Find the surface area of a cube with edge lengths of 9 centimeters.

Answer:

We can use ratios to set up a system of equations and solve for a, b, and c. Since a:b = 3:8, we can write:

a = 3x

b = 8x

Similarly, since b:c = 6:11, we can write:

b = 6y

c = 11y

Now we have two expressions for b, so we can set them equal to each other and solve for y:

8x = 6y

y = 4x/3

Substituting y back into the expression for c, we get:

c = 11y = 44x/3

To find the smallest possible values of a, b, and c, we want to choose values of x that are as small as possible while still being positive integers. Since x must be a multiple of 3 (because a = 3x is a multiple of 3), let's try x = 3. Then we get:

a = 3x = 9

b = 8x = 24

c = 44x/3 = 44

So the smallest possible values of a, b, and c are 9, 24, and 44, respectively.

Step-by-step explanation:

Answer: 4 2/5

Step-by-step explanation:

1 divided by 2 is 1/2, so if 1/2 times 2 equals one cup, then all we have to do is times 2 1/5 by two. 2 x 2 is 4, and 1/5 times 2 is 2/5.  Add them together, and you get 4 2/5. Alex will need 4 2/5 cups of dip.

Answer:

Median is 9

mode is 10

range4:

The circumference of the circle with a radius of 6 feet would be approximately 37.7 feet.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter of the circle, which is the total length of the boundary that encloses the area of the circle.

The formula for the circumference of a circle is

C = 2πr

Where C is the circumference, r is the radius, and π is approximately 3.14.

If a circle has a radius of 3 feet, the circumference would be

C = 2πr

C = 2π(3)

C ≈ 18.85 feet

When the radius doubles to 6 feet, the circumference would be

C = 2πr

C = 2π(6)

C ≈ 37.7 feet

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Answer:

double, and 36

Step-by-step explanation:

Mc graw hill

Q...

The product of -10(15 + 25h) is -150 - 250h.

In mathematics, a product is the result of multiplying two or more numbers or quantities together. The product is a fundamental operation in arithmetic and algebra, and it is denoted by the symbol "×" or "." or by placing the numbers or quantities next to each other without any symbol.

In the given question,

To use the area model to multiply -10(15+ 25h),We can label the dimensions of the rectangle as 15 and 25h, and we can label the value we want to multiply by (-10) as -10. Then, we can find the area of each of the smaller rectangles by multiplying the corresponding dimensions together:

To find the product of -10(15 + 25h), we can add the areas of the two smaller rectangles:

-10(15 + 25h) = -150 - 250h

Therefore, the product of -10(15 + 25h) is -150 - 250h.

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Answer:

80

Step-by-step explanation:

First, let's mark all animals as x. Now we can form an equation:

[tex] \frac{1}{3} x + \frac{1}{4} x + \frac{1}{5} x + \frac{1}{6} x + 4 = x[/tex]

Then, let's multiply this whole equation by 60, since it's a common denominator:

20x + 15x + 12x + 10x +240 = 60x

57x = -240 + 60x

57x - 60x = -240

-3x = -240 / : (-3)

x = 80

The difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.

The Mean Value Theorem is a fundamental result in calculus that relates the average rate of change of a function over an interval to its instantaneous rate of change at some point within the interval. It states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists some c in (a,b) such that:

f'(c) = [f(b) - f(a)] / (b - a)

In this problem, we are given that f(x) is continuous on [4,8] and differentiable on (4,8), and we are asked to estimate f(8) - f(4) using the Mean Value Theorem.

To do this, we first apply the Mean Value Theorem to obtain an expression for f(8) - f(4) in terms of f'(c) for some c in (4,8):

f'(c) = [f(8) - f(4)] / (8 - 4)

Rearranging, we get:

f(8) - f(4) = f'(c) [tex]\times[/tex] 4

So we need to find an estimate for f'(c) to find an estimate for f(8) - f(4).

We are given that −4≤f′(x)≤3 for all x in (4,8), which means that f'(x) lies between -4 and 3 for all x in (4,8). Since c is also in (4,8), it follows that f'(c) is also between -4 and 3. Therefore, we can say that:

-4 ≤ f'(c) ≤ 3

Substituting this inequality into our expression for f(8) - f(4), we get:

-4 * 4 ≤ f(8) - f(4) ≤ 3 [tex]\times[/tex] 4

Simplifying, we get:

-16 ≤ f(8) - f(4) ≤ 12

This means that the difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.

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After answering the provided question, we can conclude that Therefore, trigonometry the helicopter's horizontal distance to the hiker is approximately 388 feet.

The study of the relationship between triangle wall lengths and angles is known as trigonometry. The topic first emerged in the Hellenistic era, around the third century BC, because of the utilization of geometry in astronomical studies. The branch of mathematics known as precise methods deals with certain quaternion functions and about there potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, buying new furniture, secant, and cosecant are their person names and acronyms (csc). The study of triangle properties, specially those of right triangles, is known as trigonometry. As a result, geometry is really the study of the properties of all geometric shapes.

We can use trigonometry to solve this problem. Let's start by drawing a diagram:

             Hiker

               /|

              / |

             /  | 1500 ft

            /   |

           /θ   |

          /     |

         /14°   |

        /_______|

     Helicopter

We are looking for the horizontal distance between the helicopter and the hiker, which we can call x. We know the altitude of the helicopter (1500 ft), and we know the angle of depression (14°).

From the diagram, we can see that:

tan(14°) = x / 1500

We can solve for x:

x = 1500 * tan(14°)

x ≈ 387.7 ft

Therefore, the helicopter's horizontal distance to the hiker is approximately 388 feet.

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The derivative of [tex]fm(x) = Xm * x^n / (2^{(n+1)})[/tex] with respect to x is [tex]fm'(x) = (Xm-1)x^{n(n+1)}/2^{(n+1)}[/tex].

We can start by using the power rule of differentiation. Taking the derivative of Xm with respect to x gives mXm-1.

Next, we need to find the derivative of the series n=1 n x · x n !2, which involves using the product and chain rules.

First, we can rewrite the series as:

[tex]x(1!/2) * x^{2(2!/2)} *x^{3(3!/2)} * ... * x^n(n!/2)[/tex]

Taking the derivative of each term in the series with respect to x, we get:

[tex]1/2x^{(1-1)} * 1/2x^{(2-1)} * 2/2x^{(3-1)} * ... * n/2x^{(n-1)}[/tex]

Simplifying each term, we get:

[tex]1/2x^{(0)} * 1/2x * 1/x * ... * n/2x^{(n-1)}[/tex]

Combining all the terms, we get:

[tex](1/2 + 1/4 + 2/6 + ... + n/2n) * x^{(-1)}[/tex]

To simplify the series 1/2 + 1/4 + 2/6 + ... + n/2n, we can factor out 1/2 and simplify the remaining terms:

1/2(1/1 + 1/2 + 1/3 + ... + 1/n)

This is the harmonic series, which does not have a closed-form solution. However, we can approximate it using the integral test:

∫(1 to n) 1/x dx = ln(n)

So, the harmonic series can be approximated as ln(n), and the derivative of the series can be written as:

[tex](1/2 ln(x) ) * x^{(-1)}[/tex]

Putting it all together, we get the derivative of fm(x) as:

[tex]f0m(x) = mXm-1 *(1/2 ln(x)) * x^{(-1)}[/tex]

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Median is 67. We see comparing the medians that the Allstars are likewise taller on average than the Champs. Conclusion is that the Allstars have taller players than the Champs based on central tendency from data.

We may compare the measures of central tendency of the heights of the players on both teams to see which team normally has the tallest players. The median and mean are the two often used measurements of central tendency based on data.

We add together all the heights and divide by the total number of players to determine the mean height for Allstars:

(73+62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15 = 1006 / 15 = 67.1 inches

We add together all the heights for the Champs and divide by the overall player count:

(15) = 996/15 = 66.4 inches (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)

We can observe from comparing the means that the Allstars are taller on average than the Champs.

Outliers or extremely high or low numbers in the data, however, can have an impact on the mean. We may determine the median, which is the midpoint value when the data is sorted in either ascending or descending order, to further evaluate the data.

We order the data according to Allstars:

60 60 62 63 65 66 67 68 69 70 70 71 71 72 73

The centre number, or median, is 68.

We order the information for the Champs:

58 60 60 62 65 66 67 68 69 70 70 75

The centre number, or median, is 67.

We can observe from comparing the medians that the Allstars are likewise taller on average than the Champs.

We can therefore draw the conclusion that the Allstars typically have taller players than the Champs based on the metrics of central tendency.

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Answer:

For the second set of numbers, 23, 16, 4, 10, 16, 65, 8:

Mean: To find the mean, we add up all the numbers and divide by the total number of numbers:

(23 + 16 + 4 + 10 + 16 + 65 + 8) / 7 = 142 / 7 = 20.2857 (rounded to 4 decimal places)

Median: To find the median, we need to first arrange the numbers in order from smallest to largest:

4, 8, 10, 16, 16, 23, 65

There are an odd number of numbers (7), so the median is the middle number, which is 16.

Mode: The mode is the number that appears most frequently in the set. In this case, 16 appears twice, which is more than any other number, so the mode is 16.

Range: To find the range, we subtract the smallest number from the largest number:

65 - 4 = 61

So the mean is 20.2857, the median is 16, the mode is 16, and the range is 61.

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Answer:

A = 47 degrees

Step-by-step explanation:

cosineA = adjacent/hypotenuse

cosineA =  34/50

cosineA = 0.68

reverse cosine

A = 47 (rounded to the nearest whole number)

Therefore, the statement that is true is: "The solution to the equation is x = 0.1."

In mathematics, an equation is a statement that shows the equality between two expressions. It is made up of two sides: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equal sign (=). An equation indicates that the two expressions on either side of the equal sign have the same value. Equations can take different forms, depending on the types of expressions involved and the operations used.

Here,

However, we can solve the equation ourselves to find the solution and then check the options.

5x − 6 + 7 = 15x (Given equation)

Simplifying the left-hand side of the equation, we get:

5x + 1 = 15x

Subtracting 5x from both sides, we get:

1 = 10x

Dividing both sides by 10, we get:

x = 1/10

Now we can check each option to see which statement is true:

x = 0.1: This is true, as 1/10 is equal to 0.1.

x = -0.1: This is false, as we found that x = 0.1, not x = -0.1.

x = 10: This is false, as we found that x = 0.1, not x = 10.

The equation has no solution: This is false, as we found a solution for x, namely x = 0.1.

The solution to the equation is x = 1: This is false, as we found that x = 0.1, not x = 1.

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Complete question:

The steps to solve equation 5x−6+7=15x are shown. Which statement about the solution is true?

x = 0.1

x = -0.1

x = 10

The equation has no solution

The solution to the equation is x = 1

The equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

What is the rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity. It is expressed as a ratio of two different units, and it indicates how fast or slow one quantity is changing in relation to another quantity.

If we assume that a person's height decreases by 0.06 cm per year starting at age 30,

we can use the following equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

where h(30) represents the person's height at age 30.

This equation assumes that the rate of height decrease is constant and linear over time.

Hence, the equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

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Answer: 17y - 12

Step-by-step explanation:

By distributing the 3 with the numbers inside the parentheses (2y - 4),

you would get: 6y - 12

You are left with: 11y + 6y - 12

Finally, by adding like terms, your answer would be 17y - 12

The required equation of change is : C= $40 - 10x, where x is the highest price of gas and C is the change.

Let's start by finding the total cost of the 10 gallons of gas. Let's assume that the price of gas is x dollars per gallon at the gas station with the highest price. Then, the total cost of 10 gallons of gas is:

10x dollars

Since Steve paid with two $20 bills, the total amount he paid is:

$40

Therefore, the equation we need to solve to find Steve's change is:

$40 - 10x = C

where C is the amount of change that Steve will receive. We can simplify this equation by subtracting 10x from both sides:

$40 - 10x - 10x = C - 10x

$40 - 20x = C - 10x

Then, we can simplify further by adding 10x to both sides:

$40 - 20x + 10x = C

$40 - 10x = C

Now, we have an equation that relates the price of gas to the amount of change that Steve will receive. To solve for C, we need to know the price of gas at the gas station with the highest price. Once we know that value, we can substitute it into the equation and solve for C.

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The complete question is :

Steve bought 10 gallons of gas at the gas station with the highest price. He paid with two $20 bills. Write and solve an equation to find his change.

Answer:

116in2

Step-by-step explanation:

Top Rectangle Shape: 2in x 3in = 6in2

Middle Rectangle Shape: (9in+3in) x (9in-2in) = 84in2

Far Left Rectangle Shape: (9in-2in-5in) x (6in) = 12in2

Bottom Triangle Shape: [6in - (9in-5in-2in] x [(9in+3in-11in)+6in] x 1/2 = 14in2

Total: 6in2 + 84in2 + 12in2 + 14in2 = 116in2

*Recommend dividing shape to avoid trapezoids

Answer:

3(y-2)=2(y-1)-3

or, 3y-6 =2y-2-3

or, 3y-6 =2y-5

or 3y-2y =6-5

or y=1

hence, the value of y is 1

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Answer:

it 50°

Step-by-step explanation:

D is the reflection of x

Hong opened a money investment account with $6600, which increased by 7.5% by the end of the year. The final amount in the account was $7095.

Hong opened an money investment account with $6600. At the end of the year, the amount in the account had increased by 7.5%. To solve the problem, we can start by calculating the amount of the increase in Hong's account:

Increase = $6600 x 7.5% = $495

Then, we can add the increase to the initial amount to find the final amount:

Final amount = $6600 + $495 = $7095

Therefore, there was $7095 in Hong's account at the end of the year.

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Answer:

132 in.

Step-by-step explanation:

C = πd

C = 22/7 × 42 in.

C = 132 in.

To compare the two accounts, we need to calculate the final amount in each account after the given period.

For the simple interest account:

I = P * r * t

I = 250 * 0.03 * 3 = $22.50

Final amount = P + I = $272.50

For the compound interest account:

Final amount = P * (1 + r/n)^(nt)

Final amount = 250 * (1 + 0.04/2)^(22) = $276.16

Therefore, the compound interest account earns more by $3.66 ($276.16 - $272.50).

Answer:4% over 2 years

Step-by-step explanation:

Answer:

85 points per minute

Step-by-step explanation:

the points earned per minute is calculated as

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₂, y₂) = (200, 17007) and (x₁, y₁ ) = (100,8507) ← 2 ordered pairs from table

points earned per minute = [tex]\frac{17007-8507}{200-100}[/tex] = [tex]\frac{8500}{100}[/tex] = 85

[tex] \texttt{2(x + 2) = - 8} \\ \: \: \: \: \texttt{2x + 2 = - 8} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 8 - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{x = \cancel\frac{ - 10}{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\texttt \purple{ x = - 5} \: }[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps-

The specified circle's center is at (-7, 4). The revised center will therefore be (-7 - 3, 4 - 4) = (-10, 0).

We must deduct 3 from x and 4 from y in order to move the circle 3 units to the right and 4 units below. The revised center will therefore be (-7 - 3, 4 - 4) = (-10, 0).

By inserting the new center and simplifying, it is possible to find the equation for the resulting circle. The equation for a circle has the conventional form[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the circle's center and r is its radius. Since the original equation is[tex](x+7)^2+(y-4)^2=36[/tex], we may substitute the new center (-10, 0) and the radius 6 to obtain [tex](x + 10)^2 + y^2 = 36[/tex]as the equation of the translated circle.

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1. Option 1 multiply 18 m by 0.09361 yd is the correct answer.

2. The cost of the wallpaper will be $1013.

A conversion factor is a ratio used to convert a measurement in one unit to the equivalent measurement in another unit.

In order to convert 18 meters to yards, we must multiply 18 m by 0.09361 yd.

This is because when converting from one unit to another, we must use the conversion factor to multiply, rather than divide.

In this case, the conversion factor is 0.09361 yd/m.

Therefore, we must multiply 18 m by 0.09361 yd to get the answer.

Therefore, the correct answer is option 1, which is to multiply 18 m by 0.09361 yd.

2. To answer the second question, Ken is buying wallpaper. It costs $6.49 per meter.

He needs 512 feet.

To calculate how much the wallpaper will cost, first convert 512 feet to meters.

1m = 3.28ft,

therefore 512ft ÷ 3.28ft = 156.1m.

Then multiply the cost of wallpaper per meter, $6.49, by the number of meters needed, 156.1m.

156.1*$6.49=$1013.07.

To round the nearest half dollar, the cost of the wallpaper will be $1013.

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The closest answer choice is A. Domain: All real numbers; Range: All real numbers.

What are the domain and range?

The domain of a function is the set of all possible input values (often represented by x) for which the function is defined. The range of a function is the set of all possible output values (often represented by y) that the function can produce, based on its input values. In other words, the domain is the set of all valid inputs, and the range is the set of all possible outputs.

The domain and range of an exponential growth function depend on the specific equation of the function.

However, in general, an exponential growth function has a domain of all real numbers and a range of y > 0.

This is because an exponential growth function always has a positive output, and it can take any positive input value.

Therefore, the closest answer choice is A. Domain: All real numbers; Range: All real numbers.

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