Prove that there exists a positive integer n < 10^6 such that 5^n has six consecutive zeros in its decimal representation

Answer:

D

Step-by-step explanation:

because

( 5 + 2 + 1 ) is (x + y + z)

Answer:

=> A/Q,

m + 3m + 2m+ 3m 360° =

9m = 360°

m = 360/9

m = 40°

Angle A = m = 40°

Angle B = 3m = 120°

Angle C 2m = 80° =

Angle D = 3m = 120°

the set of all z ∈ (-3,1) such that neither 2+z nor 2-3z is in the interval (-1,2].

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities.

the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2].

here, we shall assume two cases,

case first.

z > -1,

2+z > -1

z > -1 -2

z > -3

and,

2-3z > -1

-3z > -3

z > 1

z belongs to ( -3 , 1)

case 2nd,

z<=2

2+z < = 2

z <= 2-2

z ≤ 0

and 2-3z ≤ 2

-3z ≤ 0

z ≤ 0

z is less than equal to 0

So, by above conditions

z belongs to (-3,1).

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If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.

In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.

Here,

If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.

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The total distance traveled by the particle over 5 units of time is 140 units.

What is the total distance?

To find the total distance a particle travels over a certain time interval, we need to find the definite integral of its velocity function over that interval. The velocity function is the derivative of the position function.

In this case, the position function of the particle is x(t) = t³ - 6t + 9t - 2 and we need to find the total distance traveled by the particle over 5 units of time.

The velocity function is x'(t) = 3t² - 6 + 9 = 3t² + 3

The total distance traveled over 5 units of time is the definite integral of the velocity function evaluated between 0 and 5.

∫(3t²+3) dt from 0 to 5

= [t³ + 3t] from 0 to 5

= (5³ + 3*5) - (0 + 0) = 125 + 15 = 140

The total distance traveled by the particle over 5 units of time is 140 units.

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The most appropriate time-series plot will depend on the data being visualized. The title, axes labels, and scale should all be chosen to accurately describe the data and provide the clearest understanding of the data.

The most appropriate time-series plot for a particular dataset will depend on the data being visualized. The title, axes labels, and scale should all be chosen carefully to accurately describe the data and provide the clearest understanding of the data. For example, for a time series of stock prices, the title could be "Stock Price Over Time", the axes could be labeled "Time" and "Price", and the scale could range from the lowest to the highest stock price. Additionally, the time intervals should be appropriately labeled, such as monthly, quarterly, or annually. It is important to choose the right type of plot to ensure that the data is accurately and clearly represented.

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The complete question is

which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale should all be chosen to accurately.

Answer: ASA postulate

Step-by-step explanation:

There is a congruent side included between two pairs of congruent angles.

The rate at which shadow is decreasing On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long and is 10.4 inches per minute.

Given,

Height of the building, [tex]h[/tex] = 80 ft = 960 inches

Length of shadow, [tex]x[/tex] = 60 ft = 720 inches

The angle that the sun makes with the ground is increasing,

[tex]\frac{d\theta}{dt} = 0.27[/tex] degree [tex]= \frac{3\pi }{2000} rad/min[/tex]

[tex]tan\theta = \frac{960}{x} \\\frac{d }{dy} tan\theta = \frac{d}{dy} \frac{960}{x} \\sec^{2}\theta \frac{d\theta }{dt} = -\frac{960}{x^{2} } \\\\\frac{dx}{dt} = \frac{(60^{2})(\frac{5}{3})^{2} }{960} \\\\\\\frac{dx}{dt} = 10.4 inches /min[/tex]

Hence, the shadow is decreasing at a rate of 10.4 inches per minute.

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Answer:

-2

Step-by-step explanation:

y = −2− x 2 y = - 2 - x 2

Answer:

[tex]24x^{2}y^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}[/tex]

We can use the Binomial Theorem to find any term of a binomial expansion.  

The first term is when k = 0, so the third term is when k = 2.

Compare the given expression (x + 2y)⁴ with the formula to find the values of a, b and n.  

Therefore:

Substitute the values into the formula to find the third term:

[tex]\implies \displaystyle\binom{4}{2}x^{4-2}(2y)^2[/tex]

[tex]\implies \dfrac{4!}{2!(4-2)!}x^{2}2^2y^2[/tex]

[tex]\implies \dfrac{4 \times 3\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}{2\times 1\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}\;x^{2}4y^2[/tex]

[tex]\implies \dfrac{12}{2}\:x^24y^2[/tex]

[tex]\implies 6x^{2}4y^2[/tex]

[tex]\implies 24x^{2}y^2[/tex]

The number of years after 2003 that the car's value will be $11,250 is t = 7.5 years.

In 2003, the price of a certain automobile was approximately with a depreciation of 1,750 per year. After how many years will the cars value be $11,250 A) write an equation to model the problem. Let the represent the number of years after 2003.

A) The equation to model the problem is:

Price in year t = 2003 Price - (t - 1)(1,750)

B) To solve the equation for t, we can rearrange it to isolate t:

t = (2003 Price - 11,250) / 1,750

Therefore, the number of years after 2003 that the car's value will be $11,250 is t = 7.5 years. This means that the car's value will be $11,250 in the year 2010.5.

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The maximum area of a triangle with a base and height of 10 cm is 50 cm^2. The dimensions for this would be a base of 5 cm and a height of 5 cm.

1. The area of a triangle is calculated by taking the base multiplied by the height, then dividing by 2.

2. Since the sum of the base and the height of the triangle is 10 cm, the base and the height must be equal.

3. Therefore, the base and the height are both 5 cm, and the area of the triangle is (5 cm * 5 cm) / 2, which equals to 50 cm^2.

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The measure of the angle ∠ABC  is given by 45°

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: ΔABC with AB=√2, AM=1,BM=1 and BC=2

Now in ΔABM we have two sides equal AM=1,BM=1

and AB=√2

Thus AM²+BM²=AB²

Thus the triangle must be a right angled triangle with AB as its hypotenuse

let ∠B=Ф then we have TanФ=1/1

                                         ⇒ Ф=45°

Hence, The measure of the angle ∠ABC  is given by 45°

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Answer:

2290
ignore this--> (I need 20 words to answer the question lol)

Answer:

2290

Step-by-step explanation:

2290*3 gives 6870

Step-by-step explanation:

that's so easy just learn it times

An inequality which represents the value of t for which the water temperature is still safe is t ≤ 2 and it has been plotted in the graph attached below.

In order to write, solve, and graph an inequality that represents the value of t for which the water temperature is still safe, we would take note of the following important information;

Now, we can write an inequality that represents the value of t for which the water temperature is still safe as follows;

102 + t ≤ 104

By subtracting 102 from both sides of the inequality, we have the following:

102 - 102 + t ≤ 104 - 102

t ≤ 2

Next, we would use an online graphing calculator to graph the above inequality as shown in the image attached below.

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The required total income generated by planting corn in 2008 is the amount of $1917.85.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5

Let's find the amount of corn produced in 2008:

N(7) = 10 x 7 + 88.5 = 158.5 (kilograms)

Next, let's find the price of corn in 2008:

P(7) = 81 - 10 x 7 + 1.1 = 12.1 ($/kilogram)

Finally, we can multiply the amount of corn by the price per kilogram to find the total income:

158.5 x 12.1 = 1917.85

Rounding to the nearest cent, the total income generated by planting corn in 2008 is $1917.85.

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The smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

The smallest amount of rotation about a vertex from one ray to the other can be calculated using the formula θ = 180° - (α + β), where θ is the measure of the angle of rotation, α and β are the measures of the two rays that are connected by the vertex. The amount of rotation between two rays is measured in degrees, which is equal to the angle between the two rays. The formula used to calculate the amount of rotation is the arctangent of the ratio of the difference in the y-coordinates to the difference in the x-coordinates. For example, if the two rays have measures of 90° and 30°, the smallest amount of rotation from one ray to the other would be 60°. This can be calculated by taking 180° - (90° + 30°) = 180° - 120° = 60°. In conclusion, the smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

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The value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest. The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given first expression as 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex]

The answer for this expression can be a positive or a negative number depending on the fact which of the terms is greater.

The second expression is (-7[tex]\frac{5}{6}[/tex] ) + (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a negative number because addition of two negative numbers is always negative.

The third expression is (-7[tex]\frac{5}{6}[/tex] ) . 9[tex]\frac{3}{4}[/tex]

The answer for this expression will be a negative number because multiplication of one negative number and one positive number is always  negative.

The fourth expression is (-7[tex]\frac{5}{6}[/tex] ) ÷ (- 9[tex]\frac{3}{4}[/tex])

The answer for this expression will be a positive number because division of two negative numbers is always positive. But, dividing two numbers will give us value close to 1 because the numbers 7 and 9 are very close to each other.

Hence, the value of 7[tex]\frac{5}{6}[/tex] - 9[tex]\frac{3}{4}[/tex] is the greatest.

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A specific example of a non-representative sample can be seen in the 2016 US presidential election.

The national polls indicated that Hilary Clinton had a lead in the polls, but Donald Trump went on to win the election. This is because the sample used in the polls was not representative of the population. The sample was disproportionately composed of college-educated individuals, when the actual electorate was more evenly balanced between college-educated and non-college-educated individuals. This caused the samples to be biased and not representative of the population.

For example, if we assume that the population is composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample should also be composed of 50% college-educated individuals and 50% non-college-educated individuals to be representative. If the sample is not composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample is not representative of the population.

This can be calculated by using the formula: (Number of College Educated Individuals in Sample/Total Sample Size) X 100.

For example, if the sample size is 100 and there are 75 college-educated individuals in the sample, then the sample is not representative of the population because (75/100) X 100 = 75%, which is not equal to the 50% of the population that is college-educated.

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The third side is represented by the inequality 7 < x < 43, where x is the third side.

When you know two sides of a triangle, you can calculate the range for the third side.

Let x would be the third side.

First, since 25 - 18 = 7, the third leg must be greater than 13. Otherwise, the two smaller legs would not be able to connect to form the third leg.

Second, if we combine 18 with 25 and get 63, the third leg must be smaller than 69. Otherwise, the third leg would be able to reach further than the previous two legs.

This means 7 < x < 43.

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The interval over which the function is continuous equation is (-∞, 3) U (3, +∞).

The function f(x) = (x2 - 5x - 6)/(x - 3) is continuous over all real numbers except x = 3, since the denominator is equal to 0 at x = 3.

We can use the properties of combinations of continuous functions to determine the interval(s) over which the function f(x) is continuous equation.

First, we need to consider the function f(x) in two parts. The first part is f(x) when x ≠ 3, and the second part is when x = 3.

For the first part, when x ≠ 3, the function f(x) is continuous over all real numbers, since both the numerator and denominator are continuous over all real numbers.

For the second part, when x = 3, the function f(x) is discontinuous, since the denominator is equal to 0.

Therefore, the interval over which the function f(x) is continuous is (-∞, 3) U (3, +∞).

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The correct option is C for the frequency table.

A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.

The correct two-way frequency table for the date will look like this:

                                               RAP      ROCK     COUNTRY     TOTAL

Grades 9-10             40           30            55                  125

Grades 11-12            60           25            35                  120

TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total

125 + 120 = 100 + 55 + 90

245 = 245

The correct option for the frequency table is C.

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Using the formula for the average value between two numbers, we will see that bag B weighs 11.9 kg

If we have two values x and y, the average value between these two is given by the formula below.

average = (x + y)/2

Here we know that the average between the wheights of bags A and B is 6.4 kg, and A = 0.9kg

Then we can write the equation:

6.4kg = (B + 0.9kg)/2

We can solve that equation for B to get:

2*6.4kg = B + 0.9kg

12.8kg - 0.9kg = B

11.9kg = B

Bag B weighs 11.9 kilograms.

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Answer:

26

Step-by-step explanation:

32 - 14 + 26 - (81/9)2

Dividing

32 - 14 + 26 - (9)2

Multiplying

32 - 14 + 26 - 18

Adding & Subtracting from left to right

18 + 26 - 18

44 - 18

26

In the given oblique triangle , the required value of c using cosine rule is given by c = 34.4.

As given in the question,

In the given oblique triangle ABC,

a = 12 feet

b = 30 feet

∠A = 20°

Let us consider in triangle side opposite to angle A, B, and C are a, b, and c respectively.

Using cosine rule we have,

a² = c² + b² - 2cbcos A

Substitute the values we get,

⇒ 12² = c² + 30² - 2(c )(30) cos 20°

⇒ 144 = c² + 900 - 60c ( 0.9396)

⇒ c² -56.376c + 900 - 144 = 0

⇒ c² -56.376c +756 = 0

using quadratic formula :

c = [ ( 56.376) ± √56.376² -4(1)(756) ]/ 2

  =  [ 56.376 ± 12.42 ] / 2

  =  (56.38 + 12.42) / 2 or (56.38 - 12.42) / 2

  = 34.4 or 21.98

Correct value is c = 34.4

Therefore, using the cosine rule the required values c of the triangle is equal to 34.4 .

The above question is incomplete, the complete question is :

One of the cases for the known measures of an oblique triangle is given. In triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. State whether the Law of Cosines can be used to solve the third side of the triangle .

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The general statement for the previous question is that if a homogeneous system of equations has at least one non-zero solution, then it has infinitely many solutions, which can be found by taking multiples of the non-zero solution.

(a) (i)

Let p = (1,3,4) and q = (5,8,12) be two points in R3. The line joining p and q can be written as lq + (1-\p) where l is a real number. By substituting in the coordinates of p and q, we get l(5,8,12) + (1-\1,3,4) = (l + 1-\, l+3-\, l+4-\). This is the equation for the line joining p and q, where l can be any real number.

(ii)

To check that all points on the line joining p and q are also solutions to the system of linear equations, we substitute the equation of the line into the system of equations.

01111 + 212.22 + 213.43 = 21

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 21

Simplifying, this gives: l + 6 - \ = 21. Therefore, all points on the line joining p and q are solutions to the system.

(b)

To check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system, we substitute the equation of the multiple of p into the system.

01111 + 212.22 + 213.23 = 0

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 0

Simplifying, this gives: l + 6 - \ = 0. Therefore, all multiples of p are solutions to the system.

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The dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

What is a rectangular prism?

A rectangular prism is a solid geometric shape that has three mutually perpendicular rectangular faces, and is also known as a rectangular parallelepiped or a box. It has six faces, eight vertices, and twelve edges.

The shape is defined by three dimensions: length, width and height, and is specified by the three sets of parallel and mutually perpendicular edges that form its six faces. The opposite faces of a rectangular prism are equal in area and parallel to each other. The opposite edges are also parallel and equal in length.

You can’t get a perfect match, but you can get pretty close, with dimensions of (1,8,9), (2,5,7), (3,4,6)

Hence, the dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

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Answer:0.3

Step-by-step explanation:

answer my question next please its about zara sells apples one

Answer:3/10

Step-by-step explanation: 4x3 is 12 and 4x10 is 40, so 12/40, the GCF of these numbers are 4 so 12/4=3 and 40/4= 10

So 3/10