Translate words to mathematical expressions : 3 times a number​

Absolute minimum value is -4/81 and the Absolute maximum value is 72 at x = 9.

To find the absolute maximum and absolute minimum values of the function f(x) = x(x² - x)/9 on the interval [0, 9], we need to follow these steps:

1. Find the critical points by taking the derivative of f(x) and setting it to zero.

2. Evaluate the function at the critical points and endpoints of the interval.

3. Compare the values obtained to determine the absolute maximum and minimum.

1. f'(x) = (3x² - 2x)/9

Set f'(x) to 0: (3x² - 2x)/9 = 0

Solve for x: 3x² - 2x = 0 -> x(3x - 2) = 0

Critical points: x = 0, x = 2/3

2. Evaluate f(x) at critical points and endpoints: - f(0) = 0(0² - 0)/9 = 0 - f(2/3) = (2/3)((2/3)² - (2/3))/9 = -4/81 - f(9) = 9(9²- 9)/9 = 72

3. Comparing the values:

- Absolute minimum value: -4/81 at x = 2/3

- Absolute maximum value: 72 at x = 9

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(a) The probability is, 0.242

(b) The probability is, 0.0034 or 0.34%.

(c) The minimum salary is $49538 and the maximum salary is $67962.

What is probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

(a) For normal distribution z - score = (X - μ) / σ

Here, mean (μ) = 58750  and

Standard deviation (σ) = 4700

Probability = P( X > 62000) = P( Z > ((62000 - 58750) / 4700) = P( Z > 0.7) = 1 - P( Z < 0.7) = 1 - 0.7580 = 0.242

Hence, the probability is, 0.242

(b)

Probability = P( X > 45000) = P( Z > ((45000 - 58750) / 4700))

= P( Z < -2.93) = 1 - 0.9966 = 0.0034 = 0.34%

Hence the probability is, 0.0034 or 0.34%

(c) For middle 90% values critical z =-/+1.96

Therefore,

Minimum salaries  = mean - z x standard deviation

                              = 58750 - 1.96(4700)

Minimum salaries = 49538

Maximum salaries = mean + z x standard deviation

                              = 58750 + 1.96(4700)

Maximum salaries = 67962

Hence, the minimum salary is 49538 and the maximum salary is 67962.

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Answer:

21,704

Step-by-step explanation:

Find the volume of both the top of the silo (hemisphere) and the end bit of the silo (cylinder)

V = \(\frac{2}{3}\) \(\pi\)\(r^{3}\) is the formula for finding the volume of a hemisphere

V = \(\pi\)\(r^{2}\)h is the formula for finding the volume of a cylinder

Let's find the hemisphere first.

We're using 3.14 for pi, so the equation would look like this

V = \(\frac{2}{3}\) x 3.14 x \(12^{3}\)

V = \(\frac{2}{3}\) x 3.14 x 1728

V = 3617.28 \(ft^{3}\)

Now let's find the volume of the cylinder.

V = 3.14 x \(12^{2}\) x 40

V = 3.14 x 144 x 40

V = 18,086.4 \(ft^{3}\)

Last, you add both volumes together.

3617.28 + 18,086.4 = 21,703.68

Round it to make it 21,704.

The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 .

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

Radius(r) = 12 ft.

Then, the volume of a hemisphere is,

V = 2/3πr³

V = 2/3 x 3.14 x 12³

V = 10851.84 feet³

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder is,

V = πr²h

V = 3.14 x 12² x 40

V = 18095.57

So, the total volume is

V = 10851.84 + 18095.57

V = 28947.41

Then, total volume = total number of cubic feet of grain

Hence, the required answer is, 28947.41 .

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Answer:

18.445

Step-by-step explanation:

Multiply

Answer:

Yes

Step-by-step explanation:

y is the litters of water in the tank

x is the time in minutes

m is the change in litters

b is the initial amount of water

so the formula is y = mx + b

whereas m is -14 and b is 770

y = -14x + 770 or y = 770 - 14x

Answer:

3/10

Step-by-step explanation:

Answer:

.58 cm^3

Step-by-step explanation:

The formula for finding the volume of a cube is V = a^3 where a is a side length.

If you input the given value into the formula, you get .58 cm^3

Please mark as brainliest ;)

The statement that truly represent the diagram is

y = w and Δ ABC ~ Δ CDE

The two triangles depicted are similar triangles and similar triangle is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure shows that pair of congruent angles are

angle  y = angle  w (alternate angles)

angle D = angle B (right triangle)

angle x = angle z (alternate angles)

similar triangles is represented by ~ and only the first option match the description

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Answer: (3a + 2) • (4a2 - 2a + 9)

(no solution)

Step-by-step explanation:

Step by Step Solution

More Icon

STEP

1

:

Equation at the end of step 1

 (3a + 2) • ((22a2 -  2a) +  9)

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  4a2-2a+9

The first term is,  4a2  its coefficient is  4 .

The middle term is,  -2a  its coefficient is  -2 .

The last term, "the constant", is  +9

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -2 .

     -36    +    -1    =    -37

     -18    +    -2    =    -20

     -12    +    -3    =    -15

     -9    +    -4    =    -13

     -6    +    -6    =    -12

     -4    +    -9    =    -13

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 (3a + 2) • (4a2 - 2a + 9)

The perm pattern that includes a central rectangle and two sections at each side is the contour pattern.

The contour pattern in a perm involves dividing the hair into three sections, with a rectangular section in the center and two additional sections on each side. The hair is then wrapped around perm rods in a pattern that follows the contour of the head. This pattern is often used to create natural-looking waves or curls.

The other patterns listed - rectangle pattern, spiral bricklay pattern, and alternating oblong pattern - are not typically used in perming hair.

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Answer:

Let's solve for x. x=2y

Step-by-step explanation:

Let's solve for x.

x−2y=0

Step 1: Add 2y to both sides.

x−2y+2y=0+2y

x=2y

Let's solve for y.

x−2y=0

Step 1: Add -x to both sides.

x−2y+−x=0+−x

−2y=−x

Step 2: Divide both sides by -2.

−2y/−2=−x/−2

y=1/2x

The zero of the function, from the given graph is -5. Therefore, option A is the correct answer.

The graph of a function is given below.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.

From the given graph we can see the graph of function is passing through the x-axis at -5.

The zero of the function, from the given graph is -5. Therefore, option A is the correct answer.

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The appropriate option is "True". Adding programming to your skill-set is essential if you want to be a data scientist. Math and statistics provide a strong foundation for understanding the principles and concepts behind data analysis.

However, to effectively work with data at scale and solve real-world problems, data scientists need to use programming languages and tools.

Here are several reasons why programming is necessary for data scientists:

1. Data Manipulation: Data scientists often work with large and complex datasets that require cleaning, transformation, and manipulation. Programming allows data scientists to automate these tasks and perform them efficiently. Programming languages like Python and R offer extensive libraries and packages for data manipulation, such as Pandas, NumPy, and dplyr.

2. Data Visualization: Communicating insights from data is crucial, and data visualization plays a significant role in this process. Programming enables data scientists to create visualizations and interactive plots to explore and present data effectively. Tools like Matplotlib, Seaborn, ggplot, and Plotly provide powerful visualization capabilities.

3. Machine Learning and Data Modeling: Machine learning is an integral part of data science. Programming skills allow data scientists to implement and apply various machine learning algorithms and models. Libraries like scikit-learn, TensorFlow, and PyTorch provide the necessary tools and frameworks to build and deploy machine learning models.

4. Big Data Processing: With the exponential growth of data, data scientists often encounter big data challenges. Programming languages like Python and tools like Apache Spark enable data scientists to handle and process large-scale datasets efficiently. Knowledge of programming allows data scientists to leverage distributed computing frameworks and techniques to analyze and extract insights from big data.

5. Reproducibility and Collaboration: Programming facilitates reproducibility in data science workflows. By writing code, data scientists can document their analyses, share them with others, and ensure that the results can be reproduced. Programming also enables collaboration among data scientists and allows for version control and code sharing through platforms like GitHub.

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There are 608400 plates are possible.

If the first is A, we have 26 possibilities:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have 26 possibilities:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.

There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is:

26×26=676

The same applies for the three digits.

There are 9 choices for the first as first digit cannot be 0

10 for the second,

10 for the third

9×10×10=900

So for a license plate which has 2 letters and 3 digits, there are:

676 × 900 = 608400 possibilities

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The equations for the circle traced out counterclockwise as t goes from 0 to 2π are:

x = 3 + 4 * cos(t)

y = 2 + 4 * sin(t)

(a) To find the straight line segment traced from (3,2) to (5,8) as t goes from 0 to 1, we can use the parameterization formula for a line segment:

x = x₀ + (x₁ - x₀) * t

y = y₀ + (y₁ - y₀) * t

where (x₀, y₀) and (x₁, y₁) are the coordinates of the starting and ending points, respectively.

For the given points (3,2) and (5,8), we have:

x₀ = 3, y₀ = 2

x₁ = 5, y₁ = 8

Plugging these values into the parameterization formula, we get:

x = 3 + (5 - 3) * t = 3 + 2t

y = 2 + (8 - 2) * t = 2 + 6t

So, the equations for the straight line segment traced as t goes from 0 to 1 are:

x = 3 + 2t

y = 2 + 6t

(b) To find the circle centered at (3,2) with a radius of 4, traced out counterclockwise as t goes from 0 to 2π (a full revolution), we can use the parameterization formula for a circle:

x = cx + r * cos(t)

y = cy + r * sin(t)

where (cx, cy) are the coordinates of the center and r is the radius.

For the given center (3,2) and radius 4, we have:

cx = 3, cy = 2

r = 4

Plugging these values into the parameterization formula, we get:

x = 3 + 4 * cos(t)

y = 2 + 4 * sin(t)

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Step 1:

Draw the figure

The diagonals of a rhombus bisect each other,

therefore

FJ = JH

this implies that

JH = 4.

Opposite angles of a rhombus are equal, so

The diagonals of a rhombus bisect the interior angles.

Therefore,

The diagonals of a rhombus are perpendicular

GH = 8 (b)

Also,

Using the Pythagorean rule,

FH = FJ + JH

this implies that

FH = 4 + 4 = 8

FH = 8

right choice B

The diagonals of a rhombus bisect the interior angles.

therefore

Sum of the interior angles of a rhombus is 360degrees.

And opposite interior angles of a polygon are congruent.

Therefore

Also,

Answer:

4x-111

Step-by-step explanation:

let 'my number' be 'x'

x-15 -> (subtract from x)

4(x-15) -> (multiply result from (x-15) by 4)

4(x-15) - 51 -> (subtract 51 from result from [4(x-15)])

4x-60-51

4x-111

This is the expression for the number

The number is 37

Algebraic expressions are expressions that make use of numbers and variables

Let the number be represented with x.

So, here have;

Subtract 15 from x; x - 15

Multiply by 3; 4(x - 15)

Subtract 51; 4(x -15) - 51

The result is; x

So, the equation will be

4(x-15)-51=x

4x-60-51=x

4x-111=x

4x-x=111

3x=111

Divide both sides by 3

x=37

Therefore, the answer of the algebraic expression will be 37

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Answer:

its not 1, its the second one (B)

Step-by-step explanation:

Answer:

I know I'm 1 year late but B is the correct answer choice. I just did it on edge 2021.

The appropriate simulation applet to calculate an approximate p-value is 0.0077.

The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.

Delay or no delay, answer: the number of words remembered

The mean distance between words remembered with and without delay over time is null, or zero.

Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.

Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.

The mean distance in words remembered is 1.85.

1)0.0077 as the p-value

2)Strong data suggests that a brief delay impairs memorization.

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The final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

For the stated question-

Let initial enrollment = 100.

After one decade, the enrollment added 30% of the initial.

Thus,

= 100 + 30% of 100

= 100 + 130

= 130

Thus, the final enrollment after one decade is obtained by taking the 30% of the initial enrollment.

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Answer:

pretty sure it's b but I can't see that well can you please take a clearer picture of your question?

Answer:

Step-by-step explanation:

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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There are 16 bit strings of length eight that contain either three consecutive 0s or four consecutive 1s.

To count the number of bit strings of length eight that contain either three consecutive 0s or four consecutive 1s, we can use the principle of inclusion-exclusion.

Step 1: Count the total number of bit strings of length eight.

Each bit in the string can have two possible values (0 or 1), so the total number of bit strings of length eight is 2^8 = 256.

Step 2: Count the number of bit strings with three consecutive 0s.

We can treat the three consecutive 0s as a single block and consider the remaining five bits. The block of three 0s can start from the first position to the sixth position, so we have 6 choices for its starting position. The remaining five bits can have two possible values (0 or 1), so there are 2^5 = 32 choices for the remaining bits. Therefore, the number of bit strings with three consecutive 0s is 6 * 32 = 192.

Step 3: Count the number of bit strings with four consecutive 1s.

Similar to Step 2, we treat the four consecutive 1s as a single block and consider the remaining four bits. The block of four 1s can start from the first position to the fifth position, so we have 5 choices for its starting position. The remaining four bits can have two possible values (0 or 1), so there are 2^4 = 16 choices for the remaining bits. Therefore, the number of bit strings with four consecutive 1s is 5 * 16 = 80.

Step 4: Subtract the overlaps.

In Step 2 and Step 3, we have counted some bit strings twice. Specifically, there are bit strings that contain both three consecutive 0s and four consecutive 1s. To correct for this, we need to subtract the number of bit strings that have both patterns.

To have both patterns, we consider the starting position of the block of three 0s and the block of four 1s. The block of three 0s can start from the first position to the fourth position (leaving three positions for the block of four 1s). So, we have 4 choices for the starting position of the block of three 0s. The remaining three positions can have two possible values (0 or 1), so there are 2^3 = 8 choices for the remaining bits. Therefore, the number of bit strings with both patterns is 4 * 8 = 32.

Step 5: Calculate the final count.

To obtain the number of bit strings that contain either three consecutive 0s or four consecutive 1s, we subtract the overlaps from the total count:

Total count - Overlaps = 256 - 192 - 80 + 32 = 16.

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Answer:

1/2x + 4

1/2x + 4

= 25 + 4

= 29

It will take 29 minutes to make and pack an order of 50 parts.

Hope This Helps!

Answer:

y = -3x + 5

Step-by-step explanation:

m = -3 (slope)

y- intercept = 5

Answer:

y = -3x + 5

Step-by-step explanation:

Answer:

a=2

b=93

I hope this helps you

Step-by-step explanation:

Answer:

1. 2  

2. 93

Step-by-step explanation:

First we have to put the values of x and y into the equation

4(3)-2(5)

(4×3)-(2×5)

12-10=2

Now the second one

2(3)²+3(5)²

18+75=93

The domain is all real numbers and the Range is y ≥ 3.The correct answer is option A.

To determine the domain and range of the quadratic function based on the given table, let's analyze the values.

Domain represents the set of possible input values (x-values) for the function.

Range represents the set of possible output values (y-values) for the function.

From the given data:

x = -1, 0, 1, 4

y = 5, 3, 3, 5, 35

Looking at the x-values, we can see that the function has values for all real numbers. Therefore, the domain of the function is "all real numbers."

Now, let's consider the y-values. The minimum value of y is 3, and there are no y-values less than 3.

Additionally, the maximum value of y is 35. Based on this information, we can conclude that the range of the function is "y ≥ 3" since all y-values are greater than or equal to 3.

Therefore, the correct answer is:A. Domain: all real numbers

Range: y ≥ 3

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The probable question may be:

The table below represents a quadratic function. Use the data in the table to determine the domain and range of the function.

x= -1,0,1,4

y= 5,3,3,5,35

A. Domain: all real numbers Range: y ≥3

B. Domain: all real numbers

Range: x≥0

c. Domain: all real numbers

Range: y ≥0

D. Domain: all real numbers

Range: y ≤3

Overall, as a result of these transactions, the U.S. firm would be importing Japanese goods. Here's how the process works:

1. The U.S. firm exchanges dollars for yen: In this step, the firm converts its U.S. dollars into Japanese yen by participating in the foreign exchange market. This allows the firm to obtain the necessary currency to conduct business in Japan.

2. The firm uses yen to buy Japanese goods: With the acquired yen, the U.S. firm can now purchase goods from Japanese suppliers. These goods can vary depending on the nature of the firm's business, but they could include anything from electronics to automobiles.

3. Implications of importing Japanese goods: By purchasing Japanese goods, the U.S. firm is participating in international trade and importing these goods into the United States. This can have several implications, including contributing to the U.S. trade deficit (if imports exceed exports) and potentially impacting domestic industries.

It's important to note that this answer is based on the given information and assumes that there are no additional factors or influences at play.

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