When converting θ = π/3 to a Cartesian equation, let x = ____
1/2 r
√2/2 r
√3/2 r

If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. 

Let us take the Example.

Suppose f(x)= x/4 and g(x)=4x.

Let x=1

then f(g(x))= f(g(1))=f(4)=1

and g(f(x))=g(f(1))=g(1/4)=1

Here, f(g(x))=g(f(x))=1

Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.

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  x - 4y = 4

-3x - 4y = 12

Subtract the first equation from the second

  x - 4y = 4

-4x      = 12

Divide the second equation by (-4)

  x - 4y = 4

  x      =  -3

Subtract the second equation from the first

   - 4y  =  7

  x      =  -3          

Divide the first equation by (-4)    

       y  =  -7/4

  x      =  -3        

The dimensions (x, y, z) that minimize the amount of cardboard used for a box with a volume of 23,328 cm³ are (28, 28, 30).

1. Given the volume, V = x*y*z = 23,328 cm³.

2. The surface area, which represents the amount of cardboard used, is S = x*y + x*z + y*z.

3. To minimize S, we need to use calculus. First, express z in terms of x and y using the volume equation: z = 23,328 / (x*y).

4. Substitute z into the surface area equation: S = x*y + x*(23,328 / (x*y)) + y*(23,328 / (x*y)).

5. Now find the partial derivatives dS/dx and dS/dy, and set them equal to zero.

6. Solve the system of equations to get x = 28 and y = 28.

7. Plug x and y back into the equation for z: z = 23,328 / (28 * 28) = 30.

So the dimensions that minimize the amount of cardboard used are (28, 28, 30).

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Question options:

A. Yes, Walter is correct.

B. No 3.612 is less than 13.

C. No, both 3.612 and 3.622 are greater than

D. No, both 3.612 and 3.622 are less than 13

Answer:

C. No, both 3.612 and 3.622 are greater than the square root of 13

Explanation:

13 is a prime number and must have a decimal number as its square root and so the square root should be between √9 and √16

Using the Newton Raphson method to estimate the square root of 13 with the formula: ai +1= ai²+n/2ai

We get square root of 13 = 3.6055512

This is the same result we get using a calculator to calculate square root of 13= 3.6055512

So yes Walter is not correct

Answer:

its 4√2i i think

Step-by-step explanation:

Answer:

Answer:B

Step-by-step explanation:

Answer:

A) The Jenga game is appropriate for the middle childhood age group, typically ranging from around 6 to 12 years old.

B) Jenga promotes cognitive, physical, and socioemotional development in middle childhood through enhancing spatial reasoning and problem-solving skills, improving fine motor skills and proprioceptive input, and fostering social interaction, cooperation, and risk assessment.

Step-by-step explanation:

Jenga, a game played with rectangular blocks, can promote cognitive, physical, and socioemotional development through various concepts.

Cognitive Development: Jenga enhances spatial reasoning as players analyze the tower's structure, evaluate block stability, and strategize their moves. They mentally manipulate objects in space, building an understanding of spatial relationships and balance. Problem-solving skills are fostered as players make decisions about which block to remove, considering the consequences of their actions. They must anticipate the tower's reaction to their moves, think critically, and adjust their strategies accordingly.

Physical Development: Jenga improves fine motor skills as players carefully remove and stack blocks using only one hand. Precise finger movements, hand-eye coordination, and grip strength are required for successful manipulation of the blocks. The game also provides proprioceptive input as players gauge the weight and balance of each block, refining their sense of touch and motor control.

Socioemotional Development: Jenga promotes social interaction and cooperation when played with multiple players. Taking turns, discussing strategies, and supporting each other's successes and challenges enhance communication, collaboration, and empathy skills. Players learn to respect and consider others' perspectives, negotiate and compromise, and work together towards a common goal. Sportsmanship is nurtured as players accept both victory and defeat gracefully, fostering resilience and emotional regulation.

Furthermore, Jenga offers opportunities for developing patience and perseverance. As the tower becomes increasingly unstable, players must exercise self-control, focus, and delayed gratification. They learn to take their time, plan their moves carefully, and tolerate the suspense of potential collapse. The game also presents a low-risk environment for risk assessment, allowing children to assess the consequences of their decisions and make calculated judgments.

By engaging in Jenga, children actively participate in a multi-dimensional activity that combines physical manipulation, cognitive analysis, and social interaction. Through the concepts of spatial reasoning, problem-solving, fine motor skills, proprioceptive input, social interaction, cooperation, sportsmanship, patience, perseverance, and risk assessment, Jenga supports holistic development in cognitive, physical, and socioemotional domains.

Domain: {1, -2, -3, -6}

Range: {5, 4, 0, 2}

im not 100% sure but Im pretty sure it’s that

The sum of all possible values of n is 448.

Let n be a positive number.

We are given that 72!/n is a multiple of 2^n, but not a multiple of 2^(n-1).

We can start by finding all values of n that fit this criteria:

n = 1: 72!/1 = 479001600 is not a multiple of 2^1, but is a multiple of 2^0.

n = 2: 72!/2 = 1197500400 is not a multiple of 2^2, but is a multiple of 2^1.

n = 3: 72!/3 = 59875200 is a multiple of 2^3, but not a multiple of 2^2.

n = 4: 72!/4 = 29937600 is a multiple of 2^4, but not a multiple of 2^3.

n = 5: 72!/5 = 14968800 is a multiple of 2^5, but not a multiple of 2^4.

n = 6: 72!/6 = 7484400 is a multiple of 2^6, but not a multiple of 2^5.

n = 7: 72!/7 = 3742200 is a multiple of 2^7, but not a multiple of 2^6.

n = 8: 72!/8 = 1871100 is a multiple of 2^8, but not a multiple of 2^7.

n = 9: 72!/9 = 935550 is a multiple of 2^9, but not a multiple of 2^8.

n = 10: 72!/10 = 467775 is a multiple of 2^10, but not a multiple of 2^9.

Therefore, the sum of all possible values of n is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 = 448.

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This is a more complicated way to write \(y < 2\)

The range is the set of all possible y outputs of a function. So we use the graph to see what y values are possible. The graph shows that y can be anything smaller than y = 2. We can't actually reach y = 2 itself due to a horizontal asymptote here.

In interval notation, the answer would be \((-\infty, 2)\) with the curved parenthesis to indicate "do not include y = 2 as part of the range".

Answer:

2t+16

Step-by-step explanation:

this should 2t+16

because 2t contains a variable and there are no available numbers/figits that match up

and 9 +7 is 16

hope i could help

Answer:

2t +16

Step-by-step explanation:

2t + 9 + 7

Combine like terms

2t +16

The amount in the account after 20 years is $49530.32.

What is continuous compounding?

There is no cap on how frequently interest can compound thanks to continuous compounding. A balance can compound continuously an infinite number of times, which means interest is earned on it constantly.

Given:

Lira will not make any further investments in the withdrawals from the account until it is worth $10000.

Suppose that the interest rate for the account is 8.0% , compounded continuously.

We have to find the amount in the account after 20 years.

Consider, the compounded continuously formula

\(P(t)= P_0e^r^t\)

Where

P(t) = Value at time t.

\(P_0\) = Original principle sum = $10,000

r = Interest rate = 8.0% = 0.08

t = time in years = 20

Plug the values in the above formula

\(P(t) = 10000e^0^.^0^8^*^2^0\\P(t) = 49530.32\)

Hence, the amount in the account after 20 years is $49530.32.

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Answer:

4.7e-6 millimeters

Step-by-step explanation:

Given:

Center of dilation: (0, 0)

Scale factor = 9

Let's find the image of point L(-8, 0) after the dilation with the given scale factor.

To find the image of a point after dilation, multiply the coordinates of point by the scale factor of dilation.

We have:

L(-8, 0) ==> (-8 x 9, 0 x 9) ==> L'(-72, 0)

Therefore, the image of the point after a dilation with a scale factor of 9 is:

(-72, 0)

ANSWER:

(-72, 0)

Answer:

12 cups of pineapple juice for 16 cups of ginger ale.

Step-by-step explanation:

4+4+4+4= 16

3+3+3+3= 12

In the given scenario, we can calculate the probability of all six individuals surveyed owning a tablet using the binomial probability formula. Additionally, we can determine the mean and standard deviation of the number of individuals who own a tablet using the formulas: mean (μ) = n * p and standard deviation (σ) = √(n * p * (1-p)). C.

The probability that of the next six 18- to 29-year-olds surveyed, all six will own a tablet can be calculated using the binomial probability formula. Since each individual has a certain probability of owning a tablet, we can calculate the probability of success (p) for each trial and use the formula to find the probability of all six trials being successful.

D. The mean and standard deviation of the number of 18- to 29-year-olds who will own a tablet in a survey of six can also be determined using the binomial distribution. The mean (μ) of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of success (p). The standard deviation (σ) is found using the formula √(n * p * (1-p)).

C. To find the probability that all six 18- to 29-year-olds surveyed will own a tablet, we can use the binomial probability formula. Each individual has a certain probability of owning a tablet, and we want to find the probability of all six trials being successful. The formula for calculating the probability of exactly k successes in n trials is given by P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) represents the binomial coefficient. In this case, k=6, and p represents the probability of owning a tablet for an individual in this age group.

D. The mean (μ) of a binomial distribution is the expected number of successes in a given number of trials. For this scenario, we multiply the number of trials (n) by the probability of success (p) to find the mean. In this case, n=6 represents the number of individuals surveyed, and p is the probability of owning a tablet for an individual.

The standard deviation (σ) of a binomial distribution measures the spread or variability of the distribution. It is determined using the formula √(n * p * (1-p)). The standard deviation indicates how much the individual values in the distribution deviate from the mean.

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Answer:

see below

Step-by-step explanation:

P = 2l + 2w

Subtract 2w using the subtraction property of equality

P -2w = 2l+2w-2w

P -2w = 2l

Divide each side by 2, using the division property of equality

P/2 -2w/2 = 2l/2

1/2 P -w = l

Now we have P =40.2 and w = 6.7

l =1/2 (40.2) - 6.7

l =20.1-6.7

 =13.4

Answer:

\(2(3x + 4) + 3 \\ 2(3x) \: + 2(4) \: + \: 3 \\ 6x + 8 + 3 \\ 6x + 11\)

I hope I helped you^_^

Answer:

p≤-5/4

Step-by-step explanation:

Move variable to the left hand side and change its sign, move the constant tp the right hand side and change its sign

6p+2p+5≤-5

Collect like terms

8p≤-5-5

8p≤-10

Divide both sides of the inequality by 8

p≤-5/4

Yes, we can determine the percentage of people below 2 from the box plot. The answer is 0%

From the given data we can sketch out a box plot given as follows. Here since the left whisker ends at 2 and the right whisker ends at 43, there are no people less than 2 and no people more than 43.

5 and 15 are the 1st and the 3rd Quartile respectively.

Since the minimum value of this data is 2, there are no people who could be below 2. Therefore, the percentage of people below 2 is 0%

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The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

x = 14

Step-by-step explanation:

1. We know that all angle measures in a triangle sum to 180 degrees.

2. (Solving)

Step 1: Combine like terms.

Step 2: Add 16 to both sides.

Step 3: Divide both sides by 14.

Step 2: Check if solution is correct.

Therefore, the answer is x = 14.

Answer: the answer is B

Step-by-step explanation:

There are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

For each play date, you have 3 options for the show time.

Since the events are independent and all options are equally likely, you can multiply the number of options together to find the total number of possible outcomes.

Number of possible outcomes

= Number of play dates × Number of show times

= 4 × 3

= 12

Therefore, there are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

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Answer:

x=61

2x+3 = 125

x-6 = 55

Step-by-step explanation:

The two angles shown form a straight line so they add to 180

2x+3 + x-6 = 180

Combine line terms

3x-3 =180

Add 3 to each side

3x-3+3 =180+3

3x=183

Divide each side by 3

3x/3 =183/3

x =61

The angle on the left is 2x+3

2x+3 = 2*61+3 = 122+3 = 125

The angle on the right is x-6 = 61-6 = 55

Answer:

y = \(\frac{1}{2}\) x + \(\frac{7}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x - 2y = 7 ( subtract x from both sides )

- 2y = - x + 7 ( multiply through by - 1 )

2y = x - 7 ( divide through by 2 )

y = \(\frac{1}{2}\) x - \(\frac{7}{2}\) ← in slope- intercept form

with slope m = \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (- 3, 2 ) into the partial equation

2 = \(\frac{1}{2}\) (- 3) + c = - \(\frac{3}{2}\) + c ( add \(\frac{3}{2}\) to both sides )

2 + \(\frac{3}{2}\) = c , that is

c = \(\frac{7}{2}\)

y = \(\frac{1}{2}\) x + \(\frac{7}{2}\) ← equation of parallel line

If Southland is producing at point X, to determine the number of additional schools it can produce without giving up any movies, we need to refer to the concept of production possibilities frontier (PPF).

The PPF represents the maximum output combination of two goods that an economy can produce with its available resources and technology.

In this case, movies and schools are the two goods being produced. If Southland is operating at point X on the PPF, it means it is efficiently allocating its resources to produce a certain quantity of movies and schools. To find out how many more schools can be produced without sacrificing any movies, we need to identify a point on the PPF that lies on the same movie production level as point X.

Let's assume that at point X, Southland is producing 10 movies. To determine the number of additional schools, we need to find a point on the PPF where the movie production level is also 10. Let's say at this point, Southland can produce 20 schools.

Therefore, the answer is 20 more schools.

If Southland is producing at point X and is currently producing 10 movies, it can produce an additional 20 schools without giving up any movies. This calculation is based on the assumption that the PPF remains constant and there are no changes in resource availability or technology.

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y = -2x + 3

in the equation y = mx + b, the m represents the slope and b represents the y-intercept

remember that slope is rise over run:

   starting from the point (1, 1) you rise 2 up and go over left 1 to reach the second point shown (0, 3).

   add a negative sign to show the negative downward slope, and the m in the equation would be -2

the y-intercept is just where the line hits the y-axis, or when the x in the ordered pair is 0. In this graph, one of the points given is (0, 3) so 3 is the y intercept

just plug all that into y = mx + b

m, the slope, is -2 and b, the y- intercept, is 3.

y = -2x + 3 is your answer

To estimate errors in the approximations t8 and m8, we can use the fact that the range of the sine and cosine functions is bounded by ±1.

In part (a), we have approximations t8 and m8.

To estimate the error in t8, we can compare it to the actual value of the function. Let's denote the actual value of the function at t8 as T8. Since the range of the sine function is bounded by ±1, the maximum error in the approximation t8 would be |t8 - T8| ≤ 1.

Similarly, to estimate the error in m8, we can compare it to the actual value of the function. Let's denote the actual value of the function at m8 as M8. Since the range of the cosine function is also bounded by ±1, the maximum error in the approximation m8 would be |m8 - M8| ≤ 1.

Therefore, the estimated errors in the approximations t8 and m8 are |et| ≤ 1 and |em| ≤ 1, respectively.

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The sequence that contains all the given terms is:

aₙ = -18 + 6*n

Then the correct option is C.

Here we have the elements:

a₃ = 0

a₄ = 6

a₅ = 12

a₆ = 18

a₇ = 24

So each term adds 6 to the previous one, so trivially the relation is of the form:

aₙ = aₙ₋₁ + 6

Now we need to find the first term.

We can rewrite the above equation as:

aₙ₋₁ = aₙ - 6

Then we willget:

a₂ = a₃ - 6 = 0 - 6 = -6

a₁ = a₂ - 6 = -6 - 6 = -12

a₀ = a₁ - 6 = -18

Then the sequence is:

aₙ = -18 + 6*n

Then the correct option is C.

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Answer:

(f · g)(t - 1) = 4t² - 2t - 13

Step-by-step explanation:

First, find (f · g)(n).  You can do this by multiplying f(n) by g(n).

f(n) = 2n - 2

g(n) = 2n + 5

(f · g)(n) = (2n - 2)(2n + 5)

(f · g)(n) = 4n² + 6n - 10

Now, plug (t - 1) into (f · g)(n) and simplify.

(f · g)(n) = 4n² + 6n - 10

(f · g)(t - 1) = 4(t - 1)² + 6(t - 1) - 10

(f · g)(t - 1) = 4(t² - 2t + 1) + 6(t - 1) - 10

(f · g)(t - 1) = 4t² - 8t + 4 + 6t - 1 - 10

(f · g)(t - 1) = 4t² - 8t + 4 + 6t - 1 - 10

(f · g)(t - 1) = 4t² - 2t + 4 - 1 - 10

(f · g)(t - 1) = 4t² - 2t - 13