Let f(x) E Z[x] with deg (f(x)) ≥ 1, and let f(x) be the polynomial in Z, [x], where p is prime integer, obtained from f(x) by reducing all the coefficients of f(x) modulo p. Assume that deg (F(x)) = deg(f(x)), then: If f(x) is reducible over Q. then f(x) is irreducible over Z O This option If f(x) is reducible over Zp, then f(x) is reducible over Q If f(x) is reducible over Zp, then f(x) is reducible over Q O This option None of choices

Given parameters:

  Evaluate;

             \(\sqrt[4]{(16)^{-2} }\)

Now let us solve this;

           \(\sqrt[4]{(16)^{-2} }\);

     the fourth root can be expressed  as the power of    \(\frac{1}{4}\) ;

    \(\sqrt[4]{(16)^{-2} }\)   =     [(16)⁻²]\(^{\frac{1}{4} }\)

                     =  (16)\(^{-2 x \frac{1}{4} }\)

                      = (16)\(^{\frac{-1}{2} }\)

                      =     \(\frac{1}{16^{\frac{1}{2} } }\)

                     =    \(\frac{1}{\sqrt{16} }\)

                     =  \(\frac{1}{4}\)

The solution is \(\frac{1}{4}\)

Answer:

Step-by-step explanation:

To find the difference in temperature between the day's high and low, we need to subtract the low temperature from the high temperature.

The high temperature is 18 degrees, and the low temperature is -6 degrees.

So, the difference in temperature between the day's high and low is:

18 degrees - (-6 degrees)

= 18 degrees + 6 degrees

= 24 degrees

Therefore, the difference in temperature between the day's high and low is 24 degrees.

The solution to the system of equation is (0, 3)

Inequalities are equation that are not separated by an equal sign. Given the following system of inequality to have:

2x + 3y > -3
2x + y ≥3

Subtract to have;

3y - y ≥ -3 - 3

-2y ≥ -6

Divide both sides by -2 to have:

y ≤ -6/-2

y ≤ 3

Substitute the value of y into any of the equation to have:

2x + y ≥3
2x ≥3 - 3
x ≥ 0

Hence the solution to the system of equation is (0, 3)

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To evaluate the predictive performance of the tree model, we need to create the lift chart using the test data and analyze its shape.

A lift chart is a graphical representation of the performance of a predictive model. It can be used to evaluate the effectiveness of a model in identifying a target variable, compared to a random guess. The lift chart shows how much better the model is performing than a random guess, at different levels of the target variable.

To produce a lift chart for a decision tree model, we typically first rank the test data according to the predicted probabilities of the target variable. Then, we divide the data into equal-sized segments, called quantiles, based on the predicted probabilities. For example, if we divide the data into 10 quantiles, the first quantile will contain the 10% of cases with the lowest predicted probabilities, the second quantile will contain the next 10% of cases, and so on, up to the 10th quantile, which will contain the 10% of cases with the highest predicted probabilities.

For each quantile, we calculate the ratio of the number of cases in that quantile that have the target variable to the number of cases we would expect to see if the model was performing no better than random chance. This ratio is called the lift, and it represents how much better the model is performing than random chance, at that level of the target variable.

We can then plot the lift for each quantile on a graph, with the x-axis representing the quantiles and the y-axis representing the lift. A good model will have a lift chart that is above the diagonal line, which represents the performance of a random guess.

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Therefore:

Answer:

244140625

5¹²

it is a sequence of numbers in which each term is obtained by multiplying the preceding term by a constant. In other words, the ratio between a term and its preceding term is constant. And that constant is common ratio. Therefore, 12th term is 244140625.

Answer:

For the first attachment the answer is C

Step-by-step explanation:

Add up all the marbles which comes to 50, add the blue and green which is 15. 15/50 divided is 3/10

For the second attachment, I'm not too sure. Sorry  

Answer:

For the first attachment the answer is C

Step-by-step explanation:

Add up all the marbles which comes to 50, add the blue and green which is 15. 15/50 divided is 3/10

For the second attachment, I'm not too sure. Sorry  

Answer:

\(P(New\ House) = \frac{1}{6}\)

Step-by-step explanation:

Given

See attachment

Required

\(P(New\ House)\)

This is calculated as:

\(P(New\ House) = \frac{New\ House}{Total}\)

From the attachment, we have:

\(New\ House = 60^o\)

\({Total}= 360^o\) --- total angle in a pie chart

Note that the measurements must be converted to degrees (if not already in degrees).

So, we have:

\(P(New\ House) = \frac{60}{360}\)

Simplify

\(P(New\ House) = \frac{1}{6}\)

Answer:

y = -7/2x +17

Step-by-step explanation:

First, lets put the original equation into slope intercept form which is y=mx+b

7x + 2y = -8

subtract 7x on both sides

2y = -7x -8

divide by 2 on both sides

y = -7/2x - 8/2

y = -7/2x - 4

now we can plus in any x and y values to get a new b, which is our y intercept.

lets use (4,3)

Also, since they are parallel, their slope (m) will be the same.

y = -7/2x + b

3 = -7/2(4) + b

3 = -14 + b

b = 17

lets plug in our new b into our original equation

y = -7/2x + 17

The value of [y] = 7 and that of [x] = 6.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have a equation that represents a line as -

7x + 2y = - 8

We can write -

7x + 2y = - 8

2y = - 7x - 8

y = (-7/2)x - 4

Options are not given, so the line whose slope will be (-7/2) will be parallel to the given line with equation 7x + 2y = - 8

Therefore, line whose slope will be (-7/2) will be parallel to the given line with equation 7x + 2y = - 8

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Answer:

10

Step-by-step explanation:

if thay had 20 eggs in 3 days then u take 12 chikens witch is adding

4 new chikens from the 8  the times then its what divided by 20 givs ur answer <3 have funnn

Answer:

a)

10 days

b)

36 chicken

Step-by-step explanation:

Because i know how to do it

Therefore , the solution of the given problem of unitary comes out to be each asset class as part of the diversification plan.

By combining the information obtained using this nanosection technique with all variable additional data from two individuals who used a specific strategy, the task can be completed. Simply put, this mean that, if the desired outcome materialises, either the specified entity will be known or, actually, the colour from both enormous processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

The next two are methods for reducing the danger associated with investing out of the four you offered:

Dollar-cost averaging is the term used to describe this method of spreading investments out over time. Regardless of the investment's price, it entails making a set amount of investments at regular intervals over a length of time.

Spread your investments across various asset classes (such as stocks, bonds, real estate, etc.) and/or various companies within each asset class as part of the diversification plan.

Since currency values can be influenced by a number of variables and are sometimes unpredictable, investing in a particular currency (such as the British pound) is not always a risk management plan.

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She should use 16 quarts of sand for obtaining total of 52 quarts of mixture. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are believed to be explicable by the four fundamental operations, sometimes known as "arithmetic operations." Mathematics places operations such as quotient, product, sum, and difference after operations such as division, multiplication, addition, and subtraction.

We are given that with every 1\(\frac{1}{2}\) quarts of potting soil,, two-thirds quart of sand is to be mixed.

So, from this we get

Total mixture = 1\(\frac{1}{2}\) + \(\frac{2}{3}\)

Total mixture = \(\frac{13}{6}\) quarts

Now, on dividing sand and total mixture by 13, we get

\(\frac{2}{39}\) quarts of sand produces in total \(\frac{1}{6}\) quarts of mixture.

Now, on multiplying sand and total mixture by 6, we get

\(\frac{12}{39}\) quarts of sand produces in total 1 quarts of mixture.

So,

⇒ For 52 quarts of mixture = \(\frac{624}{39}\) quarts of sand

⇒ For 52 quarts of mixture = 16 quarts of sand

Hence, she should use 16 quarts of sand for obtaining total of 52 quarts of mixture.

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The complete question has been attached below.

Answer:

132

Step-by-step explanation:

The average rate of change over a function can be given by: f(b)-f(a)/b-a. Where b is the second part of the interval and a is the first part.

y = 6x^3-6x^2-8

____

x = 2

6(2)^3-6(2)^2-8

6(8)-6(4)-8

48-24-8

24-8

16

____

x = 4

6(4)^3-6(4)^2-8

384-96-8

288-8

280

_____

280-16/4-2 = 264/2 = 132

Using the scale factor of 4:1, the side lengths of the real objects are:

B. Side a is 5 inches long and side b is 4.5 inches long.

A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.

Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.

Therefore, the sides would be:

Side a = 20/4 = 5 in.

Side b = 18/4 = 4.5 in

The answer is B.

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Answer:

C

Step-by-step explanation:

twenty-one and ninety-five thousandths

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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Keiko purchased a prepaid phone card for $25 . long distance calls cost 9 cents a minute using this card. If the remaining credit on her card is $23.92 , then the call lasted for 12 minutes.

When Keiko made her call, she used some of the credit on her prepaid phone card. To find out how many minutes her call lasted, we need to determine the cost of the call and divide that by the cost per minute.

First, we find the difference between the original value of the card ($25) and the remaining value ($23.92), which gives us the cost of the call: $25 - $23.92 = $1.08.

Next, we need to determine the cost per minute for the long distance calls made with the card. We know that the calls cost 9 cents per minute, so we convert this to dollars: 9 cents * $0.01/cent = $0.09/minute.

Finally, we divide the cost of the call by the cost per minute to get the number of minutes: $1.08 / $0.09/minute = 12 minutes. So, Keiko's call lasted for 12 minutes.

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The total cost of an order is $900 if 50 invitations cost is $298.50

To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.

Let calculate the cost of each invitation and the one-time design fee as follows:

50 Invitations: $298.50 / 50 = $5.97 per invitation

500 Invitations: $2049 / 500 = $4.098 per invitation

Design Fee: ($2049 - ($5.97 × 50)) / 500

= $3.90 one-time design fee

If you wanted to order 150 personalized invitations, the cost would be:

150 Invitations x $5.97 per invitation = $896.50

Plus one-time design fee of $3.90 = $890.40

Total cost = $896.50 + $3.90 = $900.

Hence, the total cost of an order is $900 if 50 invitations cost $298.50

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The probability that the sample proportion will be 0.104.

What is Probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something has been likely to happen is basically what probability means. You will learn the potential outcomes for just a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total list of answers is necessary before we can calculate the likelihood that a specific event will occur.

Given that

p= 0.06

1 - p = 1 + 0 * 6 = 0 * 94

n = 221

p' = p = 0.06

sigma( p) = \(\sqrt{\frac{P(1 - P))}h{} }\)

= \(\sqrt{\frac{0.06*0.94}{221} }\)

=0.0159

p( p' > 0.1 )=1-p( p' <0.1)

= 1 - p(z < 2.51)

=1- .896

= 0.104

Hence the Probability will be 0.104

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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The correct option that accurately classifies each angle as acute, right, obtuse, or straight is:

A. LKN = 45°, acute;

HKL = 135°, obtuse;

HKN = 180°, straight

It should be noted that acute angles are the angles that are less than 90°. Therefore, in this case, LKN has 45° and is therefore an acute angle.

It should be noted that an obtuse angle is the angle that is greater than 90° and less than 180°. Therefore, HKL is 135° and is therefore an obtuse angle.

A straight angle is an angle that the sides lie in opposite directions for the vertex and it equals two right angles which will be 180°. Therefore, HKN is a straight angle.

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The trigonometric ratios of the right triangle with the given value tan A = 9 / 40 are

sin A = 9 / 41

cos A = 40 / 41

Trigonometric ratios are used to solve for the sides and angles of a right angle triangle.

Therefore,

sin A = opposite / hypotenuse

cos A = adjacent / hypotenuse

tan A = opposite / adjacent

Using Pythagoras theorem, let find the hypotenuse side

c² = 40² + 9²

c = √1681

c = 41

Therefore,

sin A = 9 / 41

cos A = 40 / 41

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(a) The probability that a pair of running shoes lasts within 2 months of the advertised average is approximately 0.2788.

(b) Approximately 63.21% of running shoes will last within 7 months of the advertised average of 13 months.

We can model the lifespan of a pair of running shoes using an exponential distribution with parameter λ = 1/13, where λ is the rate parameter. Then, the probability density function (PDF) of the exponential distribution is:

f(x) = λe^(-λx) for x >= 0

where x is the time (in months) that a pair of shoes lasts.

(a) We want to find the probability that a pair of running shoes lasts within 2 months of the advertised average of 13 months. That is, we want to find P(11 <= x <= 15). Using the cumulative distribution function (CDF) of the exponential distribution, we can calculate this probability as:

P(11 <= x <= 15) = F(15) - F(11)

where F(x) is the CDF of the exponential distribution:

F(x) = 1 - e^(-λx)

Plugging in λ = 1/13, we get:

P(11 <= x <= 15) = (1 - e^(-15/13)) - (1 - e^(-11/13))

= e^(-11/13) - e^(-15/13)

≈ 0.2788

Therefore, the probability that a pair of running shoes lasts within 2 months of the advertised average is approximately 0.2788.

(b) We want to find the percentage of running shoes that last within 7 months of the advertised average of 13 months. That is, we want to find P(x <= 20). Using the CDF of the exponential distribution, we can calculate this probability as:

P(x <= 20) = F(20)

Plugging in λ = 1/13, we get:

P(x <= 20) = 1 - e^(-20/13)

≈ 0.6321

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Answer:

It would be .841

Step-by-step explanation:

There are 1000 meters in a kilometer, and since 841 meters is 841/1000 kilometers, that is how many kilometers you would ride.

Hope this helps!

Answer:

C

Step-by-step explanation:

13/18 is .72222222

.5+.222=.722

The present worth of the tuition cost for a student planning to enroll at the university for 9 years, with the first 4 years costing $7,200 per year and a 5% annual increase for the next 5 years, can be calculated at an interest rate of 8% per year. The present worth is $23,455.297.

To calculate the present worth of the tuition cost, we need to consider the time value of money, which accounts for the fact that money in the future is worth less than money in the present. We can use the concept of present value to determine the worth of future cash flows in today's dollars.

For the first 4 years, the tuition cost is constant at $7,200 per year. To find the present value of these cash flows, we can use the formula for the present value of a fixed cash flow series. Applying this formula, we find that the present value of the first 4 years' tuition cost is

\(7,200 + 7,200/(1+0.08) + 7,200/(1+0.08)^2 + 7,200/(1+0.08)^3.\)

For the next 5 years, the tuition cost increases by 5% per year. We can use the concept of future value to calculate the value of these cash flows in the last year of the 9-year period. Applying the formula for future value, we find that the tuition cost in the last year is \($7,200*(1+0.05)^5.\)

Finally, we can sum up the present value of the first 4 years' tuition cost and the future value of the tuition cost in the last year to obtain the total present worth of the tuition cost for the 9-year period.

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The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Values that will satisfy the given inequality be 5,6 and 7.

What do you mean by natural number?

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Given inequality:

n > 4

Values that will satisfy the given inequality be 5,6 and 7.

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