Suppose $a$ and $b$ are positive integers such that $\gcd(a,b)$ is divisible by exactly $7$ distinct primes and $\mathop{\text{lcm}}[a,b]$ is divisible by exactly $28$ distinct primes. If $a$ has fewer distinct prime factors than $b$, then $a$ has at most how many distinct prime factors

it take for all the water to drain from the tank is 1 hour 11 min 26 sec for a water tank is shaped like a vertical circular cylinder

Using the Bernoulli's laws to use the conserved energy

Solve the speed and the radio of this speed of the tank is open to the air

p₀ + ρgh₀ + ½ρv₀² = p₁ + ρgh₁ + ½ρv₁²

5000Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ *

v²

v² = 25.68  m²/s²

v1 = 5.06 m/s

Because it is open the cylinder tank so P=0 pa so:

0 Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ * v²

v² = 15.68  m²/s²

v2 = 3.96 m/s

The ratio on the air is solve using both velocities so:

R = v1/v2 = 5.06 m/s / 3.96 m/s

R = 1.27

Now to find the time it takes for the tank to drain if the tank is open to the air

dh/dt = -u

dh/dt = -v * A/A'

dh/dt = v*(.02m)²/(2.0m)² = -v / 10000

and we can further substitute for v:

dh/dt = -(1/1e4)*√[(p+9800h)/500]

Solve replacing

-(1000/49)*√(49000h) = t + C

-(1000/49)*√(49000*0.8) = 0 + C

C = - 4040.6

Then when h = 0,

t = 4286 s

t = 1 hr, 11 min, 26 sec  

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So, theta = arctan(sqrt(500^2-d^2) / d) would give us the angle between the ground and the ladder where d is distance from the base of the ladder to the building.

The angle between the ground and the ladder can be found using the inverse tangent function (also known as arctan) and the Pythagorean theorem.

First, we need to find the ratio of the height of the ladder to the distance from the base of the ladder to the building. This ratio is known as the tangent of the angle between the ground and the ladder.

Let h be the height of the ladder and d be the distance from the base of the ladder to the building.

tan(theta) = h/d

Next, we can use the Pythagorean theorem to find the value of h:

d^2 + h^2 = 500^2

Now we can substitute the value of h in the first equation.

tan(theta) = sqrt(500^2-d^2) / d

To find the angle between the ladder and the ground, you can use the inverse tangent function on the above equation.

theta = arctan(sqrt(500^2-d^2) / d)

To find the exact value of the angle, you would need to know the value of d (distance from the base of the ladder to the building).

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The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

The inequality, [tex]y < -3x+6[/tex] represents the following graph.

Income gap, gender inequality, access to health care, and social class are some of the most prominent examples of social inequality. Some people receive better and more skilled care in the medical field than others.

Rule 1: An inequality symbol remains unchanged when the same amount is added to or subtracted from both sides. Rule 2: The inequality symbol remains unchanged when both sides are multiplied or divided by a positive number.

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Answer:

C) 8 : 1

Step-by-step explanation:

To find our ratio, we will multiply both sides by 20 to get rid of fractions, this gives us:

[tex]\frac{2}{5} * 20 : \frac{1}{20} * 20[/tex]

8 : 1

So, the ratio is C) 8 : 1.

The reason the answer is C), and not B) is because C) is the most simplified form.

Hope this helped!

Answer:

The answer is C) 1:8

Step-by-step explanation:

2/5 is equal to 8/20

so if you compare 8/20 to 1/20 the answer is c

Answer: Hello sorry i read the question wrong at first. but the answer id relation 1, 2 and 3.

Step-by-step explanation: all inputs (x) have to have different outputs (y) :)

Solution Grade 7 is a saturated, neutral pH liquid solution made up of a mixture of water and salt, or other electrolyte, with a specific gravity of 1.0, a boiling point of 100°C, and a high electrical conductivity.

Solution Grade 7 is a type of liquid solution used in science experiments. It is typically made up of a mixture of water and salt, or some other electrolyte. It has the following properties:

1. It is a saturated solution, meaning that it contains the maximum amount of dissolved solute that the solvent can hold at a given temperature.

2. It has a neutral pH, meaning that it is neither acidic nor basic.

3. It has a specific gravity of 1.0, meaning that it has a density equal to that of pure water.

4. It has a boiling point of 100°C (212°F), meaning that it boils at the same temperature as pure water.

5. It has a high electrical conductivity, meaning that it can easily conduct electricity.

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Check the picture below.

If Genry worked for 6 consecutive days and earned an average wage of $144 per day as a freelance handyman. Genry earned $142 on the last day.

Total amount  earned for the first 3 days =$132 × 3

Total amount  earned for the first 3 days = $396

Total amount he earned for the next 2 days =$163 ×2

Total amount he earned for the next 2 days = $326

Total amount he earned for all 6 days = $144 x 6

Total amount he earned for all 6 days = $864

Now let find the amount Genry earned on the last day

Amount earned = $864 - $396 - $326

Amount earned = $142

Therefore  Genry earned $142 on the last day.

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Answer:

x=6

Step-by-step explanation:

[tex] \cos(60) = \frac{x}{12} \\ x = 12 \cos(60) = 6[/tex]

Answer: The relationship between salary per week (s), number of weeks worked (w), and total income (t) is t = s * w.

Where t is the total income, s is the salary per week, and w is the number of weeks worked.

In Robert's case, s = $300, the equation would be t = $300 * w, where w is the number of weeks worked.

This equation shows that the total income (t) is directly proportional to the number of weeks worked (w) and the salary per week (s)

So, if Robert earns $300 every week, this equation would be t = $300 * w

Step-by-step explanation:

 If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.

  The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.

 We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.

  Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis  consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.

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According to the Pythagorean theorem length of the third side is  [tex]\sqrt{5}[/tex].

What is Pythagorean theorem?

The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagoras theorem. A and B are the triangle's two legs, and C is the hypotenuse, hence this theorem can be written as c2 = a2 + b2. These triangles are also referred to as Pythagorean triangles.

Here in given right triangle side = 2 and hypotenuse = 3.

Now using Pythagorean theorem then,

=> [tex]side^2+side^2=hypotenuse^2[/tex]

=> [tex]side^2+2^2=3^2[/tex]

=> [tex]side^2[/tex]+4=9

=>  [tex]side^2[/tex] = 9-4 = 5

=> side = [tex]\sqrt{5}[/tex]

Hence third side length of the right triangle is [tex]\sqrt{5}[/tex].

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For given data , the equation of the regression line is:

y = 2.03 ln(x) - 0.205

Consider given data.

x  1 |  2   |   3   |  4    |   5        

y  1 | 21  | 121 | 621 | 3121

We need to find the equation of the regression line, if the given data linearized using logarithms.

Now we find the logarithms of y-values.

log(1) = 0

log(21) = 1.322

log(121) = 2.0828

log(621) = 2.7931

log(3121) = 3.4943

So, we get coordinates of the points: (1, 0), (2, 1.322), (3, 2.0828), (4, 2.7931), (5, 3.4943)

from the graph of given data, the equation of the regression line is:

y = 2.03 ln(x) - 0.205

where slope of the regression line is 2.03

and the y-intercept is c = -0.205

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The US GDP (Gross Domestic Product) for 2014 was reported to be the nearest hundredth is 17. 56 trillion dollars. The current US population is about 320 million people to the nearest hundredth.

The gross domestic product (GDP) is a commonly used indicator of the value added produced by the production of goods and services in a country over a certain time period (GDP). As a result, it also takes into account the money made from that manufacturing or the sum of money spent on finished goods and services (fewer imports). Although the gross domestic product (GDP) is the most important indicator for gauging economic activity, other metrics may be better suitable for gauging people's material well-being.

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Two congruent right triangles are formed by the tangents and the line connecting P to the circle's centre. They are congruent because one of the pairs of matching sides in each of those two triangles is represented by the tangent segments from P to the sites of tangency with the circle.

The kite-shaped quadrilateral that is created by the two radii and the two tangents has two pairs of adjacent sides.

The radii, the tangents, and the line from P to the centre of the circle combine to form two congruent right triangles. The tangent segments from P to the sites of tangency with the circle are congruent because they represent one of the pairs of corresponding sides in each of those two triangles.The two radii and the two tangents combine to form a quadrilateral with two pairs of adjacent sides, which is why it is a kite.

Lines that cross a circle at a single point are known as tangents.  Where the tangent crosses the radius of the circle, it is perpendicular to the tangent. Any curved shape can take into account tangent. Since the tangent is a straight line, its equation will take the form y = m x+ c .

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Devon's expression had the greatest value which is 20.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a mathematical value or relationship. Expressions can be simple or complex, and they can take on many different forms depending on the context.

They are also used to represent real-world problems, and also used to evaluate mathematical expressions to get numerical results.

Step-by-step explanation:

Let's use t=1 to compare all the expressions:

1. -5(12t+9)

if t = 1, -5(12+9) = -5(21) = negative number

2. 2(-6t-8)

if t = 1, 2(-6-8) = 2(-14) = negative number

3. -6(-2t+18)

if t = 1, -6(-2+18) = -6(16) = negative number

4. (-4(-3t-2)

if t = 1, -4(-3-2) = -4(-5) = 20 positive number

Therefore, Devon's expression had the greatest value which is 20.

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The negative z-score = -0.84 and the Positive Z-score = 0.84.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The shaded region in the question is symmetric about z = 0 and forms the middle part of the distribution.

Standard deviation is a measure of the spread or dispersion of a set of data. It tells us how much the individual observations in a dataset vary from the mean of the dataset.

The formula for the standard deviation of a dataset is:

σ = √( Σ (x_i - μ)^2 / n)

The middle shaded region is known as the central region, it represents the middle part of the distribution, and it covers the area between two Z-scores, one negative and one positive. The area of the central region is typically given as a percentage.

For example, if the shaded region represents 68% of the total area under the standard normal distribution curve, then the two Z-scores that form the boundaries of the shaded region are the Z-scores that correspond to the 16th and 84th percentiles of the standard normal distribution. These Z-scores are -0.84 and 0.84 respectively.

So, the negative z-score = -0.84 and the Positive Z-score = 0.84.

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The total time that will have elapsed when 12.5 grams of the original co-60 sample at the hospital remains unchanged is 16 years

A radioactive isotope of cobalt with a half-life of 5.2713 years is cobalt-60.Nuclear reactors are used to artificially create it. Neutron activation of bulk samples of the monoisotopic and mononuclidic Co-59 is necessary for deliberate industrial manufacture.

Let, the initial amount of the Co 60 = 100 = A

Final amount = 12.5 = A'

We will use the following relation for calculating time elapsed in the decay

[tex]A' = A\frac{1}{2} ^{\frac{t}{t1/2} }[/tex]

Thus,

   [tex]A' = A\frac{1}{2} ^{\frac{t}{t1/2} }[/tex]

[tex]12.5 = 100(\frac{1}{2}) ^{\frac{t}{5.2713} }[/tex]

(1/2)³ = [tex](\frac{1}{2}) ^{\frac{t}{5.2713} }[/tex]

3 = t/ 5.2713

t= 3 x 5.2713

t = 15.8139 ≅ 16 years

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Answer:

Step-by-step explanation:

A five-digit palindromic number is a number that has 5 digits and is the same when read forwards and backwards. A multiple of 45 is a number that is divisible by 45.

To find the largest five-digit palindromic number that is a multiple of 45, we need to find the largest five-digit palindrome and then find the largest multiple of 45 that is less than or equal to that palindrome.

The largest five-digit palindrome is 99999. The largest multiple of 45 less than or equal to 99999 is 99945.

To find the smallest five-digit palindromic number that is a multiple of 45, we need to find the smallest five-digit palindrome and then find the smallest multiple of 45 that is greater than or equal to that palindrome.

The smallest five-digit palindrome is 10001. The smallest multiple of 45 greater than or equal to 10001 is 10035.

To find the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45, we can subtract the smallest from the largest:

99945 - 10035 = 8910

So the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45 is 8910.

The ratio of 2 or more integers is known as fraction. The answer to the given expression is 3 13/16

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

Given the expression below:

15/4 + 7/12 x 3/28

Required

Simplified form of the expression

On solving, we will have;

15/4 + (7/12 x 3/28)

15/4 + (1/4 x 1/4)

15/4 + 1/16

Find the LCM of the resulting sum

15/4 + 1/16= [4(15)+1]/16

15/4 + 1/16 = 61/16

15/4 + 1/16 = 3 13/16

Hence the answer to the given expression is 3 13/16

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it would be 1oclock the next day

Data about a population is collected, recorded, and counted in a census.  The numerical summary measures obtained from the analysis of this population data are referred to as parameters.

Censuses of agriculture, traditional culture, businesses, supplies, and even transportation are also prevalent, while the phrase is most often associated with national population and housing counts.

The UN defines the essential characteristics of population and housing censuses as "individual enumeration, universality within a defined territory, simultaneity, and defined periodicity," and suggests that population censuses be conducted at least once every ten years.

The United Nations has made recommendations for what information should be collected in a census, including official definitions, classifications, and other data that might help international organizations coordinate their efforts.

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Answer:

t - 2 = the number of treats remaining.

Step-by-step explanation:

Answer:

Step-by-step explanation:

t-2

Answer:

x=27.5 hope it helps you..... and hi

Answer:

Step-by-step explanation:

1....Re-order terms so constants are on the left;

2(x - 3) =49

2.. Distribute;

2x-6 =49

3... Add 6 to both sides;

2x-6+6=49+6

4... Simplify;

2x=55

5..Divide both sides by the same factor;

2x=55

[tex]\frac{2x}{2}[/tex]  = [tex]\frac{55}{2}[/tex]

6...Simplify;

x=[tex]\frac{55}{2}[/tex]

Paying from his UK account will be More profitable.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A Kenyan businessman US$100 to a company in the United States of America. The Kenyan can either pay through his account in Kenya or through his account in the United Kingdom.

if he pays in US Dollars:

1 US Dollar = 76.84 Kenya Shillings

100 US Dollars = 7,684 Kenya Shillings

If he pays in UK pounds:

1 Sterling Pound = 1.53 US dollars

And, 1 Sterling pound = 115.70 Kenya shillings

1 US Dollar = 1/1.53 US Pound

Thus,  1 US Dollar = 1/1.53 * 115.70 Kenya shillings

 1 US Dollar = 75.62  Kenya shillings

100 US Dollar = 7,562.09  Kenya shillings  

Therefore, Paying from his UK account will be More profitable.

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Answer:

Step-by-step explanation:

It is unclear what is being asked in this question. The information provided does not make logical sense and it's hard to understand what is being asked. Could you please provide more information or rephrase the question?

There are 30240  different id cards can be made if there are five digits on a card and no digit can be used more than once.

a) If repetition is allowed, then there are 10 ways to choose each of 5 digits. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is:

10⋅10⋅10⋅10⋅10 = 10⁵= 100000.

b) If repeats are not allowed, there are 10 ways to choose the first number, 9 ways to choose the second number (because we chose 1 digit as the first number), and 9 ways to choose the third number. There are 8 ways, 7 ways, and 7 ways to choose the 4th number. 6 ways to select the digit to select and the 5th digit.

So according to the multiplication rule the answer is:

10 × 9× 8×7×6 = 30240.

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The probability that the sample mean nicotine content is less than 0.77 is approximately 0.0003.

The probability that the sample mean nicotine content will be less than 0.79 can be found by using the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. Since the sample size is 100, we can assume that the sample means nicotine content is approximately normally distributed.

The mean of the sample means nicotine content is equal to the population means, which is 0.8 mg. The standard deviation of the sample means nicotine content is equal to the population standard deviation divided by the square root of the sample size. So, the standard deviation of the sample means nicotine content is 0.1 mg/sqrt (100) = 0.01 mg.

Using these values, we can find the probability that the sample mean nicotine content is less than 0.79 by using the standard normal distribution table or calculator.

z = (0.79 - 0.8) / 0.01 = -1

Using a standard normal table or calculator, P(z < -1) = 0.1587.

So, the probability that the sample mean nicotine content is less than 0.79 is approximately 0.1587.

Similarly, for the sample mean nicotine content less than 0.77

z = (0.77 - 0.8) / 0.01 = -3

P(z < -3) = 0.0003

So, the probability that the sample mean nicotine content is less than 0.77 is approximately 0.0003

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