An engineer is designing a fuel tank in the shape of a cylinder. The tank must have a volume of 3,500 cubic inches. The height of the cylinder must be twice the radius. What is the approximate radius of the cylinder?


8.2 inches


10.4 inches


12.1 inches


23.6 inches

Answer:

7.2

Step-by-step explanation:

The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this  helps!

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

The answer is: 0 = 0

True for all x

Answer:

A) We know that she make $7 per hour, with this we can make a table:

1hr | $7

2hr | $14

3hr | $21

etc...

B)  If in one week she earns $105 and 1w = 7h (1hr = $7) holds true, that means that we have to divide 105 by 7 which gives us 15hrs

C) If she baby-sat for 24hrs, we just have to multiply that by 7 and we get $168

Hope that helped!

The Solution for the given system of equations is (-2) and \((\frac{5}{3})\).

The given are linear equations as follow:
y = \(\frac{2}{3}x\) + 3              .. ... ...(1)
and x  = -2.          .. .... ...(2)

We already know the first part of the solution (x) which is -2.  We can find the other part (y) by putting the value of equation (2) in equation (1).

By putting the values of x in equation (1), we get

y = \((\frac{2}{3})(-2)\) + 3
y = \(\frac{-4}{3}\) + 3

Taking the L. C. M of denominators which will be '3', we get:

y = \(\frac{-4 + 9}{3}\)

y = \(\frac{5}{3}\)

So the second part (y) of the solution of the given equation is \(\frac{5}{3}\).

Hence, the overall solution to the given system of equation is \((-2, \frac{5}{3})\).

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Answer:

Step-by-step explanation:

Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following

\(E[X^k] = \int_{4}^{7}x^k f(x) dx\)

\(Var(X) = E[X^2]- (E[X])^2\)

Standard deviation = \( \sqrt[]{Var(X)}\)

Mean = \(E[X]\)

Then,

\(E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}\)

\(E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31\)

Then, \(Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}\)

Then the standard deviation is \(\frac{\sqrt[]{3}}{2}\)

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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Answer:

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Step-by-step explanation:

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The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.

This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.

For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.

This question is using the percentage decrease theory. According to this theory,

you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.

Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).

Original - Current = Change

120,000 - 3200 = 116,800

Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)

Change / Original = Percentage Change

116,800 / 120,000 = 97%

Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)

Percentage Change x Original = Estimated Original

97% x 120,000 = 116,400

Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

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The quadratic function f(x) = 4x² + 16x + 8 can be expressed in vertex form

Max's error is in step 3

The function is given as:

\(f(x) = 4x^2 + 16x + 8\)

Factor out 4

\(f(x) = 4(x^2 + 4x) + 8\)

Take the coefficient of x

\(k = 4\)

Divide by 2

\(k/2 = 2\)

Square both sides

\((k/2)^2 = 4\)

Add and subtract 4 to the bracket

\(f(x) = 4(x^2 + 4x + 4 - 4) + 8\)

Expand

\(f(x) = 4(x^2 + 4x + 4) + 8 - 16\)

By comparing the above equation to step 3 of Max solution, we can determine that Max's error is in step 3

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Solving equations with algebra tiles or balance scales is difficult due to its limitation which is explained below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Because of their 2-d existence, algebra tiles can only model graduate degrees or reduced polynomials. Their physical nature furthermore restricts the number of different factors that can appear in the algebraic expressions they model, as well as the complexity of their understanding of contradiction and subtraction.

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The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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Answer: 6 units

Step-by-step explanation:

|-5.4| + |0.6|

5.4 + 0.6 = 6 units

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The value of \(f\) is \(0\), by using the concept of slope of a line.

The equation to find the slope of a line is given by:

\(\(\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)\)

Given that the slope is -8 and the points (-7, f) and (-6, -8) lie on the line, we can substitute the coordinates into the equation:

\(\(-8 = \frac{{-8 - f}}{{-6 - (-7)}}\)\)

Simplifying the equation:

\(\(-8 = \frac{{-8 - f}}{{1}}\)\)

Multiply both sides by 1:

\(\(-8 = -8 - f\)\)

Rearranging the equation:

\(\(-8 + 8 = -f\)\(0 = -f\)\)

The concept used in this problem is finding the slope of a line using two given points. The slope represents the rate of change of the line, indicating how much the line rises or falls for each unit of horizontal distance.

By substituting the coordinates of the two given points (-7, f) and (-6, -8) into the formula, we can calculate the slope.

Thus, the value of \(f\) is \(0\).

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The statements that are true regarding the areas are that each palette icon will always allow you to drag only one fill area onto the graph. Changing the position of the other objects on the graph may change the shape of the possible regions you may fill.

The statement "Each palette icon will always allow you to drag only one fill area onto the graph." is true.

The statement "Areas can be used to shade a region of any shade." is false. Areas can be used to shade a region in a specific colour or pattern, but not necessarily any shade.

The statement "Changing the position of the other objects on the graph may change the shape of the possible regions you may fill." is true.

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Answer:

okkkkkk???

Step-by-step explanation:

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

Answer:

a idk

Step-by-step explanation:

Answer:

$150

Step-by-step explanation:

I = prt

I = 5000(.06)(.5)

I = 150

Hey there!

\( \displaystyle{ \red{ \boxed{ \green{ \bold{m = - 1}}}}}\)

\( \\ \)

To find the slope of a line using two points \( \displaystyle{(x_1 , y_1)} \) and \( \displaystyle{(x_2 , y_2)} \) , we can use the slope formula.

This formula corresponds to the quotient of the change in y \( \: \) over \( \: \) the change in x :

\( \displaystyle{m = \frac{ \blue{y_2} - \orange{y_1}}{ \green{x_2} - \red{x_1} }}\)

\( \\ \)

\( \hookrightarrow \) We are given the points (-2 , 3) and (-5 , 6) where:

\( \\ \)

\(\displaystyle{ \hookrightarrow m = \frac{\blue{6} - \orange{3}}{\green{-5} - \red{(-2)}}} \\ \\ \displaystyle{\implies m=\frac{3}{-3}} \\ \\ \displaystyle{\purple{\implies} \boxed{\bold{m=-1}}}\)

Therefore, the slope of the line is -1.

\( \\ \)

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The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

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

To mark all points on the same coordinate plane, we simply plot the graphs of the three functions on the same graph

Using the above as a guide, we have the following:

The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

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Nice work on selecting "invalid" as the correct answer.

The reason why this argument is invalid is because the 'x' could be in circle B or could be outside circle B. There's simply not enough information.

The venn diagram would either be (A) or (D).

The only information we know is that Fred is does not live in San Francisco, so the 'x' will not be placed inside circle A.

Ignore any diagram where x is on the edge of a circle. That isn't allowed in venn diagrams because a person is either in San Francisco, or they aren't (same goes with California). We can't have blurry boundaries like that. This means venn diagrams (B) and (C) are nonsensical.

Answer: A 15/100

Step-by-step explanation:

1. Convert 17/20 into percents

2. You get 85% Which is how much of her homework she has completed

3. To find what she has left subtract 85 from 100

4. You get 15 or 15/100 or 15% more of the test she hasn’t completed and needs to complete

[i] … … … x + 3y - z = 9

[ii] … … … 2x + 9y + 4z = 12

[iii] … … … x + 4y + z = 7

Eliminate z by combining …

• … 4 times equation [i] and equation [ii] :

4 (x + 3y - z) + (2x + 9y + 4z) = 4•9 + 12

(4x + 12y - 4z) + (2x + 9y + 4z) = 36 + 12

6x + 21y = 48

2x + 7y = 16

• … equation [i] and equation [iii] :

(x + 3y - z) + (x + 4y + z) = 9 + 7

2x + 7y = 16

Since we ended up with 2 copies of the same equation, we have infinitely many solutions for x, y, and z. That is, we have infinitely many choices for x and y that satisfy 2x + 7y = 16, and consequently infinitely many choices for z to satisfy any of the 3 original equations.

We can parameterize the solution by letting, for instance, x = t; then the solution set is

x = t

2x + 7y = 16   ⇒   y = (16 - 2t)/7

x + 3y - z = 9   ⇒   z = t + 3 (16 - 2t)/7 - 9   ⇒   z = (t - 15)/7

where t is any real number.