2 positive integers have hcf of 12 and their product as 6336 number of pairs possible for the number is​

Answer:600 students

Step-by-step explanation:

Answer:

There are 600 students participating. The operation you have to carry out is 800 × .75 = 600.

Or you can simply divide 800÷4= 200. 3/4=200×3. The percentage of students is 3/4 that would be 600 students participating.

To determine the sample size needed for work sampling to estimate a proportion with a 4% maximum error and 95.45% confidence, Hill should take 125 observations.

To determine the sample size needed for work sampling in order to be 95.45% confident that the results will not be more than 4% from the true result, we can use the following formula:n = (z*σ/E)^2

where n is the sample size, z* is the critical value from the standard normal distribution corresponding to a 95.45% confidence level, which is approximately 1.8, σ is the standard deviation of the proportion, and E is the maximum error we are willing to tolerate, which is 4% in this case.

Since we are given an initial estimate of the proportion, we can use it as an approximation for the true proportion. Therefore, the standard deviation can be estimated using the following formula:

σ = sqrt(p*(1-p)/n)

where p is the initial estimate of the proportion.

Substituting the values from the problem, we get:

1.8*sqrt(0.15*(1-0.15)/n) = 0.04

Simplifying and solving for n, we get:

n = 1.8^2*0.15*(1-0.15)/0.04^2 = 124.74

Rounding up to the nearest whole number, the answer is 125. Therefore, Hill should take 125 observations to be 95.45% confident that the results will not be more than 4% from the true result.

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Here's a possible implementation of the DivideByThree function in C:

int DivideByThree(int number) {

   int count = 0;

   while (number > 0) {

       if (number % 10 == 3) {

           count++;

       }

       number /= 10;

   }

   return count;

}

This function takes an integer number as input and returns the quotient of the division by 3 by counting how many times the number 3 appears in the original number. The function works as follows:

Initialize a counter variable count to 0.

While number is greater than 0, do the following:

a. If the last digit of number is 3 (i.e., number % 10 == 3), increment count.

b. Divide number by 10 to remove the last digit.

Return the final value of count.

For example, if we call DivideByThree(123456333), the function will count three occurrences of the digit 3 in the input number and return the value 1. If we call DivideByThree(33333), the function will count five occurrences of the digit 3 and return the value 1. If there are no occurrences of the digit 3 in the input number, the function will return 0.

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Answer:

(3,0)

Step-by-step explanation:

Answer:

x = 5, x = \(\frac{5}{2}\)

Step-by-step explanation:

Given

\(\frac{x-1}{x-2}\) + \(\frac{x-3}{x-4}\) = 3 \(\frac{1}{3}\)

\(\frac{(x-1)(x-4)+(x-3)(x-2)}{(x-2)(x-4)}\) = \(\frac{10}{3}\)

\(\frac{x^2-5x+4+x^2-5x+6}{x^2-6x+8}\) = \(\frac{10}{3}\)

\(\frac{2x^2-10x+10}{x^2-6x+8}\) = \(\frac{10}{3}\)  ( cross- multiply )

10(x² - 6x + 8) = 3(2x² - 10x + 10) ← distribute both sides

10x² - 60x + 80 = 6x² - 30x + 30 ← subtract 6x² - 30x + 30 from both sides

4x² - 30x + 50 = 0 ( divide through by 2 )

2x² - 15x + 25 = 0 ← in standard form

(2x - 5)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = \(\frac{5}{2}\)

x - 5 = 0 ⇒ x = 5

Answer:

Step-by-step explanation:

x-1/x-2+x-3/x-4=31/3

3(x²-4x-x+4)+3(x²-2x-3x+6)=31(x²-4x-2x+8)

3(x²-5x+4)+3(x²-5x+6)=31(x²-6x+8)

3x²-15x+12+3x²-15x+18=31x²-186x+248

3x²+3x²-31x²-15x-15x+186x+12+18-248=0

-25x²+156x-218=0

-(25x²-156+218)=0

By using quadratic equation

The probability that all three wires will meet the specifications is approximately 0.173 .

Expected value (mean) of wire resistance = 0.13 ohms Standard deviation of wire resistance = 0.005 ohms

the probability for each wire, we need to standardize the range of resistance values using the expected value and standard deviation. We can use the Z-score formula:

Z = (X - μ) / σ

Z is the standard score (Z-score) X is the observed value (resistance) μ is the mean (expected value) σ is the standard deviation

For the lower specification of 0.10 ohms

Z1 = (0.10 - 0.13) / 0.005

For the upper specification of 0.17 ohms

Z2 = (0.17 - 0.13) / 0.005

Using a standard normal distribution table , we can find the probability associated with each Z-score.

Lower bound of standardized range = (0.10 - 0.13) / 0.005 = -0.06

Upper bound of standardized range = (0.17 - 0.13) / 0.005 = 0.80

Let's calculate the probabilities for each wire

P(z < -0.60) ≈ 0.2743

P(z < 0.80) ≈ 0.7881

Since we want the probability that all three wires meet the specifications, we need to multiply these probabilities together since the wires are selected independently.

P(all three wires meet specifications) = P(z < -0.60) × P(z < 0.80) × P(z < 0.80)

P(all three wires meet specifications) ≈ 0.2743 × 0.7881 × 0.7881 ≈ 0.1703

Therefore, the probability that all three wires will meet the specifications is approximately 0.173, or 17.3% .

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Given :

You order 1.5 pounds of turkey at the deli.

You will accept the turkey if its weight is between 1.54 and 1.46 pounds.

To Find :

What absolute value inequality can be used to describe the tolerance of the weight of the turkey.

Solution :

It is given that the weight cannot be less that 1.46 pounds.

So, mathematical equation is :

x ≥ 1.46 .....1 )

Also, weight cannot be greater than 1.54 pounds.

x ≤ 1.54 ......2)

Combining equation 1 and 2 we get :

1.46 ≤ x ≤ 1.54

Hence, this is the required solution.

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:

\(\frac{29}{8}\)

Step-by-step explanation:

3\(\frac{3}{8}\) equals to \(\frac{27}{8}\), then we can write out the equation:

\(\frac{27}{8} + x = 7\)
then subtract \(\frac{27}{8}\)on both sides of the equal sign,

\(x = 7 - \frac{27}{8}\)

and then we calculate x

\(x=\frac{56-27}{8}\)

\(x=\frac{29}{8}\)

Thus the answer is \(\frac{29}{8}\)

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}\)

The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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Answer:

400

Step-by-step explanation:

To make this easier, you could do 352+48 and get 400 like that.

The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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The p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

The general recurrence of z-scores empowers us to decide a few things in regards to the comparing crude scores, except for deciding qualities concerning goodness or disagreeableness. The number of standard deviations a given data point has from the population mean is measured using Z-scores. In statistics, particularly normal distribution, these are frequently used to normalize data and evaluate a data point's position for improved data analysis. One of the purposes of the general recurrence of z-scores is that it permits us to work out the likelihood of an occasion happening in a standard typical conveyance.

Using mathematical software or a standard normal table, the probability distribution for z-scores can be found and used to calculate the probabilities of occurrences below, above, or between two z-scores. The general recurrence of z-scores is additionally utilized in deciding whether a noticed contrast is impressive and measurably critical. By determining whether the difference is significant if the corresponding z-score falls outside the range of 1.96, this can be accomplished. Since the p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

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The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

To calculate the confidence interval, we can use the formula:

Confidence interval = Sample mean ± (Critical value * Standard error)

Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.

Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard error = (Standard deviation) / √(Sample size)

Standard error = 4.2 / √85 ≈ 0.456

Now we can plug in the values into the confidence interval formula:

Confidence interval = 42 ± (1.66 * 0.456)

Confidence interval ≈ (41.29, 42.71)

Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.

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Answer:

30

Step-by-step explanation:

add 2 to 4, which =6, then divide 6 by 1/5 to get x

The probability of obtaining a sum less than or equal to 4 is:  1/12

An experiment consists of tossing two ordinary dice and adding their numbers together. To determine the probability of obtaining a sum of 8, we need to first count the number of ways we can get a sum of 8. We can do this by listing all the possible combinations of dice rolls that add up to 8:

2+6, 3+5, 4+4, 5+3, 6+2

So there are 5 ways to get a sum of 8.

Next, we need to determine the total number of possible outcomes for this experiment. Each die has 6 sides, so there are 6 x 6 = 36 possible outcomes.

Therefore, the probability of obtaining a sum of 8 is:

Number of ways to get a sum of 8 / Total number of possible outcomes = 5/36

Now let's determine the probability of obtaining a sum less than or equal to 4. We can use the same method as before:

1+1, 1+2, 2+1

So there are 3 ways to get a sum less than or equal to 4.

The probability of obtaining a sum less than or equal to 4 is:

Number of ways to get a sum less than or equal to 4 / Total number of possible outcomes = 3/36 = 1/12

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Answer:

Cleaning

Step-by-step explanation:

Answer:

t = 2 seconds

Step-by-step explanation:

Given that,

h = -16\(t^{2}\) + 64 t

where h and t have their usual meaning.

To determine the number of seconds required of the ball to hit the ground, differentiate the given equation with respect to t.

0 = -32 + 64

So that,

32t = 64

t = \(\frac{64}{32}\)

t = 2

The ball will hit the ground in 2 seconds.

1) Dora may be incorrect because we can't use the data to generalize that most people spent at least 4 hours reading last week because the research pertained to only her friends.

2) We can't find the range of time spent because the interval does not show us the highest nor lowest time spent in reading by the friends.

3) Mean = 4.8 hours

1) From the given table from the values gotten from the question Dora asked her friend, we can see that 11 of her friends out of a total of 20 friends spent a minimum of 4 hours reading.

However, we can't use this to generalize that most people spent at least 4 hours reading last week because the research pertained to only her friends.

2) We can't find the range of time spent because the interval does not show us the highest nor lowest time spent in reading by the friends.

3) The mean of the data is:

Mean = [(1 * 4) + (3 * 5) + (7 * 11)]/20

Mean = 96/20

Mean = 4.8 hours

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There were 7 big dogs, 10 small dogs, and 13 average size dogs in total. The prices were $36.00 for big dogs, $12.50 for small dogs, and $14.00 for average size dogs.

Let's assume the number of big dogs is "x". The number of small dogs would then be "x + 3" since there were 3 more small dogs than big dogs.

The number of average size dogs would be 30 - (x + x + 3) = 30 - (2x + 3) = 27 - 2x.

The total revenue from the big dogs would be: x * $36.00.

The total revenue from the small dogs would be: (x + 3) * $12.50.

The total revenue from the average size dogs would be: (27 - 2x) * $14.00.

According to the given information, the total revenue from all the dogs is $559.00, so we can set up the following equation:

x * $36.00 + (x + 3) * $12.50 + (27 - 2x) * $14.00 = $559.00.

Now, let's solve this equation to find the value of "x" and calculate the number of dogs in each category.

36x + 12.5(x + 3) + 14(27 - 2x) = 559

36x + 12.5x + 37.5 + 378 - 28x = 559

20.5x + 415.5 = 559

20.5x = 559 - 415.5

20.5x = 143.5

x = 143.5 / 20.5

x ≈ 7

Therefore, there were approximately 7 big dogs.

The number of small dogs would be x + 3, which is 7 + 3 = 10.

The number of average size dogs would be 30 - (2x + 3), which is 30 - (2 * 7 + 3) = 30 - 17 = 13.

So, there were approximately 7 big dogs, 10 small dogs, and 13 average size dogs.

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The complete question is:

The dog wash washes 30 dogs for charity. they had different prices for the dogs. big dogs cost $36.00, small dogs cost $12.50, and average size dogs cost $14.00. they made $559.00. there were 3 more small dogs than big dog.How many big dogs, small dogs, and average size dogs did The Dog Wash wash for charity?

The solution to the inequality -48 - 3x > 6x - 8 is x < -40/9

From the question, we have the following parameters that can be used in our computation:

-48 - 3x > 6x - 8

Collect the like terms in the above inequality

So, we have

-6x - 3x > 48 - 8

When the like terms are evaluated, we have

-9x > 40

Divide both sides by -9

x < -40/9

Hence, the solution to the inequality is x < -40/9

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The cost of the chocolate for 110 bon-bons  as per given radius , density and cost is equal to $8.80 to the nearest cent.

Volume of a sphere with radius r is ,

V = ( 4/3 )πr³

Radius 'r' of each chocolate bon-bon is 0.8 cm,

Volume of each bon-bon is equals to,

V = ( 4/3 )π (0.8)³

   = 2.144 cm³

Density 'ρ' of the chocolate is 1.3 g/cm^3,

Mass 'm'  of each bon-bon is equals to,

m = ρV

   = ( 1.3 ) ( 2.144 )

   = 2.78grams

The cost of the chocolate used in each bon-bon is $0.03 per gram,

This implies,

Cost of the chocolate used in one bon-bon is ,

= ( 0.03 ) × 2.78

= 0.0834

Rounding to the nearest cent, the cost of the chocolate for one bon-bon is $0.08.

Cost of the chocolate for 110 bon-bons,

= 110 × 0.08

= 8.8

Therefore, the chocolate for 110 bon-bons would cost $8.80 to the nearest cent.

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The inequality which can be used to determine the number of days he can afford as required is; 74.90x + 22.75 ≤ 210.

The solution of the inequality is; x = 2 days.

As evident in the task content; the company charges $74.90 per day to rent a car and $0.13 for every mile driven, hence, since he drives 175 miles.

The total mileage cost = 175 × 0.13 = $22.75.

since, x = number of days he can afford to rent the car.

74.90x + 22.75 ≤ 210.

74.90x ≤ 210 - 22.75

74.90x ≤ 187.25

x ≤ 2.5 days.

Ultimately, the number of days Tes can afford the car within his budget is; 2 days.

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The correct integral to express the arc length is:

∫₀^(π/3) √(1 + sec⁴(x)) dx

The correct integral to express the arc length of the curve y = tan(x) for 0 ≤ x ≤ π/3 is:

∫₀^(π/3) √(1 + (dy/dx)²) dx

To find the derivative dy/dx, we differentiate y = tan(x) using the chain rule:

dy/dx = sec²(x)

Substituting the derivative into the integral expression:

∫₀^(π/3) √(1 + (sec²(x))²) dx

Simplifying the expression inside the square root:

∫₀^(π/3) √(1 + sec⁴(x)) dx

the correct integral to express the arc length is:

∫₀^(π/3) √(1 + sec⁴(x)) dx

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40 of these small cubes are painted red on at least two faces.

To determine the number of small cubes that are painted red on at least two faces, we need to consider the cubes at the corners and edges of the large cube.

The large cube consists of 8 corner cubes, each having 3 faces painted red, and 12 edge cubes, each having 2 faces painted red. These corner and edge cubes are the ones that have the potential to be painted on at least two faces.

Number of corner cubes = 8

Number of faces painted red on each corner cube = 3

Total number of faces painted red on corner cubes = 8 * 3 = 24

Number of edge cubes = 12

Number of faces painted red on each edge cube = 2

Total number of faces painted red on edge cubes = 12 * 2 = 24

Now, we need to subtract the double-counted faces where the corner and edge cubes overlap. Each corner cube shares one painted face with three edge cubes, so there are 8 * 1 = 8 double-counted faces.

Therefore, the total number of small cubes painted red on at least two faces is:

Total number = Total number of faces painted red on corner cubes + Total number of faces painted red on edge cubes - Double-counted faces

Total number = 24 + 24 - 8 = 40

Hence, there are 40 small cubes out of the 1000 congruent cubes that are painted red on at least two faces.

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