5. Construct a DFA over \( \Sigma:=\{a, b\} \) that accepts the following language: \{w \( \in \Sigma^{*} \mid \) each a followed by exactly 1 or 3 b's \( \} \) (5 Marks) 6. Draw a deterministic and n

Answer:

No Solution

Step-by-step explanation:

I used a graphing tool to graph the equations. When graphed, the lines are parallel and they do not intercept at a point.

There is no solution; your answer should be correct.

Answer:

yes it is no solution

Step-by-step explanation:

this is because since they both have the same slope, that means the two lines are parallel

and so therefore they will never intersect

so the answer is no solution

Answer:

A)  236 cm³

Step-by-step explanation:

To calculate the volume of the composite solid, sum the volume of the cone and the volume of the cylinder.

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\vphantom{\dfrac43}\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)

From inspection of the given diagram, the diameter of the circular base of the cone and cylinder is 6 cm. As the radius is half the diameter, the radius is:

\(\implies r=\dfrac{6}{2}=3\; \sf cm\)

The height of the cone is 4 cm. The height of the composite solid is 11 cm. Therefore, the height of the cylinder is:

\(\implies h_{\sf cylinder}=11-4=7\; \sf cm\)

Using π = 3.14, the volume of the composite solid is:

\(\begin{aligned}\implies V_{\sf composite\;solid}&=V_{\sf cone}+V_{\sf cylinder}\\\\&=\dfrac{1}{3} \cdot 3.14 \cdot 3^2 \cdot 4+3.14 \cdot 3^2\cdot 7\\\\&=\dfrac{1}{3} \cdot 3.14 \cdot 9 \cdot 4+3.14 \cdot 9\cdot 7\\\\&=37.68+197.82\\\\&=235.5\\\\&\approx 236\; \sf cm^3\;(nearest\;whole\;number)\end{aligned}\)

Therefore, the volume of the composite solid is 236 cubic centimeters, rounded to the nearest whole number.

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

The appropriate order for the given calculations would be (b) Calculate the (vector) forces acting on the objects, (c) Update the (vector) momentum of each object, and (a) Update the (vector) position of each object.

First, we need to calculate the (vector) forces acting on the objects. This involves considering factors such as the mass of each object, their positions, and any other relevant forces such as gravitational force (if applicable) determined by constants like G. By calculating the forces, we can determine the interactions and influences between the objects.

Once the forces acting on the objects are calculated, we can proceed to update the (vector) momentum of each object. The momentum is updated based on the forces acting on the object and the time step, which determines the change in momentum over a given period. This step takes into account the initial momentum and the forces acting on each object.

Finally, after updating the momentum, we can update the (vector) position of each object. This involves using the updated momentum, the initial position of each object, and the time step to determine the new position of the objects in the next time interval. This step ensures that the objects move and change their positions according to the forces and momentum they experience.

Therefore, the appropriate order for the given calculations is (b) Calculate the (vector) forces acting on the objects, (c) Update the (vector) momentum of each object, and (a) Update the (vector) position of each object.

to learn more about calculations click here:

brainly.com/question/29678854

#SPJ11

Answer:

x=34

Step-by-step explanation:

Again we are given an angle's ( x to be more specific )  opposite side length and the adjacent side length so we will use trig ratio tangent

Recall that tan = opposite over hypotenuse

\(tan(x)=\frac{29}{43}\)

* multiply each side by the inverse of tan ( \((tan)^-^1\) )

\(tan(x)*tan^-^1=x\\tan^-1*\frac{29}{43} =33.99645915\\x=33.99645915\)

Finally we round to the nearest tenth of a degree and get that x = 34

The minimum number of supports required is 7.

To determine the minimum number of supports required for the twenty-four feet (six 4-ft sections) of track lighting to be installed in a continuous row in a retail store, follow these steps:

1. Determine the total length of the track lighting: 6 sections * 4 feet per section = 24 feet.

2. Consider that a support is needed at the beginning and end of the track.

3. Assess the spacing between supports. For instance, let's assume supports can be placed every 4 feet.

4. Calculate the number of supports in between the ends: (24 feet - 4 feet) / 4 feet = 5 supports.

5. Add the supports at the beginning and end: 5 supports + 2 supports = 7 supports.

The minimum number of supports required is 7.

Learn more about length here,

https://brainly.com/question/31573578

#SPJ11

The expected number of heads in 90 tosses of an unbiased coin is 45.

The probability of obtaining a head is 0.5, and the probability of obtaining a tail is 0.5. Since there are only two possible outcomes, heads and tails, a coin is classified as a binomial distribution.

Binomial distribution can be used to calculate the expected number of heads in 90 tosses of an unbiased coin. The expected value of a binomial distribution is μ = np. where n is the number of trials, and p is the probability of success.In the given case, n = 90, and p = 0.5.

Thus, the expected value of the number of heads would be:

μ = npμ = 90 x 0.5

μ = 45.

The expected number of heads in 90 tosses of an unbiased coin is 45. The expected value can be used to predict the outcomes of a large number of tosses.

However, it cannot predict the exact outcome of any single toss since the result of each toss is a random variable that is independent of the previous tosses.

Know more about the binomial distribution.

https://brainly.com/question/15246027

#SPJ11

Answer:

y=6/5x -2

Step-by-step explanation:

An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

Read more on algebraic expression here: https://brainly.com/question/17615109

#SPJ4

Answer:

24

Step-by-step explanation:

it is correct

...,..............

(c) The statement "If xy is irrational, then x is irrational or y is irrational" is false. Here's a counterexample:

Let x = √2 (which is irrational) and y = 1/√2 (which is also irrational).

In this case, xy = (√2) * (1/√2) = 1, which is a rational number.

Therefore, we have an example where xy is irrational, but neither x nor y is irrational, disproving the statement.

(d) The statement "If x+y is irrational, then x is irrational or y is irrational" is true. Here's a proof:

Suppose x+y is irrational, and we want to prove that either x is irrational or y is irrational.

By contradiction, assume that both x and y are rational.

If x is rational, then we can write x = p/q, where p and q are integers with q ≠ 0 (and q ≠ 1 for simplicity). Similarly, we can write y = r/s, where r and s are integers with s ≠ 0 (and s ≠ 1 for simplicity).

Now, let's consider x+y:

x+y = (p/q) + (r/s) = (ps + qr) / (qs),

where ps + qr and qs are integers. Therefore, x+y is a rational number since it can be expressed as a ratio of two integers.

However, this contradicts our initial assumption that x+y is irrational. Thus, our assumption that both x and y are rational must be false.

Hence, if x+y is irrational, at least one of x or y must be irrational.

Therefore, the statement is true.

To learn more about irrational:https://brainly.com/question/25466696

#SPJ11

Answer:

the third one

Step-by-step explanation:

You substitute 1 into the Y's place and solve the equations until you get x=0

Answer:

Polynomial 1:

Simplified Form: 6x^2 - x - 1

Name by Number of Terms: trinomial

Polynomial 2:

Name by Degree: linear

Name by Number of Terms: binomial

Polynomial 3:

Simplified Form: 2

Name by Degree: constant

Step-by-step explanation:

Polynomial 1:

(x-1/2)(6x+2)

6x^2 - 3x + 2x - 1

6x^2 - x - 1

It has 3 terms, so it's a trinomial.

Polynomial 2:

There is one term with x and x is raised to the first degree, so it's linear.

There are 2 terms, so it's a binomial.

Polynomial 3:

4(5x^2-9x+7)+2(-10x^2+18x-13)

20x^2 - 36x + 28 -20x^2 + 36x - 26

28 - 26

2

Since there are no variables and the answer is just 2, it's a constant.

Answer:

Step-by-step explanation:

The system of linear equations is:

y = -1/4 x + 1

y = -2x - 1

To find the solution to the system, we need to find the point where the two lines intersect. We can do this by graphing the two lines and finding their point of intersection, or by solving the system of equations algebraically.

Using the second method, we can substitute the first equation into the second equation for y:

-1/4 x + 1 = -2x - 1

Simplifying and solving for x, we get:

15/8 x = 2

x = 16/15

Substituting this value of x into the first equation to solve for y, we get:

y = -1/4 (16/15) + 1

y = 19/15

So the solution to the system is (16/15, 19/15).

Looking at the graphs, we can see that only the first option has a point of intersection that matches the solution we found algebraically. Therefore, the graph that shows the solution to the system of linear equations is a coordinate grid with one line that passes through the points 0,1 and 4,0 and another line that passes through the points 0,-1 and 1,-3.

Answer:

5 - (3n)

n starts at 0

5 - 3(n-1)

if you want n to start at 1

Step-by-step explanation:

u have to multiply both of the numbers

Answer:

Nijah has 6 stickers left.

Step-by-step explanation:

Starting stickers:

45

2/5 are given away:

\(\frac{2}{5}\) * 45

\(\frac{2}{5}\) * \(\frac{45}{1}\)

\(\frac{90}{5}\)

18

1/3 of the remaining are given away:

\(\frac{1}{3}\) * 18

\(\frac{1}{3}\) * \(\frac{18}{1}\)

\(\frac{18}{3}\)

6

Nijah has 6 stickers left.

Answer:

18

Step-by-step explanation:

Find the part she gave to her sister

45 *2/5 = 18

The part remaining is

45 - 18 = 27

She gives 1/3 to Brett

27 * 1/3 = 9

She has 27 - 9 = 18

She has 18 remaining

Answer:

9

Step-by-step explanation:

The height of a cone is dependent on its radius.
The height for a cone radius of 1 is 9.

Volume is the amount of space that is occupied by a three dimensional object.

The volume of a cone (V) is given by:V = (1/3)πr²

Where r is the radius and h is the height.

For a radius of 1:3π = (1/3)π*(1)² * hh = 9

The domain of f∘g is (-∞, -6) U (0, 1) U (7, ∞).

The given functions are: f(x)=√(42−x) and g(x)=x²−xTo find the domain of the function f∘g, we need to find the range of g(x) such that it will satisfy the domain of f(x).The domain of g(x) is the set of all real numbers. Therefore, any real number can be plugged into the function g(x) and will produce a real number.The range of g(x) can be obtained by finding the values of x such that g(x) will not be real. We will then exclude these values from the domain of f(x).

To find the range of g(x), we will set g(x) equal to a negative value and solve for x:x² − x < 0x(x - 1) < 0

The solutions to this inequality are:0 < x < 1

Therefore, the range of g(x) is (-∞, 0) U (0, 1)

Now, we can say that the domain of f∘g is the range of g(x) that satisfies the domain of f(x). Since the function f(x) is defined only for values less than or equal to 42, we need to exclude the values of x such that g(x) > 42:x² − x > 42x² − x - 42 > 0(x - 7)(x + 6) > 0

The solutions to this inequality are:x < -6 or x > 7

Therefore, the domain of f∘g is (-∞, -6) U (0, 1) U (7, ∞).

Explanation:The domain of f∘g is found by finding the range of g(x) that satisfies the domain of f(x). To find the range of g(x), we set g(x) equal to a negative value and solve for x. The solutions to this inequality are: 0 < x < 1. Therefore, the range of g(x) is (-∞, 0) U (0, 1). To find the domain of f∘g, we exclude the values of x such that g(x) > 42. The solutions to this inequality are: x < -6 or x > 7. Therefore, the domain of f∘g is (-∞, -6) U (0, 1) U (7, ∞).

To know more about domain visit:

brainly.com/question/30133157

#SPJ11

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

Learn more about null hypothesis here:

https://brainly.com/question/29387900

#SPJ11

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

To know more about the right circular cylinder, here

https://brainly.com/question/12762578

#SPJ4

Answer:

A. –x – 6y = 42

Step-by-step explanation:

Multiply everything by 6:  

6y = x + 42

The answer you are looking for is -6y+x=-42

We start by multiplying everything by 6

·6y=X+42

We then need to move X to the other side of the equation so we subtract X rom both sides.

·6Y-X=42

In order to solve the question X must be positive so we multiply everything by a quanitity of -1

·-6y+x=-42

Now this is in stardard form, so in conclusion your answer is -6y +x = -42

-I hope this is the answer you are looking for, feel free to post your questions here on brainly in the future.

The standard form of a straight line equation is: Ax%2BBy%2BC=0

.

In your example, we would write:

x-y%2B6=0

Write in standard form.

x

−

6

y

=

−

42

Answer:

2x−3y=6

Step 1: Add 3y to both sides.

2x−3y+3y=6+3y

2x=3y+6

Step 2: Divide both sides by 2.

2x2=3y+62

x=32y+3

Answer:

x=32y+3

The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Know more about probability here:

https://brainly.com/question/251701

#SPJ11

Answer:

1. <

2. <

Step-by-step explanation:

Have a good day :)

Answer: 234

Step-by-step explanation:

Given function is f(x) whose second derivative is f″(x)=8x+6sin(x). We have to find f(x) if f(0)=4 and f′(0)=4.For this we have to find f′(x) and f(x) using the second derivative of function f(x).

Steps to follow: Using f″(x) and integrating with respect to x we get the first derivative

f′(x) i.e.f′(x) = f″(x) dx∫f″(x) dx

=∫(8x+6sin(x))dx

=4x² - 6cos(x) + C1

Differentiating the above expression to get f′(0), we have

f′(0) = 0 + 6 + C1

Therefore, C1 = -6

Thus, we havef′(x) = 4x² - 6cos(x) - 6Using f′(x) and integrating with respect to x we get f(x) i.e.

f(x) = f′(x) dx∫f′(x) dx

=∫(4x² - 6cos(x) - 6)dx

= (4/3)x³ - 6sin(x) - 6x + C2

We know f(0) = 4

Therefore,C2 = f(0) - (4/3) * 0³ + 6sin(0) + 6 * 0 = 4

Therefore,f(x) = (4/3)x³ - 6sin(x) - 6x + 4

Answer: f(x) = (4/3)x³ - 6sin(x) - 6x + 4

To know more about second visit:

https://brainly.com/question/31828197

#SPJ11

Answer:

Obtuse triangle.

Step-by-step explanation:

The rule to know what type of triangle it is, you do A^2 + B^2 and if it is less than C^2, then it is obtuse. If it is equal, then it is right, and if it is more than, it is acute.

Do this equation fo 7, 8, and 12

7^2 + 8^2 =? 12^2

49 + 64 =? 144

113 < 144

113 is less than 144 which means that it is an obtuse triangle