Algebraic expression for a number divided by 12

[tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.

What are rational exponents?

Rational exponents are exponents that are expressed as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.

When we talk about rational exponents, we are referring to exponents that are written as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.

So, in the case of ∛7, we can rewrite the cube root symbol (∛) as a rational exponent with a denominator of 3. That is, ∛7 can be expressed as [tex]7^{(1/3)}[/tex] , where the 1/3 exponent means "take the cube root of 7".

Therefore, [tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.

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The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.

The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:

Perimeter

p = n · l

Area

A = (n · l · a) / 2

Where:

Where the apothema is:

a = 0.5 · l / tan (180° / n)

If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:

Perimeter

p = 5 · (4 in)

p = 20 in

Area

a = 0.5 · (4 in) / tan (180° / 5)

a = 0.5 · (4 in) / tan 36°

a = 2.753 in

A = [5 · (4 in) · (2.753 in)] / 2

A = 27.53 in²

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Answer:see below

Step-by-step explanation:

10.600

11.80000

12.17

13.48

14.4000

21. 1km=100m;0.5km=500m;0.1km=100m

22.50m=5000cm; 5m=500cm; 0.5m=50cm

Answer: 70% of the brownies are caramel.

Step-by-step explanation: First take 56/80 because 56 of the brownies were caramel out of the 80. Which divided that give you 0.7. Multiply then by 100 which will give you 70. So the answer is there are 70% caramel brownies.

When two coins are repeatedly flipped, the probability of getting two heads is 1/4, the probability of getting a head and a tail is 1/2, and the probability of getting two tails is also 1/4.

Therefore, the expected ratio of two heads : heads/tails : tails/heads : two tails is 1:2:2:1, respectively. This means that out of every six flips, we would expect to see one outcome of two heads, two outcomes of heads/tails and tails/heads each, and one outcome of two tails.

However, it is important to note that this is only a prediction and the actual results may differ due to chance.

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Answer:miami is 43431.16 rounded to 43431 because you can't have .16 of a person.

washington dc is 4249.22 which is round to 4249 because you can't have .22 of a person.

and new york city is 27348.99 which is rounded to 27349 because you can't have .99 of a person.

Step-by-step explanation:

im smart and im really good at math

The area of the shaded sector is approximately 463.8 square yards.

To find the area of the shaded sector, we need to use the formula for the area of a sector, which is given by

Area of sector = (central angle / 360°) x πr²

where r is the radius of the sector, and the central angle is the angle between the two radii that form the sector.

In this case, we are given that the central angle of the shaded sector is 167°, and the radius is 17.8 yards. So, we can substitute these values into the formula as follows

Area of sector = (167° / 360°) x π(17.8)²

Simplifying this expression, we get:

Area of sector = 0.464 x 998.92

Multiplying these two numbers, we get

Area of sector = 463.8 square yards

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The given question is incomplete, the complete question is:

Find the area of the shaded sector. Round to the nearest tenth.

1. The equation she was supposed to solve was sin(x) = cos(2x), but she mistakenly added an extra "= 0" term.

2. The correct answers are x = π/6 and x = 5π/6.

To find the correct answers, we will solve the correct trigonometric equation sin(x) = cos(2x).

Since cos(2x) = 1 - 2sin²(x), the equation becomes:

sin(x) = 1 - 2sin²(x)

Now we can rewrite this equation as a quadratic equation in sin(x):

2sin²(x) + sin(x) - 1 = 0

This equation can be solved using the quadratic formula:

sin(x) = [-b ± sqrt(b² - 4ac)] / 2a

where a = 2, b = 1, and c = -1:

sin(x) = [-1 ± sqrt(1² - 42(-1))] / (2*2)

sin(x) = [-1 ± sqrt(9)] / 4

sin(x) = (-1 ± 3) / 4

There are two possible solutions for sin(x):

sin(x) = 1/2

sin(x) = -1

For sin(x) = 1/2, we have:

x = π/6, 5π/6

For sin(x) = -1, there is no solution in the interval 0 < x < 2π because the sine function does not reach -1 within this range.

So the correct answers are x = π/6 and x = 5π/6.

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The first term acute classifies the angle m∠AHB which have a measure of 84°.

An acute angle is an angle that measures less than 90 degrees. In other words, it is an angle that is smaller than a right angle (which measures exactly 90 degrees).

The angles H, 34°, and 62° lie in the straight line FC which implies their sum is equal to 180° so;

H = 180° - (34 + 62)°

H = 84°

angles m∠AHB and H are vertical angles which makes them equal, so;

H = m∠AHB = 84°.

In conclusion, the term acute classifies the angle m∠AHB which have a measure of 84°.

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The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:

P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800

P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674

P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474

b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:

P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498

Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

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Complete Question:

Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.

a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)

b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)

Therefore, the correct answer is (B) No, she needs 1/2 cup more.

To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.

Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.

Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.

She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.

needs 3 - 2.5 = 0.5 cups more.

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Answer:

The answer for this is B 15/36

Answer:

x=2

Step-by-step explanation:

x^4=16

x=[tex]\sqrt[4]{16}[/tex]

x=[tex]2[/tex]

From the plot we deduce that

x intercept = 0

y intercept = 0

Domain = all real numbers

Range = all real numbers

Transformations

The transformation for the function

y = 2(x - 8)^1/3 + 4

Shows a movement from the parent function y = x^1/3

(x - 8)^1/3  represents translation 8 units to the right

(x - 8)^1/3 + 4  represents translation 4 units upwards

2(x - 8)^1/3 + 4  represents vertical stretch by a factor of 2

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There are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).

To calculate the total number of different passwords, we can break the problem down into several steps:

Step 1: Calculate the number of possible characters for each position in the password. Since the password consists of four alphanumeric characters, there are 26 letters (A-Z) and 10 digits (0-9) for each position.

Therefore, there are 36 possible characters for each position.

Step 2: Calculate the total number of possible passwords without any restrictions.

Since there are 36 possible characters for each position and the password has four positions, the total number of possible passwords without any restrictions is:

36 x 36 x 36 x 36 = 1,679,616

Step 3: Calculate the number of passwords that do not contain at least one digit or at least one letter.

To do this, we can calculate the number of passwords that do not contain any digits and subtract it from the total number of possible passwords, and then do the same for passwords that do not contain any letters.

The number of passwords that do not contain any digits is:

26 x 26 x 26 x 26 = 456,976

The number of passwords that do not contain any letters is:

10 x 10 x 10 x 10 = 10,000

However, we have to be careful not to double-count the passwords that do not contain both letters and digits.

The number of passwords that do not contain both letters and digits is:

26 x 26 x 10 x 10 = 67,600

So the total number of passwords that do not contain at least one digit or at least one letter is:

456,976 + 10,000 - 67,600 = 399,376

Step 4: Subtract the number of invalid passwords from the total number of possible passwords:

1,679,616 - 399,376 = 1,280,240

Therefore, there are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).

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The answer of the given question based on the probability is ,  the probability of pulling a black chip from the bag is 2/15 or approximately 0.133 or 13.3%.

Probability is  measure of  likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. For example, the probability of flipping a coin and getting heads is 0.5, or 50%, assuming a fair coin. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes

The total number of poker chips in the bag is:

total = 4 + 6 + 3 + 2 = 15

The probability of pulling a black chip from the bag is the number of black chips divided by the total number of chips:

P(black) = number of black chips / total number of chips

P(black) = 2 / 15

Therefore, the probability of pulling a black chip from the bag is 2/15 or approximately 0.133 or 13.3%.

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The probability that the average coyote weight for a sample of 20 coyotes is less than 13 kg is approximately 13.14%.

we need to know the mean and standard deviation of the coyote weight population. Let's assume that the population mean is μ = 13.5 kg and the population standard deviation is σ = 2 kg.

Since we are measuring a sample of 20 coyotes, we can use the central limit theorem to approximate the distribution of sample means. According to the central limit theorem, if the sample size is large enough (in general, if n > 30), then the distribution of sample means will be approximately normal, regardless of the distribution of the population.

The mean of the sample means will be equal to the population mean (μ) and the standard deviation of the sample means (also known as the standard error) will be equal to σ / √(n), where √(n) is the square root of sample size.

Using this information, we can calculate the z-score for a sample mean of 13 kg as follows;

z = (13 - 13.5) / (2 / √(20)) = -1.118

Next, we can use a standard normal distribution table (or a calculator or software that can calculate normal probabilities) to find the probability that a z-score is less than -1.118. The area to the left of this z-score is approximately 0.1314, or 13.14%.

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Both functions have the same axis of symmetry equation, which is x = -3.

Given that, Maxine graphs a function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8).

Ricardo graphs p(x) = (x+3)² + 4

We need to check if both the function axis of symmetry equation.

So,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

Axis of symmetry = The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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When we compare this to the options provided, we can see that the equation is: a. y = -x²/2+x+1. The answer is (a) y = -x²/2+x+1.

A parabola's equation can take many different forms, such as vertex form, standard form, or intercept form, depending on its particular shape and orientation.

The parabola's typical vertex form equation is y = a(x - h)² + k

We must locate the vertex form of the parabola in order to get its equation, which is:

y = a(x - h)² + k

Using to determine the vertex

h = -b/2a

To begin, we can locate the vertex:

(-1,0) (1,1.5) (3,0) (-2, -3) (4,-3) (-3,-6) (5,-6)

In order to average the x-values of the two sets of x-intercepts, the vertex must be halfway between the parabola's x-intercepts:

h = (-1 + 3)/2 = 1

The vertex and another point can then be used to find the value of "a":

y = a(x - 1)² + k

Using the point (4, -3):

-3 = a(4 - 1)² + k

-3 = 9a + k

Using the point (1, 1.5):

1.5 = a(1 - 1)² + k

1.5 = k

k = 1.5 is substituted into the second equation:

-3 = 9a + 1.5

-4.5 = 9a

a = -0.5

y = -0.5(x - 1)² + 1.5

When we multiply the equation, we get:

y = -0.5x² + x + 1

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The expression in terms of the first power of sine is 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x. The solution has been obtained by using the trigonometric identities.

What are trigonometric identities?

All possible values of the variables in the equation must satisfy the equality condition known as a trigonometric identity. A triangle's side length and angle can be used to express a variety of unusual trigonometric identities.

We are given expression as [tex]cos^{6}[/tex] (x).

This can be written as a cosine function as  [tex](cos^{2} x)^{3}[/tex].

We know that [tex]sin^{2}[/tex]x + [tex]cos^{2}[/tex]x = 1.

So, we get

⇒ (1 - [tex]sin^{2}[/tex]x[tex])^{3}[/tex]

⇒ 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x

Hence, the required expression has been obtained.

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The value of z is 14.

What is the fraction?

A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.

To solve for z, we can start by cross-multiplying the fractions, which gives:

5z = 14 * 25

Simplifying the right side, we get:

5z = 350

Finally, we can solve for z by dividing both sides by 5:

z = 70/5

Simplifying the right side, we get:

z = 14

Therefore, the value of z is 14.

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The complete question:

Solve for the value of z: 14/5 = z/25

The correct answer is: Aaliyah’s gray paint will be darker.

What is proportion?

In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two numbers or quantities that are usually written in the form of a fraction. For example, the ratio of apples to oranges in a basket could be written as 3/5, meaning that there are three apples for every five oranges.

Hassan mixed 2 cups of black paint and 3 cups of white paint, so the total amount of paint he mixed is 2 + 3 = 5 cups. The proportion of black paint in his mixture is 2/5.

Aaliyah mixed 4 cups of black paint and 5 cups of white paint, so the total amount of paint she mixed is 4 + 5 = 9 cups. The proportion of black paint in her mixture is 4/9.

Comparing the two proportions, we see that Aaliyah's proportion of black paint is greater than Hassan's proportion of black paint, so Aaliyah's gray paint will be darker.

Therefore, the correct answer is: Aaliyah’s gray paint will be darker.

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Answer: it would be (b) because the number 64 7th graders hights are less than

65 inches tall

Step-by-step explanation:

Hoped this helped have a good day pl z mark me as brainliest :)

Answer:

Step-by-step explanation:

5989.87

The perimeter of the rectangle is 16x + 2

The perimeter of a rectangle is given by P = 2(L + B) where

Given the rectangle in the figure, we desire to find its perimeter. We proceed as follows.

We notice that its length and breadth are

So, since the perimeter of the rectangle is P = 2(L + B), we substitute the values of the variables into the equation.

So, with

We have that

P = 2(L + B)

= 2(5x + 2 + 3x - 1)

= 2(5x + 3x + 2 - 1)

= 2(8x + 1)

= 16x + 2

So, the perimeter is 16x + 2

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Answer:

[tex] \frac{11}{13} \times \frac{1}{4} \times \frac{1}{3} = \frac{11}{156} [/tex]

So the volume of this rectangular prism is 11/156 of a cubic foot.

Answer:

To find the value of a4, we need to use the recursive formula for the sequence. The formula gives us the nth term in the sequence in terms of the (n-1)th term.

We are given that a1 = -7, so we can use the recursive formula to find a2, a3, and a4:

a2 = a1 - 4 = -7 - 4 = -11

a3 = a2 - 4 = -11 - 4 = -15

a4 = a3 - 4 = -15 - 4 = -19

Therefore, the value of a4 is -19.

Using the fact that the triangles are similar we can see that the value of x is  36

We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.

So we can write:

20*k = 48

k = 48/20 = 2.4

Then:

x = 15*2.4

x = 36

That is the value of x.

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The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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