solve for x round to the hundredth placement

D) 81 is equivalent to 27^(4/3).

The expression 27^4/3 can be simplified using the rule that (a^m)^n = a^(m*n). Therefore, we can write,

27^(4/3) = (3^3)^(4/3)

Using the power of a power rule, we can simplify further,

(3^3)^(4/3) = 3^(3*4/3)

Simplifying the exponent, we get,

3^(4)

To check the other answer choices,

A. 4^3 is not equivalent to 27^4/3.

B. (27^1/3)^4 is equivalent to 27^(4/3), which we already simplified to 3^4. Therefore, this expression is also equivalent to 3^4.

C. 3^1/4 is not equivalent to 27^4/3.

D. 81 is equivalent to 3^(4).

Therefore, the expression 27^4/3 is equivalent to 3^4, which is answer choice D) 81.

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the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

What is Total fixed cost?

Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.

The Contemporary Resort costs $239 per night, so the total cost for four nights would be:

$239 × 4 = $956.

The Fun Times Resort costs $189 per night, so the total cost for four nights would be:

$189 × 4 = $756.

The regular cost is $219 per night, so the total cost for three nights would be:

$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:

$657 + $0 = $657.

Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

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The triangle is given as equilateral and the length of the perpendicular of the given equilateral triangle is 13.85.

It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, the longest side of the triangle. This theorem can be used to determine the length of the sides of a right triangle if two sides are known.

The triangle is given as equilateral. As we know he perpendicular in a equilateral triangle divides a line into to equal parts, so

Base= 8+8

= 16

As it is a equilateral triangle, all the sides will be equal.

Now, we can use the Pythagorean theorem to find the length of the perpendicular, which can be found by using the formula:

16²= 8² + x²

x² = 16²- 8²

x = √192

x = 13.85

Thus, the length of the perpendicular of the given equilateral triangle is 13.85.

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The probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes, respectively, is 1 in 6,497,400.

The probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in the contest with 52 entrants and no one winning more than one prize can be calculated as follows:
1. Probability of Bo winning the first prize: 1/52 (since there are 52 people, and Bo is one of them)
2. Probability of Colleen winning the second prize after Bo has won the first prize: 1/51 (since there are now 51 people left)
3. Probability of Jeff winning the third prize after Bo and Colleen have won: 1/50 (50 people remaining)
4. Probability of Rohini winning the fourth prize after Bo, Colleen, and Jeff have won: 1/49 (49 people left)
To find the overall probability, multiply all individual probabilities together:
(1/52) x (1/51) x (1/50) x (1/49) = 1/6,497,400

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The probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in the drawing is approximately 1.0625 × 10^-9.

To find the probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes, respectively, follow these steps:
Calculate the total number of ways to choose 4 winners from 52 people (order matters, since the prizes are distinct). This is a permutation, so use the formula nPr = n! / (n - r)!,

where n = 52 (total number of people) and r = 4 (total number of prizes). In this case, 52P4 = 52! / (52 - 4)! = 52! / 48!.
Calculate the probability of Bo winning the first prize:

There is 1 favorable outcome (Bo winning) out of 52 possible outcomes, so the probability is 1/52.
Calculate the probability of Colleen winning the second prize, given that Bo has already won:

There is 1 favorable outcome (Colleen winning) out of the remaining 51 possible outcomes, so the probability is 1/51.
Calculate the probability of Jeff winning the third prize, given that Bo and Colleen have already won:

There is 1 favorable outcome (Jeff winning) out of the remaining 50 possible outcomes, so the probability is 1/50.
Calculate the probability of Rohini winning the fourth prize, given that Bo, Colleen, and Jeff have already won: There is 1 favorable outcome (Rohini winning) out of the remaining 49 possible outcomes, so the probability is 1/49.
To find the overall probability of this specific order of winners (Bo, Colleen, Jeff, Rohini), multiply the individual probabilities: [tex](1/52) × (1/51) × (1/50) × (1/49) ≈ 1.0625 × 10^-9.[/tex].

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The volume of the basketball is 4.19x³

The volume of the box is 8x³

The volume of air is 3.81x³

We know that the basketball is a sphere of radius x, and the volume of a sphere of radius R is:

V = (4/3)*pi*R³

Where pi = 3.14

In this case the radius is x, so the volume is:

V = (4/3)*3.14*x³

V = 4.19x³

b) The cube has a side length of 2x, then the volume (the cube of that) is:

V = (2x)³

V = 8x³

c) The volume of air is the difference between the volume of the cube and the volume of the ball:

volume of air = 8x³ -  4.19x³ = 3.81x³

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It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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Answer:

Assuming that "5 mi Lo" means a sphere with a radius of 5 miles, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius, and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given radius of 5 miles into the formula, we get:

V = (4/3)π(5^3)

V = (4/3)π(125)

V = (4/3)(3.14159)(125)

V = 523.59833 cubic miles

Therefore, the volume of the sphere is approximately 523.6 cubic miles (rounded to the nearest tenth).

The volume of the sphere is 523.6 mi³

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Since we require to find the volume of the sphere with radius 5 mi, we substitute the value of the radius into the equation.

So, we have that V = 4πr³/3

So, substituting the value of the radius into the equation, we have

V = 4π(5 mi)³/3

= 4π × 125 mi³/3

= 500π mi³/3

= 1570.796 mi³/3

= 523.6 mi³

The volume is 523.6 mi³

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1. Mean = 54

2. Standard Deviation = 6.3

3. Probability = 0.077

4. Probability = 0.845

5. Probability = 0.155

6. Probability = 0.323

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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All the possible angle measures are given as follows:

25º and 35º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

On the first quadrant, we have that:

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The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.

Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.

The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]

Now, Speed of car (s) = 50 miles per hour

Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]

=> x = 4 × 50 miles

=> x = 200 miles

Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]

=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]

= 5 hours.

Hence, required value of time is 5 hours.

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Complete question :

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?

1. A hamburger combo meal in Poland costs approximately $1.13.

2. A hamburger combo meal in Mozambique costs approximately $5.12.

To find the dollar price of a hamburger combo meal in Poland, we need to divide the price in Polish Zlotys by the exchange rate for January:

= 5.08 Polish Zlotys / 4.5

= $1.13

To find the dollar price of a hamburger combo meal in Mozambique, we need to divide the price in Mozambique Meticals by the exchange rate for February:

= 338 Mozambique Meticals / 66.00

= $5.12

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The value of the given trigonometric ratio: Cos A = 4/5,  tan C = 4/3 for the given right angle triangle ABC.

A collection of mathematical functions that relate the angles and sides of a right triangle are known as the trigonometric functions.

Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse is known as the cosine of an angle in a right triangle.

⇒ Cos(θ) = adjacent/hypotenuse

⇒ Cos A = AB/AC

⇒ Cos A = 32/40

⇒ Cos A = 4/5

Similarly;

Tan tangent: The ratio of the length of the side opposite to the length of the side adjacent to is what is referred to as the tangent of an angle in a right triangle.

⇒ tan(θ) = opposite/adjacent

⇒ tan C = AB/BC

⇒ tan C = 32/24

⇒ tan C = 4/3

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Answer:

Step-by-step explanation:

b.  the sample statistic is larger than the claimed population parameter.

The transformation in the triangle will be as follows:

Translation by (-Rx, -Ry)

Rotation by counterclockwise around the origin

Reflection across the x-axis

Translation by (-Ux, -Uy)

In order to find a congruence transformation that maps triangle RST to triangle UVW, we need to find a combination of rotations, translations, and reflections that will transform one triangle into the other while preserving their size and shape.

Translate triangle RST so that vertex R is at the origin. We can do this by subtracting the coordinates of vertex R from each of the other vertices:

S' = (Sx - Rx, Sy - Ry)

T' = (Tx - Rx, Ty - Ry)

R' = (0, 0)

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Answer:

29 inches

Step-by-step explanation:

This problem can be solved using the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the ramp (13 in.) and the adjacent side is the length of the base of the ramp (x in.). We can set up the following equation:

```

tan(24°) = 13/x

```

To solve for x, we can take the inverse tangent of both sides of the equation. This gives us:

```

x = 13 / tan(24°)

```

```

x = 13 / 0.447213596

```

```

x = 29.23 in.

```

To the nearest inch, the length of the base of the ramp is **29 in.**

The percentage that is equivalent to the portion of lots in the neighborhood with three or more trees is 30%.

A percentage is a number or a ratio represented by fractions of 100. It is denoted by the percentage sign '%'. The percentage is represented by the abbreviations 'pct' or 'pc'. In other words, the percentage is defined as how much of one quantity is produced by another, and it is expressed in terms of 100.

To find the percentage that is equivalent to the portion of lots in the neighborhood with three or more trees, we can use the following formula:

Percentage = (Part/Whole) x 100

where Part is the portion we want to find as a fraction, and Whole is the total number of lots in the neighborhood.

In this case, we are given that 12/40 of the lots have three or more trees. This means that the Part is 12/40, and the Whole is all the lots in the neighborhood.

To find the percentage, we substitute these values into the formula:

Percentage = (12/40) x 100

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common factor, which is 4:

Percentage = (3/10) x 100

Multiplying 3/10 by 100, we get:

Percentage = 30%

Therefore, the percentage that is equivalent to the portion of lots in the neighborhood with three or more trees is 30%.

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Answer:

-2 & -2

Step-by-step explanation:

-2 * -2 = 4 (+ve 4)

-2 + -2 = -4 (-ve 4)

Answer:

-2 and -2

Step-by-step explanation:

-2 + -2 = -4

-2 x -2 = 4

James will need to pay £70 per month for 10 months to fully pay for the washing machine.

The cost of the washing machine is £640 + 20% of £640 = £768.

To find out how much James needs to pay in total, we subtract the deposit from the total cost:

Total amount to be paid = £768 - £68 = £700.

James will pay this amount in 10 equal monthly installments. To find out how much each installment will be, we divide the total amount by the number of installments:

Each monthly payment = £700 ÷ 10 = £70.

Therefore, James will need to pay £70 per month for 10 months to fully pay for the washing machine.

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Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

The number of pies that Kyla brought to the picnic were eaten = 2

The correct answer is an option (C)

According to the statement 'after the picnic, Kyla noticed 16/8 of the pies were eaten.'

We can observe that the number of pies that Kyla brought to the picnic were eaten is given by the fraction 16/8

Now we simplify this fraction.

We know that 16 = 8 × 2

So the numerator of the above fraction becomes,

16/8 = (2 × 8) / 8

       = (2 × 8)/(1 × 8)

       = 2/1           ........(cancelling common factor)

       = 2

Therefore, 2 pies were eaten.

The correct answer is an option (C)

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The answer to this question is  0.1754

Answer: I’m pretty sure it’s B

Step-by-step explanation:

Thus, all the prime factors of 56 are found as- 2, 2, 2 and 7 means  2³ and  7.

Factors have are numbers that divide into your target number in an even number of parts.

First, all prime numbers, with the exception of 2, are odd because an even number can be divided by two, making it composite.

Prime numbers are those that only have the number one and themselves as factors. Factors that are prime numbers are known as prime factors. 2, 3, 5, 7, 11, and 13 are the first six prime numbers.

After completing all definitions, it is time to identify the prime factors of 56.

For finding the all prime factors, start breaking the number using prime factorization:

56 = 2×2×2×7

56 = 2³ x 7

Thus, all the prime factors of 56 are found as- 2, 2, 2 and 7 means  2³ and  7.

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The range for the data set is equal to 48.

In Mathematics and Statistics, a range is the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 95.

Lowest number = 47.

By substituting, we have:

Range = 95 - 47

Range = 48.

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So, 174 children, 100 students, and 87 adults attended the movie theater.Let's denote the number of children as x, the number of students as y, and the number of adults as z. We can use the given information to form the following equations:

1) x + y + z = 361 (Total seating capacity)
2) z = 0.5x (Half as many adults as children)
3) 5x + 7y + 12z = 2614 (Total ticket sales)
Now, substitute equation (2) into equation (3):
5x + 7y + 12(0.5x) = 2614
5x + 7y + 6x = 2614
11x + 7y = 2614
Next, substitute equation (2) into equation (1):
x + y + 0.5x = 361
1.5x + y = 361
Now we can solve these two linear equations:
11x + 7y = 2614
1.5x + y = 361
Multiply the second equation by 7 to match the y-coefficients:
10.5x + 7y = 2527
Subtract the new equation from the first equation:
0.5x = 87
x = 174
Now, find y:
1.5(174) + y = 361
261 + y = 361
y = 100
Finally, find z:
z = 0.5x = 0.5(174) = 87

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There are 174 children, 100 students, and 87 adults in attendance.

Let's use the following variables to represent the number of attendees for each category:
C = number of children
S = number of students
A = number of adults
We are given the following information:
The theater's seating capacity is 361.
[tex]C + S + A = 361[/tex]
There are half as many adults as there are children.
[tex]A = 0.5C[/tex]
The total ticket sales amount to $2614.
[tex]5C + 7S + 12A = 2614[/tex]
Now, we will solve the system of equations.
First, let's rewrite equation (2) to express C in terms of A:
[tex]C = 2A[/tex]
Next, substitute this expression for C in equation (1):
[tex]2A + S + A = 361[/tex]
[tex]3A + S = 361[/tex]
Now, substitute the expression for C in terms of A into equation (3):
[tex]5(2A) + 7S + 12A = 2614[/tex]
[tex]10A + 7S + 12A = 2614[/tex]
[tex]22A + 7S = 2614[/tex]

We already have an expression for S from equation (1):
[tex]S = 361 - 3A[/tex]
Now, substitute this expression for S in the last equation:
[tex]22A + 7(361 - 3A) = 2614[/tex]
[tex]22A + 2527 - 21A = 2614[/tex]
[tex]A = 2614 - 2527[/tex]
[tex]A = 87[/tex]
Now that we have the number of adults [tex](A = 87)[/tex], we can find the number of children (C) and students (S) using the expressions we derived earlier:
[tex]C = 2A = 2(87) = 174[/tex]
[tex]S = 361 - 3A = 361 - 3(87) = 361 - 261 = 100[/tex]

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