18 Miles

Change in distance = 25 - 18

= 7 miles

Percentage decrease = change in distance / original distance × 100

= 7/25 × 100

= 0.28 × 100

= 28%

Percentage decrease = 28%

Answer:

This is a function y = mx + b:

So, the function would be y = 20x + 50, where y is the dollar amount after x weeks and x cannot be greater than 12.

c) in the long run, the amount of oil leaked per day will decrease. Hence, the conclusion is that the amount of oil leaked per day is decreasing to 0 in the long run.

(a) The total number of barrels leaked on the first day of an oil tanker:

The function given isL′(t)=t+1/80 ln (t+1)To find the total number of barrels leaked, we need to integrate this function over the interval

0 ≤ t ≤ 24 (hours in a day):

∫₀²⁴ L′(t) dt = ∫₀²⁴ (t+1/80 ln (t+1)) dt= [(1/2)t²+1/80(t+1)ln(t+1)]₀²⁴= 312.99 ≈ 313

Thus, the tanker will leak 313 barrels on the first day. Rounding it to the nearest whole number, we get 313. Therefore, the main answer is 313 barrels of oil on the first day.

(b) The total number of barrels leaked on the second day of an oil tanker:

To find the number of barrels leaked on the second day, we need to integrate L′(t) from 24 to 48:∫²⁴⁺²⁴ L′(t) dt = ∫²⁴⁺²⁴ (t+1/80 ln (t+1)) dt= [(1/2)t²+1/80(t+1)ln(t+1)]²⁴⁺²⁴≈ 316.

Therefore, the total number of barrels leaked on the second day is 316 barrels. The main answer is 316.

(c) :The amount of oil leaked per day will decrease in the long run. To see why, we take the limit as t approaches infinity of L′(t).∞lim L′(t) = lim (t+1/80 ln (t+1))∞→∞

This limit is equal to infinity, so the amount of oil leaked per day will increase at first. However, since the natural logarithm function grows more slowly than any polynomial function, L′(t) will eventually grow more slowly than t.

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bc Answer: They form an obtuse triangle

Step-by-step explanation:

the length of one side must be greater than the difference and less than the sum of the lengths of the other two sides. In this case the third side must be greater than 3 and less than 31. 3(squareroot) 55 is 22.25 so it fits.

The table, we cannot determine the probability of a student participating in exactly two activities.

The probability distribution table is not provided in the question, but assuming that it is a valid probability distribution, we can use it to find the probability that a student participates in exactly two activities.

Let X be the random variable representing the number of extracurricular activities a college freshman participates in, and let p(x) denote the probability of X taking the value x.

Then, we want to find p(2), the probability that a student participates in exactly two activities. This can be obtained from the probability distribution table.

Without the table, we cannot determine the probability of a student participating in exactly two activities.

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The ship's distance from its starting point is 7.810 km and the ship's bearing is 49°.

(a) Distance from the starting point:

To find the distance, we have to consider the two legs of the ship's journey as vectors and use the Pythagorean theorem.

Using the cosine rule, we can find the magnitude of the resultant vector:

=√(25 + 16 - 40cos(240°))

=√(41 - 40cos(240°))

=√(41 + 40 * 0.5)

=√(41 + 20)

=√(61)

≈ 7.810 km (rounded to three significant figures)

(b) Bearing from the starting point:

To find the bearing, we have to use the tangent of the angle between the resultant vector and the east direction.

=tan((4 sin(240°)) / (5 - 4 cos(240°)))

=tan((-4 * 0.866) / (5 - 4 * 0.5))

=tan((-3.464) / (5 - 2))

=tan((-3.464) / 3)

=tan(-1.154)

≈ -49° (rounded to the nearest degree)

Therefore, the ship's bearing is 49° and is at 7.810 km from its starting point.

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Answer:

13

Step-by-step explanation:

See attachment

The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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Answer:

9

Step-by-step explanation:

add all the numbers: 6+12+10+8=36

then divide by the amount of numbers there are: 36/4=9

Answer:

Step-by-step explanation:

Correct option is A)

The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The pair of lines are shown in figure.

Now,

By figure, we see that;

The lines are perpendicular because they intersect at a right angle.

Thus, The correct statement about the pair of lines will be;

''The lines are perpendicular because they intersect at a right angle.''

Option 4 is true.

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Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.

Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc. 

According to the information in the question:

Deposit = $50

Rent cost per day for the car = $20

Total amount that Justice has to pay = $490

∴ Total number of days that Justice kept the car = (490 - 50)/20

                                                                                 = 440/20

                                                                                 = 22 days

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The number of days did he have the car are 22.5 days.

a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.

Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.

To find out how many days he had the car, we can set up an equation:

$50 + (number of days x $20) = $490.

Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.

So Justice had the car for approximately 22.5 days.

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Answer:

B.

Step-by-step explanation:

Since all bulbs are connected in series, by opening switch A, you break the series connection, and all bulbs go out.

Answer:

34

Step-by-step explanation:

Step 1: form an equation

n + 4 = 38

Step 2: isolate the variable (n)

n = 38 - 4

Step 3: solve the equation

n = 34

The domain of the function is  x ≤ 1.

x ≤ 1 because your domain cannot have h(x) because that is your function and would be your range but in this case it is your domain and your domain, also known as the x coordinate, would have to be the number on the x axis that your line starts at, which would be your domain.

Your line starts on line 1 on the x axis, which would be your domain.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

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Based on the linear pair theorem, the measure of angle 5 is: A. 83 degrees.

The linear pair theorem states that if two angles are on a straight line, the sum of their measures equals 180 degrees.

∠5 and ∠6 are a linear pair. Therefore:

m∠5 = 180 - m∠6

m∠5 = 180 - 97

m∠5 = 83°

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Answer:83 degrees

Step-by-step explanation:topG

Answer:

Answer:

2.215=2 43/200

Step-by-step explanation:

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

2.215=2.215/1

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000

2.215/1×1000/1000=2215/1000

Find the Greatest Common Factor (GCF) of 2215 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5,

2215÷5/1000÷5=443/200

Simplify the improper fraction,

=2 43/200

In conclusion,

2.215=2 43/200

Answer:

\(\frac{731}{330}\)

Step-by-step explanation:

We require 2 equations with the repeating numbers placed after the decimal point.

let x = 2.2151515... ( multiply both sides by 10 and 1000 )

10x = 22.1515.... → (1)

1000x = 2215.1515.... → (2)

Subtract (1) from (2) thus eliminating the repeating decimal

990x = 2193 ( divide both sides by 990 )

x = \(\frac{2193}{990}\) = \(\frac{731}{330}\)

Thus

2.2151515..... = \(\frac{731}{330}\)

The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.