Find the sum of \sqrt{25}
25
​
and 4\sqrt{2}4
2
​
in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

[tex]ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)[/tex]

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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A random variable is a variable whose possible values are determined by chance, while a discrete random variable can only take on certain values, and a continuous random variable can take on any value within a given range

There are two types of random variables: discrete random variables and continuous random variables.

The difference between these two types of random variables is as follows:

Discrete random variables: A discrete random variable is one that can only take on a finite or countably infinite number of distinct values. These values are usually represented by integers.

Examples of discrete random variables include the number of students in a class, the number of cars in a parking lot, or the number of heads that come up when a coin is flipped. In other words, a discrete random variable is one that can be counted.

Continuous random variables: A continuous random variable is one that can take on an infinite number of values, and these values can be represented by any real number within a given interval.

Examples of continuous random variables include height, weight, temperature, and time. In other words, a continuous random variable is one that can be measured.

Continuous random variables are usually represented by a function called the probability density function, which describes the likelihood of any given value occurring within the given interval.


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The numbers in Z84 that are relatively prime to 84 are: 1, 5, 25, 29, 43, 47, 61, 65, 79, and 83.

To find the numbers in Z84 that are relatively prime to 84, we need to find the numbers that do not have any common factors with 84 other than 1.

First, we can factorize 84 as 2^2 * 3 * 7.

Next, we can remove all the factors of 2, 3, and 7 from the set Z84, since any number in Z84 that has any of these factors would have a common factor with 84 other than 1.

So, we are left with the set of numbers {1, 5, 25, 29, 43, 47, 61, 65, 79, 83}.

Therefore, the numbers in Z84 that are relatively prime to 84 are 1, 5, 25, 29, 43, 47, 61, 65, 79, and 83.

As a comma-separated list, the answer would be: 1, 5, 25, 29, 43, 47, 61, 65, 79, 83.

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The maximum acceleration attained on the interval 0 < t <3 is 27 m/s²

To find the maximum acceleration of the particle, we need to find its acceleration function by taking the derivative of its velocity function with respect to time

a(t) = v'(t) = 3t^2 - 6t + 12

To find the maximum acceleration attained on the interval 0 < t <3, we need to find the critical points of the acceleration function within the interval and evaluate the function at these points and at the endpoints of the interval.

The critical points of the acceleration function occur where its derivative equals zero

a'(t) = 6t - 6 = 0

t = 1

So the only critical point of the acceleration function within the interval 0 < t <3 is t=1. We also need to evaluate the acceleration function at the endpoints of the interval

a(0) = 12

a(3) = 27

Therefore, the maximum acceleration attained on the interval 0 < t <3 is either at t=0, t=1, or t=3. To determine which one is the maximum, we can evaluate the acceleration function at each of these points and compare the values

a(0) = 12

a(1) = 9

a(3) = 27

Thus, the maximum acceleration attained on the interval 0 < t <3 is 27m/s², which occurs at t=3.

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The number of participants that will not get two cups of water if Mr. Mohan is the only person that donated water, obtained using basic arithmetic operations are 40 participants

Basic arithmetic operations includes addition, subtraction, division and multiplication.

Mr. Mohan donated 8 five-litre bottles of water, which is equivalent to 40 litres of water;

8 × 5 litres = 40 litres

Each cup contains 125 ml of water which means that each liter can fill 8 cups. So the total number of cups that can be filled from the 8 five-litre bottles of water containing 40 litres of water is; 40 × 8 = 320 cups

Since each participant takes one cup at each stop and there are two stops in total, each participant will take a total of 2 cups during the walkation. This means that only 160 participants will get two cups of water if Mr Mohan is the only person who donated water.

So, 200 - 160 = '40 participants' will not get two cups of water if Mr. Mohan is the only person who donated water.

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Answer:0.6

Step-by-step explanation: because i got it correct

The relationship between the two confidence intervals will be that the width of i81 will be 3 times the width of i9. So, the correct answer is option D.

In statistics, a confidence interval is a range of values that is used to estimate the unknown population parameter. They are used to express the degree of uncertainty associated with a sample estimate of a population parameter.

Two 99 percent confidence intervals are going to be constructed to estimate the difference in means of two populations, r and w. One confidence interval, i9, is going to be constructed using samples of size 9 from each of r and w.

The other confidence interval, i81, is going to be constructed using samples of size 81 from each of r and w. When all other things remain the same, the width of 181 will be 3 times the width of Ig.

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The probability that at any given time instant, 4 or more users are transmitting simultaneously is 0.3297

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

(a) 21 users

No. of users supported = 2.4 Mbps/450 kbps

= (2.4 x 1000000) / ( 450x 1000)

=20

(b)  Probability = 10% of a time

=1/10

=0.1

(c)  By using binomial distribution,

probability for N users = [tex]120 CN* (0.1) ^ N * (9/10) ^ 120 - N[/tex]

(d)  Total number of chances = 17

probability for more than 4 users = 0.6703

So, 4 and more user's probability = 0.3297

=0.3297

The probability of 4 or more users are transmitting simultaneously is 0.3297.

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the worker will have earned $231,584.10 from the period of beginning 1962 through the end 1980.

To solve this problem, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $8,400 and the common ratio is 1.05 (since the worker's salary increases by 5% each year). We need to find the sum of the series from 1962 to 1980, which is 19 years. So, the total amount that the worker will have earned from the beginning of 1962 through the end of 1980 is:

S = 8,400(1 - 1.05¹⁹)/(1 - 1.05)

S ≈ $231,584.10

Therefore, the worker will have earned approximately $231,584.10 during this period.

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The type of study which the student is conducting is a survey

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

This is because the student stands in the main dining hall during dinner 3 times and asks every 10th student how much he/she exercises in a week, in minutes and this is to get reasonable and valuable statistical feedback from the students

The correct answer is A. Survey

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No, it is not less likely that you will get one of the four types of juice, as they are the only options available.

Probability of getting apple juice = 29%

                                                      = 0.29

probability of getting grape juice = 31%

                                                       = 0.31

Probability of getting orange juice = 19%

                                                      = 0.19

Probability of getting pear juice = 21%

                                                      = 0.21

The total probabilities of getting apple, grape, orange, and pear juice sum up to

= 29% + 31% + 19% + 21%

= 100%.

or

= 0.29 + 0.31 + 0.19 + 0.21

= 1.00

This implies,

That every customer will get one of the four types of juice, and there is a 100% chance of getting one of them.

Therefore, the given probabilities are not less likely as it represents chances of one type of juice definitely will be given.

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Answer:

1.83 pounds of fruit in all

Step-by-step explanation:

1 pound of melon + 0.83 pounds of cherries = 1.83 pounds in all

Answer: He bought 1.83 pounds of fruit

Step-by-step explanation:

Hope this helps :3

The length of the arc of circle with radius 13m and with angle of arc [tex]2\pi /3[/tex]would be 13.6 meters.

The part of a circle's circumference known as an arc.It is defined by two endpoints on the circle and the points that lie on the circle between these endpoints.

An arc can be measured by its length, angle, or other properties, and is often used in the calculation of the perimeter and area of a sector of a circle.

Arcs can also be part of other curves, such as ellipses or parabolas, but they are most commonly associated with circles.

To find the length of an arc, you need to know the radius of the circle and the measure of the central angle subtended by the arc.

Arc length = (central angle / 360 degrees) x (2 x pi x radius)

where pi is approximately equal to 3.14.

For example, if the radius is 13m and the central angle is 60 degrees, then the length of the arc would be:

Arc length = (60 / 360) x (2 x 3.14 x 13) = 13.6 meters.

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The best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.

Given, the mean GPA for the 127 residents of the local apartment complex is 1.6.

The mean or sample mean is used as a point estimate for the population mean or population parameter when the value of the mean of the sample is unbiased and accurately represents the mean of the population.

Here, we are given the mean GPA of 127 residents of the local apartment complex, which is 1.6.

Therefore, the best point estimate for the mean GPA for all residents of the local apartment complex would be 1.6.

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Answer:

We can use exponential decay formula to solve this problem:

N(t) = N0 * e^(-kt)

where N(t) is the number of employees with petrol cars at time t, N0 is the initial number of employees with petrol cars (in 2013), k is the decay constant, and e is the base of the natural logarithm.

We need to find N(2019), the number of employees with petrol cars in 2019. We know that N0 = 1536, and we need to find k.

Let's assume that the number of employees with petrol cars decreases by 5% each year. This means that the ratio of the number of employees with petrol cars in two consecutive years is:

0.95

Therefore, we can write:

N(2019) = 1536 * 0.95^(2019-2013)

N(2019) = 1536 * 0.95^6

N(2019) = 1133.76

Rounding to the nearest integer, we get:

N(2019) = 1134

Therefore, we can estimate that about 1134 employees owned a petrol car in 2019, assuming that the number of employees with petrol cars decreases exponentially at a rate of 5% per year.

To make a stable structure, the method of joints can be used to calculate the force BD in the truss shown.

This method uses the equations of equilibrium to determine the forces in the members of a truss. To calculate the force BD, one needs to sum the moments about point A and equate them to zero.

The moment is given by M = FxD, where F is the force, and D is the perpendicular distance from the point of interest to the line of action of the force. Therefore, the force BD can be calculated using the equation:

MAB = 0 = (BD)(2) - (AE)(5)

BD = 5AE/2

To find the forces in members CD and CE using the method of sections, one needs to cut through the truss along a line passing through points C and E.

Then, the force in member CD can be found by using the equation of equilibrium, where the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. Similarly, the force in member CE can also be calculated using the same method.

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If the length of a rectangle is nine inches more than its width and its area is 442 square inches, the width of the rectangle is 17 inches and its length is 26 inches.

Let's denote the width of the rectangle as "w" and its length as "l". From the problem statement, we know that:

l = w + 9 (since the length is nine inches more than the width)

The area of the rectangle is given by the formula:

A = l * w

Substituting in the expression for "l" in terms of "w", we get:

A = (w+9) * w

Simplifying, we get a quadratic equation:

w^2 + 9w - 442 = 0

We can solve this equation by factoring or using the quadratic formula. Factoring gives:

(w+26)(w-17) = 0

Therefore, the possible values for "w" are -26 and 17. However, since the width of the rectangle cannot be negative, we can eliminate -26 as a possible value. Thus, the width of the rectangle is 17 inches.

Using the expression for "l" in terms of "w", we can find the length:

l = w + 9 = 17 + 9 = 26 inches

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The percentage  of known edible plants is cultivated or collected by humans for food : 23%

We need to find the percentage  of known edible plants is cultivated or collected by humans for food.

From the infographic, the number of known edible plants are 30,000

and the total number of terrestrial plants known to be edible is about 130000

We know that the percenage of 'x' out of 'n' is given by formula,

p = (x / n) × 100%

here, x = 30,000 and n = 130000

Using above formula of percentage:

p = (30,000/130000) × 100%

p ≈ 23%

the required percentage is: 23%

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The complete question is:

What percentage of known edible plants is cultivated or collected by humans for food? Find that number on the infographic and divide by the total number of terrestrial plants known to be edible. (Round your answer to the nearest whole number.)

Answer: Option A: x=4

The approximate diameter of the largest pillow Sarita can use is 12 inches.

Sarita has 38 inches of fringe to sew around a circular pillow.

To calculate the approximate diameter of the largest pillow she can use, we can use the formula 2 × (fringe length ÷ 3.14) = diameter. In this case, the diameter would be approximately 12 inches (38 ÷ 3.14 = 12.1).

To solve this problem, we need to divide the length of the fringe (38 inches) by the value of pi (3.14). Dividing 38 by 3.14 gives us 12.1. Since we are looking for the approximate diameter, we can round this number down to 12 inches.

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The  least common denominator of 7/9 and 2/3 is 9

To find the least common denominator of 7/9 and 2/3, we need to find the smallest multiple that both denominators share.

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

We can see that the smallest multiple that both denominators share is 9.

To convert 7/9 and 2/3 to have a denominator of 9, we need to multiply the numerator and denominator of 7/9 by 1 (which is equivalent to 9/9), and the numerator and denominator of 2/3 by 3:

7/9 * 1 = 7/9

2/3 * 3/3 = 6/9

Now both fractions have a denominator of 9, so we can compare them easily:

7/9 and 6/9

Therefore, the least common denominator of 7/9 and 2/3 is 9.

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Answer: i believe its 15.12

Step-by-step explanation:

The probability of getting a tail on the coin and at least a 5 on the die is 0.1667 rounded to four decimal places.

The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes. This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).

If a coin is fair and impartial, the likelihood of getting a tail is equal to half.

On a six-sided dice, the likelihood of getting at least a 5 is 2/6, or 1/3. Either rolling a 5 or rolling a 6 will result in a 5 or a 6 on the die. The likelihood of rolling at least a 5 is 2/6 or 1/3 because there are a total of six possible results.

You can multiply the probabilities of the two occurrences to determine the likelihood that they will occur simultaneously (assumed to be independent events). As a result, the likelihood of getting at least a 5 on the die and a tail on the coin is:

1/2 * 1/3 = 1/6

Thus, there is a 1 in 6 possibility of rolling at least a 5 on the die and getting a tail on the coin in a single trial. Another way to say this is as a percentage:

1/6 * 100% = 16.67%

Thus, rounded to four decimal places, the likelihood of receiving a tail on the coin and at least a 5 on the die is 0.1667.

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Answer:

500 vehicles

Step-by-step explanation:

let t represent number of tolls and v represent number of vehicles.

given that t varies directly with v then the equation relating them is

t = kv ← k is the constant of variation

to find k use the condition t = 129 from v = 20 , then

129 = 20k ( divide both sides by 20 )

6.45 = k

t = 6.45v ← equation of variation

when t = 3225 , then

3225 = 6.45v ( divide both sides by 6.45 )

500 = v

the number of vehicles is 500

The probability that a randomly selected unit will contain at least one surface-finish defect is 0.0952.

The number of surface finish flaws in this issue will follow a Poisson distribution, and since the mean is given, it is necessary to obtain the probability. More solutions will be found by using the Poisson distribution's normal approximation.

The following formula can be used to determine the likelihood that a randomly chosen unit will have at least one surface finish flaw:

The distribution's average and standard deviation are λ = 0.1

P(X ≥ 1) = 1 − P(X < 1)

P(X ≥ 1) = 1 − P(X = 0)

P(X ≥ 1) = 1 − [tex]\frac{e^{-0.1}(0.1)^0}{0!}[/tex]

After simplification

P(X ≥ 1) = 0.0952

​

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Answer:

27..

Step-by-step explanation:

w - 10 ≤ 16

w - 10 + 10 ≤ 16 + 10

w ≤ 26

all apply except 27.

The trigonometric expression cosAcotA = 8x/(4x² - 1)

A trigonometric expression is an expression that contains trigonometric ratios.

Given that for any acute angle A if sin A = 2x-1/2x+1, we desire to find the value of cos A cot A?

So, we proceed as follows

cosAcotA = cosA × cosA/sinA  (since cotA = cosA/sinA)

= cos²A/sinA

Now using the trigonometric identity

sin²A + cos²A = 1

⇒ cos²A = 1 - sin²A

So, substituting this into the equation, we have that

cosAcotA = cos²A/sinA

=  (1 - sin²A)/sinA

= 1/sinA - sin²A/sinA

= 1/sinA - sinA

Substituting the value of sinA into the equation, we have

= 1/(2x - 1)/(2x + 1) - (2x - 1)/(2x + 1)

= (2x + 1)/(2x - 1) - (2x - 1)/(2x + 1)

Taking the L.C.M, (2x - 1)(2x + 1), we have

= [(2x + 1)² - (2x - 1)²]/[(2x - 1)(2x+ 1)]

=  [(2x + 1)² - (2x - 1)²]/[(2x)² - 1²)]

=  [(2x + 1 + 2x - 1)(2x + 1 - (2x - 1)]/(2x)² - 1²)

=  [(2x + 1 + 2x - 1)(2x + 1 - 2x + 1)]/4x² - 1)

=  [(4x)(2)]/4x² - 1)

= 8x/(4x² - 1)

So, cosAcotA = 8x/(4x² - 1)

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The slope of the line of best fit in the scatterplot below can be determined using the formula for the slope of a line:
Slope = (y2-y1)/(x2-x1)

In this case, x1 = 3, y1 = 12, x2 = 6, y2 = 19. So, the slope of the line of best fit is (19 - 12) / (6 - 3), which equals 7/3 or 2.33.
The line of best fit is the line that best represents the data on a scatterplot. It is the line that is closest to all the data points in the graph. The slope of the line of best fit helps to indicate whether the data points are moving in a positive or negative direction. If the slope is positive, the data points are increasing, and if the slope is negative, the data points are decreasing.
A positive slope, like the one in this example, means that as x increases, y also increases. This means that in this case, as the x-values (3 and 6) increase, the y-values (12 and 19) also increase.

The slope of the line of best fit can also be used to make predictions about values of y, given values of x. For example, if x = 8, then y = 26, because the slope of the line of best fit is 2.33, and 8*2.33 = 19.8, which is approximately equal to 26.
Overall, the slope of the line of best fit on this scatterplot is 2.33, which is a positive number. This indicates that as the x-values increase, the y-values also increase, and it can also be used to make predictions about y-values, given x-values.

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