​Hank's pickup can travel 65 miles on 5 gallons of gas. How many gallons will​ Hank's pickup need to travel 39 ​miles?

The statements that are true about automata and formal languages are b, c and d

The term empty does not exist in any language. There are dialects that do not use the empty word in their lexicon. The empty word, for instance, would not exist in a language where all words have lengths higher than zero.  There exist Irregular finite languages. A language with all possible combinations of a limited number of symbols is one example.

While this language is finite, a conventional grammar cannot adequately define it. Additionally, contextless languages are a subset of regular languages. Because of this, there are irregular context-free languages. A regular grammar can be used to describe L1 if L1 is a subset of L2 and L2 is regular.

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Complete Question:

Which of the following statements about automata and formal languages are true? Briefly justify your answers. Answers without any substantiation will not achieve points!

(a) Every language contains the empty word.

(b) There exist finite languages which are not regular.

(c) Not every context free language is regular.

(d) For two arbitrary languages L1 and L2 the following always holds: If L1 <L2, L2 is regular than L1 is also regular.

(e) Let L = (ba) be a language which contains only one word. There exists only one (unique) regular expression which generates L, and this expression is a = ba.

40 middle school students preferred sweet coconut-flavored frozen yogurt.

According to the circle graph, the percentage of middle school students who preferred sweet coconut-flavored frozen yogurt is 10%.

To find the actual number of students, we can calculate 10% of the total number of students:

10% of 400 = (10/100) x 400

= 0.10 x 400

= 40

Therefore, 40 middle school students preferred sweet coconut-flavored frozen yogurt.

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Answer:

y = 110

Step-by-step explanation:

The formula for the sum of the interior angles of a polygon with n sides is: (n-2) x 180 degrees. A hexagon has 6 sides, so if we plug this value into the equation, we get (6-2) x 180 = 4 x 180 = 720 degrees. Since we have one angle which is 170 degrees and the other five angles are the same (y), we can make the equation 170 + 5y = 720. We subtract 170 on both sides and get the equation 5y = 550. Dividing both sides by 5, we get y = 110, which is our answer.

The person who starts Priya does not always win, but rather the outcome depends on whether the total number of players is even or odd.

Let's record the game on paper for different numbers of players and see if the person who starts always wins.

Case 1: Two Players (Priya and Jada)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 2: Three Players (Priya, Jada, and Han)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Priya is the winner. The person who starts (Priya) wins.

Case 3: Four Players (Priya, Jada, Han, and Diego)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

From these examples, we can see that when the number of players is even, the person who starts always wins.

To find more numbers where the person who starts always wins, let's consider some additional cases:

Case 5: Six Players (Priya, Jada, Han, Diego, Alex, and Mia)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 6: Eight Players (Priya, Jada, Han, Diego, Alex, Mia, Ethan, and Lily)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Round 7: Ethan says SAFE.

Round 8: Lily says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Based on these examples, we can observe that when the number of players is a multiple of 2, the person who starts always wins. There seems to be a pattern here: if the number of players is even, the starting person wins, while if the number of players is odd, the starting person loses.

Therefore, the person who starts does not always win, but rather the outcome depends on whether the total number of players is even or odd.

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Answer:

The Correct answer is C ( -7, 4)

Step-by-step explanation:

The Correct answer is C ( -7, 4) yepppp

Answer:

20 % decay

Step-by-step explanation:

Exponential equations are in the form

y = a * b^x

a is the initial value

b is the growth or decay

b>1 is growth b-1 rate  of growth

b <1 decay  1-b rate of decay

1-.8 = .2

Change to decimal form

20 % decay

The equation -20,000(F/P, i*, 4) + 10,000 + 5,000 = 0 is used to calculate the project's internal rate of return (i*). The Option A/

The internal rate of return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.

To get internal rate of return (i*), we need to solve the equation: \(-20 000(F/P, i*, 4) + 10 000 + 5 000 = 0\)

The initial cost of the project is -$20,000, the net annual cash inflow is $10,000 and the salvage value is $5,000. The equation represents the present value of cash flows over the project's duration.

Therefore, by solving the equation, we can determine the internal rate of return (i*) for the project.

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Answer:

1) 3.25 gallons

2)12-1.75tt

Step-by-step explanation:

1) gallons per hour x number of hours

1.75x5 = 8.75 gallons

subtract your answer from what he currently has

12 - 8.75 = 3.25 gallons

Answer:

18

Step-by-step explanation:

Because -1 q would make it a positive 1q (q) so q=18

Answer:

Step-by-step explanation:

A factor in an experiment that changes from the manipulation of the independent variable is the dependent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

The variable being measured or tested in an experiment is known as the dependent variable. 1 The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.

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Answer:

0.5

Step-by-step explanation:

0.5=0.42 then the answer is 0.5

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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For a point P plotted on a given number line, the number represented by the point P is 5.80⁻³.

A number line is a linear visual representation of numbers and integers. This line is used to compare equally spaced numbers on an infinity line that extends horizontally or vertically on either side. A number line shows point values ​​and equal divisions on the line. Between point 5.10⁻³ and point 6.10⁻³ there are 10 evenly spaced points.

Counting from the left, it looks like this:

5.10⁻³, 5.20⁻³, 5.30⁻³, 5.40⁻³, 5.50⁻³, 5.60⁻³, 5.70⁻³, 5.80⁻³, 5, 90⁻³, 6.00⁻³, 6.10⁻³.

Point P drops to 5.80⁻³, so the value of point P is 5.80⁻³.  

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The complete question is as follows:

The opportunity cost of 1 lunch box is 3 sandwich containers. This means workers are giving up the opportunity to produce 3 sandwich containers

The opportunity cost represents the value of the next best alternative forgone when making a choice. In this case, the workers at Shadowland have the option to produce either lunch boxes or sandwich containers.

Given that they can produce 6 lunch boxes or 18 sandwich containers per hour, we can calculate the opportunity cost.

To find the opportunity cost of 1 lunch box, we compare the number of sandwich containers that could have been produced in the same amount of time.

Since they can produce 18 sandwich containers per hour, the opportunity cost of 1 lunch box is the number of sandwich containers that could have been produced instead, which is 18/6 = 3.

Therefore, the opportunity cost of 1 lunch box is 3 sandwich containers. This means that for every lunch box produced, the workers are giving up the opportunity to produce 3 sandwich containers, which represents the trade-off in their production choices.

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Answer:

19 tickets

Step-by-step explanation:

Nadine sold two kinds of tickets to her class play

The student tickets cost $3

Adult tickets cost $5.50

Nadine sold a total of 25 tickets for $90

We are required to find the number of students tickets that were sold

Let x represent the number of tickets sold to students

Let y represent the number of tickets sold to adults

x + y= 25

x= 25-y..........equation 1

Since the total cost of the ticket is $90

3x + 5.50y=90..........equation 2

Substitute 25-y for x in equation 2

3(25-y) + 5.50y= 90

75-3y+5.50y= 90

75+2.5y= 90

Collect the like terms

2.5y= 90-75

2.5y=15

Divide both sides by 2.5

2.5y/2.5=15/2.5

y= 6

Substitute 6 for y in equation 1

x= 25-y

x= 25-6

x= 19

Hence Nadine sold 19 student tickets

Answer:

12.5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Only one in which x is not more than one number matching y in function.

The table 4 represent the function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

The function should have distinct input with corresponding output.

If there are 2 same input vales then it not said to be a function.

So, according the definition the table 4 represent the function because the table 1, 2 and 3 have repeated input value,

Hence, the table 4 represent the function.

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The term q^2 in the Hardy-Weinberg equation represents the frequency of homozygous recessive individuals in a population.

In the Hardy-Weinberg equation, the term q^2 is used to calculate the frequency of homozygous recessive individuals in a population. The equation is based on the principle that in the absence of evolutionary forces, such as mutation, migration, selection, and genetic drift, the allele frequencies in a population remain constant from one generation to the next.

In the equation, q represents the frequency of the recessive allele, and q^2 represents the frequency of individuals who are homozygous for the recessive allele. By squaring q, we obtain the proportion of individuals who carry two copies of the recessive allele. This is because in a population in Hardy-Weinberg equilibrium, the probability of an individual inheriting the recessive allele from both parents (represented by q * q) is q^2.

To understand this better, let's consider an example. Suppose we have a population in which the frequency of the recessive allele (q) is 0.3. To calculate the frequency of homozygous recessive individuals (q^2), we square q: (0.3)^2 = 0.09. This means that 9% of individuals in the population would be expected to be homozygous for the recessive allele.

The Hardy-Weinberg equation and its components are valuable tools in population genetics. They help us understand how genetic variation is maintained or changes over time in populations and provide a baseline against which we can compare real-world data to detect deviations that may indicate evolutionary processes at work.

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Answer:

x=9.717

y=18.275

Step-by-step explanation:

First solve for x and then use x to help you solve for y

The true statement about the function is that (c) the domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

The complete question is added at the end of this solution

From the complete question, we have the following equation

f(x) = g(x)/h(x)

The above equation means that

The function f(x) is the quotient of the functions g(x) and h(x)

For the function f(x) to have real values, the function h(x) must not equal 0

i.e. h(x) ≠ 0

This is so because

A number or an expression divided by 0 is not a real number

Hence, the true statement is that the domain of f(x) consists of all values of x where h(x) does not equal 0.

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Complete question

which of the following statements is true about a rational function of the form where g and h are polynomial functions?

A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote. g(x)

B. The rational function f(x) h(x) will have a removable discontinuity at x = a if g(a) = 0. g(x)

C. The domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

D. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote.

Answer:

y = mx + b

Step-by-step explanation:

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

272 cm²

Step-by-step explanation:

Surface Area :

Hey! there

Answer:

Step-by-step explanation:

In this question we are provided with length 4 cm , height 15 cm and width 4 cm which are basically of a cuboid.

And we are asked to find the Surface Area . For finding surface area of cuboid we need to know its formula . So ,

\( \quad \underline{ \boxed{ \frak{Surface \: Area_{(Cuboid)} = 2 ( lw + wh + hl )}}}\)

Where ,

SOLUTION : -

Step 1 : Substituting value of length , width and height in formula :

\( \quad \: \longmapsto \: \qquad2((4 \times 4) + (4 \times 15) + (4 \times 15)\)

Step 2 : Solving parenthesis :

\(\quad \: \longmapsto \: \qquad2(16 + 60 + 60)\)

Adding 16 , 60 and 60 :

\(\quad \: \longmapsto \: \qquad2(136)\)

Step 3 : Multiplying 2 with 136 :

\(\quad \: \longmapsto \: \qquad \: \blue{ \underline{ \boxed{ \frak{272 \: cm {}^{2} }}}} \quad \bigstar\)

The answer is eight.

Given the fraction of each colored chalk, Andrea is right that less than 1/2 the chalk in the bucket is blue.

Total = 2/6 + 5/12 + 3/12

= (4+5+3) / 12

= 12/12

= 1

Fraction of blue : Total chalk

= 5/12 : 1

Blue = 5/12 ÷ 1

= 5/12 × 1/1

= 5/12

= 0.42

So,

1/2 = 0.5

Therefore, Andrea is right that less than 1/2 the chalk in the bucket is blue.

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Answer:

the mean is 8

Step-by-step explanation:

To find the mean, add the numbers together and then divide by the number of numbers

( 6+11+7+4+12+15+1)/7

56/7

8

Answer:

3⅓

Step-by-step explanation:

2/12•20=

1/6•20=

20/6=

10/3=

3⅓