A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 45 minutes? In 1 hour?

The regular expression is ^(a(aa)*b)$.

To create a regular expression for the language L = {w = {a,b}* | w has an odd number of 'a's and ends with 'b'}, we can use the following expression:

^(b|(a(aa)*b))$

Breaking it down:

^ indicates the start of the string.

(b|(a(aa)*b)) matches either 'b' or a sequence of 'a's followed by an odd number of 'a's and 'b'.

(aa)* matches zero or more pairs of 'a's.

$ indicates the end of the string.

This regular expression ensures that the string starts with 'b' or a sequence of 'a's, followed by an odd number of 'a's, and ends with 'b'. Any additional characters or sequences in between are not allowed.

Please note that regular expressions can have different notations and conventions depending on the context or programming language you're using. The expression provided here follows a general pattern that should work in most cases.

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A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

A. 2(8)+2(w)=26

B. 16+2w=26

Subtract 16 from both sides of the equation

2w=10

Divide both side by 2

The width is 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

yeah

Answer: C Is the answer  

Step-by-step explanation:

All four statements given about logarithms are true.

The logarithm is exponentiation's opposite function in mathematics.

This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.

The solution of a logarithm can be zero as anything raised to the power zero is 1.

The x inside the logarithm can never be zero as there are no such numbers and their exponent which results in zero.

The argument inside a logarithm must always be greater than zero.

The x inside the logarithm must always be greater than zero is also true.

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The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

Data;

Using poission formula,

\(P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute\)

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

\(p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431\)

b)

The probability the next call arrives after 2 hours.

\(\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488\)

c)

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

\(\lambda = 0.3 * 50 * 24 = 360\)

The mean = 360

The standard deviation is given as

\(S.D = \sigma =\sqrt{360} = 18.974\\\)

The probability the sum of these 50 number is less than 356 is

\(p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165\)

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The equation of the line (y+10)=4(x−3)  or  y=4x−22

We can use the point-slope formula to find an equation for this line.

The point-slope formula states: \((y-y_{1} )=m(x-x_{1} )\)

Where m is the slope and \((x_{1}, y_{1} )\) is a point the line passes through.

Substituting the values from the problem gives:

(y − −10) = 4(x − 3)

(y + 10) = 4(x − 3)

To transform this into the more familiar slope-intercept form we can solve for y:

y + 10 = (4 × x) − (4 × 3)

y + 10 = 4x − 12

y + 10 − 10 = 4x − 12 − 10

y + 0 = 4x − 22

y = 4x − 22

Hence the answer is the equation of the line is (y+10) = 4(x−3)  or  y = 4x−22

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Answer:

= -2/7

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 6-14)/(13 - -15)

    = (6-14)/(13+15)

    = -8/28

   = -2/7

Answer:

4x - 3

Step-by-step explanation:

x + x + x + x = 4x

- + - + - = - 3

So, finally 4x - 3

For Question 7, the man must take out 4 socks to be sure that he has at least two socks of the same color. This is because he could potentially take out 3 brown socks and 3 black socks before getting a matching pair, but with 4 socks, there must be at least two of the same color.

For Question 8, the man must take out 3 socks to be sure that he has at least two black socks. This is because he could potentially take out all 12 brown socks before getting a black one, but with 3 socks, there must be at least one black sock and then a potential for a second.

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Answer:

$6.90 is the cost of 9 tennis balls

Answer:

18

Step-by-step explanation:

The range is the highest data minus the smallest data.

Hence range is 27 - 9 = 18.

Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.

What is quotient?

In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

0. 48 ÷ 0. 8

=0.06

The solution for Long Division of \($\frac{4.8}{8}$\) is 0.6

The solution for Long Division of \($\frac{0.48}{0.08}$\) is 6.

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y = -7

x = 56/45

see the pic, hope its correct

Answer:

4/13

Step-by-step explanation:

We can first find the GCD or GCF of 28 and 91. 91 in its simplest form is 13*7. 28 in its simplest form is 2*2*7. The only common factor they have is 7, so 7 is the GCD. We can divide both by 7 to get \(\frac{4}{13}\)

Answer: B. alternate interior angles.

Step-by-step explanation:

Answer:

20 miles

Step-by-step explanation:

x = break even miles

$10 + x($1.50 = x($2.00)

10 + 1.5x = 2x

0.5x=10

x = 20 miles

The solution for the system of equations is (21.5, 2).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the sum of two numbers is 23.5.

Let the two unknown numbers be x and y.

x+y=23.5 --------(i)

The difference of two numbers is 19.5.

x-y=19.5 --------(ii)

From equation (ii), x=19.5+y

Substitute x=19.5+y in equation (i), we get

19.5+y+y=23.5

2y=4

y=2

Substitute y=2 in equation (i), we get

x-2=19.5

x=21.5

Therefore, the solution for the system of equations is (21.5, 2).

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Answer:

7:5

Step-by-step explanation:

35:30

7:5

Your pay on the next paycheck will be $263.50

To calculate the amount of your next paycheck, we need to determine your total earnings for the pay period.

Given that you make $7.75 per hour and work 17 hours each week, we can calculate your weekly earnings by multiplying your hourly rate by the number of hours worked:

Weekly earnings = Hourly rate * Hours worked per week

Weekly earnings = $7.75 * 17 = $131.75

Since you are paid biweekly, we can now determine your total earnings for the pay period by multiplying your weekly earnings by 2:

Total earnings = Weekly earnings * Number of weeks in the pay period

Total earnings = $131.75 * 2 = $263.50

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Answer: The Earth makes one rotation every day.

Step-by-step explanation:

Answer:

8,000,000,000 text messages every month.

Step-by-step explanation:

\(8*10^9\)

\(10^9\) means there will be 9 zeroes at the end of 1. So it will be 1,000,000,000.

So 8* 1,000,000,000 will be 8,000,000,000 text messages every month.

Answer:

I think its A

Step-by-step explanation:

x=√13 I think it is that one makes sense

Answer:

A.)

Step-by-step explanation:

First you need to take the square root from both sides to isolate x. Since you cannot find an exact decimal answer for the square root of 13 you leave it as + or - \(\sqrt{13\\}\).

As a general rule, the larger the degrees of freedom for a chi-square test, the more reliable and accurate the test results become.

In statistical hypothesis testing using the chi-square distribution, degrees of freedom (df) play a crucial role. The degrees of freedom represent the number of independent pieces of information available for estimation or inference in a statistical analysis.

For a chi-square test, the degrees of freedom are calculated based on the number of categories or cells involved in the analysis. As the degrees of freedom increase, it allows for more variability in the data and provides a better approximation of the chi-square distribution.

Having a larger degrees of freedom value provides a more accurate estimation of the expected frequencies under the null hypothesis. This, in turn, leads to a more reliable assessment of the goodness-of-fit or independence in the data being tested.

Therefore, in general, larger degrees of freedom provide greater statistical power and precision in chi-square tests, allowing for more confident conclusions to be drawn from the analysis.

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The syntax \large{1. 8\overline{3} = ?}1.83  can be re-written as \(\large{1. 8\overline{3} = \frac{8}{9}}1. 8 3\). This means that the decimal form of \(\large{1. 8\overline{3}\) is equal to 8/9 in a fraction.

Here’s how we can convert a repeating decimal to a fraction:

Let x be the repeating decimal. Then we can write:

x = 0.833333…

Multiplying both sides by 10 gives:

10x = 8.333333…

Subtracting the first equation from the second equation gives:

10x - x = 8.333333… - 0.833333…

Simplifying both sides gives:

9x = 8

Dividing both sides by 9 gives:

x = 8/9

Therefore, \large{1. 8\overline{3} = \frac{8}{9}}1.83, or \(\large{1. 8\overline{3}\) = 8/9

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Answer:

75.245 or 75.25

Step-by-step explanation:

The number of steps he would have to take to make the cut for the top 5% for his distribution is 12,031.5.

The number of steps he would have to take to make the cut for the top 5% for his distribution is 12,031.5.

Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. So, the population parameters are:

Mean=μ=10,000

Standard Deviation=σ=1,500

We need to find the number of steps he would have to take to make the cut for the top 5% for his distribution.

Step 1: We need to find out the z-score for the top 5% of the distribution.

We can find out the z-score for the top 5% of the distribution using the standard normal distribution table. The table value of z for 0.05=1.645. Check the attachment.

Step 2: We can use the z-score formula to find out the value of X for the top 5% of the distribution.

z=(X-μ)/σ

Rearranging the above equation, we get:

X=μ+z.σ

X=10,000+1.645×1,500

X=12,031.5

Therefore, It would take him 12,031.5 steps to make the top 5% for his distribution.

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Answer: D. Subtracting 9 from each side

Step-by-step explanation:

Always start with numbers without variables first before doing anything with x. And make sure one side must not equal 0 unless you're doing polynomials.