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Two boats were 400 miles apart at midnight and were both sailing to the same port on Honolulu. One boat was heading west and the other was heading east. If they both arrived at 8:00am, find the speed of each boat if one was 20MPH faster than the other.

It will take 14 weeks for the insect population to exceeds 10,000 insects.  It will take 17 weeks for the insect population to exceeds 10,000 insects when 40% of the insect is killed by a disease every 4 week.

The code for this function of Java is : class InsectPopulation {

   public static void main(String[] args) {

       int week = 1;

       double population = 2;

       System.out.println("Week 1: 2 insects");

       while (population <= 10000) {

           population = population * 2;

           week++;

           if (week % 4 == 0) {

               population = population - (population * 0.4);

           }

           System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");

       }

   }

}

The second function for the loop is : class InsectPopulation {

   public static void main(String[] args) {

       int week = 1;

       double population = 2;

       System.out.println("Week 1: 2 insects");

       do {

           population = population * 2;

           week++;

           if (week % 4 == 0) {

               population = population - (population * 0.4);

           }

           System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");

       } while (population <= 10000);

   }

}

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The expression for the perimeter of the triangle is 6x + 15 units.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, an art class is making a mural for their school which has a triangle drawn in the middle.

Let x represent the bottom of the triangle.

One side if the triangle is 12 more than four times the length of the bottom of the triangle, hence:

Length of the side = 4x + 12

The last side is 3 more than the bottom of the triangle, hence:

Length of the side = x + 3

Perimeter of the triangle = x + (4x + 12) + (x + 3)

Perimeter = 6x + 15 units

Therefore, the expression for the perimeter of the triangle is 6x + 15 units.

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Answer:

10

Step-by-step explanation:

Use the pythagorean theorem/distance formula.

AB = \sqrt{(4-(-2))^2+(7-(-1))^2} = \sqrt{36+64} = \sqrt{100} = 10

The probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced can be calculated using combinatorics.

The number of ways to choose two types of phones out of three and the number of ways to arrange twelve phones of these two types need to be determined. The probability can then be calculated as the number of favorable outcomes divided by the total number of possible outcomes. This method can help determine the likelihood of a specific event happening in a given scenario.

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To find the mean of the data set, we will simply take the average of the data as:  Mean= 345+340+400+625/ 4=  427.5

So we have mean as, 427.5

Now we have to calculate the variance of the data.

As we know, for variance we take the difference of each value from mean, take its square and then average of all.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Now

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

So, the variance is 13556.2

Now we have to calculate the Standard deviation (S.D) of the data.

And the Standard Deviation is just the square root of Variance, so:

σ = √13556.25

σ =116.43

So, the Standard deviation of the data is 116.4

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Answer:

19.6666666667

Step-by-step explanation:

it A

Step-by-step explanation:

Answer:

[tex]2.28*10^7[/tex]

Step-by-step explanation:

[tex](2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7[/tex]

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

To answer this question, you cannot do it all at once. Since the percentage will change every year because of how percents work, you must do seven calculations for each of the seven decades.

To decrease a number by 6%, you multiply it by 0.94, which is the same as finding 94% of that number, as you have taken 60% away.

1. 1200*0.94 = 1128

2. 1128*0.94 = 1060.32

3. 1060.32*0.94 = 996.7008

4. 996.7008*0.94 = 936.898752

5. 936.898752*0.94 = 880.68482688

6. 880.68482688*0.94 = 827.843737267

7. 827.843737267*0.94 = 778.173113031

You probably don't need 9 decimal places, so we can round to 778.17.

After seven decades, the mountain will be 778.17 meters.

The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

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The length of the rectangle in centimeters is 15.60 cm.

The correct way to report the length of the rectangle in centimeters is 15.60 cm. To calculate the length of the rectangle, we must first calculate the distance between the two edges of the rectangle. To do this we can use the formula Distance = Final Position - Initial Position. Therefore, the distance between the two edges of the rectangle is 15.600 cm - 0 cm = 15.600 cm. This is the length of the rectangle, so the correct way to report the length of the rectangle in centimeters is 15.60 cm.

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The equation that represents the total amount of kites for a given number will be y = 2x + 20.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The rate of the kite is $2 per kite and the shipping charge is $20.

Let 'x' be the number of kites and 'y' be the total amount. Then we have

y = 2x + 20

Then the table is completed below.

Number of kites      Total amount

         0                             20

          1                             22

         4                             28

         7                             34

        10                            40

The equation that represents the total amount of kites for a given number will be y = 2x + 20.

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As percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 is 25%.

A percentage is a fraction of a whole number expressed as a fraction of 100. It is often used to describe the change in a quantity over time or between different groups.

There were 50 more full-time students enrolled in the fall of 2000 than in the fall of 1999, we can calculate the change in the number of full-time students as follows:

Change in full-time students = 50

To calculate the percentage change, we need to know the initial number of full-time students in the fall of 1999. This information is not provided, so we will use the information that the total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.

Let's call the total number of students enrolled at College T in the fall of 1999 "x". Then, the total number of students enrolled at College T in the fall of 2000 would be x + 5% of x.

x + 5% of x = x + 0.05x = 1.05x

To find the number of full-time students in the fall of 2000, we can subtract the change in full-time students from the total number of students enrolled at College T in the fall of 2000:

Number of full-time students in fall of 2000 = 1.05x - 50

To calculate the percentage change, we divide the change in full-time students by the initial number of full-time students and multiply by 100:

Percentage change = (50 / x) * 100

Where the value of x as 2000, then the percentage is

=> (50/2000) * 100 = 25%.

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Answer:

3/2 of a mile

Step-by-step explanation:

The equation is 1/2 times something = 3/4 (because length times width is area)

you would divide 1/2 on both sides to get an unknown number(that represents the width)

3/4 divided by 1/2 is 3/2 of a mile !

The wechsler intelligence scale has a mean of 100 and a standard deviation of 15.  the z score that corresponds to an iq score of 115 is 1.

To calculate the Z score, you subtract the mean from the score and divide it by the standard deviation. In this case, 115-100=15, and 15/15=1.  A Z score of 1 indicates that the score is one standard deviation above the mean. This means that a score of 115 is higher than 84% of the population. It is in the top 16% of scores.

This score is considered to be in the high average range on the Wechsler Intelligence Scale.  The Z score can be interpreted in a variety of ways. It can be used to compare scores or to see how far a score is from the mean. It also can be used to compare scores across different tests. For example, a Z score of 1 on the Wechsler Intelligence Scale could be compared to a Z score of 1 on another test to see how the scores compare.

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Answer:

The mean is 8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

add all numbers together and divide by how many numbers there are so:

8+12+4+3+14+1+9+13=64

64÷8=8

Feel free to ask me any questions if you don't understand it :)

The perimeter of the playground is 92 meters

The figure is added as an attachment

To calculate the perimeter, we simply add the side lengths of the playground

i.e. Perimeter = Sum of side lengths

Using the above as a guide, we have the following:

Perimeter = 10 + 14 + 10 + 10 + 6 + 6 + 6 + 14 + 6 + 10

Evaluate the like terms

Perimeter = 92

Hence, the perimeter is 92 meters

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The standard deviation of the sample proportions (i.e., the standard error of the proportion) is 10.5.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

n = 525

Population Proportion(p) = 0.3

q = 1 - 0.3

q = 0.7

σ = √npq

σ = √(525 × 0.3 × 0.7)

σ = √110.25

σ = 10.5

So The standard deviation of the sample proportions = σ/n

The standard deviation of the sample proportions = 10.5/525

The standard deviation of the sample proportions = 0.02

The standard deviation of the sample proportions = 2%

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The complete question is:

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

a.0.0004

b.0.2100

c.0.3000

d.0.0200

Answer:

The marginal profit function can be found by subtracting the marginal cost from the marginal revenue. The marginal cost is given by the derivative of the cost function, and the marginal revenue is given by the derivative of the revenue function.

The derivative of the cost function is:

C'(x) = dC(x)/dx = 0.9

The derivative of the revenue function is:

C'(x) = dC(x)/dx = 0.9

The derivative of the revenue function is:

R'(x) = dR(x)/dx = 9 - 0.04x

Therefore, the marginal profit function is:

P'(x) = R'(x) - C'(x) = 9 - 0.04x - 0.9 = 8.1 - 0.04x

Answer:

4 inches

Step-by-step explanation:

Let b = base length

h = height

A = area

[tex]A = \dfrac{1}{2}\cdot b \cdot h\\\\[/tex]

Multiply throughout by 2

[tex]2 \cdot A = 2\cdot \dfrac{1}{2}\cdot bh\\\\2A = bh\\\\h = \dfrac{2A}{b}[/tex]

We are given A = 16 in² and b = 8 inches

So, h = 2(16)/8 = 32/8 = 4 inches

Check to see if this is correct

A = (1/2)(8)(4) = (4)(4) = 16

Points G, H, and I It seems to be the vertices of a triangle, forming the triangle GHI. Triangle GHI resembles triangle ABC.

A triangle is a three-sided polygon that is also known as the trigon. Every triangle has three sides and three angles, which might be different. In geometry, a triangle is a three-sided polygon with three edges and three vertices. The sum of a triangle's internal angles equals 180 degrees, which is its most important characteristic. This is known as a triangle's angle sum property.

Here,

Point G, H, I looks like the vertices of triangle making triangle GHI. Triangle GHI is similar to triangle ABC.

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Stratified Random Sampling is used when dividing a population into subgroups so that a random sample from each subgroup can be collected. (option 3)

Stratified Random Sampling is a type of probability sampling where the population is divided into subgroups (or strata) based on some important characteristic. The purpose of stratifying the population is to ensure that each subgroup is represented in the sample, so that the results of the study can be more accurately generalized to the larger population.

After dividing the population into strata, a random sample is selected from each stratum. This approach is used when there is heterogeneity within the population and it is important to ensure that each subgroup is adequately represented in the sample. This method can result in a more precise estimate of population parameters compared to simple random sampling, as it ensures that each subgroup is proportionately represented in the sample.

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Complete Question:

when dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

Equation can use to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

As per the given data, Naomi's carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The number of water balloons w in the bin before Naomi trips.

She counts the remaining water balloons, and there are 15 left.

According to the question, the equation is

w - 13 = 15

⇒ w = 15 + 13

⇒ w = 28

Hence, equation which is used to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

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The value of x based on the information given in the triangle will be 11.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

It should be noted that based on the information given, the value of x will be calculated thus:

24 / x + 5 = 54 / 36

Cross multiply

24 / x + 5 = 3 / 2

3(x + 5) = 24 × 2

3x + 15 = 48

Collect the like terms

3x = 48 - 15

3x = 33

Divide

x = 33 / 3

x = 11

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Graph of the equation y-4=0.75(x-1) is in the attachment.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given  equation is y-4=0.75(x-1)

y-4=0.75x-0.75

Add 4 on both sides

y=0.75x+3.25

The slope is 0.75 and y intercept is 3.25.

The graph is given in the attachment.

Hence, graph of the equation y-4=0.75(x-1) is in the attachment.

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The cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

The formula to calculate the cost of carpeting a rectangular floor is Area of the floor x Cost of carpet per square yard.

The area of the floor is calculated by multiplying the length and the width, which in this case is 9 feet x 18 feet = 162 square feet.

To convert 162 square feet into square yards, divide 162 square feet by 9, which equals 18 square yards.

Therefore, the cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

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When two finite populations are connected by migration , then (b) Fst decreases to 0 .

The Fixation Index denoted as Fst ,  is a measure of population differentiation, which is used to quantify the level of genetic differentiation between two populations.

The Fst ranges from 0 to 1, where 0 indicates complete gene flow between two populations and 1 indicates complete genetic isolation.

If the migration rate is 2% per organism per generation, over time this will lead to a reduction in genetic differentiation between the populations, and the Fst value will decrease towards 0.

This is because the exchange of genetic material will reduce the amount of variation that is unique to each population, which leads to an increase in the genetic similarities between the populations.

The given question is incomplete , the complete question is

What happens to Fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection) ?

(a) Fst increases to 1

(b) Fst decreases to 0

(c) Fst stays moderate, near 0.5

(d) Fst wanders around randomly between 0 and 1 forever  .

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The number of bricks that will be used for the entire job would be = 1000 bricks.

The amount of bricks which will be used by the Carmona Construction Company for brick patio can be calculated as follows;

The amount of rows that has been installed = 30 rows

The amount of bricks that makes up the installed rows = 600 bricks.

The amount of uninstalled rows = 20

The amount of bricks that would be required to install the remaining 20 rows ;

30 rows = 600

20 rows = X

Make X the subject of formula

X = 20×600/30

X = 12000/30

X= 400 bricks

Therefore, the total brick that will be required = 400+600 = 1000 bricks.

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