Evaluate the
expression:
(52 - 42) = 3

Answer:

Step-by-step explanation:

\(f(x)=\frac{u}{v} ,u~ and~ v~ functions~ of~ x\\f'(x)=\frac{v ~u'-u~v' }{v^2} \\f(x)=\frac{x^4}{x^2-4} \\f'(x)=\frac{(x^2-4)*4x^3-x^4(2x)}{(x^2-4)^2} \\=\frac{2x^3(2x^2-8-x^2) }{(x^2-4)^2} \\=\frac{2x^3(x^2-8)}{(x^2-4)^2}\)

In comparing the New Hampshire State Constitution to the U.S. Constitution and analyzing the New Hampshire state court structure, several similarities were found.

Both constitutions establish a system of government with a separation of powers among legislative, executive, and judicial branches. They also provide protections for individual rights and liberties, including freedom of speech and due process. In terms of court structure, both the New Hampshire state court system and the federal court system include trial courts, appellate courts, and a highest court. These similarities reflect the influence of the U.S. Constitution on state constitutions and the desire to maintain a consistent framework of governance and justice.

Both the New Hampshire State Constitution and the U.S. Constitution share common features that reflect the principles of democratic governance and the protection of individual rights. Both constitutions establish separate branches of government - legislative, executive, and judicial - to prevent the concentration of power. They also guarantee certain fundamental rights and liberties, such as freedom of speech, religion, and assembly, as well as the right to a fair trial and due process of law. These similarities demonstrate the influence of the U.S. Constitution on state constitutions, including the New Hampshire State Constitution, as many states sought to incorporate similar principles and safeguards.

In terms of court structure, both the New Hampshire state court system and the federal court system follow a similar hierarchy. They have trial courts, where cases are initially heard and decided, appellate courts that review decisions made by lower courts, and a highest court that serves as the final authority on legal matters. This parallel structure ensures that legal disputes can be resolved at multiple levels of review and allows for consistency and uniformity in the application of the law.

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Answer:

c = 2

Step-by-step explanation:

To solve this equation, you need to combine like terms and then divide by the coefficient of the variable on both sides of the equation.

To start, add 12c and 6c because they are like terms.

12c + 6c = 18c

Then, divide by 18 on both sides of the equation to solve for c.

18c = 36

----     ----

18      18

c = 2

The greater probability is the probability of winning through the use of regular defense.

If out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well

Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.

The probability to win by regular is 38 / 50 = 0.76

the probability to win by prevent defense is 29 / 50 = 0.58

0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.

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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?

Play the "regular" defense.

Play a "prevent" defense that guards against long gains but makes short gains easier.

The coach reviews the outcomes of 100 games.

Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Part A

The probability of getting diamonds on the first draw is 13/52 since we have 13 diamonds out of 52 total.

The probability of getting a non-diamond card on the second selection is 39/51 since we have 39 non-diamond cards out of 52-1 = 51 cards left over. Whatever card that was selected first is not put back. In this scenario, we are picking exactly one diamond card.

The probability of both events occurring is (13/52)*(39/51) = 13/68. I skipped a few steps but hopefully you can see how I arrived at that fraction.

The same probability shows up if we had a non-diamond card drawn first followed by a diamond card. This is because we compute (39/52)*(13/51) = 13/68.

So overall, the answer as a fraction is 13/68 + 13/68 = 26/68 = 13/34

The answer in decimal form is roughly 13/34 = 0.3824 which converts to 38.24%

---------------

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

Part B

We're told that "given the first card drawn was a diamond" so we only need to worry about the second card.

We have 13-1 = 12 diamonds left out of 52-1 = 51 total.

The probability of picking another diamond is 12/51 = 0.2353 approximately. This converts to 23.53%

-----------------

8 fluid ounces are in one serving is the required fluid ounces in one serving.

Given that,

There are 8 fluid ounces in a cup, how many fluid ounces are in one serving is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

There are 8 fluid ounces in 1 cup and in a serving of one cup there will be 8 fluid ounces.

Thus, 8 fluid ounces are in one serving is the required fluid ounces in one serving.

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Answer:

Add the lengths:

5x - 16 + 2x - 4 = 7x - 20

Answer:

55 square feet jsjjjis the answer

The number of books in her summer reading list is = 20

The number of books that has been read by Emma = 14

The percentage of books that has been read by Emma  = 70%

But the percentage of books in Emma summer reading list = 100%

∴ The number of books in her reading list= ˣ

That is ;

           70% = 14

          100% = ˣ

Make ˣ the subject of formula,

            ˣ = 100 × 14 / 70

            ˣ = 20

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Zach decided to read the Game of Thrones for his summer project. The book has 450 pages, and Zack wanted to be done reading within 10 days.

He decided to set up a table that will help him consistently read the same number of pages for a total of 10 nights. How many pages will he read each night?Zach wants to read the book of 450 pages within 10 days. He plans to read the same number of pages every night for 10 nights, to achieve this purpose.

To know how many pages Zach will read every night, we can create an equation and solve it. Let the number of pages Zach reads every night be ‘x’. Then, the total number of pages read in 10 nights = Number of pages read every night × Total number of nights= 10xOn the other hand, the total number of pages in the book is 450 pages. As Zach has to read the entire book, we can equate the two expressions of the total number of pages as: Total number of pages = 10x= 450 pages. By solving this equation, we can find the value of x, which will be the number of pages that Zach reads every night.10x = 450 pagesx = 45 pages Therefore, Zach needs to read 45 pages every night to finish reading the Game of Thrones within 10 days.

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Answer:

5.20.10

Step-by-step explanation:

Answer:

85+35 = 120

175-120 = 55

55 + 250 = 305

Step-by-step explanation:

hope it helps!

Answer:

305

Step-by-step explanation:

The difference between the masses of Jupiter and Saturn is 1.33 x 10²⁷.

Mass of Jupiter is given as, 1.898 x 10²⁷.

Mass of Saturn is given as , 5.68 x 10²⁶.

We have to find the mass difference of Jupiter and Saturn :

therefore,

Mass of jupiter is 1.898 x 10²⁷

Mass of Saturn is  5.68 x 10²⁶ = 0.568 x 10²⁷

Difference = mass of jupiter  - mass of saturn

= 1.898 x 10²⁷ - 0.568 x 10²⁷

= (1.898 -  0.568) x 10²⁷

= 1.33 x 10²⁷

Therefore, The difference between the masses of Jupiter and Saturn is 1.33 x 10²⁷.

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Complete question:

Work out the difference between the masses of jupiter and saturn, give your answer in standard form

Jupiter's Mass - 1.898 x 10^27

Saturn - 5.68 x 10^26

Answer:

(5) 84° and 96° ; (6) 40° and 50°

Step-by-step explanation:

5) Supplementary angles are in the ratio 7 : 8

So 7x + 8x = 180°

15x = 180

x = 180/15

x = 12

The angles are 7x = 7 * 12 = 84° ; 8x = 8 * 12 = 96°

6) Complementary angles are in the ratio 4 : 5

So 4x + 5x = 90°

9x = 90

x = 90/9

x = 10

The angles are 4x = 4 * 10 = 40° ; 5x = 5 * 10 = 50°

Even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

Let R be a relation that is reflexive and transitive. We want to prove that R2 = R for any relation R with these two properties.

To prove this, we need to show that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R.

First, let's consider (a, b) ∈ R2. By definition, (a, b) ∈ R2 means that there exists an element c such that (a, c) ∈ R and (c, b) ∈ R.

Since R is reflexive, we know that (a, a) ∈ R and (b, b) ∈ R.

By the transitivity of R, if (a, c) ∈ R and (c, b) ∈ R, then (a, b) ∈ R.

Therefore, (a, b) ∈ R2 implies (a, b) ∈ R.

Now, let's consider (a, b) ∈ R. Since R is reflexive, we have (a, a) ∈ R and (b, b) ∈ R.

By the definition of R2, (a, a) ∈ R2 and (b, b) ∈ R2.

Since R is transitive, if (a, a) ∈ R2 and (a, b) ∈ R2, then (a, b) ∈ R2.

Therefore, (a, b) ∈ R implies (a, b) ∈ R2.

We have shown that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R. Hence, R2 = R.

If the relation R is anti-reflexive, it is not necessarily true that R2 is anti-reflexive.

To understand why, let's consider an example. Let R be a relation defined on the set of integers such that R contains the ordered pairs (a, b) where a < b.

In this case, R is anti-reflexive because for any integer a, (a, a) is not in R.

Now, let's consider R2. R2 is the composition of R with itself. If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R2.

In our example, if we take a = 1, b = 2, and c = 3, we have (1, 2) ∈ R and (2, 3) ∈ R. Therefore, (1, 3) ∈ R2.

However, (1, 1) is not in R2 because (1, 1) is not in R. Therefore, R2 is not anti-reflexive in this case.

This example demonstrates that even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

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The perimeter for each possible region is 140 feet, 148 feet, and 160 feet when the length of the rectangle is 40 feet, 50 feet or 60 feet, respectively.

Given that you want to enclose a rectangular region with an area of 1200 square feet and a length of 40 feet, 50 feet, or 60 feet.

We are to find the perimeter for each possible region.

Area of rectangle = length x breadth

Now, we are given the area of the rectangle as 1200 square feet and length as 40 feet, 50 feet or 60 feet.

Therefore, the breadth of the rectangle can be calculated as follows:

Breadth = Area/Length

We get the following breadth for each of the given lengths:

For length 40 feet,

breadth = 1200/40 = 30 feet

For length 50 feet, breadth = 1200/50 = 24 feet

For length 60 feet, breadth = 1200/60 = 20 feet

Now, we can use the formula to calculate the perimeter of each rectangle.

Perimeter of rectangle = 2 (length + breadth)

So, the perimeter for each possible region is given by:

Perimeter when length = 40 feet

Breadth = 30 feet

Perimeter = 2(40+30) = 2(70) = 140 feet

Perimeter when length = 50 feet

Breadth = 24 feet

Perimeter = 2(50+24) = 2(74) = 148 feet

Perimeter when length = 60 feet

Breadth = 20 feet

Perimeter = 2(60+20) = 2(80) = 160 feet

Therefore, the perimeter for each possible region is 140 feet, 148 feet, and 160 feet when the length of the rectangle is 40 feet, 50 feet or 60 feet, respectively.

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Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.

The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.

Here,

Given :

Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).

In order to determine what data they use,

From the information provided, it is clear that they are using second-party data.

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.

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i. Mean: 24.8

  Standard Deviation: Approximately 3.56

ii. X-intercept with a negative value of x: (-1, 0)

   X-intercept with a positive value of x: (5, 0)

   Y-intercept: (0, 5/6) or approximately (0, 0.833)

   Vertical Asymptote: x = 6

iii. The sample space for selecting three data points is:

   {22, 22, 23}, {22, 22, 27}, {22, 22, 30}, {22, 23, 27}, {22, 23, 30}, {22, 27, 30}, {22, 27, 23}, {22, 30, 23}, {22, 30, 27}, {23, 27, 30}

   The mean of the sample space is approximately 25.25.

b. The 95% confidence interval for the mean weight of all adults is approximately (70.004, 75.996).

i. To find the mean and standard deviation of the given data set: 22, 22, 23, 27, 30.

Mean:

To find the mean, we sum up all the values and divide by the number of data points.

Mean = (22 + 22 + 23 + 27 + 30) / 5 = 124 / 5 = 24.8

Standard Deviation:

To find the standard deviation, we can use the following formula:

Standard Deviation = sqrt((sum of squared deviations) / (n - 1))

First, we find the squared deviation for each data point by subtracting the mean from each value, squaring the result, and summing them up.

Squared Deviations:

\((22 - 24.8)^2\) = 7.84

\((22 - 24.8)^2\) = 7.84

\((23 - 24.8)^2\) = 3.24

\((27 - 24.8)^2\) = 4.84

\((30 - 24.8)^2\) = 27.04

Sum of Squared Deviations = 7.84 + 7.84 + 3.24 + 4.84 + 27.04 = 50.8

Now we can calculate the standard deviation:

Standard Deviation = sqrt(50.8 / (5 - 1)) = sqrt(50.8 / 4) = sqrt(12.7) ≈ 3.56

ii. Sample space for selecting three data points:

To find the sample space for selecting three data points from the given data set, we consider all possible combinations. Since order doesn't matter, we use combinations rather than permutations.

Sample Space: {22, 22, 23}, {22, 22, 27}, {22, 22, 30}, {22, 23, 27}, {22, 23, 30}, {22, 27, 30}, {22, 27, 23}, {22, 30, 23}, {22, 30, 27}, {23, 27, 30}

Mean of the sample space:

To find the mean of the sample space, we calculate the mean for each combination and take the average.

Mean = (24.8 + 24.8 + 25 + 24 + 25 + 26.33 + 24 + 25 + 26.33 + 26.67) / 10 ≈ 25.25

iii. Probability sampling distribution for x:

Since we have only one sample of the given data, the probability sampling distribution for x will be the same as the sample space calculated in part ii. The sample space represents all the possible outcomes when three data points are selected randomly from the given data set.

Sample Space: {22, 22, 23}, {22, 22, 27}, {22, 22, 30}, {22, 23, 27}, {22, 23, 30}, {22, 27, 30}, {22, 27, 23}, {22, 30, 23}, {22, 30, 27}, {23, 27, 30}

b. To construct a 95% confidence interval for the mean weight of all adults, we can use the following formula:

Confidence Interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size)))

Given:

Sample size (n) = 8

Sample mean = (70 + 72 + 65 + 80 + 75 + 76 + 68 + 78) /

8 = 584 / 8 = 73

Sample standard deviation = calculated based on the given data set

Critical value for a 95% confidence interval = 1.96 (for a sample size of 8)

First, we need to calculate the sample standard deviation:

Squared Deviations:

\((70 - 73)^2\) = 9

\((72 - 73)^2\) = 1

\((65 - 73)^2\)= 64

\((80 - 73)^2\) = 49

\((75 - 73)^2\) = 4

\((76 - 73)^2\)= 9

\((68 - 73)^2\) = 25

\((78 - 73)^2\)= 25

Sum of Squared Deviations = 186

Sample standard deviation =\(\sqrt(186 / (8 - 1))\) =\(\sqrt186 / 7)\) ≈ 4.33

Now we can construct the confidence interval:

Confidence Interval = 73 ± (1.96 * (4.33 / sqrt(8)))

Confidence Interval = 73 ± (1.96 * (4.33 / 2.83))

Confidence Interval = 73 ± (1.96 * 1.529)

Confidence Interval = 73 ± 2.996

The 95% confidence interval for the mean weight of all adults is approximately (70.004, 75.996).

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The Solution:

Given that the volume of the cylindrical tank is:

In this case,

Substituting these values in the above formula, we get

Therefore, the correct answer is approximately 9047.8 cubic feet.

Answer:

Hello!! Your answer is 25% I think!

Hope this helps!!

Answer:

Yes, in a Cartesian Coordinate system each point is given by two numbers. If the question is "where" the function has a max or min value, that's "x", the first number in pair. If the question is "what" is that max or min function value, thats "y", the second number in the pair

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer: *x squred +3x-10*

Step-by-step explanation:

(x+5)(x-2)

x squred-2x+5x-10

x squred +3x-10

The equation ( x + 5 ) ( x - 2 ) can be simplified as x² + 3x - 10

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be = A

Now , the equation A = ( x + 5 ) ( x - 2 )

On simplifying the equation , we get

A = x ( x - 2 ) + 5 ( x - 2 )

Expanding the brackets , we get

A = x² - 2x + 5x - 10

On simplifying the equation , we get

A = x² + 3x - 10

Therefore , the value of A is x² + 3x - 10

Hence , The equation ( x + 5 ) ( x - 2 ) can be simplified as x² + 3x - 10

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Based on the information provided, we cannot conclusively determine how drivers react to sudden large increases in the price of gasoline. However, we can use the recorded speeds of cars passing the service station before and after the price increase to determine if there is a statistically significant difference in speeds.

A hypothesis test can be conducted to determine if there is a significant difference in means between the two groups. If the p-value is less than the significance level, we can conclude that the speeds differ and suggest that the price increase had an impact on driver behavior. However, if the p-value is greater than the significance level, we cannot conclude that there is a significant difference in speeds and suggest that other factors may have influenced driver behavior.

To determine how drivers react to sudden large increases in the price of gasoline, we can follow these steps:

1. Collect data: The statistician recorded the speeds (mph) of cars passing a large service station before and after the price of gasoline increased by 15 cents.

2. Analyze the data: Compare the recorded speeds before and after the price increase to see if there's a noticeable difference.

3. Conduct a hypothesis test: Perform a statistical test to determine if the observed differences in speeds are significant or due to chance. For example, you can use a paired t-test or another appropriate test based on the data collected.

4. Draw conclusions: If the test shows a significant difference in speeds, we can conclude that drivers' behavior changed in response to the price increase. Otherwise, we cannot confidently say that the speeds differ due to the price increase.

By following these steps, you can determine if drivers' speeds differ as a result of sudden large increases in the price of gasoline.

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Answer:

174

Step-by-step explanation:

All 3 angles in a triangle add up to 180.

So we are given 2 angles and we need to find angle 3. I am going to call the missing 3rd angle 'x'.

1 + 5 + x = 180.

Solve for x

6 + x = 180

Subtract 6 from both sides

x = 174