(gauß’s lemma) show that if f(x), g(x) ∈ r[x] are both primitive, then so is their product f(x)g(x).

Answer:

44.8 cm

Step-by-step explanation:

Vertical height (h) = EM = 20 cm

Slant height (l) = 30 cm

This two heights form a right angle at the interception at the base. Thus, we have a right angle triangle.

The length of the sides of the base = 2 × the base of the right triangle

✔️Use Pythagorean theorem to find the base of the right triangle formed. Thus: c² = a² + b²

a = base of the triangle

b = h = 20 cm

c = l = 30 cm

Plug in the values

30² = a² + 20²

a² = 30² - 20²

a² = 500

a = √500

a = 22.4 cm

✔️length of the sides of the base = 2 × the base of the right triangle

= 2 × a

= 2 × 22.4

= 44.8 cm

The solution is the median dress size = 12.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

given that,

from the given data we get,

dress sizes are, 10, 12 , 14, 16

no. of dresses,   16, 38, 27, 19

Hence, using the formula we get, the median dress size = 12.

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Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

see explanation

Step-by-step explanation:

\(\frac{2}{1+e^{-2} }\) ← evaluate \(e^{-2}\) using calculator

= \(\frac{2}{1+0.135}\)

= \(\frac{2}{1.135}\)

= 1.762.....

≈ 1.8 ( to 1 dec. place )

Step-by-step explanation:

Hint : we will check for each option whether it is an experiment or not by using the concepts of probability first we will check then if a coin is tossed then it is an experiment or not ? then we will check that if a dice is rolled is it an experiment or not and then we will repeat the same process for choosing a marble from a jar

complete step by step answer and event is a set of outcomes of an experiment to which probability is assigned as take an example when we and I the possibility of 5 appearing on the die is an event if for tossing a coin we do not know the result when a coin is tossed in can give any result whether it will be a head or tails so this is an example for a random experiment if a six-sided dice will be rolled then we do not know what is about to come there result can be anything from 126 so it is also an example for random experiment choosing a marble from a jar is also an experiment because we are choosing one marble from the jar and experiment is a work in which a result can be anything hence option d is the correct option not probability is how likely something is about to happen when a coin is tossed there are two possibility outcomes heads or tails show the probability of an outcome 1

( number of ways it can happen )÷

( total number of outcomes)

so when a coin is tossed the total number of outcomes are to solve the probability of a current head is 1/2

Answer: Choice A) The mode is greater than the median

Mode = 95, median = 90

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

Explanation:

The mode is the most frequent value. In this case, the mode is 95. All we do is look for the highest bar, and then record the x value connected with it. The higher the bar, the more frequent the value.

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

The median will take a bit more work, but it's not too bad.

First add up the heights of every bar shown:

2+3+4+6+7+10+5 = 37

So there are 37 scores. The median will be in the very exact middle. Divide 37 over 2 to get 37/2 = 18.5

Erase off the 0.5 and we can say that 18 values are below the median, and 18 values are above the median. So we have 18+1+18 = 37 values total.

The median will be in slot 18+1 = 19.

From here, we add up the bar heights (starting on the left and working toward the right). We're trying to see when we reach 19 or higher, since the median is in that 19th slot.

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

To summarize:

The mode is larger than the median.

This is why choice A is the answer.

Answer:

A- The mode is the greater than the median

Step-by-step explanation:

Answer:

Top right: quadrant 1

Top left: quadrant 2

Bottom left: quadrant 3

Bottom right: quadrant 4

The first number of an ordered pair is the x axis, and the second is the y axis

A: 10,3 quadrant 4

B:8, 9 quadrant 2

c: 3,2 Q 3

D: 4,0 Q4

E:4,7 Q3

F: 8,7 Q1

G: 0,7 Q4

H: 1,5 Q1

The perimeter of the isosceles trapezoid is equal to 456 feet which makes the option c correct.

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

We shall first find the length of the left and right sides which are of same length as follows:

3x - 2 = 2x + 3

3x - 2x = 3 + 2

x = 5

PQ = 6(25) - 10 = 140

QR = 3(25) - 22 = 53

RS = 9(25) - 15 = 210

PS = 2(25) + 3 = 53

perimeter of the Isosceles trapezoid = 140ft + 53ft + 210ft + 53ft

perimeter of the Isosceles trapezoid = 456ft.

Therefore, the perimeter of the isosceles trapezoid is equal to 456 feet which makes the option c correct.

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A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

         deviations of the mean.

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

a) The probability of Type I error is determined by the test level α and the rejection region R. Since the test is two-tailed, the level of significance is α/2 on each end.

The probability of Type I error is given by the area under the sampling distribution's density curve in the rejection region. When λ = λ0, the test statistic is Z0 ~ N(0,1). Let k be the positive integer such that P(Z > k) = α/2, then the rejection region is R: {Z ≥ k} ∪ {Z ≤ -k}.

b) Let c be the quantity for which P(∑Yi ≥ c | λ = λ0) = α/2, then the rejection region is R: {∑Yi ≥ c}. If λ = λa, the Poisson distribution has a mean nλa and the test statistic is Z = (∑Yi - nλa)/√(nλa), which is approximately N(0,1) for large n. For large n, the rejection region for a level α test is R: {∑Yi ≤ c'} ∪ {∑Yi ≥ c''}, where P(∑Yi ≤ c' | λ = λ0) = P(∑Yi ≥ c'' | λ = λ0) = α/2.

c) If the test from (a) is uniformly most powerful, then for any 0 < λ < λ1, the power function of the test will be greater than or equal to that of the test at λ1. However, the power function of the test at λ = λ1 is a monotonically decreasing function of λ, so the test from (a) is not uniformly most powerful.

d) If λ = λ0, the test statistic is Z0 ~ N(0,1). Let k be the positive integer such that P(Z < -k) = α, then the rejection region is R: {Z ≤ -k}.

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\( \frac{9}{ - j} \)

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer: 17

Step-by-step explanation:

First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps

Answer

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

Answer

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

Answer:x=2

Step-by-step explanation:

-1 goes to postive 1 and adds with 3 whitch ecuals 4 then it is 2x=4 and you divide 2/4 and that equals 2 so x=2

Answer:

x = 2

Step-by-step explanation:

\(2x - 1 = 3 \\ 2x - 1 + 1 = 3 + 1 \\ 2x - 2 = 3 + 1 \\ 2x = 3 + 1 \\ 2x = 4 \\ x = 4 \div 2\)

\(\boxed{\green{\boxed{\bold{x = 2}}}}\)

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Answer:

x=2

Step-by-step explanation:

-7x+14+15-5x=4x-3

-12x+29=4x-3

-12x-4x=-29-3

-16x=-32

x=-32/-16

x=2

Answer: x=2

Step-by-step explanation:

Simplify the equation

-12+29= 4x-3

Subtract 29 from both sides

12x=4x-32

Subtract 4x from both sides (Simplify)

-16x=-32

Divide both sides by -16

x=2

The inverse Laplace transform of F(s) = 10(s²+1) / [s² (s + 2)] is f(t) = 5t - 5sin(2t) + \(10e^(^-^2^t^).\)

To find the inverse Laplace transform of F(s), we first express F(s) in partial fraction form. The denominator s² (s + 2) can be factored as s² (s + 2) = s² (s + 2). Using partial fraction decomposition, we can express F(s) as:

F(s) = A/s + B/s² + C/(s + 2),

where A, B, and C are constants to be determined.

Next, we multiply both sides of the equation by the common denominator s² (s + 2) to eliminate the denominators. This gives us:

10(s²+1) = A(s + 2) + Bs(s + 2) + Cs².

Expanding and collecting like terms, we have:

10s² + 10 = As + 2A + Bs² + 2Bs + Cs².

Comparing coefficients of s², s, and the constant term on both sides of the equation, we can determine the values of A, B, and C. Solving the resulting system of equations, we find A = 5, B = -10, and C = 0.

Now, we have the expression for F(s) in terms of partial fractions as:

F(s) = 5/s - 10/s² - 10/(s + 2).

To find the inverse Laplace transform of F(s), we use the inverse Laplace transform table to obtain the corresponding time-domain functions for each term. The inverse Laplace transform of 5/s is 5, the inverse Laplace transform of -10/s² is -10t, and the inverse Laplace transform of -10/(s + 2) is \(10e^(^-^2^t^).\)

Finally, we add the inverse Laplace transforms of each term to obtain the solution f(t) = 5t - 5sin(2t) + \(10e^(^-^2^t^)\).

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Answer:

(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).

Answer:

Step-by-step explanation:

Answer:

x<2

Step-by-step explanation:

x<2;

The open circle means that this inequality is not inclusive.

If the circle was filled in the inequality would have been x\(\leq\)2

The solution for the system of equations is (-19,55).

As given the equations in the question

y = –3x – 2

Simplify the above

y + 3x = -2

5x + 2y = 15

Multiply y + 3x = -2 by 2 and subtracted from 5x + 2y = 15.

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Putting the value of x in the equation y + 3x = -2.

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

Therefore the solution for a system of equations is (-19,55).

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Answer:

d=6+2t

Step-by-step explanation:

Let

t=number of ten dollar bills

d=number of dimes

Number of dimes is six more than two times the number of ten dollar bills

d=6+2*t

d=6+2t

The final amount of salt in the tank when it is full will be 140 kilograms.

The rate of salt entering the tank is 0.1 kilograms per liter × 10 liters per minute = 1 kilogram per minute. At the same time, the rate of water leaving the tank is 5 liters per minute. Thus, the net increase in water volume is 10 liters per minute - 5 liters per minute = 5 liters per minute.

- To find the final amount of salt in the tank, we need to determine how much salt enters the tank during the time it takes to fill it completely. Since the tank initially contains 200 liters of water with 10 kilograms of salt, the ratio of salt to water is 10 kilograms / 200 liters = 0.05 kilograms per liter.

- To fill the remaining 400 liters of the tank (600 liters - 200 liters), it will take 400 liters / 10 liters per minute = 40 minutes. During this time, the amount of salt entering the tank is 1 kilogram per minute × 40 minutes = 40 kilograms.

Adding the initial amount of salt to the salt entering the tank, we get a total of 10 kilograms + 40 kilograms = 50 kilograms of salt in the tank when it is full. However, we also need to consider the removal of water from the tank. Since 5 liters per minute are being removed, after 40 minutes, 5 liters per minute × 40 minutes = 200 liters of water have been removed.

The final amount of water in the tank when it is full is 600 liters - 200 liters = 400 liters. Therefore, the ratio of salt to water in the tank is 50 kilograms / 400 liters = 0.125 kilograms per liter.

Multiplying this ratio by the tank's capacity of 600 liters, we find that the final amount of salt in the tank when it is full is 0.125 kilograms per liter × 600 liters = 75 kilograms.

However, we need to account for the 200 liters of water that was initially in the tank. This water already contained 10 kilograms of salt, so we subtract that from the total. Hence, the final amount of salt in the tank when it is full is 75 kilograms - 10 kilograms = 65 kilograms.

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Answer:

-5 1/8

Step-by-step explanation:

-5 1/8

Answer:

3486784401

Step-by-step explanation:

Hi! 9 to the 10th power is written like this: \(9^{10}\). It equals 3,486,784,401. The equation is written like this: 9×9×9×9×9×9×9×9×9×9, NOT 9×10. I hope this helps you! Good luck and have a great day. ❤️

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

The answer is D. No, because the curve indicates that the rate of change is not constant.

Step-by-step explanation:

There is not a constant rate of change which results in a curved line.

Answer:

It is the last one: No, because the curve indicates that the rate of change is not constant.

Step-by-step explanation:

You can tell in the picture that if you connected the points it would not create a straight line.

Answer: The product of 5 and a number

Step-by-step explanation:

The expression 5n represents the product of 5 and a number. For example, let the number be 8. Therefore, the value of the expression will be:

= 5n

= 5 × 8

= 40

The sum of 5 and a number will be:

= 5 + n

The difference of 5 and a number will be:

= 5 - n

Answer:

99750000 people

Step-by-step explanation:

1,750,000*57=99750000