Assume that a cell is a sphere with radius 10-3 or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter. koalas weigh 6 kilograms on average. how many cells are in the average koala? hippos weigh 1,400 kilograms on average. how many cells are in the average hippo? solution

In a genetic algorithm for the Traveling Salesman Problem (TSP), a chromosome represents a potential solution or a route through the cities. The chromosome typically consists of a sequence of genes, where each gene represents a city.

In this case, if we have 10 cities, the chromosome could be represented as a string of 10 genes, where each gene represents a city. For example, if the cities are labeled A, B, C, ..., J, a chromosome could look like:

Chromosome: ABCDEFGHIJ

This chromosome represents a potential route where the salesperson starts at city A, visits cities B, C, D, and so on, in the given order, and finally returns to city A.

It's important to note that the specific representation of the chromosome may vary depending on the implementation details of the genetic algorithm and the specific requirements of the problem. Different representations and encoding schemes can be used, such as permutations or binary representations, but a simple string-based representation as shown above is commonly used for small-scale TSP instances.

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The coordinates of the point q on the segment with endpoints a (2, −1) and c (4, 2) which partitions the segment in a 4:1 ratio. are (2, 7/5).

We can solve this question by using the section formula, which states that if we have a line segment with endpoints (x1, y1) and (x2, y2) and we want to find a point on the segment that divides it in the ratio of m:n, then the coordinates of the point can be found using the following formula:

q(x,y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

In our case,

m=4, n=1

x1=2, x2=4

y1=-1 ,y2=2

By using the given values in the formula mentioned above, we get the coordinates of q as:

q(x,y)=( [4*4+1*2]/5 ,[4*2+1*-1]/5 )

q(x,y)=( 18/5), (7/5)

So the x coordinate of q is: 18/5

the y coordinate of q is: 7/5

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5. The constant of proportionality is 1.5

The equation is p = 1.5×s

6. The constant of proportionality is 1.99

The equation is p = 1.99 × a

7. The variables Number of Pens and Cost  are not proportional

Please find attached the required graph

8. The variables Number of minutes and Words Typed are not proportional

Please find attached the required graph

The procedure for finding the answers are as follows;

5. The given data are presented as follows;

\(\begin{array}{ccc}Shirts \ (s)&&Profit \ (p)\\5&&7.50\\10&&15.00\\15&&22.50\end{array}\)

Where two variables, s and p are proportional, we get;

p ∝ s

Therefore;

p = C × s

C = p/s

Where;

C = The constant of proportionality

Therefore, the constant of proportionality, C, of the given variables, (number of shirts, s, and profit, p, is found as follows;

C = 7.50/5 = 15.00/10 = 22.50/15 = 1.5

The constant of proportionality, C = 1.5

The equation that relates the two values is p = 1.5×s

6.  For the apples to price relationship, we have;

\(\begin{array}{ccc}Apples \ (a)&&Price\ (p)\\4&&7.96\\5&&9.95\\6&&11.94\end{array}\)

Therefore;

p ∝ a

p = C × a

C = p/a

Plugging in the values gives;

C = 7.96/4 = 9.95/5 = 11.94/6 = 1.99

The constant of proportionality, C = 1.99

Therefore, the equation relating the two values is p = 1.99 × a

7. The given data is presented in a tabular form as follows;

\(\begin{array}{ccc}Number \ of \ pens &&Cost\ \\1&&52\\2&&54\\3&&56\\4&&58\end{array}\)

A set of data is proportional or has a proportional relationship if their x, and therefore, y-intercept is (0, 0)

From the graph of the data, created with MS Excel, the y-intercept is 50 which is not equal to zero, therefore, the relationship between the data is not a proportional relationship

8. The given data is presented in a tabular form as follows;

\(\begin{array}{ccc}Number \ of \ Minutes&&Words \ Typed\ \\1&&50\\2&&90\\3&&140\\4&&180\end{array}\)

From the graph of the data, we have that the y-intercept of the line of best fir is 5, therefore, the relationship is not a proportional relationship

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Here, given the percentage of college students enrolled part time and the actual percentage of the total that they are, we want to calculate the total number of students

Let the tota

Given the comopound inequality:

Let's graph the compound inequality.

Here x is greater than -1 but less than or equal to 7.

To graph the inequality, we have:

Also, x is less than or greater than 7, plot a closed dot on the point 7.

Then draw a straight line connecting both points.

Hence, we have the graph below:

Answer:

C. g(x) = (x - 4)²

Explanation

g(x) is f(x) right 4 units

When shifted right, x - a, a is the distance

So g(x) = (x - 4)² is the answer

HOPE THIS HELPS AND HAVE A NICE DAY <3

There are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.

We first need to determine the number of ways in which we can choose two of the six freshman students to receive scholarships. This can be done using the binomial coefficient formula: \(${6 \choose 2} = 15$\).

Next, we need to determine the number of ways in which we can choose two of the four sophomore students to receive scholarships. This can also be done using the binomial coefficient formula: \(${4 \choose 2} = 6$\)

Finally, we need to multiply these two values together to get the total number of ways in which the scholarships can be distributed: 15 * 6 = 90. Therefore, there are 90 different ways in which the four scholarships can be distributed such that at least two are awarded to freshman students.

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Solution of Square root,  x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30

Given,

Square root x² = 30

Then, the value of:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

x = ∛30 = ∛30² = 3.107

x = -∛30 = -∛30² = -3.107

Now,

Cube root, x³ = 30

x = √30 = √30³ = 164.317

x = -√30 = -√30³ = -164.317

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

Therefore,

Solution of Square root,  x² = 30:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30:

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

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Answer:

Option 4

Step-by-step explanation:

\(5( \frac{1}{3} x + 7) - 3( \frac{1}{2} x - 4)\)

\( \frac{5}{3} x + 35 - \frac{3}{2} x + 12\)

\( \frac{5}{3} x - \frac{3}{2} x + 35 + 12\)

\(2 \times 5x - 3 \times 3x \div 3 \times 2 + 47\)

\( \frac{10x - 9x}{6} + 47\)

\( \frac{x}{6} + 47\)

Answer:

Solution given:

5(⅓x+7)-3(½x-4)

distribute it

\( \frac{5}{3} x+35-\frac{3}{2}x+12\)

\( \frac{5}{3} x-\frac{3}{2}x+35+12\)

\( \frac{5*2-3*3}{3*2} x+47\)

\( \frac{1}{6} x+47\) is a required answer.

The product of (2x-3y)(2x+3y) is 4x^2-9y^2.

the solution of the question is as follows,

Product = (2x-3y)(2x+3y)

Product =2x(2x+3y)-3y(2x+3y)

Product = 2x(2x)+2x(3y)-3y(2x)-3y(3y)

{using distributive property of multiplication}

Product = 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0,

Product = 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

distributive property of multiplication

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a - b)(a + b) is equal to a^2 - b^2. This result is used as an identity.

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Answer:

y = -3

Step-by-step explanation:

2y +3y = -10 -5 (collect the terms then calculate)

5y = -15 ( divide both sides )

then you'll get your answer which is y = -3

The house's value Increase in dollars by $37,760.

The current value of the house is $509, 760.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A house on the market was valued at $472,000.

After several years, the value increased by 8%.

Then, the value of house increased

= 472000 x 8/100

= $37,760

So, the current value of house

= 472000 + 37760

= $509, 760

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Answer:

37,512

Step-by-step explanation:

Total # of  5 -digit numbers  =9×104=90,000

Total # of  5 -digit numbers that do not contain  3=8×94=52,488

Total # of  5 -digit numbers that contain at least one  3=90,000−52,488=37,512

Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Answer:

m = 1/2

Step-by-step explanation:

Use two points on the line given.

(0 , 2) & (-4 , 0)

You are solving for the slope. The slope formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-4 , 0)

(x₂ , y₂) = (0 , 2)

Plug in the corresponding numbers to the corresponding variables:

m = (2 - 0)/(0 - (-4))

Simplify:

m = (2)/( 0 - (-4))

m = (2)/(0 + 4)

m = 2/4

Simplify the slope. Divide the common factor 2 from both the numerator and denominator:

m = (2/4)/(2/2) = 1/2

1/2 is your slope.

~

Answer:

0.5

Step-by-step explanation:

the rise is 4 and the run is 8 so it would be 4/8 or 1/2 which would equal 0.5

The value of \($\cos \frac{7\pi}{12} \cos \frac{\pi}{12} - \sin \frac{7\pi}{12} \sin \frac\pi{12}$\) is 0.

What is trigonometric identity?

A trigonometric identity is an equation that relates different trigonometric functions of an angle or combination of angles. These identities are true for all possible values of the angles involved. Trigonometric identities are fundamental tools in solving problems involving angles and in simplifying expressions involving trigonometric functions.

We can use the trigonometric identity \($\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$\) to simplify the given expression:

\($\cos\frac{7\pi}{12}\cos\frac{\pi}{12}-\sin\frac{7\pi}{12}\sin\frac{\pi}{12} &= \cos\left(\frac{7\pi}{12}-\frac{\pi}{12}\right) $\)

\($= \cos\frac{6\pi}{12} $\)

\($= \cos\frac{\pi}{2} $\)

\($= \boxed{0}.$\)

Therefore, the value of \($\cos \frac{7\pi}{12} \cos \frac{\pi}{12} - \sin \frac{7\pi}{12} \sin \frac\pi{12}$\) is 0.

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Answer:

atq= let no.be x and y

x= 4y-3.......(1)

x-2y=7....(2)

subtracting both eqn

x-x+2y=4y-3-7

2y=4y-10

-2y= -10

y=5 ........second no.

first no...x=7+2y=7+10=17.......first no.

Step-by-step explanation:

Answer:

Taylor will earn $27.60 after the raise.

Step-by-step explanation:

If you take $24.00 and multiply it by $1.15, your answer should be $27.60. Therefore, this is the answer to your question.

Hopefully this helps, did the best I could!

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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Step-by-step explanation:

the perimeter is the sum of all sides.

it is clearly a symmetric figure.

I assume the sqrt(36) is the whole baseline (incl. the left and right x).

so, we have

sqrt(8) + 2x = sqrt(36) = 6

1/2 × sqrt(8) + x = 3

sqrt(1/4 × 8) + x = 3

sqrt(2) + x = 3

x = 3 - sqrt(2)

to get the inclined sides we use Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b being the legs of the right-angled triangle.

so,

side² = sqrt(8)² + (3 - sqrt(2))² = 8 + (9 - 6×sqrt(2) + 2) =

= 19 - 6×sqrt(2)

each inclined side is

sqrt(19 - 6×sqrt(2))

so, as perimeter we get

6 + sqrt(8) + 2×sqrt(19 - 6×sqrt(2)) =

= 15.3137085...

Answer:

126 Gallons

Step-by-step explanation:

Take 27/3 to find how many gallons it takes for 1 load which is 9

Then multiply 9 (the gallons it takes for one load) by 14 to get 126 :)

Answer:

(0, -1) or x = 0, y = -1

Step-by-step explanation:

Look for the point of intersection. (0,-1)

The solution for this system of equations is x = 0, y = -1.

To find the acceleration at the midpoint of a nozzle, calculate the velocities at the upstream end and exit, determine the time taken, and use the acceleration formula. The answer is approximately 0.02579 m/s².

To find the acceleration at the midpoint of the nozzle, we can use the equation:

a = (v₂ - v₁) / t

where v₁ is the velocity at the upstream end, v₂ is the velocity at the exit, and t is the time taken to travel from the upstream end to the midpoint.

First, let's calculate the velocities at the upstream end (v₁) and the exit (v₂):

v₁ = Q / A₁

v₂ = Q / A₂

where Q is the constant flow rate of 0.12 m³/sec, A₁ is the area at the upstream end, and A₂ is the area at the exit.

Diameter at the upstream end (D₁) = 1.3 m

Diameter at the exit (D₂) = 0.45 m

Length of the nozzle (L) = 3 m

Flow rate (Q) = 0.12 m³/sec

We can calculate the areas at the upstream end (A₁) and the exit (A₂) using the formula for the area of a circle:

A = π * (D/2)²

A₁ = π * (D₁/2)²

A₂ = π * (D₂/2)²

Now, we can substitute the values into the formulas to calculate the velocities:

v₁ = Q / A₁

v₂ = Q / A₂

Next, we need to determine the time taken to travel from the upstream end to the midpoint. Since the nozzle is 3 m long, the midpoint is at a distance of 1.5 m from the upstream end.

t = L / v

where L is the distance and v is the velocity. We can use the velocity at the midpoint (v) to calculate the time (t).

Finally, we can substitute the velocities and the time into the acceleration formula:

a = (v₂ - v₁) / t

By calculating these values, you can find the acceleration at the midpoint of the nozzle. The answer should be approximately 0.02579 m/s².

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The inverse of the given function is

(x) = (x + 12)/4

To find the inverse of a function, follow these steps:

Replace functional notation with 'y' (e.g. f(x) becomes y)

Swap the x and y variables (e.g. y = 4x becomes x = 4y).

solve y with respect to x (e.g. x = 4y becomes y = x/4)

Replace 'y' with 'f^-1' (e.g. y = x/4 becomes f^-1(x) = x/4)

To find the inverse of a function, we need to swap the x and y variables and then solve for y. So for the function f(x) = 4x − 12, we have

y = 4x − 12

Swap x and y.

x = 4y − 12

Solve for y:

y = (x + 12)/4

The inverse of the given function is similar

(x) = (x + 12)/4

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Complete question is: Find the inverse of each of the given functions.

f(x) = 4x − 12

f−1(x) = _x + _

Answer:

x=-29

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−0.64x+0.44x=5.8

(−0.64x+0.44x)=5.8(Combine Like Terms)

−0.2x=5.8

−0.2x=5.8

Step 2: Divide both sides by -0.2.

-0.2x/-0.2=5.8/-0.2

x=-29

The critical values for the given confidence levels are:

The critical value is the value of z that cuts off a specified area in the standard normal distribution. It is the value of 'z' that has a probability of 0.5 - (level of confidence) to its left.

For example, the critical value for a 95% confidence interval is 1.96. This means that there is a 0.95 probability that a standard normal variable will be less than 1.96 and a 0.05 probability that it will be greater than 1.96.

The critical value for a given level of confidence can be obtained using a Z-table or a standard normal calculator.

Hence , the critical values at the given confidence levels are 1.96, 1.65, 2.58, 1.46, 1.04 respectively.

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0.385

Take the weight of the bag and divide it by the number of oranges in the bag (12) which is:

4.5 / 12 = 0.385

Each orange weighs 0.385 pounds.

The expected value of the number of patients that will be cured is 2.78 which has been obtained by using probability.

It is feasible to determine the expected value of the number of patients who will be cured by multiplying each potential result by the appropriate probability and adding the results. The following probability and outcomes are:

0 patients cured: P(X=0) = 0.01

1 patient cured: P(X=1) = 0.08

2 patients cured: P(X=2) = 0.27

3 patients cured: P(X=3) = 0.40

4 patients cured: P(X=4) = 0.24

To calculate the expected value, we multiply each outcome by its probability and sum them up:

E(X) = (0 * 0.01) + (1 * 0.08) + (2 * 0.27) + (3 * 0.40) + (4 * 0.24)

Simplifying the calculation, we find:

E(X) = 0 + 0.08 + 0.54 + 1.20 + 0.96

E(X) = 2.78

Therefore, the expected value of the number of patients that will be cured is 2.78, rounded to two decimal places.

The expected value represents the average number of patients that would be cured if the treatment is repeated many times. In this case, based on the given probabilities, we can expect that, on average, approximately 2.78 patients out of four will be successfully cured with chemotherapy for this particular type of cancer.

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The complete question has been attached below.

The required value of x is 7.

In the given statement is:

m/HGS = 3x + 5,

m/SGF=21x +3, and m/HGF = 176º.

and, to find the value of 'x'

The two angles, ∠HGS & ∠SGF, when combined, will result in ∠HGF

m ∠HGS = 3x + 5

m ∠SGF = 21x + 3

m ∠HGF = 176°

Set the equation:

m ∠SGF + m ∠HGS = m ∠HGF

Plug in the corresponding terms to the corresponding variables:

21x + 3 + 3x + 5 = 176°

24x + 8 = 176°

24x = 176° - 8

24x = 168°

x = 168°/24

x = 7

Hence, The required value of x is 7.

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Answer:

hope it helps you ✨✨✨✨✨✨