evaluate:
2 - (-9) + (-18) / 3 x 2 -10

Answer:

8.5 cups per day

Step-by-step explanation: The answer is very simple. 85/10 equals 8.5 cups per day! Good Luck! Stay Brainy!

The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).

The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.

To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Given that the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. the domain of a function f depends on how f(x) is defined, and it's necessary to know the expression for f(x) to determine its domain.

Let f be the function defined by f(x).The domain of the function f will depend on how f(x) is defined. Without knowledge of how f(x) is defined, it's impossible to determine the domain of f. There are, however, some standard forms for which the domain can be determined.

For example, if the function is defined by a rational expression, then the domain is all real numbers except for those that would make the denominator of the rational expression equal to zero. Therefore, to determine the domain of f, it is necessary to know the expression for f(x). Once that is known, we can determine what values of x make sense to plug into the expression.

Those values of x will be the domain of f. For instance, the expression f(x) = √(x - 2) is undefined if x - 2 is negative or zero because the square root of a negative or zero number is not a real number.

Therefore, the domain of f is x > 2.

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Answer:

77.4

Step-by-step explanation:

The first term, a, of the series is 3.

It is a geometric progression, so we can calculate the common ratio, r:

3.75 / 3 = 1.25

The sum of n terms of a geometric progression is given as:

\(S = \frac{a(1 - r^n)}{(1 - r)}\)

where n =  number of terms considered

The sum of the first 9 terms will therefore be:

\(S_9 = \frac{3(1 - 1.25^9)}{(1 - 1.25)} \\\\S_9 = \frac{3(1 - 7.45)}{-0.25}\\ \\S_9 = \frac{3 * -6.45}{-0.25}\\ S_9 = \frac{-19.35}{-0.25}\\ \\S_9 = 77.4\)

The answer is that the expected waiting time until the next service completion is 7.44 minutes.



To calculate the expected waiting time, we need to first find the expected remaining service time for each server. Since the service times are exponentially distributed, the expected remaining service time for each server is equal to the reciprocal of its service rate. The service rate is the inverse of the expected service time.

Thus, the expected remaining service time for the first server is 1/λ1 = 1/0.2 = 5 minutes, where λ1 is the arrival rate for the first server. Similarly, the expected remaining service time for the second and third servers are 1/λ2 = 1/0.0333 = 30 minutes and 1/λ3 = 1/0.1 = 10 minutes, respectively.

Since each server has been busy for 5 minutes with a current customer, the expected remaining service time for each server is reduced by 5 minutes. Thus, the expected remaining service times are 0 minutes, 25 minutes, and 5 minutes, respectively.

The expected waiting time until the next service completion is equal to the sum of the expected remaining service times weighted by the probability that a customer arrives at each server while it is busy. The probability of a customer arriving at each server while it is busy can be calculated using the Erlang C formula.

Using the Erlang C formula, we can calculate that the probability of a customer arriving at the first server while it is busy is 0.016, the probability of a customer arriving at the second server while it is busy is 0.524, and the probability of a customer arriving at the third server while it is busy is 0.091.

Thus, the expected waiting time until the next service completion is (0 minutes)*(0.016) + (25 minutes)*(0.524) + (5 minutes)*(0.091) = 7.44 minutes.

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To determine the value of √2, substitute y''(1) = 3 into the equation √2 / 91 + 12 = 3 and solve for √2.

The particular solution xp for x'' + 2x^2 = 4e^(-31t) is xp = 92e^(-3t). This is obtained by matching the form of the forcing function with the solution form of the homogeneous equation.

Step-by-step explanation:

The second derivative of y, denoted as y'', is calculated as √2 * (2x^2 - 1) / (91x^3) + 12. To find the value of √2, we substitute x = 1 into the equation and set y''(1) = 3. Solving the equation √2 / 91 + 12 = 3 allows us to determine the value of √2.

In order to find the particular solution xp that satisfies the equation x'' + 2x^2 = 4e^(-31t), we match the form of the forcing function 4e^(-31t) with the solution form of the homogeneous equation. By considering the exponential form, we obtain the particular solution xp = 92e^(-3t). This solution fulfills the given equation when substituted into it.

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Answer:

4x-2=y

Step-by-step explanation:

The approximate value of E[X₂] is 2.6. The approximate values of Yxx(0) and Yxx(1) are 13.36 and -0.24, respectively.

Step 1: To approximate the expected value of X₂, we calculate the average of the values in x(n). Since x(n) is given as {5, 4, -1, 3, 8}, we sum up these values and divide by the total number of values, which is 5. The sum is 19, so E[X₂] ≈ 19/5 ≈ 3.8. Hence, the approximate value of E[X₂] is 2.6.

Step 2: To approximate the autocorrelation function Yxx(0) and Yxx(1), we utilize the formula:

Yxx(k) = E[X(n)X(n+k)] where k represents the time delay.

For Yxx(0): Using the given x(n) values, we have X(n) = {5, 4, -1, 3, 8}.

To calculate Yxx(0), we need to multiply each value of X(n) with the corresponding value of X(n), and then take the average.

Yxx(0) = (5*5 + 4*4 + (-1)*(-1) + 3*3 + 8*8)/5 ≈ 13.36.

For Yxx(1): Using the given x(n) values, we have X(n) = {5, 4, -1, 3, 8}.

To calculate Yxx(1), we need to multiply each value of X(n) with the corresponding value of X(n+1), and then take the average.

Yxx(1) = (5*4 + 4*(-1) + (-1)*3 + 3*8)/5 ≈ -0.24.

Hence, the approximate values of Yxx(0) and Yxx(1) are 13.36 and -0.24, respectively.

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The length of arc CD is 92.69

From the given circles we know that:

Circle E = Circle H

GF = CD = 28

∠CED = 75°

Arc CD?

We can imagine an imaginary radius line here are:

GH = FH = CE = DE

However we have no idea the length of the radius line of both circles.

We will use Law of Cosines to find the length of the radius line by taking GHF as a, isosceles triangle:

GF² = GH² + FH² - 2 GH FH cos H

28² = 2GH² - 2GH² cos 75°

28² = 2GH² (1 - cos 75)...(i)

Remember that:

Cos (A+B) = cos A cos B - sin A sin B

cos 75° = cos (30 + 45)°

cos 75° = cos 30 cos 45 - sin 30 sin 45

cos 75° = (√3/2)(√2/2) - (1/2)(√2/2)

cos 75° = √6/4 - √2/4

cos 75° = 1/4 (√6 - √2)

cos 75° = 0.921 ... (ii)

We subtitute equation (ii) into equation (i)

784 = 2GH² (1 - 0.921)

2GH² = 784 / (0.079)

GH = 70.78 = ED = EC

The length of arc CD is:

Arc CD = 75°/360° 2πr

Arc CD = 75°/360° 2π.ED

Arc CD = 92.69

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Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:

Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.

Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.

Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.

Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.

Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.

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Answer:

use a standard digital bathroom scale.

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

5x+2=32

Step 1: Subtract 2 from both sides.

5x+2−2=32−2

5x=30

Step 2: Divide both sides by 5.

5x

5

=

30

5

x=6

Answer:

x = 6

Step-by-step explanation:

5x + 2 = 32

Subtract 2 from both sides

5x + 2 - 2 = 32 - 2

           5x = 30

Divide both sides by 5

         5x/5x= 30/5

               x = 6

Answer: 910.22 or 8192/9

Step-by-step explanation:

The lines you've given are taking the absolute value of whatever is inside the lines. This means that you solve whatever is inside and taking the positive of it. So 6-14 is -8 but with |6-14|, the result is 8, solving the rest of it, you get 4 *8 which is 32 and raised to the third power is 32768 and then divided by 36 is approximately 910.22 or 8192/9 in fraction form.

The correct matches are:

If AB = CD, then CD = AB. - Symmetric Property

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

Segment CD is congruent to segment CD. - Reflexive Property

The matching of statements to the properties is as follows:

If AB = CD, then CD = AB. - Symmetric Property

The symmetric property states that if two objects are equal, then the order of their equality can be reversed. In this case, the statement shows that if AB is equal to CD, then CD is also equal to AB. This reflects the symmetric property.

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

The transitive property states that if two objects are equal to the same third object, then they are equal to each other. In this case, the statement shows that if MN is equal to XY, and XY is equal to AB, then MN is also equal to AB. This demonstrates the transitive property.

Segment CD is congruent to segment CD. - Reflexive Property

The reflexive property states that any object is congruent (or equal) to itself. In this case, the statement shows that segment CD is congruent to itself, which aligns with the reflexive property.

So, the correct matches are:

If AB = CD, then CD = AB. - Symmetric Property

If MN = XY, and XY = AB, then MN = AB. - Transitive Property

Segment CD is congruent to segment CD. - Reflexive Property

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Answer:

-17

Step-by-step explanation:

-2 + 5(9 − 12)

PEMDAS

Parentheses first

-2 + 5(-3)

Then multiply

-2 -15

Subtract

-17

Answer:

-17

Step-by-step explanation:

hope this helps

Answer:

Original volume = (4/3)π(6^3) = 288π

New volume = (4/3)π(18^3) = 7,776π

7,776π ÷ 28π = 27

When the radius of a sphere is tripled, the volume of the new sphere is 27 times the volume of the old sphere.

Answer:

A and E

Step-by-step explanation:

a) Write a differential equation to describe the situation.The differential equation to describe the given situation is given by the formula,dA/dt = rA - 1200 whereA = Amount of money invested by the investor at an annual interest rate r,t = time, andD = deposit made into the account at frequent intervals.

b) Find the general solution and particular solution for the differential equation in part a)The differential equation is given bydA/dt = rA - 1200The general solution to the differential equation isA = Ce^rt + 1200/rwhere C is the constant of integration.The particular solution to the differential equation can be obtained from the initial condition that the investor deposits $8000 into an account that pays 6% compounded continuously.To find C, we use the initial condition A(0) = 8000.The formula becomesA = Ce^rt + 1200/r8000 = Ce^0 + 1200/r8000 = C + 1200/rC = 8000 - 1200/rThe particular solution isA = (8000 - 1200/r)e^rt + 1200/r

c) How much will be left in the account after 2 years?Given that A = (8000 - 1200/r)e^rt + 1200/rwhere A = amount of money invested by the investor at an annual interest rate r, andt = 2 years.We know that A = (8000 - 1200/r)e^rt + 1200/rTherefore, A = (8000 - 1200/r)e^2 + 1200/rThe value of A can be calculated by substituting the given values.A = (8000 - 1200/0.06)e^2 + 1200/0.06A = (8000 - 20000)e^2 + 20000A = $11622.98Therefore, the amount left in the account after 2 years is $11622.98.

So, the given differential equation is dA/dt = rA + D, where A is the amount of money invested by the investor at an annual interest rate r, t is time, and D is the deposit made into the account at frequent intervals. Now, we know that the given amount of $8000 is deposited at a rate of 6% compounded continuously, so we have A = 8000e^(0.06t). The investor starts withdrawing from the account at a rate of $1200 per year.

So, the differential equation to describe the given situation is dA/dt = rA - 1200. The general solution to the differential equation is A = Ce^rt + 1200/r, where C is the constant of integration. The particular solution to the differential equation is A = (8000 - 1200/r)e^rt + 1200/r. The value of A can be calculated by substituting the given values. Therefore, the amount left in the account after 2 years is $11622.98.

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The set { (6, 6, 6), (6, 6, 0), (6, 0, 0) } is not a basis for ℝ3 because it is not linearly independent. However, it does span ℝ3.

To determine if the set { (6, 6, 6), (6, 6, 0), (6, 0, 0) } is a basis for ℝ3, we need to check two conditions: linear independence and spanning.

Linear Independence:

We can check linear independence by forming a matrix with the vectors as columns and finding its rank. If the rank is equal to the number of vectors, the set is linearly independent.

Forming the matrix and performing row reduction, we find that the rank is 2, which is less than 3 (the number of vectors). Therefore, the set is not linearly independent.

Spanning:

To check if the set spans ℝ3, we need to determine if any vector in ℝ3 can be expressed as a linear combination of the vectors in the set. Since the vectors in the set have non-zero entries only in the first component, any vector in ℝ3 that has non-zero entries in the second or third component cannot be obtained as a linear combination. Thus, the set does not span ℝ3.

In conclusion, the set { (6, 6, 6), (6, 6, 0), (6, 0, 0) } is not a basis for ℝ3. It is not linearly independent but it does not span ℝ3.

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Answer:

It should be option c, \(\sqrt 37 - \sqrt26\\\\\)

Step-by-step explanation: i hope this helps

When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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The longer route is 4 miles further than the shorter route.

According to the concept, the square of the hypotenuse of a right triangle equaled the square of the other sides. The formula is

\(c^{2} = a^{2} + b^{2}\),

where c is the hypotenuse length and a and b are the other two sides' lengths.

Calculate the difference between the longer route and the shorter route:

By using the Pythagorean theorem,\(c^{2} =a^{2} +b^{2}\)

Your hypotenuse is the straight path from Crimson to Sunshine, and your legs are the roadways to and from Happy Ville. \(c^{2} =6^{2} +8^{2}\)

Take the square root of both sides of the equation to eliminate the exponent on the left side: \(c=\pm \sqrt{6^{2}+8^{2}}\)

Raise 6 to the power of 2:\(c=\pm \sqrt{36+8^{2}}\)

Raise 8 to the power of 2: \(c=\pm \sqrt{36+64}\)

Add 36 and 64: \(c=\pm \sqrt{100}\)

Rewrite 100 as \(10^{2}\)

\(c=\pm \sqrt{10^{2}}\)

Pull terms out from under the radical, assuming positive real numbers.

\(c=\pm 10\)

So the distance between Crimson and Sunshine is 10 miles.It asks for the shortest path, either to Happy ville and then to Sunshine (through the legs) or to Sunshine immediately (hypotenuse),

Legs = 6+8 = 14

Hypotenuse = 10

So getting straight to Sunshine would be faster than going to Happyville than Sunshine because going straight to Sunshine is 10 miles against 14 miles for going to Happyville than sunshine.The longer path was 14 miles, while the shorter way was 10 miles, so subtract the two.14−10  = 4Hence, the longer route is 4 miles further than the shorter route.

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Answer:

18.75 or around 19

Step-by-step explanation:

You simply divide 225 by 12 and get 18.75.

We see, there is a pair of sides that have similar lengths before and after the enlargement.

-> The scale factor = 30 : 18 (or) 35 : 21 = 5/3

Recheck :

18 x 5/3 = 30
18 x 5/3 = 30
21 x 5/3 = 35

Answer:

20 i think so

Step-by-step explanation:

mabye help full

The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.

Parameter and statistic: Parameter is a value that describes the population, while statistic is a value that describes a sample.

Parameters are usually represented using Greek letters, while statistics are usually represented using Roman letters. In other words, a parameter is a population characteristic, whereas a statistic is a sample characteristic.

P and p hat: P represents the true proportion of a population with a particular attribute, while p hat represents the proportion of a sample with that attribute. P hat is an estimate of the true proportion p, which may differ from the actual proportion due to sampling error.

Sampling variability: Sampling variability is the variation in sample statistics that occurs from sample to sample. It is the result of the fact that different samples of the same size drawn from the same population will produce different estimates of the population parameter due to random sampling error. The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.

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Answer:

I believe the answer would be 6

Step-by-step explanation:

Area = length x width

4 x 3 = 12

12/2= 6 because only half of the rectangle is shaded

Answer: 6

Step-by-step explanation:

6 - 4 = 2

Im pretty sure the is the right answer! :)

Answer:

2 because

Step-by-step explanation:

2-4=2 yeah that all I got

Answer:

\(a_{n}\) = 25+(-4)(n-1)

Answer:

an = 25+(-4)(n-1)

Step-by-step explanation:

Answer:

135818564664 that the answer

The prediction is that the student will spend approximately 480 minutes (or 8 hours) mowing 12 lawns this weekend.

We know that the student takes 160 minutes to mow 4 lawns. We can use this information to make a prediction about the time he will spend mowing 12 lawns this weekend.

To calculate the time it takes to mow 12 lawns, we can use the concept of proportionality. Since the number of lawns is directly proportional to the time taken, we can set up a proportion:

Number of lawns : Time taken

4 lawns : 160 minutes

12 lawns : x minutes

To solve this proportion, we can cross-multiply:

4 × x = 12 × 160

4x = 1920

x = 480

Therefore, based on this proportion, the prediction is that the student will spend approximately 480 minutes (or 8 hours) mowing 12 lawns this weekend.

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