Still stuck on this problem, due today, I have the main idea but still can't get the right answer.

There are more than 1/4 million species of beetle. Assume the average length of a beetle is 1 cm and the average walking speed is 10 cm per second. These beetles walk up a gang-plank that is 5 meters long onto an ark. They do this in pairs, side by side, one male and one female from each species. The pairs of beetles are spaced so there is a gap of 7 cm between species. How many hours will it take for all 1/4 million species of beetles to embark onto the ark once the first pair starts up the gangplank?

The cumulative frequency distribution table is present below. Cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80 less than 120 is 100. So, correct answer is option (b).

The cumulative frequency of a variable's value is the number of values in the collection of data that are less than or equal to the variable's value. Example: Let the raw data be 2, 2, 1, 5, 5, 6, 5, 3, 7, 7, 5, 6. Cumulative frequency of 3 = 4. Cumulative frequency is a frequency distribution table for the predecessor total. The final value is always equal to the sum of all observations, since all frequencies have already been added to the previous sum. We have a data corresponds to the frequencydistribution.

Speed Number of cars

0-29 4

30-59 16

60-89 60

90-119 20

We have to construct the cumulative frequency distribution for the above frequency distribution.Using the above rules we can construct distribution as,

Speed Number of cars Cumulative Freq

0-29 4 4

30-59 16 16 + 4 = 20

60-89 60 60 + 20= 80

90-119 20 20 + 80 = 100

-----------

Total 100

Thus , cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80

less than 120 is 100.

Hence, we got the required cumulative frequencies for frequency distribution.

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Complete question:

Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Number Speed of cars 0-29 4 30-59 16 60-89 60 90-119 20 a)Speed Cumulative Frequensy

Less than 30 100

Less than 60 80

Less than 90 82

Less than 120 1

b)Speed Cumulative Frequency

Less than 30 4

Less than 60 20

Less than 90 80

Less than1 20 100

c) speed Cumulative Frequency

Less than 30 0.04

Less than 60 0.20

Less than 90 0.80

Less than120 1.00

Answer:

aₙ = aₙ₋₁ - 3, a₀ = 8

Step-by-step explanation:

Minus three every time thus the recursive equation would be aₙ = aₙ₋₁ - 3, a₀ = 8

A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. The systematic sampling method is this.

Hence, option (a) is the correct choice.

The library manager employs systematic sampling as a sample approach.

Systematic sampling is a form of probability sampling approach in which sample members are drawn from a larger population at random but with a set, periodic interval.

The sampling interval is determined by dividing the population size by the desired sample size.

Systematic sampling is a technique for picking a sample from a larger population at regular intervals. In this scenario, the library manager selects a sample of library users by tallying the number of persons every 28th day.

It is a systematic sampling approach since the intervals (28th day) are fixed and systematic.

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The estimated mean of the distribution for the given question will be 10.

Mean = 13 + 52 + 48 + 28 + 28 + 23 + 14 + 13 + 10 + 4 + 2 + 4 + 2 + 1 + 1 + 0 + 2 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1

Total number =25

Now, divided the sum by 25

We get, the mean is equal to 10.

In mathematics, particularly in statistics, there are various types of means. Every mean serves to condense a specific set of data, frequently to help understand the overall significance of a particular data set. Only numerical variables, whether continuous or discrete, can be used to calculate the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

Note that the illustration for graph is: (check the attached image)

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jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. So,  m + p ≤ 32 inequalities represents this scenario.

A relationship that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities. A mathematical connection between two expressions is known as an inequality, and it is shown using one of the following: "≤" , "≥" , "<" and ">".

Given that,

Number of mango = m

Number of papaya = p

The limit of juices should be less than or equal to 32 ounces
Thus, the sum of mass of mangoes and papaya should be less than  or equal to 32 ounces.

So, m + p ≤ 32

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The complete question is as follows:

Answer:

Altitude: Segment from a vertex of a triangle that is perpendicular to the opposite side. This segment may be inside the triangle, on the triangle, or outside the triangle. Pictured below are the altitudes (represented as black segments) of acute, right, and obtuse triangles.

Step-by-step explanation:

Answer:

Vertical Line Test

Step-by-step explanation:

If a vertical line is drawn on a graph of a relation and only intersects the graph at one point, then that graph represents a function. If there is no vertical line intersecting the graph at two or more points, then the graph does not represent a function.

The most likely way Alcmaeon will try to solve this mystery about the sudden death of the goats would be by taking blood samples to analyze a possible disease or epidemic in the goat herd.

The best option to decipher the cause of death of the Cleatus goats is to take a sample from one of the goats to do an autopsy and identify the possible cause of death. Additionally, you can take blood samples to analyze a possible disease or infection that has caused the death of the sheep.

This would be the most effective way of detecting a possible cause of death as it allows Cleatus to know if the goats left alive are sick or at risk of dying from a disease.

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Answer:

14 is a polynomial.

x+1 is a polynomial.

14vx is not a polynomial.

x-2 -2x+4 is a polynomial.

14 is a polynomial, x+1 is a polynomial, 14vx is not a polynomial, x-2 -2x+4 is a polynomial.

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

Polynomials are algebraic expressions with indeterminates and constants in them. Polynomials can be thought of as a mathematical dialect. They are used to express numbers in practically every subject of mathematics and are quite significant in others, such as calculus.

Polynomials cannot include the following:

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Answer: Its perimeter is 45 cm.

Step by step explanation:

Data :

We have a triangle with a measure of 15 cm

We must simplify taking into account that it is an equilateral triangle, all its sides are equal, therefore the perimeter is the sum of its sides:

[tex]\bf P= 15 + 15 + 15[/tex]

[tex]\boxed{\bf \: P = 45 \: cm}[/tex]

Rpt: Its perimeter is 45 cm.

The value of r is equal to the cube root of (V * (3π/4)).

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Answer:

Where is the equation?

Step-by-step explanation:

I need it to solve this problem

Answer:

5x>20 and  4

Step-by-step explanation:

x is how many packs Dave bought

5x>20 because he went over the 20 dollar budget

5(4) = 20

Buying 4 packs of cards wouldn't go above the budget, so he must've bought more than 4 packs of cards.

The length of side VY is 25.

A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Suppose that length of each side of that figure be of u units, then we have the perimeter as:

P=u+u+...+u (n times) = n xu

units.

Given;

The perimeter of the rectangle below is 120 units

The two sides of rectangle are 2y+3 and3y+2

Now,

2l+2b=120

2(2y+3)+2(3y+2)=120

4y+6+6y+4=120

10y+10=120

y+1=12

y=11

VY=2y+3

VY=2*11+3

VY=25

Therefore, the length according to given perimeter will be 25units.

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The function for distance jogged is d(t) = 3.3t and the inverse of the function is d(t)⁻¹ = 3.3/t.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Let, 'd' be the distance covered in miles, and 't' is the time in hours.

Therefore, From the given information d(t) = 3.3t.

Let, d(t) = y.

So, y = 3.3t.

t = 3.3/y.

d(t)⁻¹ = 3.3/t.

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The correct graph for the supplements is attached below.

A bar chart is a graph that uses bars to represent and compare data. The length of the bar represents the magnitude of the data being displayed, with longer bars indicating larger values.

Bar charts can be used to display data for one or more categories, and can be either vertical or horizontal. They are commonly used to compare and visualize the distribution of categorical data.

The correct bar graph that shows the distribution of the supplements have been shown in the image that is attached to the answer that we have here.

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The of sum of the fraction 2 1/3 + 5 5/16 + 2/7  is 7 313/336

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

We want the of sum 2 1/3 + 5 5/16 + 2/7 =

For convenience sake, we can convert the mixed fractions to improper fractions. That is:

2 1/3 = 7/3

5 5/16 = 85/16

2 1/3 + 5 5/16 + 2/7 = 7/3 + 85/16 + 2/7

The LCM of 3, 16 and 7 is 336

                                = (7*112 + 85*21 + 2*48)/336

                                = (784 + 1785 + 96)/336

                                 = 2665/336

                                = 7 313/336

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The number of cigarettes smoked in 1925 was approximately 1.3 billion.

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The measure of angle 2 is 38° and the value of x is 11

Geometry is a branch of mathematics concerned with the study of space, shapes, sizes, and positions of objects. It covers topics such as points, lines, angles, surfaces, and solids.

Check the attached image for labelling. From the figure:

u = 64° (base angles of an isosceles triangle are equal)

t = 180 - 64 - 64 = 52° (Sum of angles in a triangle)

y = 90 - t

y = 90 -52 = 38°

y =  m∠2  (base angles of an isosceles triangle are equal)

m∠2 = 38°

m∠2 = 3x + 5

3x + 5 = 38°

3x = 38 - 5

3x = 33

x = 33/3

x = 11

Therefore, the value of x is 11

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The LCM of 1-x^2 and (x-1)^3 is (x-1)^3.

To find the LCM, we take the polynomial with the highest degree (which determines the degree of the LCM) and then make sure that it contains all the terms from the other polynomials.

The degree of (x-1)^3 is 3 and the degree of 1-x^2 is 2.

So, we take (x-1)^3 as the starting point for the LCM and then add any missing terms from 1-x^2.

In this case, (x-1)^3 already contains all the terms from 1-x^2, so the LCM is (x-1)^3.

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The area of a sector of a circle is equal to the central angle multiplied by the radius squared, divided by 2. In this case, the sector of the circle has an area of 20 square feet, the radius is 5 feet, and we need to find the central angle.

The central angle will be 6.28 radians.

To find the central angle, we can rearrange the equation to solve for the angle:

Central Angle = (2 * Area) / (Radius^2)

Substituting the given values, we get:

Central Angle = (2 * 20) / (5^2)

Simplifying, we find that the Central Angle equals 6.28 radians.

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Therefore , the solution of the given problem of coordinate plane comes out to be Y coordinates comes out to be -3 , -2, -1 , 0, 1,2,3

By portraying the inputs and outputs as a horizontal number line (the x axis) and a vertical number line (the y axis), respectively, the Cartesian coordinate plane enables us to perceive ordered pairs. The quantity in the x component is moved horizontally. Move to the right if x is positive. Move to the left if x is negative.

Here,

Given :

=> -30 , -20 ,-10 ,0 ,10, 20 , 30

=> So ,

Y coordinates comes out to be :

=> -3 , -2, -1 , 0, 1,2,3

An ordered pair of numbers, or x-coordinate and y-coordinate on the x-axis respectively, can be used to represent each point.

Written in parenthesis are ordered pairings (x-coordinate, y-coordinate). The source is situated at (0,0).

Check your coordinates, which are two numbers enclosed in parenthesis and separated by a comma, to see how to graph a point on the coordinate plane.

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In order to divide the amount Rs.60 in the ratio 1:2

We take x as the variable that replicates the 1st amount + 2nd amount = Rs.60

Putting the values into a equation we get

1x + 2x = 60

3x = 60

x = [tex]\frac{60}{3}[/tex]

x = 20

Hence the amounts are ,

1x = 20

2x = 2 x 20 = 40

Answer:

  angle JKL is 22°

Step-by-step explanation:

You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.

The exterior angle is equal to the sum of the remote interior angles:

  angle JKL = angle I + angle J

  5x -3 = (2x +8) +(x -1)

  5x -3 = 3x +7 . . . . . . . . . simplify

  2x = 10 . . . . . . . . . . . add 3-3x

  x = 5 . . . . . . . divide by 2

  5x -3 = 5(5) -3 = 22 . . . . . degrees

Angle JKL is 22 degrees.

__

Additional comment

It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.

The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.

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Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The following are the two similarities between drawing a perpendicular line through a point on a line and drawing one through a point of a line:

Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.

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Answer:

-3y

Step-by-step explanation:

-√(9y²) = -√((3y)²)

= -3y

The side of the square cutout that gives the box the largest possible volume

Therefore the answer is d) 2450/27 in.

To find the side length of the square cutouts that give the box the largest volume, we need to find an expression for the volume of the box in terms of the side length of the square cutouts. We can start by subtracting four times the area of one square cutout from the total area of the tin sheet to find the area of the box sides. The volume of the box will then be equal to the area of the box sides multiplied by the height.

The side length of the square cutouts can be represented by x. The area of one square cutout is x^2, so the total area of the four cutouts is

4x^2

The area of the tin sheet is 8 * 15 = 120. The area of the box sides is then

120 - 4x^2

The volume of the box is then (120 - 4x^2) * 8, which we want to maximize. To do this, we can differentiate the expression for the volume with respect to x and set it equal to zero, then solve for x. The solution to this optimization problem is

x = 2450/27, which is the side length of the square cutouts that gives the box the largest volume.

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Answer: $8000 is invested for 6 years

Step-by-step explanation:P=$3,000 r= 7%= 0.07 t= 4 n= 2