Simplify: 2n (n^2 + 3n + 4)

9514 1404 393

Answer:

  DJ = 48

Step-by-step explanation:

The centroid (J) divides the median into parts that have the ratio 2:1.

  DJ : JH = 2 : 1

  DJ : (DJ +JH) = 2 : (2+1)

  DJ : DH = 2 : 3

  DJ = (2/3)DH = (2/3)(72)

  DJ = 48

Answer:

Step-by-step explanation:

1 milli liter = 0.135 grams

182.8 ml = 0.135 * 182.8 = 24.678 grams

Answer:

24.678

Step-by-step explanation:

Hope this helps :)

In July, 231 units are expected to be produced, according to the production budget.

A master budget is a comprehensive budget that is built from a collection of smaller, more specialized business budgets. The master budget process is divided into two parts: an operating budget and a financial budget, each of which is made up of a succession of smaller budgets.

A sales budget is a budget that forecasts a company's total revenue for a given time period. It forecasts the company's performance based on two factors: the number of products sold and indeed the price under which they are sold.

The word "production budget" is used specifically within film production sometimes, more broadly, in business. The term "film production budget" refers to the amount of money that will be spent on the complete film project. It entails identifying and estimating cost items for each stage of filmmaking.

The budgeted price per unit is = $65

Budgeted unit sales for  July = 15000.

Units should be manufactured in July = ?

The sales budget basically reflects the anticipated sales revenue for the next accounting quarter. It is simply prepared merely displaying the predicted sales quantity multiplied by that of the unit selling price.

sales budget for July = Units selling price ×  expected units to be sold.

15000 = 65 x expected units to be sold

expected units to be sold = 15000/65

                                           = 231 (approx.)

Units should be manufactured in July =  231 (approx.)

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Answer:

25% are red

Step-by-step explanation:

The fraction of the pencils that are red is

3/12 = 1/4

Changing to decimal form

.25

Multiply by 100 to get a percent

.25 * 100

25%

Answer:

14.42 units

Step-by-step explanation:

Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:

AB² = AC² + BC²

AB² = 12² + 8²

AB = √(12² + 8²)

AB = 14.42 units

Answer:

0.4 would represent the strongest correlation.

Step-by-step explanation:

Generally, a value of r greater than 0.7 is considered a strong correlation. Anything between 0.5 and 0.7 is a moderate correlation, and anything less than 0.4 is considered a weak or no correlation

Answer:

Julio Dempsey's taxable wages are $21,900.

Step-by-step explanation:

Taxable wages can be described as the part of the gross pay of an employee that a particular type of tax is to deducted.

Withholding allowance can be described as an exemption that reduces the amount of income tax that is deducted by an employer from the paycheck of an employee.

Gross pay refers to the total earnings of an employee before any deductions are made to arrive at the taxable wages.

Based on the explanation above, Julio Dempsey's taxable wages can be calculated as follows:

Taxable wages = Gross pay - Withholding allowance = $23,400 - $1,500 = $21,900

Therefore, Julio Dempsey's taxable wages are $21,900.

Answer:

24

Step-by-step explanation:

8*3=24

Answer:

24

Step-by-step explanation:

We are supposed to replace 'x' with '3' and then evaluate.

==========================================

\(8x; x = 3\\\rule{150}{0.5}\\8(3)\\\\8 \times 3\\\\\boxed{24}\)

==========================================

Hope this helps!

Therefοre , the sοlutiοn οf the given prοblem οf vοlume cοmes οut tο be the clοsest pοssible respοnse is 7.09, οr 0.28 in3, sο the cοrrect respοnse is:0.28 in3.

The vοlume οf a three-dimensiοnal οbject, which is measured in cubic units, describes hοw much rοοm it οccupies. Litre and in3 are the emblems fοr cubic measurements. The bulk οf an οbject, hοwever, can be used tο estimate its measurements. Usually, the οbject's weight is transfοrmed intο mass units like grammes and kilοs.

Here,

Each cοin's vοlume is calculated by multiplying its base area by its height:

=> V = πr²h

=> 3.14 x 1.2 x 0.0625 x 0.02835

=>0.02835 cubic inches (rοunded tο five decimal places)

The sum οf the weights οf all the cοins is:

=> Tοtal vοlume = V * 250, οr

=>  V * 0.02835 * 250, οr

=> 7.0875 cubic inches (rοunded tο fοur decimal places)

The cοins therefοre οccupy abοut 7.09 cubic inches οf the treasure chest (rοunded tο the nearest hundredth).

The clοsest pοssible respοnse is 7.09, οr 0.28 in³, sο the cοrrect respοnse is: 0.28 in³

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Thematic Analysis is a process that is used to analyze the text in research in qualitative research. It aims to find the patterns in the data by examining the contents of the text.

In the Qualitative Descriptive Study Design, thematic analysis is utilized to analyze the data obtained from interviews, observation, or other qualitative methods. This method involves the identification of themes and patterns in the data. It helps the researcher to organize the data, identify patterns, and develop the categories and themes that will be used to describe the findings of the study.

Thematic Analysis is used in Qualitative Descriptive Study Design to provide an in-depth understanding of the research topic. It allows the researcher to capture and analyze the rich and diverse experiences of the participants in the study. In this method, data is collected from the participants, and the researcher analyzes the data by identifying the common themes and patterns that emerge from the data. This process of analysis is done in a systematic and iterative manner until the researcher identifies all the themes that are relevant to the research question.

Thematic analysis is useful in qualitative research because it allows the researcher to identify the themes and patterns in the data that are not explicitly stated by the participants. It helps to identify the underlying meanings of the data and to develop a deeper understanding of the research topic. This method is particularly useful when the researcher is dealing with large volumes of data and wants to identify the key themes and patterns that emerge from the data.

In conclusion, Thematic Analysis is a useful method of analysis in Qualitative Descriptive Study Design. It is used to analyze the data obtained from interviews, observation, or other qualitative methods. This method involves the identification of themes and patterns in the data and helps the researcher to organize the data, identify patterns, and develop the categories and themes that will be used to describe the findings of the study.

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The z-score 30 points below the mean is -3

The normal distribution of scores has a standard deviation(σ) of 10

Below the mean is (X-μ)=-30

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Z=(X-μ)/σ

Z=-30/10

Z=-3

Therefore, the z-score is -3.

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Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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The value of y which is one of the leg of the given right angled triangle to the nearest tenth is 178.3 feet.

Given a right angled triangle.

We have to find the length of y, which is one of the leg.

Length of hypotenuse = x

Length of one of the leg = y

Length of other leg = 350 feet

Also,

One of the angle = 27°

We have to find the side opposite to 27°.

Adjacent side to 27° is given which is of length 350 feet.

So, using trigonometric ratio of tangent function,

tan (27°) = opposite side / adjacent side

tan (27°) = y / 350

y = 350 × tan (27°)

y = 178.3 feet

Hence the value of y is 178.3 feet.

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Answer:

The red marbles.

Step-by-step explanation:

It is because Red has the least amount of marbles, therefore it is most likely for you to not pull out a red marble.

The equation that describes a line passing through (4, -1) and perpendicular to y = 2x - 4 is y = 2x +6, y = 2x +6. The correct option is D.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Perpendicular lines have the same negative reciprocal slope as the line they are perpendicular to, which is important information to know.

This indicates that you may calculate the slope of the perpendicular line by taking the slope of the first line, adding a negative sign, and switching the numerator and denominator.

Therefore, the correct option is D. y = 2x +6, y = 2x +6.

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The side lengths that could be used to create a right triangle would be = 20, 21, 29. That is option C.

A right angle triangle is the type of triangle that has one side angle of 90° while the other two are less then 90°.

And in a right triangle, the square of the hypotenuse(the longest side of the triangle) is equal to the sum of the squares of the other two sides.

Thus, c²=b²+a²

The side lengths that could be used to creat a right angle triangle is 20, 21, 29.

where 29 = c = hypotenus

21= b = opposite side

20= a = adjacent side.

To prove this;

29² = 21²+20²

841 = 441 + 400

841 = 841

Therefore, the side length would be = 20, 21, 29.

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Answer:

B, negative

Step-by-step explanation:

When we look at lines on graphs, we see it from left to right. This can help you remember that if the line gets higher from left to right, it is positive. On the other hand, this line descends from left to right, meaning the slope is negative.

(a) The probability of observing a sample proportion of defective chips of 0.127 or less is approximately 0.063.

(b)The probability of observing a sample proportion within this range is approximately 0.982.  

What is the probability of collecting a sample of 212 computer chips and observing a sample proportion of defective chips of 0.127 or less, assuming a true proportion of defective chips of p = 0.1?

The probability of observing a sample proportion of defective chips of 0.127 or less, given a true proportion of p = 0.1 and a sample size of 212, is approximately 0.063. This probability can be calculated using the binomial distribution formula, taking into account the sample size, the observed proportion, and the true proportion of defective chips.

(a) To calculate the probability of observing a sample proportion of defective chips of 0.127 or less, given a true proportion of p = 0.1 and a sample size of n = 212, you can use the binomial distribution. The formula for calculating this probability is:

\(P(X\leq x)=\sum^x_{i=0}[(^nC_i) * p^i * (1-p)^{n-i}]\)

In this case, x = 0.127 * 212 = 26.924 (rounded to the nearest integer). Using R or Desmos, you can calculate the probability as follows:

\(P(X\leq 26)=\sum^x_{i=0} [(^{212}C_i) * (0.1)^i * (0.9)^{212-i}]\)

The result is approximately 0.063.

(b) To calculate the probability of observing a sample proportion of defective chips that is within two standard errors of the true population proportion, you need to calculate the standard error first. The standard error (SE) for a sample proportion is given by:

\(SE = \sqrt{\frac{(p * (1-p)}{ n}\)

In this case, p = 0.1 and n = 212. Calculate the standard error using this formula:

\(SE = \sqrt{\frac{(0.1 * (1-0.1)}{212}\)

The result is approximately 0.0169.

Next, you need to find the range within two standard errors of the true population proportion, which is (p - 2SE, p + 2SE).

Calculate this range:

Lower bound = 0.1 - 2 * 0.0169

Upper bound = 0.1 + 2 * 0.0169

The lower bound is approximately 0.0662, and the upper bound is approximately 0.1338.

To calculate the probability of observing a sample proportion within this range, you can use the cumulative distribution function (CDF) of the normal distribution. Using R or Desmos, you can calculate this probability as follows:

P(Lower bound ≤ X ≤ Upper bound) = P(X ≤ Upper bound) - P(X ≤ Lower bound)

The result is approximately 0.982.

Therefore,

(a) The probability of observing a sample proportion of defective chips of 0.127 or less is approximately 0.063.

(b)The probability of observing a sample proportion within this range is approximately 0.982.  

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The cost of the Crayons will be $4 and the cost of the Pen will be $2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Krishnan had $10. He had to purchase a box of pastels and a pen. A case of pastels costs two times as much as a pen. He got a $4 change.

Let c be the cost of crayons and p be the cost of a pen. Then the equations are given as,

c = 2p                       ...1

c + p = 10 - 4            ...2

From equations 1 and 2, then we have

2p + p = 10 - 4

3p = 6

p = 2

Then the cost of the crayons will be given as,

c = 2 x 2

c = 4

The cost of the Crayons will be $4 and the cost of the Pen will be $2.

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Answer: what is the question

Step-by-step explanation:

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

After 5 years, Account Y earns more interest than Account X, even though the annual interest rate is slightly higher for Account X.

To compare the interest earned on Account X and Account Y, we can use the following formulas

For Account X

Simple interest = P × r × t

Where P is the principal, r is the annual interest rate, and t is the time in years.

For Account Y

Compound interest = P × \((1 + r/n)^{nt}\) - P

Where P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using the given information, let's say we invest $10,000 in both accounts for 5 years.

For Account X

Simple interest = 10,000 × 0.021 × 5 = $1,050

For Account Y

Compound interest = 10,000 × (1 + 0.024/1)⁵ - 10,000 = $1,268.24

So, after 5 years, Account Y earns more interest than Account X, even though the annual interest rate is slightly higher for Account X. This is because Account Y compounds the interest annually, which means the interest earned in each year is added to the principal, resulting in a higher total amount of interest earned over time.

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Answer:

Step-by-step explanation:

use substitution and solve this 8x+4(-2x+3)=12

with the 4 distributed its

8x-8x+12=12

then you can cancel out the 8x and -8x and switch the 12 over into a -12 canceling out the 12s making it x=0

Answer:

  -6 < x < 2

  see attached for a graph

Step-by-step explanation:

You want the solution to 3 > -x -3 > -5 expressed as an inequality and as a graph.

Multiplying by -1, we need to reverse the inequality symbols:

  -3 < x + 3 < 5

Now, we can subtract 3 to get the solution as an inequality.

  -6 < x < 2

The graph is in the attachment.

__

Additional comment

There are open circles at the boundary points because the "less than" (<) inequality means the boundary points are not included in the solution set.

Therefore, the equation \(+3 + 5(2n - 1)^2 + n^2 + D(n + 2)\) is true for every positive integer n.

To verify the equation for every positive integer n using induction, we'll follow the steps of mathematical induction.

Step 1: Base Case

Let's check if the equation holds true for n = 1.

For n = 1:

\(3 + 5(2(1) - 1)^2 + 1(1) + D(1 + 2)\)

\(3 + 5(1)^2 + 1 + D(3)\)

3 + 5 + 1 + D(3)

9 + D(3)

At this point, we don't have enough information to determine the value of D. However, as long as the equation holds for any arbitrary value of D, we can proceed with the induction.

Step 2: Inductive Hypothesis

Assume that the equation holds true for an arbitrary positive integer k. That is:

\(3 + 5(2k - 1)^2 + k^2 + D(k + 2)\)

Step 3: Inductive Step

We need to prove that the equation also holds true for n = k + 1, based on the assumption in the previous step.

For n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\\3 + 5(2k + 1)^2 + (k + 1)^2 + D(k + 3)\)

Expanding and simplifying:

=\(3 + 5(4k^2 + 4k + 1) + (k^2 + 2k + 1) + D(k + 3)\\3 + 20k^2 + 20k + 5 + k^2 + 2k + 1 + Dk + 3D\)

Combining like terms:

=\(21k^2 + 22k + 9 + Dk + 3D\)

Now, we compare this expression with the equation for n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\)

We can see that the expression obtained in the inductive step matches the equation for n = k + 1, except for the constant terms 9 and 3D.

As long as we choose D in a way that makes 9 + 3D equal to zero, the equation will hold true for n = k + 1 as well. For example, if we set D = -3, then 9 + 3D = 9 - 9 = 0.

Step 4: Conclusion

Since the equation is true for the base case (n = 1) and we have shown that if it holds for an arbitrary positive integer k, it also holds for k + 1, we can conclude that the equation is true for every positive integer n.

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The speed of travel will be 4 m/s.

The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).

The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.

Total distance=10+30=40

speed=distance/time=40/10=4m/s

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Answer:

54

Step-by-step explanation:

We'll call the number "ab".

From left to right, the value of this number will be \(10a+b\).

From right to left, the value of this number will ve \(10b+a\).

From the question,

\(10a+b=1.2(a+10b)\\10a+b=1.2a+12b\\8.8a=11b\)

For a and b to be whole numbers,

\(\left \{ {{a=5} \atop {b=4}} \right.\)

So the number is 54.