Let: L1 = {bb} L2 = {a, ab} L3 = {æ € {a,b}*| |x|≤ 3} = {A, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb} (L1;L2;) ∩ L3 = what?

The side lengths are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

The length a is opposite to the angle of 73º, with an hypotenuse of 19, hence:

sin(73º) = a/19

a = 19 x sine of 73 degrees

a = 18.1698.

The length b is opposite to the angle of B = 90 - 73 = 17º, with an hypotenuse of 19, hence:

sin(17º) = b/19

b = 19 x sine of 17 degrees

b = 5.5551.

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The height of the cylinder whose area is given would be =7.6cm.

To calculate the height of a cylinder, the formula for the area of cylinder should be used and it is given below as follows;

Surface area of cylinder = 2πr²+2πhr

This can also be written as = 2πr(h+r)

surface area = 54cm²

h+r = 9cm

r = ?

54 = 2×2.14×r(9)

54 = 38.52r

r = 54/38.52

r = 1.4

h = 9-1.4 = 7.6cm

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There are 25 houseplants that are full-grown and 15 houseplants that are seedlings in the plant store. You want to know the likelihood that a plant that is bought for a friend is a full-grown houseplant.

The probability that a randomly selected plant will be a full-grown houseplant can be calculated by dividing the number of full-grown houseplants by the number of total houseplants.

Therefore, the probability of choosing a full-grown houseplant is 25/(25 + 15) = 5/8 = 0.625 or 62.5%.

The probability that a plant is a houseplant is 25 + 15 = 40.

The probability that a plant is an outdoor plant is 25 + 30 = 55.

Since there are a total of 40 houseplants and 25 are full-grown, the probability of choosing a full-grown houseplant is 25/40 or 5/8, which can be simplified to 0.625 or 62.5%.

Therefore, the chance that the plant you are buying for your friend is a full-grown houseplant is 62.5%.

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Answer:

Step-by-step explanation:

x

2

−4x+y

2

−6y+13

Answer:y=3x + 2

Step-by-step explanation: 4x+6y= 12x=-4y+ 8 y=-3x+2

A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.

If the length of a rectangular garden is twice its width, and the garden is surrounded by a rectangular concrete walk having a uniform width of 4 feet, and the area of the garden and the walk is 330 square feet, then the dimensions of the garden are 10 feet by 20 feet.

The length of a rectangular garden is twice its width, so if we let the width be x, then the length is 2x. The area of the garden is the length times the width, so it is 2x*x = 2x².Now let's add the width of the walk to the dimensions of the garden, so the width of the garden plus the walk is x + 8, and the length plus the walk is 2x + 8. The area of the garden plus the walk is the length plus the walk times the width plus the walk, so it is (x + 8)(2x + 8).

According to the problem, the area of the garden plus the walk is 330 square feet. We can set up an equation to solve for x:(x + 8)(2x + 8) = 330Simplifying and solving for x, we get:x² + 10x - 29 = 0(x + 13)(x - 3) = 0x = -13 or x = 3Since the width of the garden cannot be negative, we must take x = 3. Then the length of the garden is 2x = 6, and the dimensions of the garden are 3 feet by 6 feet.

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Answer:

slope: 3

y-intercept: 3

Step-by-step explanation:

y=3x+3

Hope this helps :) Have a good day!!!!

Answer:

The definition of parallel lines are lines that have a constant minimum distance between them at any given point along the lines, such that the lines are the same distance apart all through

Therefore, given that we have;

1) The path of the two bottle rockets are parallel,

2) The initial distance between the two rocket on level ground = 5 feet = The perpendicular (shortest) distance between the two rockets

3) The shortest distance between the rockets having the same height moving on parallel path will be constant = 5 feet

4) The height of the two rockets after 0.1 second = Constant = 5 feet

5) Therefore, by the definition of parallel lines, distance between the two rockets which are at the same height after 0.1 second will still be 5 feet

Step-by-step explanation:

Answer:

0.2083

Step-by-step explanation:

Answer:

They are zeroes when y=0

Step-by-step explanation:

For a function \(f(x)\), if \(f(x)=0\), the values of x that make the function true are known as roots, or x-intercepts, or zeroes.

Answer:

17

Step-by-step explanation:

Using PEMDAS:

5² + 2(-8 ÷ 2)​

5² + 2(-4)

25 - 8

17

Answer:

c) divide both sides by 8

hope this helps!

Answer:

Its the 3 option

A. By the given conditions, the function f has a root in the interval [a, b].

B. The given conditions provide information about the function f and its derivatives.

Let's analyze the conditions step by step:

1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.

In other words, the function changes the sign between a and b.

2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).

This indicates that the function is increasing within this interval.

3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).

This indicates that the function is concave up within this interval.

By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).

Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].

Therefore, the main answer is that the function f has a root in the interval [a, b].

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Answer:

$36,075

Step-by-step explanation:

Cheryl's annual rent as a function of her annual sales is:

\(R = 1,400*2*12+(x-100,000)*0.055\)

Where x are her annual sales, if x > $100,000. This function considers her fixed rent of $2 per square foot for 12 months, and her sales dependent rent.

Since she made $145,000 last year, her annual rent is:

\(R = 1,400*2*12+(145,000-100,000)*0.055\\R=\$36,075\)

Her annual rent is $36,075.

By fast-tracking and reducing the expected times along the critical path by a total of 14 days, the expected time of project completion is 42 days.

To calculate the expected time of project completion, we start with the sum of the original expected times along the critical path. The original times are 10-12-14, 12-21-36, 12-15-18, and 2-6-10. Adding these values gives us a total of 36 + 69 + 45 + 18 = 168 days.

Similar times along a sub-critical path are: 2-9-10, 12-15-24, and 12-18-24. Summing these values gives us a total of 21 + 51 + 54 = 126 days

Now, we will find the difference of the values.

Using the arithmetic operation, on subtracting the values, we get

168 - 126 = 42 days

Therefore, the expected time of project completion is 42 days.

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Answer:

multiplied by 3

Step-by-step explanation:

red is scaled up by 3 from blue

Answer:

3

Step-by-step explanation:

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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Answer:

5 times

Step-by-step explanation:

5*5 is 25

40-25=15$ left

any more movie tickets would be too much money spent

If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.

Two or more expressions with an Equal sign is called as Equation.

Given,

Robin was given a $40 monthly allowance.

She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.

The amount spent on movies

40-12.5

$27.5

A movie ticket costs $5.

We need to find how many times can she go to the movies.

To find this we need to divide $27.5 by 5

$27.5/5=5.5

Robin can go 6 times to the movies.

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The differential equation that represents the given property of the curve is dy/dx = 1/y. This equation expresses that the derivative of y with respect to x is equal to the reciprocal of y.

To derive the differential equation, we start by considering the slope of the tangent line to the curve y = f(x) at any point (x, y). The slope of the tangent is given by dy/dx, which represents the rate of change of y with respect to x. According to the given property, this slope is equal to the reciprocal of the y value, which can be written as 1/y.

Hence, we obtain the differential equation dy/dx = 1/y, which represents the relationship between the derivative of y with respect to x and the reciprocal of y. This equation describes the behavior of the curve y = f(x) such that the slope of the tangent at any point is reciprocal to the y value of the curve.

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There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.

When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:

P (At least one head) = 1 - 0.5n,

where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.

Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)

= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹

= 0.1718751.

The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

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Answer:

The function would be

p = $30 + $12w

or

p = $12w + 30

Step-by-step explanation:

Answer:

C

because

\(42 \div 7 = 6 \\ 7 \times 6 = 42\)

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

Step-by-step explanation:

The answer is 89 stamps. 7-4= 3 so he is adding 3 each week.  

68 + (3 x 7)=

68 + 21 = 89

Answer:

option C is correct.

Step-by-step explanation:

unit rate: \(\sf \dfrac{change \ in \ y}{change \ in \ x}\)

A)  \(\sf \frac{10}{4} / \frac{5}{6} = 3\)

B)  \(\sf \frac{1}{2} / \frac{2}{3} = \frac{3}{4}\)

C)  \(\sf \frac{4}{9} / \frac{4}{3} = \frac{1}{3}\)

D)  \(\sf \frac{3}{8} / \frac{1}{8} = 3\)

/ - refers to division symbol

Answer:

AB ≈ 3.14 in

Step-by-step explanation:

arc AB is calculated as

AB = circumference of circle × fraction of circle

     = 2πr × \(\frac{30}{360}\)

     = 2π × 6 × \(\frac{1}{12}\)

     = 12π × \(\frac{1}{12}\)

     = π ≈ 3.14 in ( to the nearest hundredth )

Answer:

The chicken closed the road.

And then he crawled up the spot

and come over the duck

The probability of a person selected at random having their birthday on the first of the month can be determined by dividing the number of possible outcomes by the total number of possible outcomes. This is because there are 12 months in a year, each with 28, 29, 30, or 31 days, resulting in a total of 365 possible birthdays for each individual.

Given that there are no leap years, it can be inferred that there are 365 possible outcomes, one for each day of the year.a. Determine the probability that a randomly selected person has a birthday on the 1st of the month.Because there are 12 months in a year, there are 12 possible ways for a person's birthday to occur on the first day of the month. This implies that the probability of selecting a person whose birthday is on the 1st of the month is:P(1st day of the month) = (12/365) = 0.0329 or 3.29%

b. Determine the probability that a randomly selected person has a birthday in May.Since there are 31 days in May, the probability of selecting a person whose birthday is in May is:P(May) = (31/365) = 0.0849 or 8.49%c. Determine the probability that a randomly selected person has a birthday in the first half of the year.Since there are 365 days in a year, the probability of a person's birthday falling in the first half of the year is:P(First Half of the Year) = (365/2)/365 = 0.5 or 50%In the first half of the year, there are a total of 181 days, which is half of the total number of days in a year. Therefore, the probability of a person's birthday falling in the first half of the year is 0.5 or 50%.d. What is the probability that a randomly selected person has a birthday in the first quarter of the year?Since there are 365 days in a year, the probability of a person's birthday falling in the first quarter of the year is:P(First Quarter of the Year) = (365/4)/365 = 0.25 or 25%The first quarter of the year comprises January, February, and March, which together have a total of 90 days. Therefore, the probability of a person's birthday falling in the first quarter of the year is 0.25 or 25%.

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