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This table shows the results of two surveys that randomly sampled 50 families about their preferred ways to travel to a vacation destination.


Which statement can be made about families' preferred ways to travel to a vacation destination based on the information in the surveys?

The value of x for the given expression is 10.

A number with both an integer and a fractional component is said to be mixed. It is expressed in the form a b/c, where a denotes the integer component, b the numerator of the fractional component, and c the denominator. An illustration of a mixed number is 3 2/9, where 3 is the integer portion, 2 is the fractional numerator, and 9 is the fractional denominator. When expressing amounts that are not whole numbers, such as measurements or fractions of a unit, mixed numbers are frequently utilised. For simpler computations, they can be changed to improper fractions or decimals.

The given expression is 3 2/9 (x ) =10.

The mixed fraction is converted into improper fraction as follows:

3 2/9 = 9(3) + 3 / 9 = 29 / 9

Multiplying both sides by the reciprocal of  29/ 9:

3 2/9 (x ) = 10

(29/9) * 3 2/9 (x ) = (29/9) * 10

x = 290/29

x = 10

Hence, the value of x for the given expression is 10.

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The complete question is:

3 2/9 (x ) =10 find x.

Answer:

There are 4^5 ways to answer 5 multiple choice questions.

Step-by-step explanation:

The functions can be matched with their correct descriptions as follows:

1. Radical function

2. Rational function

3. Absolute function

4. Piecewise function

5. Step function

6. Quadratic function

To identify the functions, you need to know the formats that each of the functions assumes when expressed mathematically. Radical functions involve radicals or roots, such as square roots (√) or cube roots (∛) while rational functions are functions that take the form p(x)/q(x), where p(x) and q(x) are polynomials, and the denominator q(x) cannot be equal to zero.

Absolute functions are functions of the form f(x) = |x-a|, where a is a constant and |x| represents the distance between x and 0 on the number line. Quadratic functions, on the other hand, are functions of the form f(x) = ax^2 + bx + c.

Piecewise functions are functions that have different rules or formulas for different parts of their domain while step functions are functions that "step up" or "step down" at specific values of x. They can be defined using the floor function (⌊x⌋) or ceiling function (⌈x⌉).

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Answer:

42 units

Step-by-step explanation:

Area of a trapezoid is always 1/2(b1+b2)*h

so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42

The greatest common factor (GCF) of x³, x⁴, and x⁷ is x³.

To find the GCF, we need to determine the largest factor that all three terms have in common. In this case, x³ is the largest factor that all three terms share.

To see why, we can factor each term into its prime factors:

x³ = x * x * x

x⁴ = x * x * x * x

x⁷ = x * x * x * x * x * x * x

As we can see, x³ is the largest factor that all three terms have in common, since it appears in all three factorizations. Therefore, x³ is the greatest common factor of x³, x⁴, and x⁷.

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the exact value of sin(θ + β) is (-3[tex]\sqrt{7}[/tex] - 4[tex]\sqrt{2}[/tex]))/15.

We can use the following trigonometric identity to solve this problem:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

Let's start by finding sin(θ) and cos(θ) using the given value of theta:

sin(θ) = -sqrt(1 - cos^2(theta))

cos(θ) = -sqrt(2)/3

We can use the Pythagorean identity to find sin(theta):

sin(θ) = ([tex]\sqrt{1 - cos^2[/tex]θ)

sin(θ) = -([tex]\sqrt{1 - 2/9}[/tex])

sin(θ) = -[tex]\sqrt{(7/9)}[/tex]

Now let's find sin(β) and cos(β) using the given value of beta:

sin(β) = 4/5

cos(β) = 3/5

Now we can substitute all these values into the trigonometric identity:

sin(θ+β) = sin(θ) cos(β) + cos(θ) sin(β)

sin(θ+β) = (-[tex]\sqrt{7}[/tex]/9))(3/5) + (-[tex]\sqrt{2}[/tex]/3)(4/5)

sin(θ+β) =  (-3[tex]\sqrt{7}[/tex] - 4[tex]\sqrt{2}[/tex]))/15.

Therefore, the exact value of sin(θ + β) is  (-3[tex]\sqrt{7}[/tex] - 4[tex]\sqrt{2}[/tex]))/15.

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The probability that the first box chosen by a mover is not a multiple of 9 is 9/10.

What is probability?

In general, Probability means possibility that is a possible chance. It is a part of mathematics which deals with the occurrence of a random event. The value is in between zero to one.

A moving company has boxes numbered 1 through 40.

Total number of boxes= 40.

Multiple of 9 is given by:

9, 18,27,36  

So the total numbers that are multiple of 9 is 4.

The probability of getting a multiple of 9 is = 4/40.

Now the probability of not getting a multiple of 9 is (1-4/40)

                                                                                      = 36/40

                                                                                      = 9/10

Hence, the probability that the first box chosen by a mover is not a multiple of 9 is 9/10.

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You must be a minimum of 18 years old to vote. The correct answer is option (b).

we have

x >= 18

The interval is the answer to this inequality-----> [18, ∞)

bigger than or equal to all real numbers

Case A:

To vote, you must be older than 18 years old.

The inequality in this instance that represents the assertion is

v > 18  is not correct

Case B:

You must be a minimum of 18 years old to vote.

The inequality in this instance that represents the assertion is

v >= 18  is correct

Case C:

Before turning 18 years old, you can cast a ballot.

The inequality in this instance that represents the assertion is

V < 18  is not correct

Case D:

When you are 18 years old, you are too old to vote.

You are unable to vote in this instance when

v = 18

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The rest of the question is,

a). You must be older than 18 years old to vote.

b). You must be at least 18 years old to vote.

c). You can vote before you turn 18 years old.

d). You cannot vote when you are 18 years old.

Answer:

132 yd²

Step-by-step explanation:

This shape is a rectangle.

Area of rectangle = L · W

L = 12 yd

W = 11 yd

We Take

12 · 11 = 132 yd²

So, the area of this shape is 132 yd².

Answer: Yes, I agree with Luna's statement that if 8^x > 0, then the value of x must be greater than 0.

The reason for this is that any positive number raised to any power will always be positive. Therefore, 8 raised to any power, including x, will always be positive.

On the other hand, any number raised to an even power will always be positive, including negative numbers. However, any number raised to an odd power can be either positive or negative, depending on whether the base is positive or negative.

Therefore, if 8^x is positive, it means that x must be an even number or zero. However, since we are given that 8^x > 0, we know that x cannot be zero or a negative even number. Therefore, the only possibility is that x is a positive number, i.e., x > 0.

In summary, if 8^x > 0, then x must be greater than 0, because any positive number raised to any power is always positive.

Step-by-step explanation:

The amount of water the farmer can put in the tank increase when the larger tank is built is 106.33%.It takes 4days for the horses to drink all the water in the larger tank.

Percentage is a way of expressing a proportion or a fraction out of 100. It represents the number of parts per hundred of a quantity.

Dimension refers to a measurable aspect of an object or a system, such as length, width, height, depth, volume, area, or mass. In mathematics, dimension also refers to the number of coordinates required to specify a point in a space. For example, a two-dimensional shape like a square has two dimensions, length and width, while a three-dimensional object like a cube has three dimensions, length, width, and height.

To find the percentage increase in the amount of water the farmer can put in the larger tank, we need to calculate the volume of the original tank and the volume of the larger tank, and then compare the two.

The original tank has dimensions of 2 4/5 ft, 2 2/5 ft, and 2 1/2 ft. We can convert these mixed numbers to improper fractions for easier calculations:

2 4/5 ft = (2 x 5 + 4)/5 ft = 14/5 ft

2 2/5 ft = (2 x 5 + 2)/5 ft = 12/5 ft

2 1/2 ft = (2 x 2 + 1)/2 ft = 5/2 ft

The volume of the original tank is then:

Volume = Length x Width x Height = 14/5 ft x 12/5 ft x 5/2 ft

Now, the farmer plans to increase measurement  by 25%. To do this, we multiply each measurement by 1.25.

The dimensions of the larger tank would be:

Length = 14/5 ft x 1.25 = 3.5 ft

Width = 12/5 ft x 1.25 = 3 ft

Height = 5/2 ft x 1.25 = 3.125 ft

The volume of the larger tank is then:

Volume = Length x Width x Height = 3.5 ft x 3 ft x 3.125 ft

To find the percentage increase, we can compare the two volumes:

Percentage increase = ((Volume of larger tank - Volume of original tank) / Volume of original tank) x 100

Plugging in the values we found:

Percentage increase = ((3.5 ft x 3 ft x 3.125 ft - 14/5 ft x 12/5 ft x 5/2 ft) / (14/5 ft x 12/5 ft x 5/2 ft)) x 100

After calculating the above expression, we find that the percentage increase is approximately 106.33%. So, the amount of water the farmer can put in the larger tank will increase by approximately 106.33% when the larger tank is built.

Now, to find how many days it will take the horses to drink all the water in the larger tank, we can assume that the rate at which the horses drink water remains constant. Since the volume of the larger tank is approximately 106.33% more than the original tank, it will take the horses approximately the same amount of time to drink all the water in the larger tank, which is 4 days.

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Answer:

[tex]396\pi \: {ft}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

l = 21 ft

r = 12 ft

Find: A (surface) - ?

[tex]a(surface) = \pi {r}^{2} + \pi \times r \times l[/tex]

[tex]a(surface) = \pi \times {12}^{2} + \pi \times 12 \times 21 = 144\pi + 252\pi = 396\pi \: {ft}^{2} [/tex]

Answer:

between 14 and 15

Step-by-step explanation:

convert fractions using 42 as the LCD, then add:

59/7 = 354/42

37/6 = 259/42

354/42 + 259/2 = 613/42 = 14.6

14 < 14.6 < 15

or,

convert fractions to decimals, then add:

59/7 = 8.4

37/6 = 6.2

8.4 + 6.2 = 14.6

The y-intercept of the function is (0, 3), which means that the initial value of the comic book is $3.

For the first problem:

Initial Amount = $1232

Growth/Decay Rate = -6.2% = -0.062 (since the value is decreasing)

Let t be the number of years since 2007, then the equation for the value of the couch in year t can be written as:

Value = 1232(1 - 0.062)^t

To find the worth of the couch in 2012 (which is 5 years after 2007), we can substitute t = 5 into the equation:

Value = 1232(1 - 0.062)^5

Value = 1232(0.938)^5

Value ≈ $888.79

Therefore, the worth in 2012 was approximately $888.79.

The information required for the third problem is given below:

Initial Value = $3

Growth Rate = 6% = 0.06 (since the value is increasing)

Let t be the number of years after the comic book is sold, then the equation for the value of the comic book in year t can be written as:

Value = 3(1 + 0.06)^t

To find the value of the comic book in 25 years, we can substitute t = 25 into the equation:

Value = 3(1 + 0.06)^25

Value ≈ $14.58

The domain of the function is all positive real numbers, since the value of the comic book can be calculated for any positive number of years after it is sold. The range of the function is all positive numbers, since the value of the comic book can never be negative.

The y-intercept of the function is (0, 3), which means that the initial value of the comic book is $3.

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The value of B, the area of the base include the following: C. 1,542 m².

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

Volume of rectangular prism = base area × Height

26,214 = B × 17

Base area, B = 26,214/17

Base area, B = 1,542 m²

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In the given problem, using Pythagorean theorem, if Ms. Smith wants to put a walkway along each diagonal, she will need a total of  40 feet of walkway.

To find the length of the walkway, we need to find the length of the diagonals of the garden. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the two sides of the rectangle are 16 feet and 12 feet. So, we can find the length of the two diagonals as follows:

Ms. Smith wants to put a walkway along each diagonal, so she will need a total of 20 + 20 = 40 feet of walkway.

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Answer:

[tex]7 \: \: and \: \: 14 \frac{1}{6} [/tex]

Step-by-step explanation:

Assume, the 1st mixed number is x and the 2nd one is y

Let's write 2 equations according to the given information:

[tex]x + y = 21 \frac{1}{6} [/tex]

[tex]x - y = \frac{43}{6} [/tex]

Let's make x the subject from the 1 equation:

[tex]x = 21 \frac{1}{6} - y[/tex]

Replace x in the 2nd equation with its value from the 1st one:

[tex]( 21\frac{1}{6} - y) - y = \frac{43}{3} [/tex]

Eliminate the brackets and collect like-terms:

[tex] - 2y = \frac{43}{6} - 21 \frac{1}{6} [/tex]

Convert the number 21 1/6 to an improper fraction:

[tex] - 2y = \frac{43}{6} - \frac{21 \times 6 + 1}{6} [/tex]

[tex] - 2y = \frac{43}{6} - \frac{127}{6} = \frac{ - 84}{6} [/tex]

Multiply both sides of the equation by 6 to eliminate the fraction:

[tex] - 12y = - 84[/tex]

Divide both sides of the equation by -12 to make y the subject:

[tex]y = 7[/tex]

[tex]x = \frac{127}{6} - \frac{7}{1} = \frac{127}{6} - \frac{42}{6} = \frac{85}{6} = 14 \frac{1}{6} [/tex]

The value of (sin x + cos x)(tan x + cot x) = sec x + csc x is proven using the trigonometric identities.

Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Identity instances include:

Mutual identities:

1/sin x 1/sec x 1/cos x 1/cot x 1/tan x = csc x

Identity of a quotient: tan = sin x/cos x, cot = cos x/sin x

These are only a few of the numerous trigonometric identities that are available. It's crucial to understand these identities in order to solve trigonometry difficulties.

The given identity is (sin x + cos x)(tan x + cot x) = sec x + csc x.

Taking the LHS we have:

(sin x + cos x)(tan x + cot x)

According to distributive property:

= sin x tan x + sin x cot x + cos x tan x + cos x cot x

Using, definitions of tangent and cotangent:

= sin x (sin x/cos x) + sin x (cos x/sin x) + cos x (sin x/cos x) + cos x (cos x/sin x)

= sin² x/cos x + sin x cos x/sin x + cos x sin x/cos x + cos² x/sin x

= sin² x/cos x + cos² x/sin x + 2sin x cos x/sin x cos x

Using, trigonometric identity sin² x + cos² x = 1:

= (sin² x + cos² x)/cos x sin x + 2

= 1/cos x sin x + 2

= (1/cos x)(1/sin x) + 2

= sec x csc x + 2

= sec x + csc x + 2

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Answer:

C 163 yd

Step-by-step explanation:

Just break it up,

12*6 + 3*9 + 2*2

72 + 27 + 4

103 yd^2 <--

Answer:

To express the given rate as a unit rate, divide the given amount by the given quantity.

$2.70 for 15 ounces can be expressed as:

$0.18 per ounce (unit rate)

Therefore , the solution of the given problem of function comes out to be  f''(3/2) at x = 3/2.

On the final exam, each subject will feature a variety of problems that cover both real and hypothetical places as well as the development of numerical factors. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

To determine the function f(x) = x⁴ - 2x³'s relative minimum,

By taking f(x)'s derivative, we arrive at:

=>  f'(x) = 4x³ - 6x²

To determine the key places, we can set this to zero as follows:

=>  4x³ - 6x² = 0

=>  2x²(2x - 3) = 0

So, x = 0 and x = 3/2 are the turning points.

The second derivative test can be used to determine the type of these key sites. By taking f(x)'s second derivative, we arrive at:

=> f''(x) = 12x² - 12x

We have f''(0) = 0 at x = 0, which indicates that the second derivative test is not convincing. To determine the nature of this crucial issue, we must employ a different technique.

We have a positive value for

=>  f''(3/2) at x = 3/2, which is 9.

This indicates that the function's relative minimum is located at x.

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Answer: $8.25

Step-by-step explanation:

Since David played 2 games and one game costs $4.50, you're gonna multiply $4.50 by 2 and that gives you $9. Then, you're gonna add the cost of the shoe ($2.75) which gives you $11.25. Since he gave the cashier a twenty-dollar bill, we're gonna subtract 11.25 by 20.00.

Therefore, the change that David will get back is $8.25

In order to create a design on a grid with 5 quadrilaterals, consisting of 3 parallelograms, 2 rectangles, 1 rhombus, 1 square, 1 trapezoid, and 1 quadrilateral with no other classification; we will to follow the below steps and ensure appropriate markings is added to each shape to label them accordingly.

By following the above steps, a design can be created on a grid with 5 quadrilaterals, consisting of 3 parallelograms, 2 rectangles, 1 rhombus, 1 square, 1 trapezoid, and 1 quadrilateral with no other classification.

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The length of a 30° arc of a circle with a radius of 6 feet is π feet.

What is circle ?

In geometry, a circle is a closed, two-dimensional figure that consists of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center). The distance across the circle through the center is called the diameter, which is equal to twice the radius.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, the circumference of this circle is:

C = 2π(6 feet) = 12π feet

Since a full circle is 360°, we can find the length of a 30° arc by multiplying the fraction of the circle represented by the arc by the circumference of the circle. In this case, the fraction of the circle represented by the 30° arc is:

30°÷360° = 1÷12

So the length of the 30° arc is:

(1÷12) × 12π feet = π feet

Therefore, the length of a 30° arc of a circle with a radius of 6 feet is π feet.

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Answer:

x = -1

y = -1

Step-by-step explanation:

−6x + 5y = 1

6x + 4y = −10

We combine the equations

9y = -9

y = -1

Now we put -1 in for y and solve for x

−6x + 5(-1) = 1

-6x - 5 = 1

-6x = 6

x = -1

Let's Check

−6(-1) + 5(-1) = 1

6 - 5 = 1

1 = 1

So, x = -1 and y = -1 is the correct answer!

Therefore, the equivalent fraction is: 126/5

A fraction is a numerical quantity representing a part of a whole or a ratio between two quantities. It is expressed as one number (the numerator) divided by another number (the denominator), separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, in the fraction 3/4, the numerator is 3, which represents three parts out of a total of four equal parts. Fractions can be used to represent many different types of quantities, such as parts of a whole, ratios, percentages, and probabilities.

To find an equivalent fraction using division, we need to divide both the numerator and denominator of the given fraction by the same number. In this case, we can simplify the fraction 6 * 21/5 by dividing both the numerator and denominator by 5:

(6 * 21) ÷ 5 = 126 ÷ 5

Therefore, the equivalent fraction is:

126/5

Note that this fraction cannot be simplified any further.

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The DWest company has the lowest rate per minute which is 14.75.

The first company is AB and C

Given that: the price = is $ 19.95 and the time taken is 100 minute

Therefore the rate per unit of time for AB and C companies is

[tex]\frac{Price}{Time} = \frac{19.95}{100} = 0.1995[/tex]

The second company is Berizon

Given that: the price = is $ 24.95 and the time taken is 150 minute

Therefore the rate per unit of time for Berizon companies is

[tex]\frac{Price}{Time} = \frac{24.95}{150}= 0.1663[/tex]

The third company is Cinguling

Given that: the price = is $ 9.95 and the time taken is 60 minute

Therefore the rate per unit of time for Cinguling companies is

[tex]\frac{Price}{Time} = \frac{9.95}{60} = 0.1658[/tex]

The fourth company DWest

Given that: the price = is $ 14.75 and the time taken is 100 minute

Therefore the rate per unit of time for DWest companies is

[tex]\frac{Price}{Time} = \frac{14.75}{100} = 0.1475[/tex]

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Complete the question in the form of a table:

The composite function f(g(x)) has a value of -2x^2 - 6.

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

Fuctions f(x) and g(x)

To find f(g(x)), we first need to evaluate g(x) and then use the result as the input for f(x).

So we have:

g(x) = x^2 + 3

Now we substitute this expression into f(x) and simplify:

f(g(x)) = f(x^2 + 3) = -2(x^2 + 3) = -2x^2 - 6

Therefore, f(g(x)) = -2x^2 - 6.

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